The coexistence of polar and nematic interactions, observed in a broad range of biological and synthetic active systems, gives rise to a rich phenomenology that continues to challenge our theoretical understanding of non-equilibrium collective behaviour. In this paper, we numerically investigate phase ordering and defect dynamics in a newly introduced minimal single-field model for dry nematopolar systems, where competing polar and nematic contributions enter the free energy, and activity is implemented through a self-advection contribution. At optimal balance between the two alignments, the system develops depolarization strings connecting half-integer defects and separating domains with opposite polarization, together with closed depolarization loops. We first characterize the elementary relaxation mechanisms of defect pairs and loops, showing that the interplay between polar and nematic alignment gives rise to non-monotonic string-mediated interactions, finite equilibrium separations and distinct loop-collapse pathways. Large-scale simulations from disordered states instead show dynamic scaling with a characteristic length growing as $\sim(t/\ln t)^{1/2}$, consistent with coarsening in systems with non-conserved order parameters and point-like defects. Upon introducing self-advection, sufficiently strong activity leads to the coexistence of positive integer and negative half-integer defects, which we term motility-induced charge symmetry breaking, and to saturation of the characteristic length scales, ultimately resulting in arrested coarsening. Overall, our results provide a simple unified framework for understanding the ordering and defect dynamics in biological and synthetic nematopolar systems.

Despite being intrinsically athermal and strongly driven, granular materials can exhibit remarkably glass-like dynamics. Whether their rheology can be described by the same scaling concepts remains an open question. Here, we investigate the linear viscoelastic response of an air-fluidized granular bed using small-amplitude oscillatory shear over a broad range of fluidization states. We show that the frequency-dependent spectra collapse onto a single master curve when shifted by a state-dependent relaxation time, establishing a time-state superposition principle analogous to time-temperature superposition in molecular glasses. The master curve spans more than five decades in relaxation time and is quantitatively described by a Cole-Davidson relaxation spectrum. By comparison with continuous shear measurements, we identify tribocharging as the origin of history-dependent deviations from universal scaling. Our results demonstrate that fluidization primarily rescales a single structural relaxation time while preserving the underlying relaxation spectrum, establishing a direct connection between the rheology of driven granular matter and molecular glass-forming liquids.

Hyperuniform systems, defined by the anomalous suppression of large-scale density fluctuations, are a paradigm of non-equilibrium self-assembly. While mechanisms underlying the self-assembly of hyperuniform states have been widely studied, the energetics of this process remain unexplored. This raises a fundamental question: what is the energetic cost of self-assembling a hyperuniform system? Here, we address this question across several noisy particle systems drawn from soft matter and machine learning, in which hyperuniformity can be induced by tuning noise correlations. Despite their distinct microscopic dynamics, we uncover a universal behavior across all systems: hyperuniform states are maximally irreversible, as quantified by the entropy production rate. Further, we develop a path integral formulation of the entropy production rate directly from the microscopic dynamics, which explains our observations. Our work establishes a direct link between emergent long-range structure and time irreversibility and opens a new avenue of probing the energetic cost of hyperuniform self-assembly, ubiquitous across physics, biology, and materials science.

We demonstrate that the balance between polar and positional order can be systematically tuned through molecular engineering, providing direct control over the emergence of polar and modulated liquid-crystalline phases, allowing for versatile strategy for the design of functional ferroelectric soft materials. We show that polar orthogonal smectic phases (SmAF and SmAAF), promoted by the self-segregation of aromatic cores and sufficiently long terminal chains, are readily destabilized by strong longitudinal dipolar interactions that energetically penalize parallel alignment of molecular dipoles within a smectic layer. In contrast, the tilted ferroelectric SmCF phase is remarkably robust across the entire homologous series, indicating that molecular tilt efficiently relieves dipolar frustration within the smectic layers. We further demonstrate that the interplay between microsegregation and electrostatic interactions stabilizes the new modulated SmCM phase, characterized by incommensurate electron-density waves, particularly for compounds with short terminal chains. For longer homologs controlling the spatial distribution of fluorinated molecular fragments and terminal-chain length enabled the targeted formation of broken-layer-type modulated polar phases (2D or 3D).

Understanding how nonequilibrium driving modifies phase-separation kinetics remains a fundamental challenge. Here we show that phase separation in a two-temperature system exhibits a striking density-induced reentrant coarsening behavior. Using Brownian dynamics simulations and a coarse-grained field-theoretic model, we find that the characteristic domain size grows as $L(t)\sim t^{1/z}$, displaying a reentrant sequence $(t^{1/3} \rightarrow t^{1/4}\rightarrow t^{1/3})$ with increasing density. While the low- and high-density regimes are governed by classical curvature-driven bulk diffusion, the intermediate-density regime exhibits anomalously slow growth. We show that this slowdown originates from a transport bottleneck arising from the interplay of particle diffusivity, particle availability, and attachment kinetics, which suppresses the effective mass flux between domains. Unlike equilibrium phase separation, where density primarily affects morphology and crossover scales, the two-temperature drive renders density a key control parameter for coarsening pathways. Our results uncover a nonequilibrium mechanism for anomalous domain growth in two-temperature systems.

Drying of nanowire-laden elongated droplets is a ubiquitous process in printed electronics fabrication, where the resulting deposition pattern critically determines device performance by controlling nanowire alignment, connectivity, and percolating charge-transport pathways. However, the physical understanding of evaporation-driven deposition is still largely derived from studies of spherical droplets on homogeneous substrates. This gap limits the ability to predict and control deposit morphology in realistic printing scenarios. Here, we use mesoscale lattice Boltzmann simulations to investigate the drying of nanowire-laden elongated droplets on wettability-patterned substrates, focusing on the effects of droplet geometry, nanowire interactions, and nanowire length. The elongated droplet geometry is found to intrinsically induce distinct axial and transverse inhomogeneities in the final deposit. Increasing the effective attraction between nanowires, which mimics changes in surface chemistry or solvent conditions, can improve electrical connectivity but also promotes clustering and local ordering, reducing structural uniformity. In contrast, increasing nanowire length yields a dual benefit by improving long-range connectivity while simultaneously enhancing deposit homogeneity. Our findings provide design guidance for balancing electrical transport and structural uniformity in evaporation-driven printed electronics.

DNA loop formation is a key mechanism in gene regulation, and looping kinetics are sensitive to mechanical tension acting on the DNA. In both single-molecule experiments and biological settings, this tension is typically transmitted through DNA segments flanking the looping region, rather than acting directly at the looping sites. How this indirect force transmission affects the looping time has not been systematically investigated. Using molecular dynamics simulations of a wormlike chain, we show that such flanking segments significantly steepen the force dependence of the looping time, an effect that is insensitive to their length once it exceeds the persistence length, and vanishes when the junction to the looping region is made flexible. We develop an analytical framework that accounts for this effect through a force-dependent shift in the effective free energy landscape of the looping segment. In the limit of small forces, this shift reduces to a zero-force equilibrium average, after which the entire force dependence of the looping time follows analytically. Applying this framework using a coarse-grained DNA model that treats individual bases as rigid bodies, we obtain predictions in quantitative agreement with experimental looping data. Our results demonstrate that the geometry of force transmission has a significant and predictable effect on looping kinetics, with direct implications for the interpretation of tension-dependent looping in both single-molecule experiments and gene regulatory contexts.

High-resolution atomic force microscopy has transformed molecular imaging by revealing intramolecular structure directly in real space. A major remaining challenge is to extend this capability from largely planar molecules to non-planar molecular systems, where the most important structural information may be distributed across different heights above the surface. Here we use probe-particle-model simulations to predict the constant-force contours expected above molecules with increasing structural complexity. By extracting force isosurfaces from simulated three-dimensional force fields, we compare the molecular information retained in constant-height and constant-force images. For tilted benzene and pyrrole, constant-force images preserve the molecular framework across a range of adsorption angles and allow the molecular orientation to be recovered quantitatively. For larger non-planar and three-dimensional systems, simulations identify characteristic force-isosurface contrast associated with adsorption geometry, lower-lying molecular structure and curved molecular surfaces. These results provide target contrasts for force isosurfaces that could be extracted from three-dimensional force-mapping experiments, evaluating the molecular information retained by ideal force-isosurface imaging across progressively non-planar systems.

We study a bulk-driven nonlinear variant of the Kipnis-Marchioro-Presutti model of stochastic energy diffusion in which local collisions are biased to induce a net energy flow, resembling the effect of an external field. Starting from the microscopic master equation, we derive the hydrodynamic description of the driven system via a local equilibrium approximation, obtaining explicit expressions for the energy current and the associated diffusivity and mobility transport coefficients, which are nonlinear functions of the local energy density. We test our findings in kinetic Monte Carlo simulations of the model and, as a proof of concept, we demonstrate the versatility of this driving mechanism to control nonlinear energy transport by inducing time-crystalline phases. In particular, we show that appropriately designed packing fields induce the spontaneous formation of traveling energy condensates, exhibiting robust long-range temporal order reminiscent of continuous time crystals. Our results provide a simple yet powerful framework to study bulk-driven nonlinear energy diffusion in stochastic many-body systems, offering a bridge between microscopic dynamics, macroscopic transport, and controlled spatiotemporal order.

A liquid drop falling into a deep pool can create a vortex ring at the right impact conditions. Such drop-formed vortex rings are of importance in nature and technology and the dynamics of rings created by single and synchronised double drop impacts have been extensively studied. In practice, two neighbouring drops rarely impact a liquid surface exactly at the same time, yet the interaction of two unsynchronised vortex rings have not been studied. Here, we have performed experiments with two water drops impacting a water pool at varying time differences $\Delta t$. By using particle image velocimetry, we have quantified the time-evolution of the resulting vortex rings. We find four distinct categories of vortex ring evolution depending on $\Delta t$. At $\Delta t<0.5$ ms, fully symmetric merging of the vortex rings occur. An unsynchronisation larger than this drastically influences the collision and merging, which either becomes asymmetric and incomplete ($0.5 < \Delta t<7$ ms) or does not happen at all ($\Delta t \geq 7$ ms). At $7 \leq \Delta t<80$ ms, the creation of the second vortex ring is impaired, whereas at $\Delta t\geq 80$ ms, the first impact no longer affects the formation of the second ring and eventually the two rings evolve without influencing each other. We show that these different regimes can be explained by the capillary waves created by the first droplet. Our results demonstrate the importance of the time difference between drop impacts in the creation and subsequent interaction of two adjacent drop-formed vortex rings, which is important for achieving uniform and controlled mixing in high-throughput applications.

Tissue surfaces exhibit complex curvature during embryogenesis and oncogenesis. Evidence shows that cells can actively sense curvature to regulate behavior and fate, yet the underlying mechanism remains unclear. Here, we develop a vertex model for arbitrary curved surfaces and uncover spontaneous cell size patterning on ellipsoidal surfaces: cells in high-curvature regions are consistently larger than those in low-curvature regions. This non-uniformity arises from a mechanical competition encoded in Riemannian geometry: positive Gaussian curvature reduces the perimeter-to-area ratio of polygonal cells, relaxing cell-edge tension in high-curvature regions, which is compensated by area expansion to maintain global force balance. This area pattern is robust against variations in model parameters and matches observations in biological systems. The perimeter pattern, in contrast, is governed by competition between the intrinsic geometric tendency and the deformation required by force balance, and undergoes reversal beyond a critical shape index. Together, these findings establish self-organized spatial variations in cell size as a potential physical mechanism for curvature sensing.

The low-frequency dielectric response of liquid water is commonly described by a dominant Debye relaxation together with additional faster contributions whose microscopic origin remains debated. Here we show that the dielectric function of water between 0.14 and 1.21 THz can be represented by a collective Debye relaxation plus a Drude-Smith term constrained to the zero-dc-conductivity limit. The Drude-Smith spectral weight increases upon heating pure H2O from 20 C to 50 C and decreases upon isotopic substitution (D2O at 20 C vs. H2O at 20 C). Molecular dynamics simulations including nuclear quantum effects show correlated changes in the population of water molecules with unequal numbers of donated and accepted hydrogen-bonds. Ab-initio-based spectra calculations further indicate that the ~0.1-1 THz response contains both nuclear-motion and explicit electronic-polarisation/charge-redistribution contributions. We therefore interpret the excess low-frequency THz response as a localised, mixed nuclear-electronic dielectric response correlated with transient donor-acceptor imbalance in the hydrogen-bond network.

Wave turbulence is a regime of interacting nonlinear waves occurring in most physical systems. Kelvin waves are helical distortions that propagate along vortex filaments and are believed to play a central role in quantum turbulence up to atmospheric vortices. Yet, Kelvin wave turbulence has remained inaccessible to direct experimental observation. Here, we report the first direct experimental observation of Kelvin-wave turbulence along a single vortex filament in a classical fluid under controlled conditions. Using high-resolution spatiotemporal measurements, we resolve Kelvin-wave dynamics over a broad range of scales and obtain wave-amplitude spectra consistent with the predicted weak-turbulence cascade. We identify six-wave resonant interactions as the mechanism driving this energy transfer, providing direct experimental support for a long-standing prediction of weak-turbulence theory. These results establish an experimental platform for investigating energy transport along vortex filaments, with broader implications for both classical and quantum turbulent systems.

Diffuse-interface immersed boundary methods (DIBMs) provide a simple and robust approach for simulating flows involving complex geometries. However, their inherent diffusion effect can contaminate the near-wall flow field and significantly degrade wall-shear-stress prediction in wall-modeled large-eddy simulation (WMLES). To address this limitation, we develop a WMLES approach based on a fully one-sided diffuse-interface immersed boundary method (FODIBM). By performing interpolation and spreading exclusively inside the immersed body, the proposed method removes the cross-boundary diffusion effect that adversely affects wall modeling in conventional DIBMs. A wall-shear-stress enforcement strategy is developed by coupling the wall-parallel immersed-boundary forcing with the wall shear stress predicted by an explicit wall model. In addition, a tau-model based on the modeled turbulent shear-stress tensor is introduced to preserve the total shear-stress balance below the reference height. The method is first validated in high-Reynolds-number turbulent channel flows, showing good agreement with DNS data for the mean velocity, Reynolds shear stress, and skin-friction coefficient. Sensitivity studies with respect to grid resolution, reference height, wall inclination angle, and Reynolds number demonstrate the robustness of the method. Compared with the conventional DIBM, the proposed method substantially improves the overall prediction accuracy, particularly at low reference heights. The approach is further assessed for turbulent flow over a NACA23012 airfoil, where the predicted pressure distribution and lift coefficient agree well with experimental data.

Although one-sided spreading has been shown to improve the near-wall accuracy of diffuse-interface immersed boundary methods (DIBMs), the effect of its asymmetric kernel support on the effective boundary location remains insufficiently understood. In this work, a detailed analysis of the one-sided spreading operator reveals an inward displacement of the effective boundary relative to the geometric boundary. To compensate for this displacement, a target-value reconstruction strategy is developed to ensure consistency between the values imposed at the effective boundary and the prescribed conditions at the geometric boundary. The strategy is incorporated into the fully one-sided diffuse-interface immersed boundary method (FODIBM) and applies to both Dirichlet and Neumann boundary conditions. Although confined to the target-value evaluation step, the modification substantially improves boundary-condition enforcement with negligible additional computational cost. Coupled with a hybrid lattice Boltzmann solver, the improved method consistently reduces L_2 and L_{\infty} error norms across different grid resolutions while retaining approximately second-order grid convergence. The no-slip and isothermal boundary-condition errors are reduced by 77% and 85%, respectively. Simulations involving various two- and three-dimensional geometries further show improved predictions relative to both the conventional DIBM and the original FODIBM. The results agree well with body-fitted reference solutions and experimental data, demonstrating accurate and computationally efficient simulations of compressible flows around complex geometries.

A three dimensional global stability analysis is performed to investigate the problem of screeching jets under turbulent conditions. The study employs an Unsteady Reynolds-Averaged Navier-Stokes (URANS) framework, in which the compressible flow equations are discretised using the high-fidelity solver dNami, the linearised discrete system is obtained through the automatic differentiation tool Tapenade, and the global stability problem is solved in a time-stepping framework. The fixed-point solutions of the URANS equations are first validated against experimental and numerical data, then a three dimensional global stability analysis is performed around fixed points solutions at different levels of under-expanded regimes. The extracted modes are spatially analysed and examined in terms of acustic radiation and validated against experimental data. Comparison with experimental POD data shows that the linear modes reproduce the main wavenumber content and spatial organisation of the screech resonance loop, even at high levels of under-expansion. The staging behaviour is also recovered from the interaction between the Kelvin--Helmholtz wave and the dominant wavenumbers of the shock-cell structure. Finally, a Helmholtz decomposition is applied to the velocity perturbation in order to separate the vortical and irrotational parts of the modes. An energy budget of the wave components is then used to quantify the repartition of the relative feedback-loop energy perturbation. Notably, the Mach-number effects on energy partition vary depending on the type of staged mode. This insight could prove valuable for interpreting receptivity mechanisms at nozzle lips and shocks in future research.

Boundary layer theory and its analytical methods for skin friction coefficients provide an important basis for aerodynamic analysis. However, classical analytical formulas are mostly limited to flat-plate flows. High-fidelity numerical simulations are not only computationally expensive but also yield predictions that are highly sensitive to physical models, numerical schemes, and grid resolution. To overcome these limitations, symbolic AI opens a new pathway to discover novel laws of complex physical systems from data. Using limited data from surface solutions of the Euler equations and the skin friction coefficient from viscous flows over airfoils, we employ symbolic regression to progressively discover a generalizable, interpretable analytical formula chain for fast skin friction prediction in subsonic and supersonic attached flows. From the perspective of physical mechanisms, the discovered analytical expression chain reveals scaling laws for skin friction at different Mach numbers: the basic form captures the logarithmic decay of skin friction along the streamwise direction in the turbulent boundary layer; the inclusion of a pressure coefficient correction term quantifies the effect of surface pressure variation; and the Mach number correction term evolves with flow regimes, transitioning from the compressibility correction term in subsonic regimes to the thermodynamic effects term in supersonic and hypersonic regimes. This knowledge chain exhibits a unified structure across different Mach numbers, and omitting the correction terms under certain conditions recovers classical theoretical forms, further demonstrating its physical consistency. Validation against typical geometries shows that this analytical formula chain achieves a low average integrated skin friction drag prediction error, with good generalization capability across different freestream conditions and geometric shapes.

In this Letter, we show how a suspension of light solid spheres settling through a polymer solution results in a chaotic and highly-intermittent state. By leveraging particle-resolved direct numerical simulations, we investigate the effect of increasing polymer relaxation time and Deborah number $De$ on viscoelastic sedimentation at a low density ratio $\rho_s/\rho_f=5$ and a low Galilei number $Ga=3.16$. Even at moderate $De$, the spheres form gravity-aligned clusters and settle faster, while the polymer stresses energize the large scales of motion. The onset of elastic turbulence and intermittency is signaled by a $-4$ spectral scaling in the high-wavenumber range and by nonlinear high-order exponents of the velocity structure functions. These results indicate that viscoelastic effects induce pseudoturbulence in the presence of viscous-dominated sedimentation.

Reynolds-averaged Navier-Stokes (RANS) turbulence models are known to perform poorly in predicting the dynamics of Rayleigh-Taylor mixing when turbulence is not fully developed, particularly during the transition from an initially perturbed interface. In this work, we investigate the use of data-driven strategies to enhance a simple $k$-$\varepsilon$-$b$ model for this transitional regime. The turbulence model is first embedded within a surrogate physics-informed neural network (PINN), enabling the calibration of coefficients that account for parametric errors and the identification of corrective terms representing structural errors associated with missing physical processes. The learned corrections are then re-expressed onto the model state variables and relevant flow indicators, leading to explicit analytical modifications of the closure. The resulting fully interpretable corrected model is assessed against an extensive database of direct numerical simulations (DNS) of Rayleigh-Taylor flows. This framework enables improved predictions of the mixing-layer growth during the transition to turbulence.

Salt-finger plume forests in a finite layer can differ in strength and in the route by which interfacial activity becomes vertically connected. We use direct three-dimensional simulations to test whether such a route is a short-lived realization-specific transient or a persistent route family under an added mean-shear perturbation. The baseline route atlas holds density ratio, diffusivity ratio, Prandtl number, interface thickness, roughness amplitude, domain, and resolution fixed while varying the imposed interfacial roughness spectrum. Low-mode roughness forms a broad connecting endpoint, high-annulus roughness forms a localized route-memory endpoint, and mixed roughness forms a delayed scale-transfer route. A second mixed realization preserves continuous active-width, spectral, and transport measures after \(t=45\), with mean absolute differences of \(3.1\%\) in \(w\)-active width, \(1.6\%\) in salinity-active width, \(2.8\%\) in broad spectral fraction, and \(3.6\%\) in salt flux, while shifting the binary scalar-contact label. We then impose an initial tanh mean shear on the mixed route. The full-resolution shear case reaches \(t=60\) and preserves finite-depth reach: first velocity contact occurs at \(t=57.75\), first salinity contact occurs at \(t=59.5\), and both times match the unsheared mixed reference. The spectral branch is redistributed. At \(t=60\), the broad fraction is \(1.116\) times the mixed value, the intermediate fraction is \(0.530\) times the mixed value, and the short-wave fraction is \(1.278\) times the mixed value. In this finite-depth configuration, route survival means preserved reach and contact timing with a changed spectral pathway.

Unsteady thin-airfoil theory (UTAT) coupled with discrete-vortex methods has been widely employed in reduced-order aerodynamic modeling. Due to the non-uniqueness of potential-flow solutions, the Kutta condition is imposed to determine the circulation around the airfoil. Although the unsteady Kutta condition is commonly associated with the zero-loading condition at the trailing edge, its implications for the continuity of the vortex-sheet strength remain comparatively underexplored. In particular, the classical series expansion employed for the bound vorticity in unsteady thin-airfoil theory is not uniformly convergent at the trailing edge, leading to mathematical inconsistencies in the vortex-sheet and pressure distributions. In this context, the present work seeks to advance the mathematical framework of unsteady thin-airfoil theory through a physically consistent formulation of the bound vortex-sheet strength for the Wagner problem. A recurrence relation is derived for the Wagner coefficients, allowing the construction of a uniformly convergent series expansion for the bound vorticity. The proposed formulation ensures continuity between the bound and wake vortex sheets while simultaneously recovering zero pressure loading at the trailing edge, thereby providing a mathematically consistent representation of the unsteady Kutta condition. To investigate the implications of the modified framework, a discrete-vortex method based on UTAT is developed and compared with the classical formulation. The results demonstrate that the proposed approach eliminates spurious oscillatory behavior near the trailing edge and significantly improves the regularity of the computed vorticity and pressure distributions.

All published models of ultraviolet (UV) inactivation of airborne viruses in saliva droplets have neglected UV light scattering. To the best of our knowledge, this work presents the first Computational Fluid Dynamics-Discrete Dipole Approximation (CFD-DDA) platform for investigating the physical mechanisms governing UV disinfection of virus-laden airborne saliva droplets. The DDA solver predicts UV light scattering by both spherical and irregularly shaped saliva droplets, while the CFD solver predicts droplet evaporation and transport in airflow. By coupling the DDA and CFD solvers, we demonstrate that infected saliva droplets, whether spherical or irregularly shaped due to evaporation, experience highly non-uniform UV light scattering that significantly affects virus inactivation and cannot be neglected. This phenomenon has not previously been investigated within a fully three-dimensional framework. The coupled Euler-Lagrange CFD-DDA model further quantifies the effects of (i) the initial droplet size distribution and concentration, (ii) airflow rate, and (iii) droplet interactions with the surrounding airflow and bounding walls on the total number of surviving coronavirus copies $N_s$, assuming a virion diameter of 100 nm, an air temperature of 21 $^{\circ}$C, and a relative humidity of 65%. Based on the DDA results, a new virus inactivation model, referred to as the Dbouk-Yurkin law, is proposed. This model extends the classical Chick-Watson law by explicitly accounting for UV light scattering in both spherical and non-spherical airborne saliva droplets. The proposed three-dimensional CFD-DDA platform provides a powerful framework for improving the understanding of UV-based airborne virus disinfection and for optimizing the design and performance of UV air purification systems.

We present recent performance-oriented developments in this http URL , a scale-resolving incompressible flow solver written in pure Julia that runs seamlessly on CPUs and GPUs of any vendor. Supported by the newly added MPI-based parallelism, strong-scalability tests display a near-ideal linear trend, and weak-scaling efficiency is kept above 85\% before node memory-concurrency contention dominates parallel performance. Inter-node weak scalability is sustained above 96\% with grid size up to 1 billion cells. We further benchmark improvements to the geometric multigrid Poisson solver enabled by an adaptive under-relaxed red-black Gauss--Seidel smoother together with anisotropic coarsening operators.

The paper establishes extra invariant in magnetohydrodynamics (MHD) of rotating and stratified fluid layer. This invariant is conserved adiabatically, i.e. approximately over long time. The existence of the invariant is interesting by itself, as such invariants are extremely rare. However, in addition, this invariant appears to be connected to the famous dynamo phenomenon.

Nonlinear dynamics is ubiquitous in nature, ranging from chemical pattern formation to ocean circulation, yet its simulation on quantum computers is fundamentally limited by the unitary nature of quantum evolution. We propose the quantum Koopman method, a data-driven framework that embeds nonlinear dynamics into a learned linear representation and implements the resulting evolution using shallow quantum circuits. This method learns Koopman observables from trajectory data, projects the lifted dynamics onto a finite-dimensional subspace, and decomposes the corresponding non-unitary propagator into parallel spectral channels. We utilize the Koopman method on a superconducting processor to simulate three distinct nonlinear systems, comprising reaction-diffusion dynamics, fluid motion on a sphere, and satellite-derived observations of Gulf Stream currents, employing up to 32 parallel circuits of 10 qubits. These quantum simulations capture the dominant multiscale patterns and statistical signatures of the underlying dynamics, and reveal a transition from performance limited by hardware noise in weakly nonlinear systems to performance limited by finite-dimensional Koopman representations as nonlinear scale interactions increase. This transition identifies a practical boundary for quantum-amenable nonlinear dynamics, establishing a hardware-validated route for simulating moderately nonlinear dynamics on near-term quantum hardware.

Bubbly flows exhibit complex multiscale dynamics, with deformable bubbles interacting through the surrounding liquid and giving rise to strongly coupled kinematic and morphological behavior. We present BubbleSH, a bubbly flows dataset consisting of transient, three-dimensional bubble-swarm dynamics obtained from high-fidelity direct numerical simulations of bubbles rising in a periodic domain. The dataset provides time-resolved bubble trajectories, velocities, and shape evolution, with bubble morphology compactly represented using spherical harmonics. Designed to be lightweight yet physically expressive, the dataset enables data-driven modeling of bubbly flow simulators where shape deformation and bubble-bubble interactions play a central role. We characterize the dataset with bubble kinematics, morphology, and interaction patterns, and introduce evaluation metrics for both trajectory and shape prediction. The sensitivity of bubble-swarm dynamics to local perturbations makes BubbleSH particularly well suited to generative models that learn distributions over possible future trajectories. We evaluate a permutationally and translationally equivariant probabilistic emulator on BubbleSH given the proposed metrics. Therefore, we establish a compact, high-fidelity dataset and a benchmark for developing and evaluating data-driven models of deformable, chaotic multiphase systems.

Magnetohydrodynamical (MHD) simulations of isothermal compressible turbulence report that the density distribution is well described by a lognormal with a variance proportional to the flow's Mach number. The distribution of magnetic field strength also has a lognormal component, but includes long, power-law-like tails. In this work, we use semi-analytical arguments to predict the distributions of density and magnetic field strength in compressible turbulent flows. Specifically, in the Lagrangian description of the continuity and the induction equations, we model the velocity gradients of the turbulent flow as a simple random process, essentially turning these equations into stochastic differential equations. Integrating them leads to a lognormal distribution for the density field and the strength of the magnetic field. The power-law tails in the magnetic field PDF appear when we introduce intermittent shocks due to sampling rare events. Gradually increasing the frequency of these events, essentially going closer to a continuous process, leads to lognormal-like distributions again. The asymmetry is connected to the relative abundance of slow and fast shocks. An overabundance of fast MHD shocks produces a high-value tail, while the contrary produces low-value tails. We propose that the appearance of power-law tails along lognormals in turbulent flows is the signature of the co-existence of continuous, diffusion-like propagation combined with localized, intermittent events.

We present CoFINN (Conservation Flux Informed Neural Networks), a physics-informed deep learning framework for predicting compressible flow fields governed by conservation laws. Unlike conventional data-driven convolutional neural networks (CNNs), which optimize only pixel-wise similarity metrics, CoFINN embeds finite-volume conservation physics directly into the training process. Unlike classical physics-informed methods which enforce differential-equation residuals at collocation points through automatic differentiation, CoFINN adopts a finite-volume perspective consistent with modern CFD methodology. CoFINN interprets CNN output fields as structured computational grids, where each pixel represents a finite-volume cell, and enforces conservation consistency through sophisticated numerical flux calculations. The framework is evaluated on transonic flow prediction around airfoils at (M=0.7, Re=6 * 10^6), including challenging conditions involving shock waves and high angles of attack. Results show that CoFINN improves aerodynamic force prediction accuracy, reducing drag prediction error by up to 34% at extreme angles of attack and by approximately 15% on average across the test set. Improvements are particularly significant in limited-data regimes, demonstrating that the conservation-based loss acts as an effective physical regularizer. The proposed approach maintains the computational efficiency advantages of CNN surrogates while significantly improving physical consistency and conservation behavior. The framework is architecture-agnostic and extensible to broader classes of conservation-law-governed physical systems.

In homogeneous magnetohydrodynamic (MHD) turbulence without a background magnetic field driven by mechanical forces, an exact decomposition of the energy fluxes (D. Capocci et al., Journal of Plasma Physics, 91(1), E11 (2025)) has shown that current-sheet thinning is the dominant physical mechanism responsible for transferring energy from large to small scales. In contrast, mechanisms that are characteristic of hydrodynamic turbulence, such as vortex stretching and strain self-amplification, are strongly suppressed. Here, we extend this analysis to MHD turbulence in the presence of weak and strong imposed magnetic field, as previously driven by mechanical forces, and confirm that current-sheet thinning remains the leading process driving the energy cascade toward smaller scales in these more realistic configurations, and find enhanced scale invariance in the subfluxes. In addition to that, a decomposition of the contributions from the fluctuating and the background magnetic field to the conversion between kinetic and magnetic energies shows that the background-field-dependent contribution results in a nonlinear dynamo, that is an effective kinetic-to-magnetic conversion at large and intermediate scales. However, at small scales, it has the opposite effect, resulting in a net conversion of magnetic to kinetic energy.

An extended formulation of out-of-time-ordered correlators (OTOCs), which quantify noncommutative operator growth and information scrambling in quantum many-body systems, is developed for turbulence dynamics as a representative of non-canonical Hamiltonian systems. Based on the Wigner-Weyl transform and the Moyal bracket formalism, the semiclassical limit of OTOC for turbulent plasmas governed by the Hasegawa-Mima equation is derived as an ensemble-averaged squared Lie-Poisson bracket between two chosen functionals of the turbulent fields. The classical-limit OTOC provides a quantitative measure of how a variational perturbation applied to one functional propagates across scales in the turbulent dynamics and how it affects another functional at a later time, thereby capturing scale-dependent or field-dependent transfer processes. In a quasilinear approximation with a strong zonal flow, we provide a closed analytic expression of the classical-limit OTOC to characterize the interaction between zonal and non-zonal modes. An asymptotic analysis shows that the OTOC grows quadratically at early time, while in the long-time strong-shear regime it approaches a finite saturated value with an inverse-square algebraic dependence. This behavior is attributed to zonal-flow shearing, which rapidly scrambles the non-zonal perturbation toward higher wavenumbers, thereby reducing the low-wavenumber non-zonal content that can feed back onto large-scale zonal modes.

We investigate a (2+1)-dimensional nonlinear spin system containing an effective spin-current transport term. Based on its integrable structure, exact magnetic lump solutions are constructed on a rotating spin background, including both fundamental and higher-order configurations generated via the Darboux transformation. The obtained excitations are doubly localized in spatial directions, while their temporal evolution is characterized by intrinsic spin precession rather than translational motion of the localized envelope. It is shown that the effective spin-current contribution enters the localization coordinate and acts as a geometric control parameter for the spatial structure of the solutions. In particular, spin current induces anisotropic deformation of the localized profile, leading to a continuous transition toward a quasi-one-dimensional soliton-like state under specific parameter regimes. More importantly, this deformation mechanism is found to be universal across different hierarchical lump structures, including both fundamental and higher-order solutions, indicating that spin current governs a unified structural modulation law for the entire family of localized spin excitations. These results provide an analytically tractable example of spin-current-controlled anisotropic deformation and dimensional crossover in nonlinear spin systems, and further reveal a universal mechanism for geometric control of localized spin textures beyond individual solution types.

We investigated kink-antikink collisions in a $(1+1)$-dimensional $\phi^8$ scalar field theory with multiple degenerate vacua. We presented explicit soliton solutions for different vacuum structures characterized by the ratio $n = p_2/p_1$. We focused on the cases $n=2$ and $n=3$ with four distinct vacua, and performed systematic numerical simulations across all topological sectors. We revealed that there is a complete annihilation regime in the $(1/2,\,1)$ sector, where kink-antikink pairs annihilate for all initial velocities. Up to our knowledge, such phenomenon is first reported in the kink antikink collisions. We revealed a comprehensive fractal cartography of multi-bounce resonance windows across sectors $(-1,\,-1/2)$, $(-1,\,-1/3)$, and $(-1/3,\,1/3)$. Given the kink antikink ($K\bar{K}$, or $\bar{K}K$) ordering, the effective potential and the spectrum of the Schrödinger like equation were presented. By collecting all the effective potential and collision phenomena, we proposed that the effective potential classification scheme provides a predictive framework for collision outcomes including escape, bion formation, sector change, and annihilation. Especially, it is identified that, when soliton pairs pass through each other, the abrupt changes of the potential type could explain both the sector-change and annihilation phenomena. Our work highlight novel dynamical features of the $\phi^8$ model absent in lower-order field theories, and establish connections between topological structure, vibrational modes, and effective potentials.

Pair generation in time-varying media is commonly attributed to time reflection at temporal boundaries or to amplification inside momentum k gaps. Here we show that these two processes are connected by the time domain Stokes phenomenon. A finite duration photonic time crystal (PTC) slab provides the necessary Stokes connection between the incident vacuum mode, transient k gap amplification, and time boundary scattering. With Kerr nonlinearity, the otherwise unbounded amplification is arrested, spawning Kerr stabilized k gap solitons. When these solitons cross the exit boundary of the time slab, Stokes induced mode conversion produces a secondary pair generation process, yielding four spatially separated and entangled pulse branches. Detection of a backward propagating light pulse therefore heralds its forward propagating partner. We further propose combined Hanbury Brown Twiss and Hong Ou Mandel measurements to test their nonclassical correlations. These results reveal a link between asymptotic Stokes physics and quantum temporal scattering in PTCs, and suggest a route toward ultrafast heralded quantum light sources.

Biochemical traveling waves transmit signals across cells and tissues, but the thermodynamic cost of reliable propagation remains unclear. We develop a stochastic thermodynamic framework for reaction--diffusion systems with stable traveling waves and show that diffusion of the wave position is bounded by the dissipation specifically associated with propagation. The bound follows by projecting noisy field dynamics onto the adjoint translational mode, which maps the wave position to an effective biased random walk. Its tightness is controlled by the non-self-adjoint part of the linearized dynamics, with finite wave speed and antisymmetric reaction dynamics generically producing deviations from equality. For excitable trigger waves in a FitzHugh--Nagumo model, we show that the slow inhibitor dominates the propagation cost, yielding a trade-off among wave speed, inhibitor amplitude, and dissipation. We test these predictions in stochastic simulations of a microscopic Belousov--Zhabotinsky reaction--diffusion system and find consistent signatures in mitotic trigger-wave experiments in \textit{Xenopus} egg extracts. The same relation further imposes an annihilation-limited bound on the reliable signaling rate of wave trains.

We study invariant measures for soliton systems described by Mealy automata. Motivated by recently introduced soliton models associated with 2-letter, 3-state Mealy automata, we formulate the time evolution induced by Mealy automata on bi-infinite configuration spaces. We provide sufficient conditions for the invariance of Bernoulli product measures and derive a criterion for the invariance of two-sided space-homogeneous Markov distributions. We then apply these general results to three soliton models, which can be interpreted as variants of the box-ball system (BBS). For two of these models, BBS-S(2) and BBS-V(2), we prove that Bernoulli product measures are invariant. For the remaining model, BBS-C(2), we establish a more general result: the invariance of two-sided space-homogeneous Markov distributions, which include Bernoulli product measures as a special case. Furthermore, for all three models, we compute the phase shift associated with the interaction of two solitons, as well as the velocity of an isolated soliton. Although the latter has already been studied previously, both quantities constitute fundamental characteristics for understanding the generalized hydrodynamics of these systems. These results provide a foundation for the study of invariant measures, generalized Gibbs ensembles, and generalized hydrodynamic behavior in Mealy-automaton soliton systems.

We investigate the collective dynamics of a bundle of charged particles undergoing cyclotron motion in a uniform magnetic field when subjected to a short-duration electric pulse. Using the geometric framework based on the evolution of trajectory congruences, we analyze how the pulse affects the expansion, shear, and rotation of a small family of trajectories. We show that the geometric imprint persists after the pulse has vanished, manifesting as a memory of the transient perturbation. Unlike gravitational memory effects, this does not manifest itself in focusing behaviour of the trajectories, and instead implies a restructuring of the shear component before and after the pulse. We offer direct analytic and regression based arguments for the same.

We study constitutive conditions of hyperelastic potentials for incompressible material behavior in three dimensions. By means of a counterexample, we show that polyconvexity does not imply true-stress-true-strain monotonicity. Thus, polyconvexity alone is not strong enough to guarantee a physically reasonable response for idealized elasticity.

Spherical colloids with harsh repulsive forces have long been used as experimental analogs of the hard sphere model, with demonstrated good agreement with computer simulations for bulk and structural properties of the fluid, glass and crystal phases. However, an enigmatic discrepancy remains for the crystal-melt stiffness coefficient. Here we perform computer simulations of colloidal hard spheres under tunable buoyant mass and show that the long-standing discrepancy can be traced to a hitherto unrecognized gravity dependent contribution of the stiffness coefficient. This effect is one practical realization of a more general result for the external field dependence of stiffness coefficients of arbitrary interfaces.

Heat transport in nanoconfined liquids can deviate from ordinary Fourier behavior because confinement alters liquid structure and interfacial dissipation. Although such changes may lead to quasi-one-dimensional transport or overdamped sound relaxation, the conditions under which length-dependent transport persists remain unclear. Here we use molecular dynamics simulations of monatomic liquid argon confined in carbon nanotubes with systematically varied radii and lengths. We find a radius-controlled crossover: length-dependent axial thermal conductivity persists over long tube lengths in single-file and single-shell states, but is strongly truncated or nearly saturated once mixed-shell or multilayer packing develops. This crossover is accompanied by the loss of clear acoustic-like axial modes and enhanced wall--liquid friction. Thus, tube radius controls whether length-dependent heat transport persists or is truncated by coupling confined-liquid structure to wall-induced dissipation.

Membrane-deforming protein lattices play a key role in essential and pathogenic biological processes, including endocytosis and viral budding. Attaining the necessary length- and time-scales in simulation can be difficult for such large-scale membrane remodeling events. We present a model of a flexible protein lattice coupled to a Helfrich membrane propagated in Fourier space in the over-damped regime. We focus primarily on membrane-bound clathrin lattices, an essential part of the endocytic machinery. We quantify the material properties of our clathrin model lattices using buckling methods to measure the flexural rigidity as it varies with force constants of the coarse-grained potential energy function. By comparing this flexural rigidity to the effective rigidity observed when modeling the bending energy of a spherical clathrin coat using a Helfrich-like bending energy term, we show how the interpretation of the bending rigidity changes with the structure of the protein coat, resulting in an effective stiffening as the coat grows. This relatively common approximation thus must be applied with care, as it can over-estimate the stiffness of assembled lattices depending on the interpretation assumed. We validate our model by verifying that the tension of our simulated membrane results in changes to the geometry of the clathrin coat consistent with theoretical expectations. We conclude by demonstrating our newly available code for transferring structures assembled via rigid-body reaction-diffusion (using the NERDSS simulation package) into our flexible membrane-coupled dynamical framework, applying it to the membrane-bound HIV-1 immature Gag lattice.

Ferroelectric nematic liquid crystals (FNLCs) are polar fluids in which spontaneous polarization coexists with nematic orientational order, giving rise to unusual dielectric and electromechanical responses. However, the collective modes underlying their giant dielectric response remain unclear. Here, we show that this response originates from the superposition of two distinct relaxation modes rather than a single process. Dielectric spectroscopy reveals that the low-frequency mode exhibits soft-mode-like behavior associated with short-axis molecular rotation, whereas the high-frequency mode corresponds to a Goldstone-like phase displacement of an effective transverse polarization component rotating around the director. These assignments are supported by systematic analyses of temperature, electric-field, cell-thickness, and alignment-layer dependences. Our results demonstrate that the giant dielectric response of ferroelectric nematics reflects multiple collective polarization dynamics with different symmetries and restoring forces, providing a framework for interpreting dielectric spectra in polar nematic fluids.

Using theory, simulation, and experiment, we introduce a new class of active particle which we term doubly chiral active Brownian particles (dcABPs), which show robust topologically protected transport along boundaries without backscattering at corners. Their double chirality stems from the coexistence of an intrinsic angular velocity, which can cause rotation independently of translation, and a translation-rotation coupling inducing cross-alignment to the instantaneous velocity, which causes rotation only concomitantly with translation. A mechanically detailed model shows that the latter effect can arise from an asymmetric friction distribution in the direction perpendicular to the self-propulsion direction. We show that topologically protected modes emerge when the two sources of chirality have opposite sign and the intrinsic rotation is weaker than the translation-rotation coupling. In the deterministic limit, we characterize the emergence of these modes not only along straight boundaries, but also along curved boundaries and during interparticle interactions. We provide a proof-of-principle experimental realization by building a doubly chiral vibrobot. While setting the work into context, we moreover show that the topologically protected boundary-induced transport of dcABPs stands in contrast to the edge currents observed for simple chiral ABPs, which we demonstrate are not associated with boundary-induced transport, as well as to those observed for chiral active rods or self-aligning chiral ABPs, which we show to be associated with boundary-induced transport but to backscatter at corners, implying lack of topological protection.

The study of active matter has reshaped our understanding of collective states of matter far from equilibrium by proving that energy pumped into the microscopic scale leads to order on the macroscopic scale, collective motion, and anomalous mechanical responses. More recently, the discovery of odd elasticity and nonreciprocal mechanical couplings has extended these ideas to solid-like active systems, revealing materials with nonconservative elastic response. Simultaneously, innovative developments in swarm robotics , programmable metamaterials , and learning algorithms have led to the emergence of a new frontier in which collective behavior and mechanical response are no longer fixed by design, but adapted, optimized, and learned toward functional goals. This Perspective proposes a unifying trajectory, from active to odd to smart matter, organized along two intertwined axes: the traditional gas--liquid--solid progression of condensed matter, and the more recentparadigm shift from spontaneous collective dynamics to task-driven functionality. We try to highlight emerging principles, conceptual shifts, and open challenges that come along this trajectory, and argue that learning may play the role of a specific form of emergence, which could advantageously replace the more traditional view of control, at least in the realm of physics.

Spatially heterogeneous environments continually challenge the ability of active matter to sustain coherent collective motion. Understanding how collective motion remains robust under changing environments is central to both the functioning of biological systems and the design of smart active matter. Here, we extend the Vicsek model to include a circular non-noisy region surrounded by a noisy environment - a configuration in which the noise difference sets up a contrast in local directional order between the two regions. We find that, as the surrounding noise is increased, the system passes through three distinct dynamical regimes: (i) conventional global flocking at low noise; (ii) geometry-locked motion, aligned with simulation boundaries, at intermediate noise; and (iii) vortical motion within the non-noisy region at high noise. Extending the environment to multiple non-noisy regions, we find that the geometry-locked regime can develop a directional coupling, while the vortex mode leads to antiferromagnetic order between the regions. Taken together, our results demonstrate that the spatial modulation of order and disorder offers a powerful and generic strategy for steering active matter, aligning with recent experimental observations of active particles in patterned landscapes.

Motor-driven intracellular transport is often described in terms of motor activity, but macroscopic transport also depends on how effectively motor-generated force is converted into coherent motion. Motivated by cytoplasmic streaming, a minimal active transport network is examined in which motor-driven transport competes with an effective slip-related dissipative resistance. The model is not intended as a quantitative reconstruction of Nitella cytoplasmic streaming, but as a minimal system for isolating the relation between motor activity, resistance, and transport output. A controlled scan over $\gamma_{\mathrm{Slip}}$ and $\alpha_m$, with three independent seeds per condition, shows that increasing $\gamma_{\mathrm{Slip}}$ strongly suppresses mean transport speed while leaving the motor-bound fraction nearly unchanged. The mean load and motor force remain finite in the high-$\gamma_{\mathrm{Slip}}$ regime, indicating that motors remain mechanically active even when transport is suppressed. The dependence of transport speed on $\alpha_m$ progressively disappears with increasing $\gamma_{\mathrm{Slip}}$: the motor dominance ratio decreases from $R\approx1.69$ to $R\approx1.01$, and the corresponding velocity difference decreases from $\sim1.9~\mu\mathrm{m/s}$ to $\sim0.003~\mu\mathrm{m/s}$. These results indicate a dynamical crossover from motor-dominated to drag-dominated transport. The minimal model provides a compact physical scenario in which active force generation persists while its contribution to net transport is suppressed by increased effective dissipative resistance.

We investigate the effect of a high concentration (32.5 g.L$^{-1}$) of sodium chloride (NaCl) on TTAB (tetradecyltrimethylammonium bromide) vertical soap films also called foam films, pulled out of a bath under controlled humidity conditions. We observe that the film lifetime increases with relative humidity, both in the presence and absence of salt. At any given humidity, the presence of NaCl systematically enhances film stability. Our film thickness measurements show that the thinning dynamics with or without salt are nearly identical down to 100 nm. Down to that thickness, the effect of evaporation can be rationalised by a constant evaporation rate, which becomes non-negligible compared to the drainage rate at film thicknesses below 400 nm. The main effect of salt is the stabilisation of a Newton black film at a thickness of approximately 5~nm, whereas in the absence of salt, the film ruptures upon reaching a critical thickness of about 10 nm.

In confined turbulent rotating convection, the largest vertical velocities are found near the sidewalls in the form of wave-like structures known as wall modes. These structures persist deep into the turbulent regime, bias heat transport, and disrupt bulk flow organisation through radial jets. Controlling or suppressing wall modes is, therefore, essential for accessing bulk dynamics free from wall-induced effects. Here, we combine experiments and direct numerical simulations to investigate wall modes control in cylindrical cells equipped with ring-shaped sidewall barriers. Barriers suppress vertical-velocity maxima near the sidewall and disrupt the characteristic wave-like pattern. Simulations further show that the barriers reduce the wall-mode-induced enhancement of heat transport, shifting it towards values characteristic of laterally periodic domains. The suppression efficiency is governed by the ratio of the barrier width to the wall-mode scale and is enhanced by the addition of a second barrier. In the horizontal plane, radial jet ejections are attenuated, while the time-averaged flow reveals suppression of the boundary zonal flow (BZF), a ring-shaped region of positive azimuthal velocity near the sidewall, provided measurements are taken away from the immediate vicinity of the barriers. In this region, isotherms bend toward the poorly conducting barrier, creating a local misalignment with the isobars and inducing a baroclinic flow adjacent to the barrier faces. This effect weakens with increasing barrier conductivity or smoother geometry. These results demonstrate that sidewall barriers provide a robust route for suppressing wall modes signatures in experimental turbulent rotating convection, while locally inducing secondary baroclinic flows near the barriers. Their use enables access to extreme rotating-convection regimes with reduced sidewall influence.

This numerical study examines a strain-rate inconsistency in the conventional flamelet/progress-variable (FPV) formulation for non-premixed combustion and proposes an alternative coupling based on the turbulence kinetic energy dissipation rate, $\varepsilon$. Two-dimensional Reynolds-averaged Navier-Stokes (RANS) simulations of a transonic accelerating reacting mixing layer are performed using one-step kinetics, a conventional FPV model, and the proposed $\varepsilon$-$Z$ flamelet model. The analysis focuses on the relation between the RANS-computed mean strain-rate field and the local strain rate imposed on the flamelet through the coupling between the flow computation and the flamelet library. In the FPV formulation, the flamelet state is selected through a transported progress variable, whose evolution is governed by advection, diffusion, and chemical production rather than by the local strain-rate environment. The present results show that this can lead to preferential sampling of near-equilibrium flamelet states in high-strain regions, thereby weakening the intended connection between the computed flow field and the strain-rate-controlled flamelet response. In the $\varepsilon$-$Z$ formulation, $\varepsilon$ is used to infer the imposed flamelet strain rate, $S^*$, so that the local flamelet state is directly constrained by the modeled turbulence field and the pressure-dependent flammability limit. Selected species are transported explicitly, allowing products to persist through locally quenched regions, while a reactant-availability scaling limits tabulated source terms when the transported composition departs from the flamelet manifold.

The Richards equation (RE) is widely used to model water flow in unsaturated soils, but its performance in persistently wet grassland systems remains uncertain. This is particularly relevant in Irish grasslands, where soils often remain close to saturation for extended periods and seasonal waterlogging is common. Here, we evaluate the RE against three soil moisture datasets from County Wexford, Ireland, spanning different locations, soil types, and observation periods. We show that the standard RE formulation systematically over-predicts soil moisture under prolonged near-saturated conditions. We find that this arises from the commonly used Feddes plant water uptake function, which suppresses water losses under anaerobic conditions, despite continued evaporation from near-saturated soils. To address this limitation, we introduce a simple modification that retains a small non-zero water loss rate in the anaerobic regime. The modified model produces substantially improved agreement with observations across all three datasets. These results provide a systematic evaluation of RE-based soil moisture modelling in Irish grasslands. More broadly, they identify an important limitation of conventional RE implementations in waterlogged environments and demonstrate a practical approach for improving soil moisture predictions in persistently wet soils.

Large-scale circular gap closure occurs over a time scale on which cell growth and proliferation become important. Growth is the main driver of the closing process, while cell dynamics such as elongation and intercalation reflect elastic and fluidic contributions to tissue deformation. We develop a novel fluidized growth-elasticity framework as a nonlinear analogue of a Maxwell fluid with growth. The framework decomposes the experimentally observable strain rate into the additive sum of the growth, elastic, and fluidic strain rates, thus enabling the separate quantification of these contributions from tissue kinematics and allowing the roles of tissue elasticity and fluidity (the inverse of viscosity) to be characterized. We apply the model to large circular gaps ($\sim$1.7 mm in diameter) in confluent monolayers of mouse embryonic epicardial cells (MEC1) under two conditions, without and with TGF-$\beta$ treatment. We show that both tissue fluidity and the elastic properties associated with fiber reinforcement are critical for reproducing the closure kinematics. Specifically, we predict that the treated condition has lower fluidity, associated with a lower fluidic deformation rate and a higher elastic deformation rate than the untreated condition, in agreement with the experimental observations.

Compact representations of rarefied flows must preserve kinetic observables, not only smooth macroscopic fields. We introduce Gaussian kinetic representations for discrete velocity method (DVM)-Shakhov solutions of normal shocks and a lid-driven cavity. A positive log-density phase-space model reconstructs shock velocity distribution functions (VDFs) and their moments, while a moment-field model compresses wall-bounded cavity structure. Log-density training recovers heat flux, stress, and third- and fourth-order shock moments without explicit moment supervision; the cavity representation gives a compact continuous wall-transport map.

We study topological relaxation in ordered viscoelastic conformation flows at finite epsilon. In an ordered region, a positive spectral gap selects an oriented principal axis and hence an S^2-valued director with a Hopf class. We show that a change of this class must be accompanied, before the sharp-interface limit, by one of a finite list of costs: exterior gap concentration, ordered-core mass, boundary flux, FENE/collar loss, or a topology exit. The result is proved for a concrete Landau-de Gennes ordered-core closure coupled to an Oldroyd/FENE-type transport law. The structural hypotheses used in the argument are verified up to the first typed exit time: the Morse-Bott ordered well, tubular soft coordinates, massive-mode coercivity, a projected transported Ginzburg-Landau equation, exterior gap control, and tame FENE/collar coefficients. The projected Ginzburg-Landau equation separates translation modes from the remaining residuals. The translation modes give the normal line force, while the orthogonal soft, massive, geometric, and collar terms are absorbed by coercivity or charged to the corresponding exit. A modulated-energy argument propagates a nonempty class of vortex-tube data on regular intervals. On each such interval, the normalized core measures converge to an integral one-varifold satisfying a transported forced Brakke inequality with the computed force. The theorem therefore derives the force projection, open-basin propagation, and Brakke compactness estimates before invoking any limiting Brakke flow, and it records the finite-epsilon cost when the regular ordered-core description breaks down.

We compute the Lyapunov spectrum of the finite Euler ensembles, compact arithmetic fixed points of the rescaled momentum-loop equation for freely decaying incompressible Navier--Stokes turbulence. At finite cutoff \(N\), the tangential linearized problem is exactly solvable: the full Ising history \(\sigma_k=\pm1\) enters only through the closure winding \(qr=\sum_{k=1}^N\sigma_k\). The stability problem therefore reduces to an arithmetic spectral problem over reduced rational angles \(p/q\) and winding sectors \(r\). The continuum limit splits into three local sectors. For odd \(N\), both \(q\) and \(r\) are odd, so \(r=0\) is excluded by parity. For even \(N\), the zero-winding sector \(r=0\) is allowed and must be separated from the punctured sector \(r\ne0\). Their partition functions satisfy \(Z_{e,0}(N)/Z_{e,*}(N)\sim 6N/\pi^2\), so the zero-winding sector is a singular discrete zero mode, not part of the Gaussian \(r\)-continuum. The even zero-winding ensemble has a continuous tangential spectrum with positive Lyapunov exponents and is unstable. In the odd and punctured even ensembles, the spectral angle remains quantized, and for every fixed spectral label \(n\) the normalized eigenvalue law converges weakly to \(\delta_0\). Thus these two sectors are marginal fixed-mode Lyapunov limits. Their finite positive eigenvalues survive only as a vanishing arithmetic edge governed by coprime cotangent sums, Jordan totients, Dirichlet convolution, and \(\zeta(s)\). For \(d>2\), transverse perturbations are zero modes at linear order; in the two marginal sectors their quadratic obstruction is absorbed by a radial correction, leaving no quadratic spectral shift.

We consider the dynamics of inertial particles in unsteady fluid flows. At low Reynolds numbers, where the drag force is linear in the relative velocity, it is well-known that the dynamics admit an attracting, invariant, slow manifold which emerges as the perturbation of a normally hyperbolic critical manifold. However, at high Reynolds numbers, where the drag force is quadratic in the relative velocity, the critical manifold is no longer normally hyperbolic, and therefore its persistence has remained an open problem. Here, we resolve this issue by a particular application of the blowup method, which transforms the equations of motion to a generalized weighted cylindrical coordinate system, thereby desingularizing the dynamics on the critical manifold. We subsequently prove that the critical manifold persists under sufficiently small perturbations and derive the reduced equations of motion on the perturbed slow manifold to arbitrary accuracy. Our reduced equation differs from its linear-drag counterpart in its asymptotic expansion as well as its convergence rate. Using two examples, we demonstrate the validity of our slow manifold reduction. We also showcase an application of the reduced equations to the problem of source inversion in a turbulent dispersion model.

Price-based mean-field models of battery storage coordination usually assume that each agent responds to the true population-average charging power. Under that assumption, communication topology is irrelevant because the broadcast price already carries the coupling that matters. We study a nearby regime in which agents respond to a shared noisy forecast of the average, with correlation rho between agents' forecast errors. Analytically and in simulation, we find that topology remains undetectable in the effective-dimensional response of the fleet, even when neighbour observation is the only explicit communication signal. The mechanism is structural: the correlated forecast error projects onto the graph-invariant consensus mode, while topology acts through transverse modes. As rho N grows, the consensus-mode variance dominates and the spectral participation ratio approaches one independently of graph topology. Simulations on linear, star, and small-world graphs confirm that topology-induced variation is below the variation caused by redrawing the forecast noise. The result is not a claim that topology has no dynamical effect, but that shared stochastic forcing can mask topology-dependent modes in decentralized storage fleets.

We study properties of solutions, both evolving and equilibrium of the wave-kinetic equation describing ensembles of weak random waves governed by the Kadomstev-Petviashivli-I equations. The latter equation is integrable by the inverse scattering method, and yet it allows resonant wave interactions leading to redistribution of energy in the Fourier space. Such resonant interactions preserve an infinite number of invariants and we find that they preserve compactness of Fourier space supports. Numerically, we observe that the system can thermalize to one of the equilibrium states of Rayleigh-Jeans type, despite the common empirical belief that thermalization is impossible for integrable systems. The thermalized states are formed via non-local spectral transfers leading to creation of strong low-wavenumber peaks of the wave spectrum -- a process akin to Bose-Einstein condensation.

We investigate the origin and distribution of antiperiodicity -- oscillations satisfying $x(t+T)=-x(t)$ -- in the periodically driven Duffing--Holmes oscillator, combining analytical arguments with extensive numerical exploration. We first establish the minimal conditions, in terms of nonlinearity and symmetry, required for the existence of nontrivial antiperiodic trajectories, and we map how the antiperiodic, periodic, and chaotic regimes are organized in both phase space and parameter space. Antiperiodic orbits are shown to be precisely the periodic orbits that remain invariant under the half-period shift symmetry $S:(x,\dot{x},t)\mapsto(-x,-\dot{x},\,t+T_d/2)$, with $T_d$ the driving period, of the equations of motion. This invariance imposes a parity selection rule, verified without exception across our parameter sweeps: antiperiodic orbits lock to the drive only at odd multiples of the forcing period. Periodic orbits that lack the antisymmetry occur instead as conjugate pairs related by $S$, each orbit being the point reflection of its twin; the spontaneous symmetry breaking that takes place near the underlying bifurcations selects one member of each pair, while the pair as a whole restores the symmetry lost by each orbit individually. Antiperiodicity thus emerges not as an accidental property of particular waveforms but as the orbit-level manifestation of a discrete symmetry of the driven system.

When driven out of equilibrium, a Bose-Einstein condensate develops nonlinearly interacting density waves that trigger a turbulent cascade, transferring energy toward small scales. In this article, we investigate the nonstationary evolution of solutions to the two-dimensional Gross-Pitaevskii equation. Through numerical simulations of both the GPE and the corresponding Wave Kinetic Equation, we identify self-similar solutions relevant to atomic and polariton Bose-Einstein Condensates. These solutions exhibit characteristics of both first and second kind self-similarity. In particular, we show that the dynamics of the propagating front is universal, governed by a dimensionless universal constant $\beta$, which we determine numerically.

Photonic time crystals (PTCs) host momentum bandgaps, or k gaps, that enable parametric amplification and lasing of seeded fields. In nonlinear PTCs, Kerr saturation dynamically suppresses the exponential growth, reshaping k-gap amplification into an active, spatially homogeneous k gap soliton train. Here, we show that a localized perturbation on this unstable background then nucleates a transient spatiotemporal excitation: the breathing k gap event. Unlike Peregrine breathers emerging from modulational instability on a planewave background, this event extracts energy from competing host k gap solitons and remains sustained by their interaction. We identify this process as an instability on instability mechanism intrinsic to nonlinear k gap dynamics. The event is robust against noise and disorder, and can be deterministically reshaped into collective breathing patterns by periodic and phase engineered seeding. These results establish k gap engineering as a route to generating and controlling extreme spatiotemporal waves in photonic time varying media.

Aggregation and fragmentation processes are widespread in engineering and the natural world. Here, we investigate a distinct colloidal aggregation mechanism in an active system of motile bacteria in highly anisotropic environments. Specifically, we examine \textit{Escherichia coli} bacteria swimming in one-dimensional confinement within nematic liquid crystals and observe long-lived chains of bacteria swimming along the nematic director. Crucially, we find that longer chains swim faster, in apparent contradiction to fundamental force-balance models that predict the swimming speed to be independent of chain length, as chains should swim at the average speed of their individual components. The seeming discrepancy is resolved by recognizing that chains do not form randomly but self-organize due to the relative velocities between bacteria. To elucidate the physical mechanism behind this active aggregation process, we combine our experimental findings with a minimal model of nearest-neighbour aggregation and agent-based simulations of active particles aggregating in one dimension. Consistent with experimental observations, our agent-based simulations reveal a positive correlation between the length and speed of dynamically self-assembled chains of active particles, with the correlation depending on the variance of the individual speed distribution and diminishing over time. Together, our experiments and theoretical models indicate a distinct regime of swimming-limited aggregation whose evolution is constrained by the intrinsic speed distribution of active agents, providing new insight into bacterial self-organization.

We study a quasi-one-dimensional associating fluid composed of hard superellipses carrying two patches interacting through a directional Kern--Frenkel potential. Using the Transfer Operator Method, we show that the selective patch--patch association promotes horizontal alignment and chain formation at low-to-intermediate densities, whereas hard-core interaction favours vertical alignment without bonds at high densities. The competition between these two mechanisms drives a structural crossover upon compression from a horizontally aligned bonded chain structure to a completely unbonded, vertically aligned structure. While patchy ellipses undergo a tilted-to-vertical realignment, patchy rectangle-like superellipses exhibit a horizontal-to-vertical change. These structural changes manifest as a plateau in the equation of state. To capture these properties, we generalise Wertheim's first-order thermodynamic perturbation theory by introducing an orientation-dependent fraction of sites not in a bond. When combined with the Parsons--Lee hard-body theory, the orientationally resolved perturbation theory provides quantitatively reliable results for the structural properties and phase behaviour. Therefore, the generalised Wertheim theory together with Parsons-Lee theory can be suitable in higher dimensions, too.

Dielectric elastomers exhibit rich electromechanical instabilities arising from the coupling between mechanical deformations and electric fields. A widely used approach for analyzing instabilities in dielectric elastomers is the Hessian stability criterion proposed by Zhao and Suo (2007), which identifies the onset of instability of a homogeneous deformation but does not determine how the deformation develops beyond the instability threshold. To address this problem, we investigate dielectric membranes subjected to uniaxial tension and an electric field. Starting from a three-dimensional nonlinear electroelastic formulation, we derive asymptotically consistent reduced models, including a membrane model and a plate model, using the variational--asymptotic method. A linear bifurcation analysis first shows that the Hessian stability criterion is equivalent to a zero-wavenumber bifurcation condition, thereby establishing a direct connection between energy-based stability analysis and bifurcation theory. A subsequent weakly nonlinear analysis demonstrates that the zero-wavenumber bifurcation gives rise to localized necking, manifested as inhomogeneous thinning of the membrane. Furthermore, for the plane-stress configuration considered here, the membrane model accurately captures both the onset of instability and the associated localization behavior, while bending effects remain small. These results provide a physical interpretation of the Hessian instability and offer a framework for analyzing instabilities in dielectric membranes.

The conformation of polyelectrolyte (PE) brushes is highly sensitive to external conditions, particularly salt concentration and ion-specific effects. As salt concentration increases, PE brushes transition from an osmotic brush regime at low salt ($H \propto c_\mathrm{s}^{0}$) to a salted brush regime at high salt ($H \propto c_\mathrm{s}^{-1/3}$). However, deviations from this ideal scaling behavior are frequently observed in molecular simulations. In this work, we employ coarse-grained molecular dynamics simulations to systematically investigate how the sizes of counterions and co-ions affect the structural evolution and scaling behavior of PE brushes over a broad range of salt concentrations. Our results show that counterion size plays a dominant role in regulating ion penetration and coordination with PE monomers. At low salt concentration, smaller counterions penetrate more easily into the brush, leading to enhanced local charge compensation and stronger brush collapse. At high salt concentration, however, the brush height becomes largely insensitive to counterion size, while deviations from the classical scaling relation emerge. On the other hand, co-ion size mainly affects the system indirectly by modifying ion distributions and the local electrostatic environment. Smaller co-ions weaken local charge compensation and suppress brush collapse, with this effect becoming more pronounced at high salt concentration. When the sizes of counterions and co-ions are reduced simultaneously, the system exhibits a coupled response. Collectively, this work provides a microscopic understanding of how ion size and salt concentration jointly govern the structural response of PE brushes and the emergence of non-classical scaling behavior in realistic solution environments.

Fragility characterizes how rapidly a glass-forming liquid slows down upon supercooling, but whether strong and fragile behaviors arise from the same microscopic relaxation mechanism remains unclear. Here, we address this question using a density-tunable soft-repulsive binary mixture spanning distinct fragility regimes and analyze particle jump dynamics within the framework of dynamic disorder. Across these regimes, we show that increasing fragility leads to progressively broader cage-lifetime distributions and increasingly non-exponential survival probabilities, revealing non-Poisson cage-to-jump statistics governed by fluctuating jump rates and slowly evolving structural variables. To characterize their structural origin, we first identify the neighbor ranks most strongly coupled to jump motion using Kullback-Leibler divergence and Pearson correlation analyses. We then introduce a structural slowness parameter that combines these neighbor-distance fluctuations into a reduced slow coordinate for constructing the slow-fluctuation survival probability. A comparison with the actual survival probability shows that localized neighbor-distance fluctuations control the jump rate in the strong regime, whereas extended neighbor rearrangements become relevant in the intermediate and fragile regimes, increasing the effective dimensionality of the slow-variable space. In the fragile regime, distance-based descriptors alone become insufficient at the lowest temperature, where the Voronoi free volume captures additional cage-volume fluctuations in the rate-controlling slow variable. Point-to-set correlations grow with fragility, but the spatial extent of the slow variables exceeds the point-to-set length. These results show that fragility changes the structural bottleneck for microscopic rate fluctuations, linking dynamic disorder and multidimensional slow variables.

We study the inverse problem of classical density functional theory for inhomogeneous fluids: finding the wall potential that produces a constant equilibrium density profile, i.e., a perfectly flat density distribution in the accessible region adjacent to a substrate. Within Rosenfeld's fundamental measure theory, we solve this problem for a one-component fluid in planar, spherical, and cylindrical geometries, considering both a hard-sphere fluid and a fluid with an additional truncated Lennard-Jones attraction treated at the mean-field level. Explicit analytical expressions are obtained for planar walls, while spherical walls also admit an analytical treatment in a more cumbersome form. The cylindrical case is treated numerically. The construction provides an explicit microscopic realization of structure-cancelling wall fields, related to flat-profile conditions that occur under special matching conditions in interfacial theories of wetting and drying. The theory also yields a compact collection of formulae for weighted densities and one-body direct correlation functions in the three fundamental geometries, providing useful reference expressions for density-functional implementations. The resulting analytic wall potentials are validated in independent density functional calculations, which confirm that the prescribed flat profiles are recovered within numerical accuracy.

Phantom chain simulations have shown that the mean rupture properties of star polymer networks collapse onto master curves against the cycle rank density $\xi$. This study revisits this universality with a much larger ensemble than in earlier studies to discuss the statistics. Phantom Gaussian networks were made by end-linking star prepolymers, and 1,000 realizations were collected for each of 30 conditions with functionality $f=3$--$8$ and conversion $p=0.60$--$0.95$, giving 30,000 networks in total. For each realization, the breaking stretch $\lambda_b$, the breaking stress $\sigma_b$, the breaking energy $W_b$, and the cycle rank $\xi$ were recorded. The master curves are unchanged by the larger sample, demonstrating that the earlier conclusions reported for the averages of smaller ensembles hold. However, the individual realizations are inherently random, and their statistical properties, rather than the individual values, are examined. At fixed $f,p$, the fluctuation of $\xi$ is small, varying by less than 0.01, whereas $\lambda_b$, $\sigma_b$, and $W_b$ scatter by 0.05--0.3. The fluctuation of $\xi$ is almost uncorrelated with that of the breaking properties. In addition, the scatter has a definite structure; its magnitude decreases with the mean cycle rank density $\xi$, the $\lambda_b$--$\sigma_b$ correlation grows with $\xi$, and the distributions deviate from Gaussian. The $\lambda_b$ distribution is skewed to the right at small $\xi$, whereas $\sigma_b$ is skewed to the left at large $\xi$. These rupture statistics were discussed in the framework of extreme-value statistics to demonstrate that the observed trends are opposite to those of the random fuse model, in which strength decreases with size and weakest-link statistics appear for weak disorder. The difference may reflect the source of fluctuation, i.e., the cross-linking in the present networks.

Chirality gives a microswimmer something a straight-line swimmer lacks: a phase. This variable both modulates, and is affected by, the hydrodynamic interactions between microswimmers. Here we ask what collective order emerges when many such chiral swimmers are free to move, and how the shape and actuation anisotropies of an individual swimmer dictate the outcome. Using a kinetic theory for hydrodynamically interacting circle swimmers, we show that the interplay between intrinsic rotation, stresslet flows, and Jeffery-like reorientation generates effective phase-locking interactions. Asymmetries in the actuation are encoded through a non-axisymmetric stresslet tensor. At the pair level, pusher swimmers select one of two synchronized states depending on particle shape and actuation asymmetry: in-phase/anti-phase locking, or quarter-shifted locking. Extending the analysis to many-body systems, we find that these pair-level synchronization mechanisms drive emergent collective phases. The swimmers develop global \textit{synchro-nematic} order when the hydrodynamic coupling favors parallel or anti-parallel phase locking, and \textit{synchro-antinematic} local order where quarter-shifted locking prevails. A coarse-grained field theory predicts the onset of nematic order through a hydrodynamic instability criterion. In addition, we find that the collective states exhibit crystalline or disordered hyperuniform structure arising from period-averaged hydrodynamic interactions that are effectively repulsive between swimmers. Lattice Boltzmann simulations of chiral oblate squirmers, resolving finite-size and near-field flows, recover the synchro-nematic ordering. Together, these results show how a swimmer's geometric and actuation anisotropies can be leveraged to program synchronization and spatiotemporal order in chiral active matter.

Physics-informed neural networks (PINNs) for elastic contact mechanics suffer from a spectral stiffness imbalance,that is, the elastic kernel grows linearly with wave number, causing short-wavelength modes to dominate gradient updates and stall convergence of the macroscopic deformation. We introduce a spectral preconditioning strategy that reweights displacement gradients in Fourier space before back-propagation, amplifying low wavenumber components through a mass weighting (MW) function while suppressing sub-grid noise via a built-in low-pass filter. Applied to adhesive line contact problems, the mass weighted PINN reaches machine-zero residual loss within 400 Adam iterations for specified benchmark, whereas the reference benchmark stalls at three orders of magnitude higher loss. The converged displacement and contact stress fields agree quantitatively with Green's function molecular dynamics (GFMD) solutions for both smooth Hertz contact at pressures spanning tension to compression and rough surfaces with roughness covering several decades of wavelength. The method operates directly on a uniform real-space grid, requires no explicit Green's function integration or quadrature rules, and is formulated entirely in terms of minimising a scalar energy function. Extension to two-dimensional rough surfaces is direct, as both the Fourier elastic energy and the spectral preconditioner depend only on the wave-number magnitude.

We use fully resolved nematohydrodynamic simulations to study deformation statistics of a passive nematic droplet in two-dimensional extensile active-nematic turbulence. We find that the droplet aspect ratio serves as a scalar probe of the active bath. Its increments show heavy-tailed distributions with dependence on the time lag, scale-free burst statistics and multiscaling structure functions which establish temporal intermittency. While the mean deformation increases with activity, normalized intermittency is strongest at lower activity. This suggests slower and more coherent bath forcing. When compared with translational and forcing-side fluctuations, it reveals a hierarchy of intermittency: shape is more weakly intermittent than translation and active-stress fluctuations, consistent with filtering by interfacial restoring forces. Power spectra show an extended near-$1/\omega$ regime for the maximal normal interface velocity, distinct from the steeper, approximately $1/\omega^{2}$ spectrum of the interfacial active stress. Soft inclusions thus reveal how interfacial restoring forces convert active forcing into bursty, scale-rich deformation dynamics.

We formulate a continuum model for a compressible lipid-bilayer membrane immersed in Stokes flow, replacing exact local area inextensibility by conservation of an areal phospholipid density. The membrane free energy combines Helfrich bending, spontaneous curvature, and a finite area-compression penalty, so that membrane tension becomes a constitutive response to lipid-density variation rather than a Lagrange multiplier enforcing local area conservation. The resulting interfacial stress includes normal elastic forces and tangential Marangoni stresses generated by lipid redistribution; these stresses arise from membrane compressibility and can produce an effective negative tension when the local lipid density exceeds its preferred value. We further derive the linear stability of circular membranes in two dimensions and spherical membranes in three dimensions under full Stokes hydrodynamic coupling. In both cases, bending stabilizes the base shape, while excess lipid density destabilizes it by favoring increased membrane area. The first instability occurs in the lowest nontrivial shape mode, m = 2 in two dimensions and j = 2 in three dimensions. Energy expansions near onset show that the two-dimensional instability is a pitchfork bifurcation, whereas the three-dimensional instability is generically transcritical because prolate and oblate perturbations are geometrically distinct. These results provide a controlled compressible extension of classical vesicle mechanics and directly connect lipid-density variation, membrane tension, hydrodynamic coupling, and shape instability.

We give a comprehensive account of the recent entropy density functional theory for the equilibrium statistical mechanics of classical many-body systems ( arXiv:2606.28240 ). The approach is formally exact and based on a joint grand potential minimization principle for the one-body density and the global pair distance distribution. These variational fields depend respectively on position and on scalar distance, which retains the low computational complexity of standard density functional theory. Correlations effects are contained in a unique excess entropy functional, which is universal across all systems with pairwise interparticle potentials. Functional differentiation yields entropic direct correlation functionals that generate entropic response and fluctuation correlation functions via coupled Ornstein-Zernike equations. Two alternative proofs are given for the existence and uniqueness of the underlying metadensity functional map, based on generalizations of either Levy's constrained search method or Mermin-Evans proof by contradiction. Simple excess entropy approximations yield the standard mean-field and second-virial excess free energy density functionals. We describe exact entropic functional line integrals, make connections to the recent one-body fluctuation profiles, and generalize the entropy approach beyond pairwise interparticle potentials.

Shear of three-dimensional, highly compressed granular packings is simulated using a bonded particle approach that explicitly resolves elastic deformation. Varying Poisson's ratio $\nu$ produces significant changes in rheology, packing structure, and grain morphology. During flow, conventional systems ($\nu > 0$) readily crystallize while auxetics ($\nu < 0$) resist ordering. This duality reflects the fact that conventional grains develop polyhedral-like facets but conserve volume while auxetics behave oppositely, demonstrating an unexpected interaction between elasticity, geometry, and crystallization.

Classical nucleation theory (CNT) describes the formation of a stable phase from a metastable one in terms of a single reaction coordinate that corresponds to the radius of a nucleating droplet. In this work, we provide a full account of nonequilibrium nucleation theory (NNT), which generalizes CNT to non-equilibrium field theories with non-conserved order parameter. We present two equivalent derivations of the dynamics of the droplet radius: a stochastic route, based on a direct projection of the stochastic field equation onto the radial reaction coordinate, and a route based on the minimization of the Freidlin-Wentzell action. Crucially, the quasipotential barrier predicted by NNT differs from the one found when assuming the instanton to be the time-reversal of the relaxation dynamics. Whereas the interfacial density profile differs from that on the relaxation path, an analytical derivation of NNT remains possible using a careful definition of the reaction coordinate. This leverages the perturbative structure that (in common with CNT) emerges in the limit of large critical radius. We further derive with similar techniques the dynamics of capillary waves, whose stability is required for the CNT/NNT precept of a near-spherical droplet to prevail. After deriving our theory for generic non-conserved field-theories, we address two explicit examples: a non-equilibrium generalization of Model A (Active Model A), and a population dynamics model (with two choices of noise that each break time-reversal symmetry). In both cases, we validate our analytical NNT against numerical results obtained by action minimization, with excellent agreement. NNT provide a systematic framework for constructing nucleation theories in a broad class of non-equilibrium systems from active matter, reaction-diffusion systems and population dynamics.

We study a Brownian particle in a harmonic trap whose stiffness switches between two values with arbitrary waiting-time statistics, generating semi-Markovian dynamics. To treat the resulting temporal memory, we formulate the problem in an enlarged age-structured state space, restoring Markovianity and yielding a local Fokker--Planck description. Within this framework, we derive exact steady-state integral equations for the spatial and birth distributions and obtain exact expressions for stationary moments, injected power, and potential energy. In the second part of the paper, we analyze the stochastic-resetting limit, corresponding to a particle alternately released and trapped. By representing the stationary spatial distribution as a superposition of Gaussian states with fluctuating variance, the problem can be reformulated as a switching process in variance space. This yields exact integral equations for the variance distributions and leads to a simplified description amenable to direct analytical treatment.

Artificial atom-like systems are a promising candidate for next generation quantum processing. Among them, dark excitons exhibit one of the longest lifetimes at high temperatures. Here, we demonstrate coherent control of dark excitonic states in metal-organic chalcogenolates (MOChas) by using an ultrafast pulse shaper at room temperature. These dark exciton states are optically accessed via two-photon absorption and directly read out with a four-wave mixing process. The system is described by a non-perturbative, two-photon Hamiltonian based on well-known atomic physics and applied to a three level system comprised of two dark excitons. Empirical and theoretical state specific optical access is shown via a simple optical pulse shape. The developed Hamiltonian-based description is a first step towards a quantum processing platform using three-level systems and two photon transitions, one example being dark excitons in the MOCha silver benzeneselenolate (mithrene). Simple conditions for gate operations are laid out and described.

Dynamics of two short semi-flexible fibers settling under gravity in a viscous fluid are investigated at Reynolds numbers Re << 1. We focus on fibers initially relatively close to each other, and we check if later they approach an aligned horizontal configuration, previously identified numerically (Bukowicki and Ekiel-Jezewska, Soft Matter 46 (2019) 9379) as attractive for symmetric initial conditions of moderately elastic filaments. In our experiments, two semi-flexible ball chains sediment in a highly viscous silicone oil. They are initially straight and close to a parallel horizontal relative configuration. Their motion and shape deformation are recorded using two synchronized cameras. For most of the trials, ball chains stay together, with damped oscillations around the symmetric aligned configuration. For a few initial conditions, the ball chains move away horizontally or vertically. To study the behavior over a longer time, we perform numerical simulations, modeling moderately elastic filaments as chains of identical beads, with the centers of consecutive beads connected by springs and with the fibers' elastic resistance to bending. Different initial positions and orientations are considered. Their dynamics are determined by the multipole expansion of the Stokes equations, implemented in the precise Hydromultipole numerical code. For short times, we observe the similar dynamics of semi-flexible ball chains and moderately elastic filaments. We provide examples of long-time numerical simulations illustrating that elastic filaments close to each other can move away horizontally or vertically, but after a long time, come back and perform damped oscillations while approaching the aligned configuration with almost touching filament ends. We confirm the attractive nature of the aligned configuration of very close semi-flexible sedimenting fibers, even if they are far away from each other.

We present a complete field-theoretical renormalization-group (RG) analysis of the Brownian Ising Model (BIM), in which a $\mathbb{Z}_2$ order parameter is coupled to a passive conserved density, breaking detailed balance. Using the Martin-Siggia-Rose formalism and an $\epsilon=4-d$ expansion, we show that this density-order parameter coupling is RG-relevant below four dimensions and drives the system to a new non-equilibrium fixed point, distinct from the Ising universality class. Critical exponents are computed at lowest nontrivial order, some of which require a dedicated two-loop analysis. At large scales, the density acts as an effective noise that is white in time but long-range in space, enhancing order-parameter fluctuations and producing a negative anomalous dimension $\eta$. A defining feature of the new class is that the correlation and response functions acquire different anomalous dimensions, $\eta \neq 2 - \gamma / \nu$ - a direct, observable signature of fluctuation-dissipation-theorem violation at large scales that cannot occur in equilibrium. We also find a small correction-to-scaling exponent, implying large preasymptotic corrections that must be accounted for in numerical and experimental tests. We further derive a set of relations among renormalization factors that hold to all orders in perturbation theory, following from the linearity of the density dynamics and an emergent shift symmetry. These yield an exact scaling relation $\nu = 2/(d+z-2)$ at the BIM fixed point and establish that the Ising universality class, as well as that of quenched diluted-Ising, is unstable in $d=3$. This establishes the BIM fixed point as the unique infrared attractor for any nonzero diffusion constant.

The Ising universality class is remarkably robust to non-equilibrium perturbations, which generically flow to zero under renormalization. We show that this robustness fails when an order parameter is coupled nonreciprocally to a conserved diffusive density. Below $d_c=4$, the renormalization group flows to a fast-diffusion fixed point at which the density acts as a long-range multiplicative noise, producing a novel universality class. The non-equilibrium nature of the fixed point is manifest in the large-scale violation of the fluctuation-dissipation relations, reflected in a splitting of the scaling exponents of the two-point correlation and response functions--a measurable hallmark of non-equilibrium critical fluctuations. A two-loop calculation establishes the stability of this fixed point but yields a small correction-to-scaling exponent $\omega\approx0.020$ in $d=3$, implying strong finite-size corrections. An all-orders modified Harris criterion $\nu>2/(d+z-2)$ confirms that the BIM fixed point governs criticality in $d=3$, with Ising universality recovered only at $d=2$.

Fully developed isotropic turbulence exhibits a dual nature: a continuous, scale-invariant energy cascade coexists with discrete, intense vortex filaments. We show that this duality arises from a spontaneously broken SO(3) gauge symmetry. By identifying the specific angular momentum $\mathbf{L} = \mathbf{r}\times\mathbf{u}$ as a non-Abelian gauge connection and the radial velocity $u_r$ as a Higgs field, the turbulent vacuum is described by the SO(3) Georgi-Glashow model. When the radial strain condenses, the symmetry breaks SO(3) $\to$ U(1), generating a topological mass gap $M_W = gv$. This gap partitions the energy into a massless U(1) sector (the solenoidal background) that sustains the Kolmogorov cascade, and a massive SO(3)/U(1) sector that is confined to vortex filaments. Using high-resolution DNS data (JHTDB, $Re_\lambda\approx433$), we empirically verify three key predictions: (i) the energy spectra obey a strict 1:2 equipartition over the inertial range, with a sharp divergence at $M_W \approx 40$; (ii) the radial Higgs field extracted around isolated vortex cores follows the exact BPS monopole profile $H(r)=\coth(r/\eta)-\eta/r$ with $\eta = 0.0093$ domain units and the VEV $v = 0.338$, identifying the ubiquitous "worms" as macroscopic 't Hooft-Polyakov monopoles; (iii) the Wilson loop computed from the velocity field exhibits a clean area law $\langle W_C \rangle \sim e^{-\sigma A}$ with string tension $\sigma = 0.303 \pm 0.009$, directly confirming the confining nature of the turbulent vacuum.

Nanosecond-pulsed dielectric barrier discharge (DBD) plasma actuators were investigated on a generic blunt body in a Mach 6 Ludwieg tube to characterize the pressure and thermal perturbations relevant to hypersonic boundary-layer transition control. Complementary quiescent experiments were also conducted over ambient pressures representative of those predicted in the model nose region to isolate the influence of local thermodynamic conditions on actuator operation. Pulse-energy measurements and schlieren imaging showed that decreasing pressure reduced the deposited electrical energy per pulse, weakened the actuator-generated shock, and increased the spatial extent of the residual heated region owing to energy deposition over a larger plasma volume. Under Mach 6 Ludwieg-tube conditions, the actuator-generated shock interacted with and reflected from the detached bow shock, temporarily increasing the bow-shock stand-off distance by approximately 11%, while the residual heated region was advected downstream along the body. The schlieren images further permitted the evolution of the thermal disturbance to be distinguished from that of the actuator-generated shock. The results demonstrate two distinct perturbation mechanisms -- a short-duration compression wave and a longer-lived thermal disturbance -- whose relative importance is governed by the local thermodynamic conditions and which may independently promote hypersonic boundary-layer transition.

A thermal convection apparatus has been designed to study turbulent super structures at high Rayleigh numbers and Prandtl numbers of the order of unity. This apparatus consists of a rectangular cell with a length of $3.50\,\mathrm{m}$, width of $0.35\,\mathrm{m}$, and variable height, which is fixed at $0.70\,\mathrm{m}$ for the present study. This cell is installed inside a $5.6\,\mathrm{m}$ long pressure vessel facility, known as \emph{Göttingen Uboot}, which can be filled with compressed gasses (air, helium, nitrogen, or sulfur hexafluoride) at pressures up to $19\,\mathrm{bar}$, enabling Rayleigh numbers up to $ Ra \leq 5\times 10^{12}$ and Prandtl numbers of approximately $0.7 \leq Pr \leq 0.9$. The convection cell is bounded vertically by top and bottom plates consisting of a three-layer composite structure in which a thin Lexan plate is sandwiched between highly conductive aluminum plates. This allows for spatially resolved heat flux measurements. Each plate is subdivided into four longitudinal segments that can be independently temperature-controlled to enable homogeneous temperatures and the imposition of horizontal temperature gradients at both the top and bottom boundaries. While the bottom plate is electrically heated, the top plate's temperature is regulated using temperature-controlled circulating pressurized water. The apparatus is well suited for precise heat flux measurements, with the results obtained being in good agreement with those previously reported in the literature.

We present a method for estimating the hydrodynamic coefficients in the Cummins equations using time-series data from a moving body, such as a floating offshore structure. The proposed data-driven method is based on incorporating the Cummins equations governing the dynamics of a structural body interacting with water waves into a physics-informed neural network (PINN), along with available motion data. The proposed method first estimates the structure's state in terms of translational and rotational degrees of freedom, and then solves the inverse problem to determine the hydrodynamic forces acting on the body, expressed in terms of added mass, damping coefficients, and/or hydrostatic restoring. The Cummins equations are formulated as a first-order system, and both state and parameter estimation are performed using PINNs. The method is verified on the free decay of a sphere and a box. The results demonstrate that it is possible to estimate the state and hydrodynamic coefficients accurately, although accuracy depends on the volume and quality of the movement data.

This study presents a near-real-time, meter-scale three-dimensional urban wind simulation framework for low-altitude flight events in complex urban meteorological environments. It reconstructs high-resolution wind fields by combining sparse observations with efficient microscale flow modeling. The framework integrates lattice Boltzmann method large-eddy simulation (LBM-LES), high-fidelity urban morphology reconstruction that explicitly resolves real building details, and observation-driven boundary assimilation into a rapid end-to-end pipeline for realistic urban domains. Multi-site Doppler lidar measurements from dense urban Guangzhou, China, are used for evaluation. The system reconstructs three-dimensional wind fields at 5 m resolution over kilometer-scale domains within minutes. Robustness and accuracy are tested through controlled observation reduction, independent validation against withheld lidar stations, and sensitivity analyses of grid resolution and precursor domain extent. Results show stable reproduction of vertical wind structures and key local flow features under complex morphology and limited observations, providing a scalable pathway for near-real-time urban wind reconstruction.

Urban Air Mobility (UAM) requires reliable assessment of low-altitude wind hazards, because winds, gusts, and building-induced turbulence have been recognized as critical factors affecting vehicle stability, route feasibility, vertiport siting, and airspace management. While wind-tunnel experiments, computational fluid dynamics (CFD), multiscale downscaling, reduced-order models, and UAV planning datasets have advanced wind-aware analysis, public resources for data-driven, city-scale UAM planning remain limited in geographic coverage, scenario diversity, vertical extent, building realism, and task-oriented benchmarking. To address this gap, we introduce U3DWind, a building-resolved low-altitude wind-field dataset generated using our GPU-accelerated Lattice Boltzmann Method--Large-Eddy Simulation (LBM-LES) framework for rapid urban flow simulation. U3DWind covers five megacities in China: Beijing, Shanghai, Guangzhou, Shenzhen, and Hong Kong. It contains 720 simulations, with 16 inflow directions, three reference wind speeds, and three seasonal atmospheric scenarios (annual, summer, and winter) for each city. At a 10 m grid resolution, the dataset provides three-dimensional three-component (3D3C) velocity, turbulent kinetic energy (TKE), flow density, and fluid--solid masks. To support operationally relevant evaluation, we further define five baseline tasks: wind-field prediction, sparse-sensor wind-field reconstruction, site wind-exposure ranking, airworthiness wind-compliance risk scoring, and noise propagation modeling. As a multi-city, building-resolved 3D urban wind-field dataset, U3DWind enables systematic evaluation of wind-induced impacts in low-altitude traffic scenarios and provides an open benchmark for urban airspace management and data-driven high-fidelity urban flow simulation.

Data-driven turbulence closures are usually calibrated by inverse methods that place a CFD solver inside the optimization loop, tying the learned model to a particular discretization and requiring every intermediate iterate to converge. We instead train closures inside a physics-informed neural network (PINN): the RANS residual is imposed by automatic differentiation, making the inverse problem mesh-free, differentiable, and solver-agnostic. Because no forward solve runs during training, only the final closure must be solver-stable, arbitrary neural closures are admitted without deriving adjoints, and iterative solver costs are avoided. Each constitutive hypothesis trains in minutes on a single GPU, enabling rapid screening of closure forms. We develop four closures: three model the Reynolds stress on a tensor basis with built-in realizability (a local map, a non-local model transporting turbulent kinetic energy, and the same with a learned length scale l), while a fourth models the Reynolds force F = -\nabla \cdot \tau directly, free of realizability constraints. The closures are trained across six 2D bluff-body wakes at Re = 10^4 and deployed frozen in a finite-element solver. Coupled stability is enhanced by input-gradient smoothing and a Lipschitz constraint. We assess closures in-sample and under a strict leave-one-shape-out (LOSO) protocol. All four improve substantially on a steady SST k-\omega baseline. The learned-length-scale stress closure is most accurate on stress fields, while transporting kinetic energy is decisive for generalization. Notably, the force model generalizes best and attains the lowest out-of-sample error on mean velocity and drag (LOSO drag error ~8.5%). Finally, we show these closures can be efficiently trained on PIV data, enabling data-driven modeling for geometries intractable for DNS.

Repeated prediction of acoustic fields from spatially distributed boundary excitation is computationally expensive when each source realization requires a new wave simulation. This work introduces a quadrature-aware complex-linear boundary operator (CLBO) that maps complex normal velocity on a vibrating surface to complex pressure at receiver locations. The model couples learned source and receiver basis functions through an explicit complex surface-quadrature contraction, so the boundary excitation enters linearly by construction. This preserves complex superposition, homogeneity, and zero response to zero excitation, while representing the source through coordinates, normals, and quadrature weights rather than a fixed flattened input vector. Reference data were generated using a verified three-dimensional multiple-relaxation-time (MRT) lattice Boltzmann solver and stored in a solver-agnostic boundary-to-field format. CLBO was compared with a fixed-sensor complex DeepONet under matched case splits and optimization settings, with additional tests of structural consistency, receiver-coordinate interpolation, source discretization, source-family holdout, label efficiency, physics-informed ablations, unseen source mixtures, and computational cost. Across five training seeds, CLBO achieved a mean complex relative field error of 0.184 +/- 0.00771, compared with 0.367 +/- 0.00742 for DeepONet. Its measured source-superposition error was 1.31 x 10^-7, and its mean error on newly simulated mixed-source cases was 0.237, compared with 0.415 for DeepONet. Inference was 1.83 x 10^4 faster than the reference calculation for the reported query size. These results show that enforcing the known complex-linear boundary-to-field structure improves physical consistency and generalization under distributed acoustic excitation.

Uncovering the physical mechanisms of turbulent flows remains a fundamental challenge in fluid mechanics. In particular, conventional velocity-gradient analysis methods suffer from shear contamination, which hinders accurate identification of the dominant physical mechanisms. This study presents PhysMiner, an automated framework integrating the triple decomposition method of the velocity gradient tensor with large language model-driven reasoning for turbulence-physics discovery. The triple decomposition module automatically decomposes flow fields into rigid rotation, pure shearing, and normal straining components, enabling statistical analysis, contour visualization, vortex-line extraction, and threshold-insensitive vortex identification while eliminating shear contamination. These automated capabilities are validated across five benchmarks, ranging from canonical configurations to complex engineering flows. A discover-physics agent combines flow statistics, spatial structures, and literature-derived knowledge to perform pattern recognition and physical inference, while a review Agent iteratively validates physical consistency to ensure reliable conclusions. A continuously evolving Triple Decomposition Library accumulates statistical knowledge from successfully analyzed flows, enabling cross-case comparison and progressive enhancement of inductive capability. The complete PhysMiner pipeline is validated end-to-end on the periodic hill flow, where the framework autonomously generates turbulence modeling recommendations and derives an improved subgrid-scale model with superior Reynolds-stress predictions. PhysMiner is open to the public and establishes a foundation for long-term collaborative advancement in automated turbulence-physics discovery.

The mechanisms governing transverse force generation on a sphere with asymmetric dimpled roughness are investigated using wall-resolved large eddy simulation at $Re=U_\infty d/\nu=100{,}000$ for $k/d=0.004$, $0.006$, and $0.008$. Previous experiments by Sudarsana et al. (2024) showed that asymmetric roughness can generate lift comparable to the peak Magnus force on a rotating sphere while leaving the mean drag nearly unchanged. The present simulations reproduce this behavior and reveal the coupled mechanisms responsible for lift generation and drag invariance. Pressure-force decomposition shows that asymmetric dimples redistribute the streamwise pressure contribution between the upstream and downstream hemispheres with little change in net drag, while producing a finite transverse pressure imbalance that generates lift. A Fourier decomposition further shows that pressure drag is governed primarily by the axisymmetric pressure component, whereas lift is governed by the non-axisymmetric component. The dimples also produce distinct transition pathways on the two hemispheres: the dimpled side undergoes near-wall transition before separation, delaying separation non-uniformly to $\phi_s\sim105^\circ - 125^\circ$, while the smooth side separates in a laminar state at $\phi_s\sim80^\circ$. The resulting pressure asymmetry drives sidewash from the smooth to the dimpled side, which rolls up into a counter-rotating streamwise vortex pair that amplifies wake deflection beyond that expected from separation-angle differences alone. These results show that lift generation arises from the coupled interaction of asymmetric transition, non-uniform separation, pressure-driven sidewash, and coherent wake reorganization.

We extend our recently proposed framework (Chaparian, Phys. Rev. Fluids 10(9) 093301, 2025) for deriving a Darcy-type law governing viscoplastic flows through porous media to incorporate more applied aspects. In particular, the present work considers a more realistic rheological model (i.e. Herschel-Bulkley, describing the shear-thinning nature of practical yield-stress fluids) along with a wider range of porous media topologies. In our earlier work, the problem was addressed by decomposing the full Bingham number spectrum (representing the ratio of the yield stress of the fluid to the characteristic viscous stress) into three main regions: (i) low Bingham numbers (weak yield stress limit) corresponding to Newtonian flow, (ii) high Bingham numbers (strong yield stress limit) representing yield limit/plastic flow, and (iii) intermediate Bingham numbers (transition regime). By deriving theoretical models for the two asymptotic limits of the spectrum and combining them, we obtained a Darcy-type law applicable across the entire range of Bingham numbers. In contrast to our original work, where the weak yield stress limit reduces to a Newtonian flow, here, this limit instead follows a power-law asymptote that captures the shear-thinning dominated behaviour of Herschel-Bulkley fluids. In the present study, we derive a scaling to address this limit. The framework is further generalised to incorporate a broader spectrum of porous media topologies, enabling a systematic assessment of how pore geometry influences the resulting macroscopic flow law. The proposed framework provides a unified theoretical basis for predicting yield-stress fluid transport through complex porous media and establishes a pathway towards finding macroscopic models applicable to a wide range of natural systems and industrial processes.

The phase-field model regularizes sharp fractures into a diffuse representation, blurring the boundary between the fracture and the intact material. This blurring makes it difficult to capture distinct domain processes in hydraulic fracturing, where Reynolds flow governs the fracture and Darcy flow describes the surrounding porous matrix. Consequently, the blurred delineation artificially smears the pressure field across the fracture--matrix interface, which is acceptable in toughness-dominated hydraulic fracturing regimes where pressure drops within the fracture are negligible. However, in viscosity-dominated regimes, typically for actual subsurface injections due to high injection rates, the fluid pressure drops more drastically, and the fluid front may even lag behind the propagating fracture tip, a phenomenon that a smeared pressure field cannot capture. Despite its relevance, the viscosity-dominated regime has not been addressed by any existing phase-field models to date, likely due to its numerical instability. In this study, we propose a dual--continuum phase-field model based on double-porosity microporomechanics that explicitly separates mesoscale crack pressure from micropore pressure. The framework provides a variationally consistent formulation alongside phase-field--dependent poroelasticity. To ensure the numerical stability of the hydromechanical coupling, a fixed-stress split scheme is modified for two independent fluid pressures, while a variational inequality constraint is applied to reproduce fluid lag. Verified against the closed-form solutions in toughness-dominated, viscosity-dominated, and early-time transitional regimes, the model accurately captures complex fluid flow behavior and transient fluid lag within the fracture, and opens a new frontier for applying phase-field models to realistic viscosity-dominated hydraulic fracturing.

High-fidelity simulations of the Navier--Stokes equations (NSE) generate massive amounts of data, motivating the need for efficient compression and reconstruction strategies for turbulent flows. At the same time, reconstructing flow fields from sparse measurements while retaining spectral content, turbulence statistics, and coherent structures remains a major challenge. This work investigates two complementary paradigms for turbulent flow reconstruction: supervised reconstruction and physics-informed reconstruction, in the context of transition to turbulence induced by three-dimensional distributed roughness elements. We introduce a vorticity-augmented supervised approach and a physics-informed approach, implemented through a partially assisted compressible PINN formulation based on the three-dimensional unsteady compressible Navier--Stokes equations. Reconstruction performance is evaluated at different sparsity levels using instantaneous velocity fields, mean-squared error, energy spectra, Reynolds stresses, turbulent kinetic energy, and Q-criterion isosurfaces. Rather than establishing a universal winner, the present study characterises the respective strengths, limitations, and operating regimes of these two approaches. The results indicate that at lower sparsity levels, the vorticity-augmented supervised model yields the lowest reconstruction error, recovers key statistical and spectral features, and enables substantial data compression. The PINN shows potential to reconstruct turbulent flows from sparse measurements without high-resolution labels and exhibits comparatively stable held-out extrapolation behaviour at higher sparsity. These results suggest the potential of combining data-driven and physics-informed learning for flow data compression and physics-informed reconstruction of turbulent flows from sparse data.

The accurate simulation of urban flow is key to designing building ventilation, understanding cities' micrometeorology, and predicting pollutant dispersion. Reynolds-Averaged Navier-Stokes (RANS) simulations are a common modelling approach for simulating urban flow, but their accuracy depends on the closure model and its parameters. These parameters are inferred from benchmark cases, but they are not necessarily suitable for realistic urban environments, which involve different physical mechanisms. This is referred to as the transferability problem of RANS urban modelling. The objective of this work is to propose a robust Bayesian method to {sequentially} infer RANS parameters for urban flow modelling. Key to the approach is the mathematical derivation of the parameter-regularised ensemble Kalman filter (PR-EnKF), which is the analytical solution of the data assimilation problem for the sequential parameter estimation. The cost functional is regularised using the prior knowledge on the turbulence parameters, thereby ensuring that the Bayesian updates remain within physical ranges. The parameters are first inferred on an isolated building, and then transferred to three cases of increasing complexity: (i) a high-rise building, (ii) a multi-building array, and (iii) the Shinjuku district urban environment. Results show that the PR-EnKF achieves faster convergence, reducing parameter uncertainty by an order of magnitude and reconstruction errors by up to 50%. Because of the regularisation, the PR-EnKF selectively updates the most important parameters. This work enables robust large-scale urban flow simulation whilst reducing the computational overhead of model optimisation for urban planning and air quality assessment.

The energetic response of inertial particles to turbulent flow motions is important for both a fundamental understanding of the multi-phase dynamics at play, and for applications such as reduced-order models of particle dispersion processes, and their two-way coupled effects onto the flow phase. Numerous studies focus on the energetics of ensembles of particles in homogeneous isotropic turbulence, where the influence of flow anisotropy (such as that provided by boundary conditions, or other external forcing) is not considered a priori. In this work, we investigate the role of flow anisotropy on the Eulerian scale-wise particle phase energetics in a turbulent wall bounded flow for settling inertial Lagrangian particles. By using coupled Eulerian-Lagrangian direct numerical simulations at moderate Reynolds number, we aim to unravel the complex dependency of the scale-wise particle energetics on the turbulence intensity, particle inertia, and particle settling. In particular, we focus on how the developing anisotropy of the underlying turbulent flow (derived from the presence of the wall) is donated to the particle phase, and how particle inertia and settling preserve this large scale anisotropy into the formally isotropic scale range of the flow. We derive an exact (but unclosed) conservation law for the particle phase energetics at arbitrary scale, and use an asymptotic argument to help elucidate our DNS data. We discuss the relative changes to the quasi-streamwise and vertical components of the fluctuating particle field, and finish by discussing the implications of anisotropic non-local effects for more general flows, and the implications for continuum models of inertial settling Lagrangian particles.

Large-eddy simulations are performed to characterize the pressure fluctuations beneath a hypersonic boundary layer approaching a compression corner. The simulations are carried out at Mach 6.04 and an inlet momentum-thickness Reynolds number of $Re_{\theta}=4340$. The compression-corner angle is varied over $10^\circ$, $20^\circ$, $30^\circ$, and $34^\circ$ spanning attached to strongly separated regimes. The peak root-mean-square wall-pressure fluctuations intensity increases sharply with separation strength, rising by $312\%$ from R20 to R30 and a further $67\%$ from R30 to R34, with the peak located downstream of reattachment. Notably, acoustic loading increases from 140 dB in the approach flow to $\approx177$ dB downstream of reattachment in the $34^\circ$ case. Further analysis reveals that intense intermittent pressure events are concentrated near the shock foot, spatially distinct from the peak acoustic-loading region, where fluctuations are relatively sustained. With increasing interaction strength, spectral energy shifts from turbulence-dominated high frequencies to broadband low-frequency motion. Band-isolated acoustic loading maps reveal high-frequency fluctuations as the dominant contributor across the interaction zone, with low-frequency fluctuations becoming locally comparable in the R34 case near the separation region. Spatio-temporal maps of bandpass-filtered pressure fluctuations reveal downstream convecting Kelvin-Helmholtz structures and upstream propagating pressure waves near the shock foot.

Reduced-order models (ROMs) for turbulent flows based on Galerkin projection can achieve reasonable accuracy using equation-based modal bases derived from the linearized Navier-Stokes equations through the controllability and observability Gramians. The use of the modal bases obtained from linearized equations around a mean state has been seen to enhance the first- and second-order statistics in the ROM, but the use of the mean state was not necessarily extended to the equations of motion, as it implies the treatment of the divergence of the Reynolds stresses in the Galerkin projection. In this work, we present a mean-flow-based framework for ROMs in which the projection of the Reynolds stresses is solved through a modified modal basis and the knowledge of the mean flow. This framework achieves turbulence statistics comparable to those of a reference direct numerical simulation (DNS) in a minimal channel at $Re_{\tau} \approx 185$. Short-time forecasting with this framework is assessed, where balanced truncation modal bases outperform controllability modes in ROMs, yielding a reconstruction of the velocity field comparable to the Galerkin projection of proper orthogonal decomposition (POD) modes. This framework can extend analysis based on linearisations around the mean turbulent flow, which became widespread in recent years, to include explicitly non-linear interactions between modes, enabling accurate models at higher Reynolds number.

The flow of structured fluids, such as polymeric and micellar solutions, involves a strong two-way coupling between flow kinematics and internal microstructural dynamics, including polymer stretching, micellar scission, and reformation. These interactions yield complex nonlinear rheological responses, including viscoelasticity, shear-thinning, and thixotropy. In this study, we perform high-fidelity numerical simulations of micellar solution flow past a circular cylinder using the Modified Bautista-Manero (MBM) model, which couples a viscoelastic constitutive equation with a kinetic equation for fluidity to capture reversible micellar breakage and reformation. Model parameters are derived from quantitative fitting of experimental data for the EHAC-NaSal system. Our results reveal substantially richer flow dynamics than in Newtonian fluids under the same conditions. Transitions to unsteady flow occur at significantly lower Reynolds numbers, indicating greater instability driven by microstructural effects. At intermediate Reynolds numbers, micellar flows exhibit quasi-periodic behaviour, contrasting with classical periodic vortex shedding in Newtonian cases. Unlike the monotonic drag reduction in Newtonian fluids, micellar solutions show an anomalous drag increase. Wake characteristics reverse with regime: larger recirculation zones at low Reynolds numbers but more compact wakes in unsteady flows. Lift coefficients and Strouhal numbers are consistently increased. Vorticity fields display pronounced spatial localisation within thin near-wake shear layers. A dynamic mode decomposition analysis reveals coexisting unstable time-decaying and self-sustained modes in micellar flows, whereas only self-sustained modes appear in Newtonian cases.

Stability of a high-speed gas flow past a compliant solid is impacted by two distinct features: high solid-to-fluid density ratio ($\rho_r$), and flow compressibility when flow speeds are comparable to acoustic speed. This study investigates the linear stability of a shear-driven compressible gas flow past a compliant substrate modelled as a continuum Neo-Hookean solid. Numerical solutions of the eigenvalue problem reveal that at high density ratios, the dominant instabilities are the elastic shear-waves of the solid. Our study shows that flow compressibility exerts a non-monotonic effect on the growth rate of the elastic modes; the growth rate increases with increase in Mach number up to $\mbox{Ma} \approx 2$ before subsequently decreasing. Furthermore, for compressible flows, strong thermal-coupling renders the base state highly sensitive to both the solid-to-fluid thermal conductivity ratio and the substrate's bottom-surface temperature. Numerical results demonstrate that increasing the conductivity ratio destabilizes the system, whereas increasing the bottom wall temperature is stabilizing. The stability equations, analyzed in the asymptotic limit of $\rho_r \mbox{Re} \gg 1$, reveals that the fluid-solid system de-couples at the leading order with the elastic modes emerging as a solution of the linear elasticity equations under free-shear condition at the interface. We derive a closed-form expression for the leading-order growth rate of the instability, which shows an excellent agreement with the numerical solution. This expression explicitly quantifies the influence of fluid stresses at the interface, which can in-turn be expressed as integrals of the flow solution isolating the distinct physical mechanisms driving the instability.

We present a fully inertial slender-body theory (SBT) that incorporates the effect of fluid inertia on the scale of the length (the "outer" region) as well as the characteristic diameter (the "inner" region) of a steadily translating slender particle. This is achieved by matching the solution of the quasi-two-dimensional full Navier-Stokes equations in the inner region to an outer solution that consists of a superposition of a solution of the linearized Navier-Stokes equations driven by a line of forces and a potential flow solution driven by a line distribution of sources and source dipoles. The drag and lift forces result from the distribution of Oseen force singularities. These Oseenlets also predominantly govern the torque at small Reynolds numbers and large aspect ratios. However, the potential flow singularities play a crucial role in yielding a torque that grows with increasing Reynolds number at large Reynolds numbers and finite aspect ratios. By comparing the forces and torque on the steadily translating particle with those obtained from a finite difference Navier-Stokes solution, we demonstrate the accuracy of the resulting inertial SBT for $\mathrm{Re}_D$ up to 10, where $\mathrm{Re}_D$ is the Reynolds number based on the smallest dimension, i.e., the characteristic cross-sectional diameter of the slender particle.

We investigate turbulent dissipation in a von Karman flow using PIV and Diffusing Wave Spectroscopy measurements to directly compare bulk and wall dynamics. While bulk dissipation conforms to the dissipative anomaly, wall dissipation exhibits a clear excess that grows with Re, consistent with velocity-gradient dominated scaling. Decomposition into dissipation intensity bands reveals that this excess is mainly driven by progressive redistribution toward high-intensity events, larger than 10 x mean, as Re increases. From these measurements, we infer the skin-friction coefficient, finding a decreasing trend with Re fairly consistent with classical power-law behavior despite increasing dissipation. Statistically, the wall shows strong departures from log-normality at low Re that diminishes with increasing Re, reflecting an increase in the effective dimensionality of the near-wall gradient field with Re. In contrast, the bulk dissipation remains near log-normal across all Re with slowly growing log-dissipation variance, consistent with K62 refined similarity. These results suggest distinct origins of log-normal behavior which are multiplicative cascade dynamics in the bulk versus the combined effect of persistent shear and a superposition of an increasing number of independent gradient contributions at the wall.

We experimentally study the two-way coupling between a swarm of centimetre-scale active swimmers (Artemia salina) and an electromagnetically driven quasi-two-dimensional cellular flow. The swimmer loading $N$ and the background forcing $E$ are varied independently across 85 conditions, and the coupled dynamics are characterized through Lagrangian diagnostics built on the attracting Lagrangian coherent structures (LCS) of the flow. In the dilute limit, swimmers accumulate onto the attracting LCS most strongly when their speed is comparable to the flow speed, recovering the mobility-selective accumulation predicted by one-way-coupled simulations at the fixed aspect ratio of A. salina. As the loading increases, this accumulation is progressively suppressed, a collective effect inaccessible to single-swimmer models. The back-action of the swarm on the flow is itself bidirectional and regime-dependent: at low forcing the swarm disorders the attracting-LCS web and scatters the topological critical points of the cellular pattern, whereas at high forcing it reorganizes and reinforces the skeleton. The temporal stability of the skeleton is correspondingly non-monotonic in both $N$ and $E$, with the conditions of maximal stability migrating systematically through the $(N,E)$ plane. This reinforcement of coherent structures has no counterpart in prior simulations, which reported a predominantly disruptive back-action. Resolving both directions of the coupling shows how collective activity can either erode or reinforce the transport skeleton of a structured flow.

When two low-Ohnesorge-number drops impact a dry substrate simultaneously, their spreading lamellae collide and lift a free-standing vertical sheet. The sheet grows by inertial feeding from the spreading drops and is pulled back by capillary retraction at its rim. We develop a semi-analytical model for this rising sheet by extending the single-drop impact description of~\citet{Gordillo2019} to the two-drop geometry. The thin-film flow in the sheet is coupled at its base to the colliding lamellae and at its apex to a capillary-retarded rim. The sheet interior is then solved along ballistic characteristics in two stages: a lamella-fed stage, for which the velocity and thickness fields can be obtained in closed form, and a post-lamella stage, for which the inlet conditions are taken from simulations. The resulting framework gives the three-dimensional velocity and thickness fields and therefore the full sheet shape. On the centreline, the apex height and local thickness are obtained explicitly, showing that the different Weber-number exponents reported in the literature arise from a crossover rather than from a single universal scaling law. At sufficiently large Weber number, the apex pinches off. A linear Rayleigh--Plateau analysis, using the time-dependent jet diameter and deceleration predicted by the model, then bounds the maximum attainable height and closes the description of the pinch-off regime.

This self-contained theoretical study treats incompressible, free-boundary flows in a gravitating, ideal hydromagnetic star abutting vacuum, centered on the steady field-aligned flows of Chandrasekhar, Prendergast and Tsinganos, together with a novel family of steady cross-field flows, all as solutions of the axisymmetric Tsinganos equation. In the absence of compressive waves and shocks, an incompressible fluid evolves by its frozen-in magnetic field propagating as transverse Alfvèn waves along the field lines, with pressure reacting instantly in place. The origin of the steady flows rests on the Parker theory that everywhere-continuous flows are the exception rather than the rule because of a basic propensity for tangential field/flow discontinuities. Astrophysical viscosity and electrical resistivity are not zero but are significant only over scales much smaller than macroscopic scales. Such near-ideal fluids have the same propensity for tangential discontinuities but the near-discontinuities readily dissipate by small-scale, viscous-resistive magnetic reconnections. The study treats the strictly ideal fluid separately in its own right, to construct a conceptual understanding of the turbulent creation of a steady flow in a self-organizing near-ideal fluid via irrepressible energy loss and field-topology changes as episodic reconnections run out of free energy. The study suggests that metastable storage of steady vortices and twisted fields is a natural product of the solar internal dynamo, to explain a recent, multi-instrument observation of solar-coronal eruptions persisting coherently in preferred longitudinal locations over solar-rotational timescales.

Pulse experiments in the temporal analysis of products (TAP) reactor are one of the most important methods for studying transient kinetics of gas-solid catalytic reactions. The Y-procedure (Yablonsky et al., Chem. Eng. Sci. 62, 6754, 2007) is a model-free analysis framework for inferring the relationship between the reaction-rate $R$ and the reactant concentration $C$ from measurements of the outlet flux of gas. While elegant in conception, its application is hindered by the amplification of measurement noise that results from having to backtrack diffusive transport from the outlet to the reaction zone. Here, we explicitly recognize the inverse problem inherent in the Y-procedure and treat it using well-developed tools from the field of inverse problems. While previous implementations of the Y-procedure used Fourier-based filtering, we do not pre-process the measurements with an ad hoc noise-filter. Instead, we use a basis of localized square pulses to formulate a discrete inverse problem, whose regularized solution is obtained via the truncated singular value decomposition (TSVD) method. This method requires one to select a cutoff mode number; while we show how the choice of this regularization parameter can be guided by a Picard plot, we also develop an objective selection strategy for state defining experiments, for which $R(C)$ is a single-valued function. We apply our proposed inverse-problem approach to synthetic data corresponding to linear and nonlinear reactions and compare the results with the Fourier-filtration method. The former produces better reconstructions of the $R$ vs $C$ relationship, especially for nonlinear reactions. Our work facilitates the automation of pulse response analyses and enables the application of other discrete inverse-problem techniques, such as Tikhonov regularization or machine-learning methods.

Double-diffusive convection in the ``fuzzy'' cores of giant planets has been widely discussed as a mechanism for redistributing heavy elements, but its efficiency in evolutionary models remains uncertain. Previous estimates rely on idealized compositional structures and have not treated double-diffusive transport self-consistently in planetary evolution calculations. Here we implement a prescription for transport across convective staircases in the planetary evolution code \texttt{APPLE} and apply it to post-formation interior models of Jupiter and Saturn containing compositional gradients produced during formation. These models are evolved for 4.56 Gyr including convection, diffusion, and double-diffusive transport. We find that double-diffusive convection produces limited mixing between the deep interior and the envelope. In both Jupiter and Saturn, less than $\sim 1\,M_\oplus$ of heavy material is redistributed over the full cooling history, leaving the primordial compositional gradients largely intact. This inefficiency arises because the buoyancy work available to drive compositional transport is constrained by the thermal energy budget of the deep interior, in contrast to idealized Boussinesq simulations that operate in regimes more favorable to layer merging and efficient mixing. As a result, double-diffusive convection alone cannot significantly erode the compositional gradients generated during formation. The observed heavy-element distributions in Jupiter and Saturn therefore likely require additional transport mechanisms or formation pathways, including large collisional events, that produce broader initial mixing than standard accretion models predict.

We present a surrogate modeling strategy for Stokes flows with liquid droplets suspended in a carrier fluid. Our approach is based on a multi-fidelity framework. At the lowest fidelity, droplets are treated as passive tracers, neglecting their influence on the ambient flow field. Building on this approximation, we derive a PDE that represents the current modeling error. This error equation is then solved approximately to correct the flow field and the procedure is iterated. Two fidelities are employed in an alternating fashion: Stokes flow in the absence of droplets and flow around a single droplet in free space. By systematically combining these models, the method captures droplet-flow, droplet-boundary, and droplet-droplet interactions. For geometrically similar droplets, we further develop an efficient offline-online strategy that exploits this structure by reusing precomputed single-droplet solutions. Numerical experiments demonstrate the accuracy and efficiency of the proposed surrogate in a variety of tests, including scenarios with up to 10,000 droplets. Notably, we show that the proposed surrogate achieves substantially reduced computational cost compared to fully resolved multi-fluid simulations with state-of-the-art software.

Small-scale dynamos (SSDs) are believed to be the primary source of magnetic fields in all turbulent astrophysical systems, especially those with weak rotation such as elliptical galaxies and galaxy clusters. The initial kinematic phase of these dynamos is relatively well understood. Here we demonstrate analytically and numerically that, in an appropriate limit, the eddy-damped quasi-normal Markovian (EDQNM) closure for incompressible magnetohydrodynamic turbulence is strictly equivalent to the earlier models of kinematic dynamos. Moreover, it allows the extension of the kinematic dynamo framework to multi-scale turbulent flows and into the nonlinear regime. The EDQNM closure also enables us to explore a wide parameter range which is inaccessible to direct numerical simulations of the SSD. Using nonhelical EDQNM simulations, we identify several asymptotic regimes of nonlinear dynamo action when the system is highly turbulent with fluid Reynolds number $Re \gtrsim 10^6$ for magnetic Prandtl number $Pm > 1$ and magnetic Reynolds number $Rm \gtrsim 10^6$ for $Pm < 1$: 1) the kinematic growth rate approaches a value independent of $Pm$, 2) the saturated magnetic to kinetic energy ratio similarly converges to $\simeq 0.55$ across $Pm$, while the ratio of magnetic to kinetic integral wavenumbers asymptotes to $\simeq 3$. For all $Pm$, we further find strong feedback between magnetic field and velocity field largely via Alfvénisation leading to a saturated kinetic and magnetic spectra with almost the same inertial range with a slope of $-3/2$. These findings could provide guidance for future global simulations and for modeling the nonlinear regime of astrophysical systems living in these extreme limits.

In this paper we consider solutions $\boldsymbol{u}$ of the three-dimensional Navier-Stokes system and investigate sharpness of the a priori bound \begin{align*} \frac{d}{dt}\|\boldsymbol{u}\|_q^q \leq C\|\boldsymbol{u}\|_q^{q\frac{q-1}{q-3}}, \qquad q > 3. \end{align*} This bound is closely related to the Ladyzhenskaya-Prodi-Serrin conditions characterizing classical solutions of the Navier-Stokes system. Velocity fields maximizing the rate of growth $(d/dt)\|\boldsymbol{u}\|_q^q$ under certain constraints are found as solutions of a suitable optimization problem which is solved numerically using a Riemannian conjugate gradient approach. The results obtained for different $q$ and increasing values of $\|\boldsymbol{u}\|_q$ indicate that the bound is indeed sharp, up to a numerical prefactor, and therefore cannot be fundamentally improved. Additionally, the results also suggest that the rate of growth $(d/dt)\|\boldsymbol{u}\|_q^q$ diverges as $q\to 3$.

The periodically forced Duffing--Holmes oscillator possesses a discrete symmetry under sign reversal of the coordinate combined with a half-period shift of the drive. When this symmetry is dynamically realized, the system supports \emph{antiperiodic} solutions, whose state at any instant is the point reflection of the state half a driving period earlier. We show that a standard recurrence plot (RP) is blind to this symmetry, whereas a complementary \emph{anti-recurrence plot} (anti-RP), built from the cross recurrence between a trajectory and its point-reflected image, detects it directly. Across four regimes -- periodic and chaotic single-well motion, and antiperiodic and chaotic two-well motion -- the anti-RP is empty when the attractor occupies one well and densely diagonal when the motion respects the symmetry. Crucially, the antiperiodic fingerprint persists into the chaotic two-well regime, where the anti-recurrence rate stays high relative to the ordinary one ($\mathrm{RR}_a/\mathrm{RR}\approx0.8$) despite the chaos. Recurrence quantification of both matrices separates order from chaos, while the anti-RP independently distinguishes one- from two-well, symmetry-respecting dynamics, giving a compact classification of all regimes. Requiring only a time series and the symmetry operation, the anti-RP is a model-free probe of dynamical symmetry for any system with a sign-reversal invariance, including experimental signals where phase-averaged observables fail.

Models of complex systems often have many parameters, yet are constrained by far fewer experimentally accessible observables: similar activity can emerge from coordinated parameter changes. We formalize these compatible parameter sets as \emph{viable parameter manifolds}: the inverse images of a system's target dynamical behaviors under a parameter-to-feature map. The relevant codimension is not the number of reported features, but the effective rank of that map at the target scale. Co-varying features lower the codimension, while poor conditioning, high curvature, or regime mixing degrade learnability. We train conditional score-based diffusion models on simulated parameter--feature pairs and use them as amortized samplers of prior-weighted viable sets. In the Lorenz system, scalar trajectory statistics generate thin viable sheets, and two-feature conditioning localizes a transition-adjacent corridor. In the Izhikevich neuron model, four firing descriptors lie close to a nearly two-dimensional family of features, and the learned inverse images reveal distinct regular and irregular compensation geometries. In a recent ODE reduction of finite spiking networks, the same framework reveals excitatory--inhibitory compensation, timescale--coupling tradeoffs, and input-dependent viable manifolds across 4--12 parameter dimensions. In this view, robustness, compensation, and hidden parameter dependencies are organized as inverse geometry, with diffusion models providing practical tools for sampling, visualizing, and interrogating that geometry.

We present a method for computing reducible, normally hyperbolic, invariant tori with internal quasiperiodic dynamics in autonomous ordinary differential equation systems. The approach is based on the parameterization method of KAM theory; thus, it is a Newton scheme with small divisors. Since the inner dynamics of the torus is prescribed, the corresponding system parameters for which such a torus exists are simultaneously determined. The method is amenable to a form of pseudo-arclength continuation, enabling the traversal and computation of saddle-node bifurcations. We give explicit algorithms for the methods and demonstrate their applicability with two numerical examples.

We estimate the strength of chaos of probe waves and probe geodesics in different smooth supergravity backgrounds of decreasing supersymmetry and/or increasing length of the AdS throat in the interior (LLM geometry, supertubes, superstrata). We find that the wave chaos becomes stronger and stronger with less supersymetry and longer throats; in other words, chaos becomes stronger as we approach black hole solutions. Geodesic motion shows the opposite trend, becoming more and more regular. Testing the wave chaos by its compliance with the Berry random wave hypothesis and the geodesic chaos by computing Poincare sections, we explain the dichotomy between wave and geodesic motion by the existence of stable periodic orbits inside long throats while the overall measure of KAM tori decreases. Computing the Renyi entropies for the dual CFT states in the weak coupling regime, we show that they do not have such universal trends and the complexity depends on the specifics of the state rather than just the amount of supersymmetry and throat length. We conclude that the hierarchy of BPS chaos works differently in the bulk and in field theory, and in either case cannot be simply extrapolated to black holes.

We demonstrate that realistic excitonic many-body Hamiltonians obtained from first-principles GW-Bethe-Salpeter equation calculations can exhibit quantum chaos governed by random-matrix universality. Considering a prototypical van der Waals heterostructure (WS$_2$-graphene), with and without lattice disorder, we analyze their energy-resolved spectral correlations and identify a disorder-driven crossover from regular to complete chaotic dynamics. We show that while pristine samples exhibit incomplete chaos (non-ergodicity) due to an approximate valley symmetry that restricts excitonic mixing, the presence of disorder-induced electronic flat bands act as a catalyst for valley mixing to drive the system into a fully developed chaotic (ergodic) regime with reduced symmetry. Crucially, fluctuations in many-body oscillator strengths are shown to follow universal Porter-Thomas statistics, directly linking the underlying quantum chaos and experimentally accessible optical observables. Finally, by examining long-range spectral correlations, we estimate the Thouless time associated to excitonic mixing across the entire many-body bandwidth. Our results establish excitons as a highly tunable platform for probing many-body ergodicity and its spectroscopic signatures in realistic interacting 2D materials.

Phononic frequency combs offer a rich platform for nonlinear sensing, yet how their observable properties respond to changes in physical parameters remains poorly understood. Using a reduced two-mode autoparametric resonance model, we investigate how primary and secondary detuning, drive amplitude, and relative damping jointly shape amplitude and frequency sensitivity across the nonlinear parameter space. We find that sensitivity is far from uniform: primary detuning shifts the comb response smoothly, secondary detuning produces sharply localized transitions near resonance manifolds, and drive amplitude concentrates peak sensitivity close to the activation threshold rather than deep within the comb state. The relative damping redistributes energy continuously between modes without introducing discontinuities. The nonlinear sensitivity of amplitude and frequency observables across all parameters points to a common physical origin in autoparametric resonance, nonlinear saturation, and coupling-induced synchronization, offering a coherent basis for designing nonlinear sensing platforms with deliberate, parameter-aware sensitivity engineering.

Width-balance conditions at a junction are often associated with reflectionless transmission, or transparency, in some one-dimensional wave models on networks. We show that, on cyclic networks, this identification is incomplete: local balance is a vertex-level condition, while transparency also requires synchronization of the path travel times. To make this precise, we consider a shallow-water wave model and derive the channel-width-weighted scattering law for a vertex of arbitrary degree and introduce a source-relative definition of balance, reflecting the fact that the same junction may be reflective or reflectionless depending on which edges carry incoming waves. Under this definition, a balanced vertex is transparent only to the synchronized incoming-amplitude direction. For an \(N\)-path island, the resulting first-generation upstream reflection is governed in frequency space by the width-weighted distribution of path delays. Exact broadband cancellation requires all path travel times to agree; when they do not, commensurability of the path-length differences produces a periodic comb of frequency-selective zeros, independent of channel widths. At $N\ge 4$ we further exhibit a hybrid regime in which the reflection factor vanishes without commensurability among the path lengths.

At first glance, combining Newton's laws of motion with his law of gravitation seems straightforward. Students learn to distinguish inertial from gravitational mass and that their empirical equality is a remarkable fact about nature that will later serve as the conceptual gateway to general relativity. However, a closer look reveals a further and often neglected distinction within Newtonian gravity: that between active and passive gravitational mass. A common textbook argument maintains that these must be equal, for otherwise Newton's third law would be violated. We review and critically re-examine this familiar reasoning and show that the supposed theoretical proof is not compelling. Our analysis highlights subtle structural assumptions within Newtonian mechanics and offers physics teachers and researchers a fresh opportunity to explore foundational questions with potentially interesting applications in observational astronomy. In addition, an extended appendix, which is not part of the published AJP paper, offers some mathematical background material on the Galilean group and its action as group of dynamical symmetries for the type of dynamical equations considered here.

This work focuses on the two-dimensional, nine-velocity (D2Q9) lattice Boltzmann model. First, we show that the D2Q9 scheme cannot achieve secondorder accuracy unless the cubic velocity terms are neglected, and we explain how some of these parasitic terms can be eliminated. Second, we demonstrate that the standard choice of the equilibrium distribution has no effect on the equivalent PDE at second order. Finally, we numerically investigate the effect of these cubic terms and study different choices of equilibrium distributions using a new benchmark called the Oblique Dipole Benchmark, which describes obliquely propagating 2D vortex dipoles with periodic boundary conditions.

Battery discharging is governed by a fundamental trade-off between output power and energy conversion efficiency due to internal dissipation. In this paper, we demonstrate that such a trade-off universally yields a parabolic envelope $P\propto\eta(1-\eta)$. The efficiency at maximum power is exactly one half, mirroring the well-known half-Carnot limit in finite-time thermodynamics. To extend this bound into practical operational rules, we formulate a multistage constant-current discharging (MSCD) schedule subject to simultaneous real-time load demands and a global discharging deadline. Analytical resolution via the Karush--Kuhn--Tucker conditions reveals a remarkably compact optimal policy: $I_{i}^{\star}=\max(I_{i}^{-},I_{0})$. Under this rule, stages limited by external demand run exactly at their minimum required currents, while all remaining stages are elevated to a uniform baseline $I_{0}$ fixed by the deadline constraint. By tracing the dissipation--time Pareto front, we quantify how internal resistance shifts the operational boundaries and sharpens the trade-off corner. This analysis establishes a rigorous thermodynamic baseline for the scheduling layer of battery management systems, offering natural extensions to nonlinear models incorporating temperature and state-of-charge dependencies.

Polar collective motion commonly arises from alignment interactions, particle anisotropy, or an imposed directional bias. Here we identify a distinct route to polar order that does not rely on alignment interactions between the active particles. We show that non-aligning active Brownian particles embedded in a dense passive medium can develop polar coherence when confined to a compact curved surface. Persistent active motion redistributes stress through the host and creates passive-depleted regions. When the stress-spreading length becomes comparable to the sphere radius, these regions merge into elongated scars that channel active motion and, through feedback with the active flux, promote a common direction of motion. Removing the passive host suppresses polar coherence even though the active particles continue to cluster on the same sphere. Our results establish an environment-mediated route to collective polarity in which symmetry breaking emerges from the coupling between active motion, passive stress redistribution, and compact geometry.

Universality is one of the central organising principles of modern physics, explaining why systems with vastly different microscopic constituents can exhibit identical large-scale behaviour. While the classification of equilibrium critical phenomena through hydrodynamics and the renormalization group (RG) is now well established, our understanding of universality far from equilibrium remains far less developed. In recent years, however, rapid progress - driven in large part by developments in active and living matter - has uncovered a growing range of genuinely nonequilibrium universality classes (UCs) with no equilibrium counterparts. In this review, we present a pedagogical and unified introduction to hydrodynamic and RG approaches to nonequilibrium many-body systems. We first show how hydrodynamic theories can be systematically constructed from symmetry and conservation laws alone. We then introduce perturbative dynamic RG methods and demonstrate how hydrodynamic theories are organised into distinct UCs according to their scaling behaviour. Building on these foundations, we review the diverse nonequilibrium UCs uncovered since 2015, while emphasizing the conceptual connections and unifying physical principles underlying their emergence. We conclude by discussing open theoretical and experimental challenges for the field.

Single-molecule (SM) rotational dynamics of fluorescent probes in polystyrene near the glass transition temperature ($T_g$) are investigated over long times to reconstruct susceptibility spectra. The loss spectrum, commonly recorded using external field-driven (frequency-domain) spectroscopy, such as dielectric spectroscopy, is reconstructed from purely thermal SM rotational fluctuations. The results reproduce time-temperature superposition typically seen in dielectric spectroscopy for materials near $T_g$ and show that the ensemble spectrum is comprised of individual molecular responses to distinct environments.

Suspensions of motile microswimmers such as bacteria and other active colloids frequently encounter porous environments where obstacles and complex shear flows strongly influence their dynamics. Here, we study the distribution and transport of a dilute suspension of active particles in a square lattice of pillars, which serves as a model porous medium. The microswimmers are modeled as slender point particles, and Brownian Dynamics simulations are performed to determine how their number density and polarization fields change with systematic variations in the medium porosity, polydispersity, flow strength, and self-propulsion strength. We find that in the absence of flow, self-propulsion drives particle accumulation and radial polarization at the pillar surfaces. In the presence of a background flow, particles preferentially accumulate in the wake of pillars and exhibit upstream polarization near their surface, consistent with experimental observations. At moderate flow strengths, topological defects nucleate in the polarization field. These defects are of purely kinematic origin and mark the transition from global upstream swimming at low flow strengths to the coexistence of upstream and downstream swimming regions in the lattice at high flow strengths. The structured lattice studied here provides a controlled framework for isolating the physical mechanisms governing active transport in complex geometries, with direct relevance to transport in structured microfluidic settings.

We study a dilute system of non-motile chiral active particles confined in geometries ranging from straight channels to circular enclosures. Activity is introduced through chiral particle-wall interactions, modeled as tangential wall forces that generate the edge currents characteristic of chiral active matter. Remarkably, although the particles lack self-propulsion, these boundary currents induce density inhomogeneities. We show that boundary curvature drives a wall accumulation phenomenon: particles remain uniformly distributed in straight channels but accumulate near the boundaries of circular confinements. Numerical simulations and a hydrodynamic theory for the density and momentum fields consistently capture this curvature-induced wall-accumulation. These results identify boundary curvature as a fundamental control parameter for chiral edge transport and confinement-induced organization, with potential experimental relevance to spinning colloids and granular spinners.

The instabilities of slender structures power biological locomotion across scales, and offer a compelling method to actuate soft robots. Nonreciprocal elastic solids have been found to amplify flexural waves in one direction only, but design principles to tune and stabilize these waves are missing. Here we develop a geometrically exact theory of nonreciprocal filaments and provide simulations that capture their post-instability nonlinear dynamics. We find that nonreciprocity, when coupled to inertia or pre-stress, amplifies and advects curvature variations. The resulting one-way patterns of shape morphing can then be selected via dissipative interactions with the environment. Our work offers a continuum-based strategy for how internal stresses can drive active unidirectional waves without need for additional degrees of freedom.

We investigate fluid mixing induced by microswimmers using mutual information as a global, information-theoretic measure of mixing efficiency. For a two-dimensional squirmer model in a confined domain, we compute numerically the swimmer-generated flows and solve the advection-diffusion equation for the transport of tracer particles in the fluid. We show that the spatial distribution of swimmers strongly affects mixing, which is suppressed by swimmer aggregation and enhanced by positional and orientational disorder. At fixed energy dissipation, mixing efficiency depends non-monotonically on the squirmer parameter, with an optimal finite value arising from the balance between swimmer translation and dipolar flow generation. When hydrodynamic interactions are included, pushers outperform pullers. The mutual information as a function of time decays in three stages: an initial diffusion-dominated stage, an intermediate advection enhanced regime, and a final relaxation stage controlled by system size. Our results demonstrate that mutual information, previously validated as a measure of mixing efficiency only in simplified model systems, can equally be used in complex flows. Its application reveals that mixing by microswimmers is subject to a trade-off between the generation of strong shear flows and achieving optimal dispersion across the fluid domain.

We investigate the low-Reynolds-number propulsion of a slender elastic filament with a dipolar magnetic head actuated by an oscillating field in a viscous fluid by studying its strokes and net forward motion. To capture these dynamics, we employ an elasto-hydrodynamic (EH) framework that couples Euler-Bernoulli beam mechanics with resistive force theory. Unlike prescribed-kinematics models, filament shapes here emerge self-consistently from the actuation and the force and torque boundary conditions (BCs). We demonstrate that viscous boundary contributions are crucial for quantitative agreement and show that the swimming dynamics are governed by the EH length and a magneto-viscous-elastic stroke amplitude introduced here. The swimming speed is non-monotonic with increasing ratio of the swimmer length to the EH length, and is shown to reach a maximum when the swimmer length is on the order of the EH length. We further discuss the analytical limit in which the tail BCs can be described as free, and the limitations that arise when viscous contributions to the BCs are ignored.

We investigate homogeneous populations of smart active agents that exchange information with their neighbors to perform a decentralized learning process aimed at achieving a prescribed macroscopic state. Such agents may, for example, represent simple microrobots. The exchanged information comprises tunable parameters governing the agent dynamics, referred to as the individual policy, together with an internal memory encoding previously visited states. This memory is used to evaluate a reward that quantifies the success of a policy to achieve the prescribed state. We extend the kinetic-theory description of collective learning in spatially homogeneous systems [Phys. Rev. Lett. 134, 248302 (2025)] and derive formal evolution equations for the distribution of policies across the population. A central outcome of our theory is the emergence of an effective reward function that fully determines the evolution of the policy distribution and encapsulates the microscopic details of the agents physical and memory dynamics. We obtain closed equations for the policy mean and variance which admit explicit time-dependent solutions under the assumption of Gaussian-distributed memories and polices. To illustrate the framework, we present a series of minimal microscopic models, considering both perfect and partial separation of physical, memory and policy exchange time scales, as well as models with one- and two-dimensional policies. The obtained theoretical results compare well with agent-based numerical simulations. The theory captures key aspects of collective learning, including the influence of population diversity and reward fluctuations on learning performance. Finally, we discuss potential applications to swarm robotics and machine learning, and highlight connections with classical models of biological evolution, including the Replicator equation and the Moran model.

Cyclic pore-pressure or normal stress variations arise both in relation to natural earthquakes and in engineered subsurface systems, yet their effect on fault stability remains poorly constrained at the grain scale. Here we numerically model, using a coupled Discrete Element--fluid dynamics model, the response of a sheared, fluid-saturated or dry, gouge-filled fault to effective normal stress oscillations over a wide frequency range (0.5-10000 Hz). The effective normal stress is oscillated either by cycling the pore-pressure or by directly cycling the normal stress, while keeping the stress state below the Mohr-Coulomb threshold measured in continuous loading. Despite this sub-critical loading, we observe failure across most frequencies, with a non-monotonic frequency dependence. A distinct non-failure window emerges at intermediate frequencies (30-200 Hz), bounded by failure at both lower and higher frequencies; the system exhibits four regimes from cyclic failure-and-arrest to continuous sliding. Pore-pressure and normal stress oscillations produce the same regime structure, confirming that they act as equivalent forcings via Terzaghi's principle, with fluid coupling adding only a delay due to dilatant hardening. Sub-critical failure arises from dilation-induced strength deterioration via two mechanisms: (i) low-frequency cycles allow sufficient time for shear-driven ratcheting dilation, while (ii) high-frequency cycles induce dynamic dilation (acoustic fluidization) via amplified seepage forces, stress gradients and inertial forces. The intermediate non-failure window represents the gap between these mechanisms. These results identify frequency as a controlling parameter for failure in granular materials, with implications for dynamic earthquake triggering and cyclic injection protocols.

We have conducted Direct Numerical Simulations of turbulent half-channel flow over realistic surface deformations at friction Reynolds number $Re_\tau=200$. We generated the surface deformations using piezoelectric actuators. We simulated the piezoelectric actuation over the practical actuation frequency range $(119Hz\le f_\mathrm{act}\le543Hz)$ and voltage range $(250V\le Q \le500V)$ beneath an Aluminum sheet using Finite Element Analysis. The sheet deformation amplitude and actuation frequency in viscous units vary within the range $2 \le \eta^+_\mathrm{max} \le 34$, and $-0.58 \le \omega^+ \le 0.70$. The vertical surface deformations from our actuation setup generate three types of waves: travelling, hybrid, and standing waves. Surface deformations are applied as bottom-wall boundary conditions of the turbulent channel flow to generate waves in the upstream, downstream, and spanwise directions. We achieved maximum drag reductions of 1.6\%, 5.4\%, and 27.6\% for upstream, downstream, and spanwise waves, respectively. The streamwise waves generate alternating adverse and favorable pressure gradients, which locally increase and decrease drag, leading to a marginal net change in drag. In contrast, spanwise waves introduce transverse shear, accompanied by high- and low-streamwise-momentum zones that respectively attenuate and energize the near-wall turbulence. Such disruption of the near-wall turbulence-regeneration cycle produces up to $27\%$ drag reduction for the realistic spanwise hybrid wave; such an outcome demonstrates the efficacy of unconventional realistic surface deformations in achieving significant drag reduction.

In canonical turbulent wall-bounded flows, the inner-scaled wall-pressure variance is empirically well described by a constant offset plus a slope logarithmic in the friction Reynolds number ($\delta^+$). Because the fluctuating pressure is predominantly a Poisson response to only two source terms -- a linear contribution from the mean shear coupled to a fluctuating velocity gradient, and a nonlinear contribution from the fluctuating velocity field -- the origin of this growth can be pinned down by elimination: if the linear source saturates at a Reynolds-number-independent value, the nonlinear source must carry the logarithmic growth. Here we supply the complementary evidence for inner-scaled invariance of the linear source at $\delta^+$ up to $O(10^4)$, using the simultaneous velocity and velocity-gradient hot-wire measurements of Zimmermann \textit{et al.} (2019 \textit{JFM} vol. 869 pp. 182--213) acquired with a single eight-sensor probe in both a zero-pressure-gradient turbulent boundary layer and a high-Reynolds-number pipe flow. The inner-scaled factors entering the linear source collapse across Reynolds number, and the inertial-layer variance of the relevant fluctuating velocity gradient decays inversely with wall distance. Together with the established inner scaling of the mean shear, this is consistent with a linear wall-pressure contribution that, under inner normalisation, remains $O(1)$ as $\delta^+\to\infty$. Both source terms then trace to one structural mechanism: the near-wall depletion of mean spanwise vorticity that caps the linear source also feeds, through vortex stretching, the inertial-layer fissures that carry the growing nonlinear contribution.

We study pressure-driven Poiseuille flow of a one-component fluid between adiabatic plates in liquid-gas coexistence. The analysis uses Poiseuille flow and Fourier heat conduction in the bulk regions together with particle and energy conservation. From these bulk equations, we identify extremely small dimensionless parameters $A^\mathrm{L}$ and $A^\mathrm{G}$ describing coexistence Poiseuille flow, whose smallness comes from squared microscopic-to-macroscopic length ratios. In weak driving with macroscopic liquid and gas regions, the pressure difference is concentrated across the interfacial region, and the ordinary Poiseuille particle current is strongly reduced. For equal-temperature reservoirs, this residual particle current produces interfacial cooling.

We experimentally analyze the effect of a surfactant on wetting following drop impact on rough surfaces, paying special attention to the role of dynamic surface tension. To this end, we compare the results obtained with Triton X-100, SDS, and Surfynol 465. For concentrations below the critical micelle concentration $c_{\textin{cmc}}$, the evolution of the coverage area is nearly identical for all three surfactants, suggesting that the surfactant concentration is too low to significantly influence droplet spreading. In contrast, pronounced differences emerge due to the distinct dynamic surface tensions of the surfactants at $c/c_{\textin{cmc}}=2$. The evolution of the coverage area during spreading is nearly the same for pure water droplets and those containing Surfynol 465, indicating that surfactant depletion is negligible during the rapid spreading stage. As the Weber number increases, droplet spreading becomes progressively less sensitive to surface tension, thereby reducing the influence of surfactant adsorption kinetics. Nevertheless, Surfynol 465 produces larger coverage areas than Triton X-100 and SDS. The final coverage area is governed by the quasi-static recession of the triple contact line, which is controlled by the receding contact angle. Surfynol 465 consistently yields substantially larger final coverage areas across the range of surface roughness considered in this study.

Gliding mammals exhibit diverse patagium and tail/uropatagium morphologies that may influence aerodynamic performance and maneuverability. Here, we use computational fluid dynamics to isolate the aerodynamic effects of representative gliding-mammal-inspired morphologies under controlled flow conditions. Three patagium configurations were compared to evaluate the effects of membrane outline on lift generation, drag, stall behavior and pitching moment. Three tail/uropatagium configurations were further tested under baseline, symmetric-deflection and asymmetric-deflection conditions to assess their longitudinal and lateral control authority. The results show that a broader patagium configuration generated the highest lift and lift coefficient, whereas an intermediate patagium morphology showed a smoother post-stall response with lower drag. For the tail configurations, the colugo-like integrated uropatagium enhanced lift and pitch-control authority under symmetric deflection, while the flat-tail configuration produced stronger rolling and yawing responses under asymmetric deflection. These findings indicate that gliding-mammal-inspired morphologies produce distinct aerodynamic trade-offs rather than a single optimal design. The results provide insight into the functional diversity of gliding mammal morphology and offer design guidance for bioinspired morphing aerial robots.

We investigate a stably stratified flow driven by deterministic Kolmogorov forcing that generates horizontal shear, using direct numerical simulations over a broad range of stratification strengths characterized by the Froude number $Fr$. As the stratification is progressively weakened, the flow exhibits a sequence of regimes: a buoyancy-dominated, strongly stratified regime, an intermediate regime characterized by Kelvin--Helmholtz instabilities and enhanced mixing, and a nearly isotropic turbulent regime. A key feature of the intermediate stratification range is the emergence of energetically significant vertically sheared horizontal flows (VSHFs), accompanied by a marked steepening of the reduced one-dimensional perpendicular kinetic energy spectra. The spectral energy transfer remains predominantly forward, although the perpendicular flux becomes negative at large horizontal scales; this apparent upscale transfer reflects anisotropic energy redistribution rather than a true inverse cascade. Strong stratification enhances intermittency, producing increasingly non-Gaussian vertical velocity fluctuations and large kurtosis associated with localized vertical bursts. The energetics-based mixing coefficient remains of order $10^{-1}$ over the parameter range investigated, with a modest enhancement near the Kelvin--Helmholtz instability regime.

Numerical modeling of aortic valve dynamics is essential for understanding the complex fluid-structure interaction (FSI) governing valve biomechanics in health and disease. Immersed methods provide a flexible computational framework for simulating the large deformations of valve leaflets and associated blood flow without requiring body-fitted meshes. Among these approaches, the Resistive Immersed Surface (RIS) and Immersed Boundary (IB) methods are widely used. However, systematic comparative analysis of these methods for realistic aortic valve simulations has not been performed. In this work, we compare a prescribed-kinematics RIS workflow implemented in SimVascular's svMultiPhysics solver with a fully coupled IB workflow using IBAMR for trileaflet and bicuspid aortic valve configurations. The RIS method represents the valve as a surface with prescribed kinematics embedded in the fluid domain and introduces a penalty force that drives the surrounding fluid velocity toward the prescribed leaflet velocity. This formulation reduces modeling complexity and provides useful hemodynamic predictions when representative leaflet kinematics are available. In contrast, the IB method models the leaflets as elastic structures fully immersed in the fluid domain and resolves leaflet deformation through fully coupled two-way FSI. The study focuses on the extent to which RIS reproduces bulk hemodynamic features and transvalvular pressure gradients. Results show that the RIS method captures the large-scale flow structures and predicts the mean transvalvular pressure gradient with a relative error within 15% of the fully coupled IB simulation, improving to within 5% when inlet boundary conditions are matched, while reducing computational cost by approximately 60%.

Accurately resolving interfacial gradients is critical for simulating two-phase flows, particularly those involving phase transitions or active matter. The traditional diffuse-interface immersed boundary methods (IBMs) are highly efficient for such problems, but they typically suffer from a reduction to first-order accuracy near the phase-changing boundaries. We clarify that the main reason is the local derivative discontinuities. Here, we propose a smooth extension strategy to restore formal second-order spatial accuracy. By extrapolating the scalar field across the interface, the method structurally ensures derivative continuity. To preserve the divergence-free condition in incompressible fluid solvers, this smooth extension is applied exclusively to the scalar transport equations. The velocity field retains the standard diffuse-interface treatment. The proposed framework is systematically validated against classical phase-change benchmarks, specifically one-dimensional evaporation and boiling problems. Additionally, the method is applied to the spontaneous autophoretic motion of isotropic particles. The numerical results confirm the capability of our method in resolving the complex multi-physics boundary couplings.

We study hydrodynamic spin coupling in a two-rotor corral using DNS of 2D incompressible viscous fluid flow. An active rotor is driven at angular velocity W, and a nearby torque-free passive rotor selects an angular velocity w through hydrodynamic torque balance. The signed gear ratio Gamma=w/W distinguishes corotation from counterrotation, with Reynolds number Re=|\Omega|r^2/\nu. Motivated by a recent quasi-two-dimensional experiment, we use a DLM/FD method to compute planar phase diagrams of $\Gamma(G,Re)$ at corral sizes C=3, 4.5, and 6. The planar model recovers the benchmark gap route at Re=20: an intermediate counterrotation band, a wide-gap transition to corotation, gear-ratio magnitudes of order 10^{-2}, and the observed sequence of vortex attachment, detachment, and merger. It also produces a reentrant-like gap structure with a small-gap corotation region whose relation to the experimental close-range geometric state remains unresolved. The main discrepancy is the high-Re boundary. At the experimental mid-gap transect G about 0.3, the planar gear ratio approaches zero from the counterrotating side but does not cross through Re=400; at the narrower gap G=0.22, by contrast, the planar terminal spin reverses near Re=44. Wall-traction diagnostics show that this crossing is not the experimental shear-competition mechanism: the gap-facing counterrotating arc narrows but does not collapse or deflect as in the experiment, and the reversal at G=0.22 occurs by redistribution of the integrated planar torque. The strictly planar model therefore captures the broad gap-route architecture and the existence of a Reynolds-driven spin boundary, but displaces that boundary in gap and alters its surface-stress mechanism. The remaining mismatch points to finite-depth secondary motion, end-wall stresses, and apparatus geometry as plausible contributors to the experimental shear balance.

Polymeric stresses in viscoelastic flows arise from the deformation of polymer chains and are commonly computed using Eulerian constitutive models, in which the conformation tensor is evolved as a transported field over the entire domain. This approach is computationally intensive, prone to numerical instabilities, and not directly applicable to experimentally measured velocity fields. In this work, we develop a Lagrangian integration scheme that reconstructs the polymeric stress field from the deformation-gradient history along fluid element trajectories in a known, steady velocity field. This approach avoids solving the full Eulerian constitutive transport equation, which we develop for the nonlinear FENE-P model as well as the Oldroyd-B model as a reference case. After validation on unidirectional, canonical flows, the scheme is applied to non-trivial channel flows past circular obstacles using velocity fields quantified from both numerical simulations and microfluidic experiments. The reconstructed stress fields across both experiments and simulations are in agreement with traditional Eulerian reference solutions. Not only does this new Lagrangian scheme enable the quantification of stress fields directly from experimental velocity field data, but it also enables partial or whole-field mapping of stresses without solving fully-coupled viscoelastic constitutive equations.

Operator learning has emerged as a powerful tool for modeling complex physical systems in functional spaces. However, their neural network-based architectures make them opaque models, obscuring the reasoning behind their predictions. In this work, we introduce a self-explainable operator learning framework that overcomes this challenge by reformulating operator learning as a linear combination of generalized functional linear models expressed through integral equations. Exploiting the additive decomposability of these integral equations, we divide the input domain into subdomains and compute localized integrals to evaluate the contribution of each region to the final prediction. This decomposition enables direct interpretability where the model explains both inputs and outputs by linking specific input regions to corresponding output patterns, thereby revealing which spatial features drive predictions. We demonstrate the framework on function-to-scalar and function-to-function mappings in fluid flow problems involving blood flow and unsteady aerodynamics. The results show that the operator most often prioritizes regions with strong feature gradients, providing physically meaningful insight into the model's decision-making process. Comparisons with established post-hoc explainability methods demonstrate qualitative agreement while highlighting the key advantage of the proposed approach: explainability is embedded directly within the operator structure itself and does not require an external tool. Therefore, our framework provides a mathematically transparent and physically interpretable approach to uncover relationships within data, fostering trust in machine learning for scientific applications by enabling more informed data-driven analysis of physical systems.

We propose an improved Fourier Neural Operator (FNO) for modeling two-dimensional Rayleigh-Bénard convection by predicting time increments instead of full solutions, achieving higher accuracy than a standard FNO baseline. The resulting model is compact (314k parameters, 1.26 MB) and fast (7 ms inference), while maintaining similar accuracy as demonstrated in previous benchmarks. We show that although FNOs generalize to finer meshes, accuracy remains limited by the resolution of the training data.

We investigate modular Laplacian automata on triangular lattices with evolution governed by binary and ternary moduli. Extending previous studies on square lattices, we examine how lattice geometry influences long-term growth, density, fragmentation, and the emergence of self-similar structures. We further investigate whether sparse ternary interventions can stabilize predominantly binary dynamics. The experiments reveal that mask geometry is the primary determinant of large-scale morphology. Full hexagonal masks generate recurrent density crises and fragmentation, whereas triangular masks support persistent growth and reveal a threshold phenomenon governed by growth-capable nuclei. Although seed symmetry influences transient behaviour, the asymptotic morphology is inherited mainly from the mask. To control binary fragmentation, we investigate sparse developmental ternary perturbations in which a small number of carefully timed occurrences of modulus 3 are inserted into an otherwise binary sequence. A Monte Carlo optimization demonstrates that as few as three interventions are sufficient to redirect the subsequent binary evolution toward substantially denser carpet-like configurations. The effectiveness of this strategy depends primarily on the timing of the interventions rather than on their number. Analysis of the post-intervention dynamics shows that ternary shaping does not replace binary evolution. Instead, it produces denser self-similar structures, substantially reduces crisis depth, and resets the phase of the binary crisis clock. The results suggest that geometry determines the family of admissible morphologies, whereas sparse developmental perturbations select favourable long-term trajectories within that family.

Electronic neurons are a keystone for construction of the spiking neural networks which have numerous applications in neuroprosthetics, artificial memory, intensive calculations etc. A number of concepts of electronic neurons has been already proposedm with some of them implemented in hardware. However, new schemes are of significant interest since the existing ones do not fit all requirements: either they are too complex and expensive in realization, or they are not able to demonstrate all demanded regimes, or their do not have a appropriate mathematical description and therefore may be investigated only experimentally etc. In this study we propose a new design of bursting electronic neuron constructed as a circuit implementation of the equations of a phase-locked loop system. To succeed, we use a novel hybrid approach: we start from the phenomenological equations providing the demanded, then we adjust and modify these equations to simplify the implementation rather than implementing the biophysical equations into thee hardware directly or writing equations for the already constructed circuit. The resulting circuit is simple in implementation and well matches the underlying equations. It can be used for description of not only a single neuron, but small neural circuits too.

We investigate the interaction of small-amplitude waves called phonons, with an initially static kink in an exceptional discretization of the $\phi^4$ model that is free of the Peierls-Nabarro potential. Phonons are generated by a localized harmonic source and scattered from one side of the kink. By computing the transmission and reflection coefficients over the entire phonon band, we demonstrate that the scattering properties depend strongly on the lattice spacing. In the weak-discreteness regime ($h<1$), the kink is nearly transparent and phonons are transmitted through it over most of the phonon spectrum. In contrast, for strong discreteness ($h>1$), significant reflection emerges even though the corresponding continuum $\phi^4$ kink is reflectionless. We further show that depending on the frequency of the incoming phonons, the kink experiences negative radiation pressure and is accelerated toward the incoming phonons for all lattice spacings considered, and this effect is much stronger for the strong discretness. The frequency dependence of the kink velocity and energy transfer is explained in terms of resonances associated with Doppler-shifted phonon frequencies and extrema of the phonon group velocity. Our results reveal that strong lattice discreteness can qualitatively modify phonon-kink interactions even in systems where the static Peierls-Nabarro potential is absent.

It has been known for several decades that the third moment of the multifractal spectrum of the harmonic measure for diffusion-limited aggregates is linked to the underlying fractal dimension of the cluster. We demonstrate, using an argument based on the Hastings-Levitov formulation of diffusion-limited aggregation (DLA) in two dimensions, an even stronger link, connecting the universal amplitude of the third moment to the cluster fractal dimension. This argument can be used for both the standard circular DLA as well as DLA in a cylinder (i.e., with periodic boundary conditions).

Quantum droplets (QDs) are self-bound states of ultradilute quantum fluids stabilized by the interplay between the Lee Huang-Yang (LHY) quantum-fluctuation correction and the mean-field interaction, providing a useful platform for exploring macroscopic quantum phenomena. Recent studies on three-dimensional QDs have introduced the concept of bulk modulus and revealed its connection with the breathing-mode frequency, thereby linking the elastic response of QDs to their collective dynamics. Motivated by this progress, we investigate the elastic modulus of one-dimensional QDs. Based on a super Gaussian variational ansatz, we systematically derive the elastic modulus B and analyze its dependence on the interaction strength and particle number. The analytical predictions are further validated by numerical simulations based on imaginary time evolution and the spatial scaling method. We also establish a quantitative relation between the elastic modulus and the eigenfrequency of the breathing mode. In addition, by incorporating corrections to the droplet width beyond the Thomas Fermi approximation, we obtain the dependence of the ratio {\eta} = B/2 on the control parameters g and N. Unlike the three-dimensional case, where the corresponding ratio follows a simple power-law scaling, the one-dimensional system is affected by the soliton-to-droplet crossover, leading to a more intricate dependence of {\eta} on g and N. Our results show that, in the high-particle-number regime, the elastic modulus asymptotically approaches a limiting value determined mainly by the interaction strength, whereas in the low-particle-number regime it depends on both the particle number and the interaction strength.

Metainterfaces can realize specified evolutions of their friction force as a function of the confining normal force (friction law), thanks to the design of the individual radii and heights of a population of independent hertzian asperities. However, not all friction laws are achievable. Here I show that, contrary to a suggestion from the literature, the slope of the friction law has a finite positive lower bound. This result is useful to identify friction laws that are not accessible to metainterfaces.

In Hermitian topological systems, topological modes (TMs) are bound to interfaces or defects of a lattice. Recent discoveries show that non-Hermitian effects can reshape the wavefunctions of the TMs and even turn them into extended modes occupying the entire bulk lattice. In this letter, we experimentally demonstrate such an extended TM (ETM) in a one-dimensional (1D) non-Hermitian acoustic topological crystal. The acoustic crystal is formed by a serie of coupled acoustic resonant cavities, and the non-Hermiticity is introduced as the non-reciprocal coupling coefficient using active electroacoustic controllers (AECs). Our work highlights the potential universality of ETMs in different physical systems and resolves the technical challenges in the further study of ETMs in acoustic waves.

Chemical gradients are ubiquitous in porous and crowded environments, including soils, filters, fabrics, tissues, hydrogels, biofilms and living cells. They arise from displacement fronts, dissolution and precipitation, ion exchange, metabolism, root exudation, evaporation, gas dissolution, freeze--thaw cycles and externally imposed chemical treatments. These gradients can drive colloids, macromolecules and emulsion droplets by diffusiophoresis, while simultaneously driving diffusioosmotic flows along confining surfaces. Classical models of colloid transport in porous media emphasize hydrodynamic dispersion, surface interactions, straining, deposition, detachment and filtration. This chapter places diffusiophoresis within that broader transport framework and reviews how porous media generate, stretch, disperse and sustain the solute gradients that drive phoretic motion. We first discuss sources of chemical gradients and the distinction between spreading and mixing, then summarize classical colloid transport, the minimal physicochemical model for diffusiophoresis and diffusioosmosis, and the experimental platforms used to study these effects. Particular emphasis is placed on recent results showing that diffuse solute fronts can enhance phoretic removal from dead-end pores by prolonging the duration of forcing, and that cross-streamline migration within flowing pathways can change macroscopic breakthrough and dispersion by orders of magnitude. We close by discussing emulsion droplets, multiphase flows, confined and living media, and open problems, including the transition from algebraic mixing in two-dimensional micromodels to chaotic mixing in three-dimensional porous media.

We use self-consistent field theory to investigate the free energy landscape for single-chain expulsion from a diblock copolymer micelle with a dense corona. Using the distance from the micelle center-of-mass to the hydrophilic-hydrophobic junction of the chain as the reaction coordinate, we compute the free energy landscape for chain exchange. Our results show that the expulsion free energy barrier scales linearly with both the hydrophobic block length and the solvent selectivity, consistent with recent experiments. To accurately resolve chain conformation, we introduce a second reaction coordinate: the distance between the junction and the free end of the hydrophobic block, and construct a two-dimensional free energy surface. Using the string method to identify the minimum energy path, we find that all pathways converge to a nearly degenerate reaction channel, irrespective of the initial path. Within this channel, the end-to-end distance of the hydrophobic block exhibits a broad distribution, yet the corresponding expulsion barriers remain nearly indistinguishable. Together, these findings establish a continuum-level theoretical foundation for understanding the hyperstretching mechanism and the transition state ensemble in micellar chain exchange.

We investigate the role of compressibility in the modified quasi-linear viscoelastic (MQLV) constitutive framework for soft solids at finite strain, where shear and bulk responses are governed by distinct relaxation functions. Analytical and semi-analytical results are derived for simple shear and torsion, under incompressible and slightly compressible assumptions. We show that compressibility affects the response only when volume changes occur: under isochoric deformations, the bulk contribution vanishes, while even small deviations from isochoricity significantly alter the normal response. Shear stress and torque are largely insensitive to compressibility, whereas normal stress and axial force exhibit pronounced sensitivity due to the coupling between shear and bulk relaxation. We further demonstrate that volumetric effects interact with the Poynting effect: in simple shear they oppose each other, reducing relaxation, while in torsion they reinforce each other, enhancing it. These trends agree with brain tissue experiments but reveal limitations of the slightly compressible model for highly compressible materials, such as agarose gels. Overall, the results emphasise the importance of accounting for compressibility in modelling normal stress responses and motivate the development of fully compressible formulations and numerical implementations.

For many decades, researchers have been studying various types of electro-hydrodynamic instabilities in liquid crystals. A significant amount of experimental data has been collected, however, the theoretical interpretations of the results typically rely on linear analysis. In response to this limitation, we investigate the nonlinear stage of the flexoelectric instability in nematics, focusing on liquid crystals with a negative anisotropy in their dielectric permittivity and electrical conductivity. We base our analysis on a comprehensive set of nonlinear electro-hydrodynamic equations for these nematics influenced by an external alternating electric field. The equations predict an instability that is driven by the flexoelectric effect. In order to examine the peculiarities of this phenomenon, we use a model that was proposed in our previous publications, Refs. [1,2], which allows us to perform numerical simulation of nonlinear dynamics. We examine patterns that are formed above the instability threshold. Through numerical simulations, we have identified static and dynamic patterns that occur over a timescale that is much longer than the period of the external electric field. The static patterns are one-dimensional structures and dynamic patterns are standing or traveling one-dimensional waves. The type of the realized pattern depends on the material and experimentally controlled parameters. We found that the standing waves are stable with respect to small transverse perturbations, whereas the propagating waves are unstable. We present a Ginzburg-Landau-like phenomenology that applies near the instability threshold. This approach allows us to rationalize our numerical findings with a few parameters.

A double-occupancy cell model of a fluid with Curie-Weiss interaction is studied. First, we show that the model is isomorphic to the Blume-Capel model on a complete graph through a simple transformation from spin to occupancy variables. We then investigate its phase behavior within the grand-canonical ensemble using a combination of analytical and numerical methods. Despite its simplicity, the model exhibits a remarkably rich thermodynamic behavior depending on the ratio between the local repulsive and global attractive interactions. We identify regimes characterized by a single critical point, two distinct critical points, tricritical behavior, and triple-point formation. For sufficiently strong repulsion, the system possesses three fluid phases of different densities, leading to both gas-liquid and liquid-liquid coexistence. The locations of the critical, tricritical, and triple points are determined, and the corresponding phase diagrams are constructed. These results demonstrate that the competition between double-occupancy repulsion and long-range attraction is sufficient to generate complex phase behavior in a minimal multiple-occupancy lattice-gas model.

Complex interactions among regulatory molecules determine the rules underlying cell growth and division in microbial cells. While the governing molecular network may not always be obvious, it is well known that correlations among certain physiological quantities measured in experiments, such as birth-size, division-size, division-time, and division-added-size, can differentiate among various cell-division models, such as Timer, Sizer, and Adder. Here we show that, apart from these correlations, which we extend for the case of stochastic single-cell growth and stochastic asymmetric partitioning, probability distributions of these quantities and statistical relationships between them can also be used to differentiate between these division models. Interestingly, we show that these quantities can not only differentiate the division models, but also distinguish among the single-cell growth paradigms, such as linear and exponential growth. We then demonstrate this differentiability among various division and growth models by comparing our analytical results with published experimental data. We further show that these results remain valid even when the growth rate of a cell is correlated with the growth rate of cells from previous generations in the lineage.

Fusion of two epithelial cell sheets brought together in a bilayer configuration is a common step in animal morphogenesis, yet, in contrast to other epithelial fusion processes such as wound healing in a monolayer of cells, it has not been a strong focus of modeling efforts. Here we consider a preliminary stage of bilayer fusion, recently termed "docking." In multiple instances of docking that span apical and basal varieties, cells appear to have a tendency to remodel so as to co-localize their bilateral junctions (match their edges) across the bilayer. Motivated by this observation, we introduce a bilayer cellular Potts model that couples two standard 2D area- and perimeter-elasticity models via short-range, out-of-plane interactions between cell edges. The new coupling involves a single adjustable parameter that minimally models the combined effect of dynamic cytoskeletal protrusions, cadherins, and other potential edge-associated adhesion molecules. Our model predicts that bilayer edge matching is maximized when the two monolayers are in their fluid-like regimes (average cell shape index greater than 4.6 in our implementation), and when the bilayer coupling strength strikes a balance between in-plane and out-of-plane energy scales. At higher coupling strengths, the system tends to get stuck in metastable states with sub-optimal edge matching. Exploration of the mechanisms of edge matching reveals that pairs and quadruplets of coordinated T1 transitions play a particularly important role. We also find numerous examples of emergent features we term "domain walls" - branching or unbranching curves that cross no matched edges, but that separate regions of nearly complete matching. These domain walls can be both system spanning and long lived. Finally, we extend our model to crudely account for bending of the two sheets, and study the distributions of docking front speeds that result.

Synchronization and swarming are canonical manifestations of self-organization, observable across scales from cellular processes to animal flocks. This study investigates the collective dynamics of a novel agent-based model where individuals exhibit both spatial mobility and internal, two-mode stochastic oscillatory states. By introducing a local, distance-dependent coupling between the agents' spatial configuration and their internal state transitions, we establish a mutual feedback loop that drives complex pattern formation. Through large-scale numerical simulations, we identify seven distinct morphological configurations, ranging from stationary \textit{Filled-disk} states to highly disordered \textit{Intense-motion} regimes. By performing a rigorous quantitative analysis of the rotational energy and radial dispersion, we transcend simple morphological classification and demonstrate that the system organizes into discrete, quantized topological attractors. We derive a macroscopic scaling law, $\Omega \propto r^{-1/2}$, which proves that the emerging rotating states are not rigid-body rotations, but rather composite differential vortex structures characterized by spontaneous chiral symmetry breaking. Our results suggest that these stable, quantized dynamical states are fundamental features of systems governed by bidirectional spatial-phase feedback, offering a robust framework for designing autonomous, decentralized robotic swarms.

Gravitational collapse creates large amounts of kinetic energy that could potentially seed turbulence. If such turbulence were also suitable to initiate dynamo action, the resulting magnetic field would further modify the dynamics, especially on small length scales. However, a small-scale dynamo requires vortical turbulence, while the collapse produces mainly irrotational motions, which may not be efficient for dynamo action. Here, we study the efficiency of vorticity production during a turbulent collapse. We use a barotropic equation of state, where pressure and density gradients are parallel, and no magnetic field, so that vorticity can only be produced by viscosity. Using direct numerical simulations of gravitational collapse, we show that, for the parameter space accessible to our numerical resolution, this effect is related to the initial irrotational turbulence and is not a consequence of the collapse flow.

The novelty of this work is that it takes a result of macromolecular theory that is not objective, and fixes it. To do so we use an objective vorticity tensor to obtain a fully frame invariant form of the classical constitutive equation for FENE dumbbell fluids obtained within the conceptual framework of kinetic theory for polymer solutions. The influence of such an objective formulation is discussed for steady shear flows.

Direct Numerical Simulations (DNS) of a spatially developing supersonic turbulent shear layer are conducted for a range of convective Mach numbers ($M_c$) and velocity parameters ($\lambda$) to examine the effects of compressibility and advection on the growth rate, self-similarity, flow statistics, asymmetry, and entrainment of the layer. At distant downstream locations, self-similarity is attained for all cases. The self-similar region is identified by the collapse of normalized mean streamwise velocity, the constant peak of normalized Reynolds stresses, and the linear growth rate of the shear layer thickness and momentum thickness. Despite significant variations in lower-order and higher-order statistics across different $M_c$ and $\lambda$ values, profiles of all turbulence quantities examined collapse within the self-similar region using our proposed self-similar scalings. The self-similar forms of continuity, momentum, and energy equations have been formulated, incorporating compressibility and centerline shifts. The self-similar normalized density distribution inside the layer is used to explain the effects of compressibility on various flow statistics, including the far-field cross-stream velocity. The density variation is linked to dissipation effects as revealed by our analysis of the self-similar energy equation. An approximate equation for the cross-stream velocity is developed, and the profiles of cross-stream velocity obtained from this equation show good agreement with the DNS results. A geometric interpretation of the entrainment ratio is presented, and the approximate equation for the cross-stream velocity is used to provide a general closed-form expression of the entrainment ratio. The entrainment ratio increases with $M_c$ and $\lambda$, favoring excess entrainment on the high-speed side.

In this paper, we develop a physics-informed convolutional neural network (PICNN) assisted physics-preserving method for a thermodynamically consistent model of incompressible and immiscible two-phase flow in porous media. Following the physics-preserving prediction-correction scheme of Li et al. \cite{li2025class}, the prediction step is performed by a PICNN trained with finite-volume residuals, where the interfacial fluxes are evaluated by the two-point flux approximation (TPFA) using two-point difference quotients of neighboring cell-centered unknowns to approximate interfacial normal gradients. The PICNN output is further corrected by a post-processing procedure to obtain energy-stable, mass-conservative, and bounds-preserving solutions. Numerical results show that the finite-volume residuals trained PICNN can replace the traditional prediction solver within the physics-preserving framework. Compared with conventional physics-informed neural networks (PINNs), the PICNN better captures local spatial interactions between each control volume and its neighboring cells, while the finite-volume residuals accommodate discontinuous permeability fields and interfacial flux continuity.

The flow and density field characteristics around a bubble curtain in a laboratory scale lock-exchange setup are investigated using two-phase large-eddy simulations. We study the detailed hydrodynamics and show that there are three qualitatively distinct (sub)regimes within the previously classified breakthrough regime. The occurrence of these regimes depends not only on air Froude number that characterises the relative strength of the bubble curtain and the gravity current, but also on an additional non-dimensional parameter: the density ratio between the salt and fresh water. The dependence on this additional parameter is also observed in how effective bubble curtains are in blocking the transport of salt to the fresh part of the lock. Hence, it has important implications for the optimisation of bubble curtains in ship locks.

Convective heat transfer is traditionally visualized from a Eulerian perspective using scalar temperature fields, offering limited insight into the underlying transport mechanisms. A Lagrangian view, analogous to mass transport along fluid paths, can reveal coherent structures and transport routes invisible from a Eulerian view of temperature. However, heat transport is aperiodic and non-conservative, hampering the application of fluid mixing and transport visualization techniques, developed primarily for time-periodic, conservative transport. We present a particle-based visualization technique that addresses these challenges by advecting massless particles along a time-reparameterized spacetime formulation of thermal transport, accumulating path contributions to reveal coherent transport routes and finite-time attracting and repelling structures that conventional methods cannot show.

Superfluid $^4$He subjected to steady rotation develops a regular lattice of quantum vortices aligned with the rotation axis. We prepare this lattice in a rotating cryostat, perturb it with a constant heat flux, and visualize vortex deformation waves that propagate in the lattice and grow in energy with the forcing. Below twice the rotation rate, we show that these waves feature a continuous frequency spectrum whose structure corresponds to inertial waves. At larger frequencies, we report evidences supporting the observation of a turbulent cascade of Kelvin waves. Our experiments hence provide a direct approach to deepen our understanding of collective dynamics in perturbed quantum vortex systems across all quantum fluids.

We propose the arbitrary Lagrangian-Eulerian (ALE) form of the Galerkin-Boltzmann formulation for the simulation of nearly incompressible flows with moving boundaries. The continuous Boltzmann equations are mapped to a reference state to compensate the mesh motion with an advection term. The resulting system is discretized in space using the discontinuous Galerkin method on unstructured meshes. A semi-analytic Runge-Kutta time discretization is used to overcome the stiffness introduced by the continuous Boltzmann equations. The well-known geometric conservation law is shown to be satisfied by the time and space discretizations and consistent update of geometric factors of the discretization. The implementation is on the GPU accelerated kernel library libParanumal and validated by a free stream preservation and moving Taylor-Green vortex test cases. Then, the capabilities are shown using a plunging symmetric airfoil in two-dimensions and moving carangiform fish in three-dimensions using perfectly matched layers.

Phytofluidic platforms have enabled controlled studies of plant roots, however, most existing systems either impose geometric confinement without flow or introduce hydrodynamics in single-channel devices that limit throughput and disrupt downstream analysis. New experimental platforms are therefore needed to investigate how roots integrate mechanical confinement and hydrodynamic nutrient transport, two defining features of the rhizosphere that remain difficult to reproduce under controlled laboratory conditions. Here, we present the Plant-on-a-Disc (POD), a phytofluidic platform that enables the parallel cultivation of eight seedlings under controlled hydrodynamic conditions while allowing non-invasive, in situ multimodal analysis of the intact root-shoot system. The device is fabricated in PDMS using a cost-effective wire-drawing technique to generate radial microchannels that converge into a central sump beneath an optical window. This design enables sequential bright-field, fluorescence, and Raman measurements using a single microscope objective without disturbing neighbouring seedlings. Dimensionless transport analysis and finite-element modelling confirm that the radial architecture equalizes hydraulic resistance across channels, establishing creeping laminar flow with convection-dominated nutrient transport under physiologically safe shear conditions. Using Brassica seedlings, we show that hydrodynamic flow drives coordinated root responses across multiple scales. Roots grown in flow condition exhibit accelerated elongation, substantial ROS generation and anisotropic cortical cell expansion, accompanied by carotenoid signatures detected by Raman spectroscopy.

We reveal a pristine, scale-invariant 3D Kolmogorov velocity cascade ($\alpha_V^{\mathrm{3D}} \sim 2/3$) spanning $0.05$--$20$~pc in the Polaris Flare using \texttt{PPCOS} $^{12}\text{CO}$ data. A transition scale at $\sim 0.5$~pc marks a bifurcation in the structure functions' exponents, below which the degree of intermittency is also saturated. By deriving an analytical mapping relation ($\alpha_V^{\mathrm{3D}}=\alpha_V-\frac{1}{3}\alpha_I$), we obtain the scale-invariant value of $\alpha_V^{\mathrm{3D}}$, proving that the apparent transition stems from geometric projection and a changing density fractal dimension rather than a turbulent mode shift. Kolmogorov turbulence is smoothly inherited from the large-scale cold neutral medium, remaining uninterrupted by compression or gravity below 0.1 pc.

We study a slow heat-driven flow in a gas of elastically colliding hard disks confined to a long channel. The initial state consists of two regions with large temperature and density contrasts but nearly equal pressures, leading to a low-Mach-number, nearly isobaric evolution. In the dilute limit, the corresponding isobaric hydrodynamic theory reduces to a previously known ideal-gas description. We extend this theory to finite densities by incorporating a non-ideal equation of state of a hard-disk fluid, and solve the resulting one-dimensional equations numerically. Finite-density effects produce appreciable deviations from the ideal-gas prediction. We then test the theory directly against event-driven molecular dynamics simulations of hard disks and find very good agreement in both the dilute and finite-density regimes. The results provide, to our knowledge, the first particle-level test of isobaric gas dynamics of a strongly inhomogeneous cooling flow.

Population immunity carried over from past epidemics of an antigenically variable pathogen influences the epidemic of new variants based on their antigenic similarity to the previous ones. We develop a recurrent SIR model where a population faces sequential, antigenically related variants. The model yields a recurrence map for the population susceptibility to successive variants under the assumption of status-based population immunity. The model reveals that stable, equal-sized recurrent epidemics occur across broad parameter ranges, but can be destabilized when transmission is strong and antigenic escape is limited, leading to period-2 or more, or even more complex epidemic dynamics. Epidemic size is maximized at an intermediate basic reproduction number: higher transmissibility boosts immediate infection but also enhances cross-immunity, reducing future susceptibility of the population. Our results clarify how immune history shapes recurrent epidemics and why success in one wave does not ensure larger future epidemics.

The simplest point-particle description of classical matter is incompatible with Einstein's General Relativity because the stress-energy tensor of a point particle is distributional and concentrated on a one-dimensional worldline. For such higher-codimension sources, smooth spacetime solutions generally do not exist. This obstruction was established by Geroch and Traschen for sources of codimension $\geq2$. Motivated by this result, this thesis proposes codimension-zero tubes as a fundamental description of gravitating matter. Timelike tubes are constructed within the tubular neighbourhood of an auxiliary timelike curve. The tube interior is foliated by timelike codimension-one hypersurfaces whose dynamics are governed by a brane-like action. The resulting collective stress-energy tensor is smooth, unlike that of a point particle. For a broad class of tension and potential profiles, the strong energy condition is violated inside the tube, while the null and weak energy conditions remain satisfied. In the ultraviolet limit, where the tube radius vanishes, an appropriate rescaling of the Lagrangian density reduces the tube action to the point-particle action together with a canonical self-force-like term. The particle's rest mass then emerges as an effective quantity rather than a fundamental localized parameter. Perturbative stability is analysed at two levels. Field perturbations yield an infinite squared sound speed, showing that the foliation-generating scalar is non-dynamical and cuscuton-like. Small deformations of the leaves lead to the Jacobi equation for timelike hypersurface congruences, further constraining admissible tension and potential profiles. These results establish gravitating tubes as a geometrically and dynamically consistent description of matter that respects the Geroch--Traschen obstruction.

Moons tidally interact with their host planets and stars. A close moon is quickly synchronised by the planet, or becomes captured in a higher spin-orbit resonance. However, the planet requires much more time to significantly alter its rotation rate under the influence of moon-generated tides. The situation becomes more complex for close-in planets, as star-generated tides come into play and compete with the moon-generated tides. Synchronisation of the planet by its moon changes the tidal dynamics of the entire star-planet-moon system and can lead to long-term stable configurations. In this paper, we demonstrate that a certain initial condition must be met for this to occur. Based on the angular-momentum conservation, the derived condition is universal and bears no dependence upon the planet's internal structure or tidal dissipation model. It is applicable to dwindling systems as well as tidally expanding orbits, and to the cases of initially retrograde motion. We present calculations for specific planet-moon systems (Earth and the Moon; Neptune and Triton; Venus and its hypothetical presently-extinct moon Neith; Mars, Phobos, and Deimos; Pluto and Charon), to constrain the dynamically plausible formation and evolution scenarios. Among other things, our analysis prompts the question of whether Pluto and Charon evolved into their current state from an initially more compact configuration (as is commonly assumed) or from a wider orbit -- a topic to be discussed at length elsewhere. Our results are equally applicable to exoplanets. For example, if asynchronous close-in exoplanets are detected, the possibility of tidal synchronisation by an exomoon should be considered.

The paper addresses the possibility of a young Mars having had a massive moon, which synchronised the rotation of Mars, and gave Mars an initial asymmetric triaxiality to be later boosted by geological processes. It turns out that a moon of less than a third of the lunar mass was capable of producing a sufficient initial triaxiality. The asymmetry of the initial tidal shape of the equator depends on timing: the initial asymmetry is much stronger if the synchronous moon shows up already at the magma-ocean stage. From the moment of synchronisation of Mars' rotation with the moon's orbital motion, and until the moon was eliminated (as one possibility, by an impact in the beginning of the LHB), the moon was sustaining an early value of Mars' rotation rate.

Magnetic active particles offer a versatile route to externally controlled microscale transport by combining self-propulsion with field-tunable orientation, as realized in both synthetic and living magnetic microswimmers. Here, we develop a theoretical framework for three-dimensional active Brownian motion in a uniform magnetic field, incorporating coupled translational and rotational dynamics and providing analytical approximations for low-order displacement moments. At long times, the system dynamics reduces to a combination of enhanced diffusion and permanent drift absent in regular active Brownian particles. The field acts as an external controller, channeling activity toward one of these two types of motion. At intermediate time scales, the interplay between rotational noise, self-propulsion, and magnetic alignment results in pronounced non-Gaussian displacement statistics. First-passage properties exhibit strong field sensitivity, highlighting the potential of magnetic guidance to optimize search processes and targeted delivery in active matter systems. Theoretical predictions are validated by numerical simulations.

There are many situations in nature and industry where small particles are exposed to gradients of charged polymers, such as enzymes in biological gradients of DNA or RNA, virus particles in respiratory droplets, and colloidal particles in stratifying paint layers. Here, we study the phoretic propulsion of charged microparticles in a polyelectrolyte gradient. We theoretically predict the emergence of a macroscopic electric field from charge-separation dynamics in a polyelectrolyte gradient under a continuous diffusive driving force. We confirm the presence of this self-generated electric field experimentally and show that it significantly increases the phoretic velocity of the microparticles. Finally, for high molecular weight polyelectrolytes we observe that propulsion becomes gradient-independent, consistent with diffusiophoretic predictions for asymmetric electrolytes. Our results show that self-generated electric fields in polyelectrolyte gradients can enhance microparticle transport, with potential applicability wherever charged species of different mobility are continuously driven out of equilibrium.

Achieving robust functionality in active matter driven away from thermal equilibrium is a current theoretical and experimental challenge. Several recent studies have reported edge currents--persistent transport along walls and density inhomogeneities--in chiral active matter. Yet, the microscopic rules that render these edge currents robust with respect to the confinement geometry and defects remain elusive. Here, we introduce a simple particle model of two-dimensional chiral active swimmers that undergo chirality switching and demonstrate that the model exhibits robust edge currents, i.e., when a single particle is confined, edge currents arise regardless of the confinement geometry or the presence of defects. We also investigate the collective behavior of interacting particles in bulk and find that chirality switching induces phase separation accompanied by edge currents along interfaces. This phase separation is distinct from motility-induced phase separation and is qualitatively explained by an effective hydrodynamic theory derived via bottom-up coarse-graining. Furthermore, by analyzing the topological properties of the linearized hydrodynamic equations, we show that the edge currents in our system are genuine topological edge modes. Notably, phase separation induced by chirality switching can be regarded as the coexistence of two topologically distinct domains. Our results provide guidelines for designing robust edge currents in active matter systems.

Addressable self-assembly asks that each building block assemble into a particular location in a target structure. Although particles may all be distinct, achieving high yield is a challenge because of monomer depletion: more target structures can nucleate than there are building blocks for, so they form partial fragments which cannot complete growth. We ask how to design the interactions between building blocks to achieve the highest yield in a given time. Using reaction equations describing all the intermediate steps of assembly, combined with numerical optimization, we show that the optimal interactions are such that (i) all bonds are either very strong or very weak, and (ii) the strong bonds form a spanning tree of the target structure. We then prove that when interactions form a spanning tree, monomer depletion cannot occur: assembly can always proceed downhill in energy space, with no kinetic traps. This result is a combinatorial property of the underlying interaction graph, and does not depend on the particular model for the kinetics. It suggests a robust design principle: create a network of strong interactions that has no loops, and make all other interactions much weaker. We validate this principle in numerical simulations of larger structures, and we further show that spanning trees that are more compact have typically better yield. Our results suggest a new framework for understanding monomer depletion and addressable self-assembly, which may be applied to DNA nanotechnology and which may give insight into the assembly pathways of certain multiprotein complexes.

Many subcellular condensates continuously produce biopolymers. Coupling Flory-Huggins thermodynamics to two-fluid viscoelasticity, we probe the diffusion of such source-driven polymeric droplets, and identify a universal structural compressive rim at their diffusion front. Integrating analytical scaling laws, numerical simulations, and experimental data, we show that this framework captures key structural and dynamic characteristics of the nucleolus, demonstrating the role of polymer diffusion in non-equilibrium biological transport.

We employ large-scale Dissipative Particle Dynamics simulations to investigate dilute solutions of linear polymers and unknotted, non-concatenated ring polymers in explicit solvent. By systematically varying solvent quality, we examine the interplay between hydrodynamic interactions, chain architecture, and intermolecular association. Under good solvent conditions, both linear and ring polymers remain expanded and well dispersed, displaying center-of-mass dynamics consistent with normal diffusion. In poor solvents, attractive polymer-polymer interactions drive the formation of irregular aggregates characterized by partial chain collapse, substantial interpenetration, and slower dynamics. Despite their different topologies, the two polymer architectures exhibit remarkably similar structural and dynamical responses across the solvent conditions considered. These results indicate that solvent quality largely determines the organization and transport properties of dilute polymer solutions, whereas topological effects remain comparatively weak in the investigated regime.

Many biological machines function through controlled conformational transitions, yet designing synthetic nanostructures with prescribed dynamical behavior remains a major challenge. Here, we develop a modular inverse-design framework for bistable nanostructures whose function is controlled by an energy profile along a geometric reaction coordinate. Inspired by proteins with rigid domains connected by flexible hinges, we introduce a hinge-arm paradigm in which a small bistable hinge controls the energetics of a conformational transition, while rigid arms map this transition onto the separation between external binding sites. Specifically, we ask which features of a target energy profile can be programmed under different design constraints. We find that the energy barriers and the binding-site separations in the two metastable states can be readily designed, while controlling the location of the transition state or the full shape of the energy profile requires additional design freedom. Using a differentiable design framework, we find that some optimized solutions are numerically inexact but still display the functional behavior for which the target profile was selected, emphasizing the importance of function-based evaluation criteria. These results establish a practical hierarchy of designability for bistable nanostructures and provide a route toward synthetic nanomachines that couple conformational transitions to target behavior.

Wormlike micellar fluids exhibit complex rheological behavior driven by the continuous breakage and recombination of self-assembled micellar networks. Existing two-species models provide a coarse binary representation of the micellar population, limiting their ability to resolve intermediate structural states and broad relaxation spectra. To address this limitation, we develop a three-species cascade breakage model consisting of gel-network, long chains, and short chains. By introducing an intermediate micellar state, the model links the rapid relaxation of short fragments to the slow recovery of the gel-network within a unified kinetic framework. This additional structural pathway gives rise to a three-mode viscoelastic response, improves the high-frequency description of the dynamic moduli, and produces a non-monotone constitutive curve that evolves into a stress plateau with coexisting shear bands in Couette flow. This cascade mechanism also governs the transient response, including stress overshoot, hysteresis, and multistep relaxation after shear cessation. Overall, the proposed three-species model provides a physically interpretable framework for worm-like micellar shear banding, capturing the connection between cascade microstructural evolution, broad relaxation dynamics, and macroscopic flow localization.

The linear response of wormlike chains in the nematic phase is studied by self-consistent field theory. The model Hamiltonian incorporates Maier--Saupe orientational interactions together with an isotropic excluded volume interaction. The latter models implicitly solvent mediated chain interactions, as appropriate for a lyotropic nematic. An effective free energy description for uniform nematic states is constructed in terms of the chain segment density and uniaxial nematic order parameter, providing a unified framework for density--degree of order coupling, isotropic-nematic coexistence, and the limit of stability of the nematic phase. Our results show that strong density--nematic degree of order coupling can destabilize the nematic state. The location of the instability depends on the ratio of excluded volume and nematic interaction, $u_0/u_2$. In contrast, director distortions couple to density and nematic order variations only at higher order, remaining effectively decoupled in the linear response regime. The Frank elastic constants and the correlation lengths are obtained from a linear response analysis based on the self-consistent field theory free energy. Increasing flexibility strongly suppresses twist and bend elasticity while affecting splay elasticity comparatively weakly, leading to a crossover from bend-dominated to splay-dominated elasticity. The correlation lengths and Frank elastic anisotropy obtained from the linear response analysis explain well director profiles around a +1/2 disclination core, including the core size. The latter is proportional to the equilibrium correlation length, in agreement with Landau--de Gennes scaling.

Indentation is a practical route for probing soft materials when standard tests are difficult, destructive, or cannot be performed in situ. Conventional indentation is usually interpreted in the shallow-depth regime, where the indentation depth D is small compared with the indenter radius R. In this limit, the response is controlled by local contact geometry and primarily identifies the small-strain Young's modulus E. Here, we show that at deep indentation, D >> R, flat and spherical indenters converge to the same parabolic force-depth law, F = beta E D^2. The coefficient beta is independent of indenter radius and tip shape, only mildly affected by interfacial friction, and controlled by the hyperelastic strain-stiffening response. Finite-element simulations show that this scaling arises from strain-energy delocalization: the region where SED/mu > 0.01 expands into a spheroidal domain whose size scales with D. The activated volume therefore scales as D^3, giving stored elastic energy U ~ E D^3 and force F = dU/dD ~ E D^2. Far from contact, the strain-energy-density fields collapse toward the Boussinesq far-field solution when distances are normalized by a = sqrt(F/E), which scales as D in the deep-indentation regime. These results provide a mechanistic basis for tip-shape independence and link beta to the Ogden strain-stiffening parameter alpha, enabling hyperelastic parameter extraction from deep-indentation data.

Photoelasticity is a qualitative and quantitative optical technique to image internal stress distributions in transparent materials. In the past few decades, discrete photoelastic particles have been used as a proxy for dry granular materials in both static, quasistatic, and dynamic analogue experiments. The technique allows the visualization of force chains, determination of the location and magnitude of contact forces, and outputs a stress tensor for each particle with shear and normal stress components. To date, little to no work has investigated photoelastic suspensions, where photoelastic granular particles are immersed in a fluid medium, despite its relevance in industrial and natural applications. The introduction of a fluid phase yields additional considerations in the rheological and photoelastic behavior of our proxy particles. In this manuscript, we summarize the state-of-the-art in resolving forces in immersed photoelastic granular materials. We introduce characterization techniques to probe changes in rheological and optical properties of hydrated photoelastic particles, and we report considerations for use of photoelastic particles in immersion-based experiments. We intend for this work to provide the leading framework to study the hydrodynamic interactions in 2D systems of photoelastic particles immersed in a fluid medium.

For particles of fixed mass, classical equilibrium statistical mechanics dictates a Maxwellian velocity distribution determined solely by the temperature, regardless of the interactions, density, or structure. Supercooled glass forming liquids realize long lived metastable states that evade equilibrium crystallization and may thus violate assumptions underlying Maxwellian statistics. We numerically demonstrate that supercooled liquids can exhibit persistent non-Maxwellian velocity distributions with deviations connected to their exceptionally slow super-Arrhenius relaxation. Our work is motivated by a general result establishing that long lived metastable states may exhibit finite width distributions of intensive variables. A distribution of temperatures implies non-Maxwellian velocity statistics. We test this prediction by introducing stochastic thermostats that generate stationary states while, unlike conventional thermostats, not imposing Maxwellian velocity distributions. Simulations with these thermostats yield long lived states that have, by comparison to Maxwellian velocity distributions, an excess kurtosis $0<\kappa\lesssim0.3$. Crystallization is strongly impeded with increasing $\kappa$. In a minimal description, temperature fluctuations are characterized by a dimensionless width $\overline{A}$ with $\kappa\simeq3\overline{A}^{2}$. The nearly constant $\overline{A}$ (of an average value $0.08$ and standard deviation $0.03$) found in viscosity data collapse across $45$ glass formers and in specific heat signatures is consistent with kurtosis found in our simulations. Long time non-Maxwellian velocity statistics may thus link slow relaxation, transport, and thermodynamic measurements. Independent of the tested theory, the stochastic thermostats that we introduce offer a molecular dynamics route to non-Maxwellian velocity statistics.

We conduct direct numerical simulations of homogeneous isotropic turbulence in dilute polymer solutions to investigate the Lagrangian velocity statistics. We show how polymers modulate the power spectral density of the Lagrangian velocity and the Lagrangian integral timescale by varying the Reynolds number, forcing method, and polymer relaxation time. As the polymer relaxation time increases, the attenuation of the power spectral density extends successively from high to low frequencies, and the Lagrangian integral timescale increases. To clarify the mechanism underlying the modulation of the Lagrangian velocity statistics, we decompose the Lagrangian velocity into the contributions from vortices at different length scales. Using this scale-decomposition analysis, we demonstrate that the observed modulation of the Lagrangian velocity statistics results from polymer-induced suppression of vortices that proceeds from smaller to larger scales.

Nature has equipped jet-propelled swimmers with flexible nozzles that outperform rigid ones, yet the origin of this advantage has remained unexplained. By tracking where and when energy is exchanged between fluid and structure, three-dimensional numerical simulations resolve the underlying mechanism: a standing-wave response of the nozzle, in which the structure dilates and then recoils synchronously, charging and releasing energy to enhance thrust. Outside of this regime, the structure exhibits a traveling wave response, with expansion and contraction coexisting along the nozzle, reducing the thrust gain. We propose a physics-based model that captures the boundary between standing and traveling responses in a closed form, showing that the optimum occurs when the natural period of the structure matches the pulse duration. Beyond this optimum the strain imposed by the nozzle curvature required for steering selects the geometry observed across marine species. The propulsion and maneuverability are reconciled within a single framework that yields design principles for soft robotic propulsors.

Adjoint-based sensitivity analysis is an indispensable tool for large-scale fluid-dynamic design and distributed control problems, yet its application to unsteady and turbulent flows is frequently hindered by the prohibitive memory footprint of transient checkpointing and the divergence of gradients in chaotic regimes. To address these computational bottlenecks, this paper presents a mean-flow adjoint sensitivity analysis framework for unsteady flows around porous cylinders using the homogenized lattice Boltzmann method (HLBM). Within this framework, solid structures are efficiently modeled as local porous media utilizing a Brinkman penalization approach. We systematically investigate HLBM-based adjoint gradients for drag and energy dissipation objective functionals, transitioning from steady laminar to unsteady, and finally to turbulent flow regimes. For the turbulent case at Re = 3900, a proof-of-concept is conducted where the framework relies on automatic differentiation to automatically generate adjoint kernels containing subgrid-scale (SGS) turbulence models for large eddy simulations (LES), circumventing manual derivation and allowing for a direct comparison against the frozen turbulence assumption (FTA).

New numerical methods are proposed for the mixing entropy maximization problem in the context of Miller-Robert-Sommeria's (MRS) statistical mechanics theory of two-dimensional turbulence, particularly in the case of spherical geometry. Two of the methods are for the canonical problem; the other is for the microcanonical problem. The methods are based on the original MRS theory and thus take into account all Casimir invariants. Compared to the methods proposed in previous studies, our new methods make it easier to detect multiple statistical equilibria and to search for solutions with broken zonal symmetry. The methods are applied to a zonally symmetric initial vorticity distribution which is barotropically unstable. Two statistical equilibria are obtained, one of which has a wave-like structure with zonal wavenumber 1, and the other has a wave-like structure with zonal wavenumber 2. While the former is the maximum point of the mixing entropy, the wavenumber 2 structure of the latter is nearly the same as the structure that appears in the end state of the time integration of the vorticity equation. The new methods allow for efficient computation of statistical equilibria for initial vorticity distributions consisting of many levels of vorticity patches without losing information about all the conserved quantities. This means that the statistical equilibria can be obtained from an arbitrary initial vorticity distribution, which allows for the application of statistical mechanics to interpret a wide variety of flow patterns appearing in geophysical fluids.

In this experimental and theoretical study, we assess the extensional relaxation time of sodium alginate solutions by using dripping-onto-droplet capillary breakup rheometry (DoD), e.g., the capillary thinning and breakup of viscoelastic filaments formed following the coalescence of a millimetric-nozzle-generated pendant drop with a lower droplet cap of the same fluid contained in a millimetric pool in ambient air. Hence, we extend the analyses conducted by El Khoury et al. (2026) from Newtonian to viscoelastic fluids. Our approach relies on experiments recorded with a high-speed camera using sodium alginate in deionised water, with alginate concentrations ranging from 0.1% to 8% by weight. The results are depicted by considering the dynamics of fluid filament thinning, stress balances, and scaling laws. Extensional relaxation times are resolved from the filament diameter evolution. Three flow regimes are highlighted: capillary-inertial, capillary-elastic, and mixed capillary-inertio-elastic. The findings are summarised in a two-dimensional diagram that correlates the filament breakup time with different flow regimes using the important dimensionless parameter of the problem, e.g., the intrinsic Deborah number (which relates the extensional relaxation time to the characteristic capillary-inertial time). This diagram can be used to quantify both the solution's extensional relaxation time and the liquid/air surface tension solely from filament breakup times.

Wind shear and wind veer (gradients of wind speed and direction, respectively) are ubiquitous in the atmospheric boundary layer (ABL), and wind turbines therefore routinely operate in sheared and veered conditions. Previous field campaigns have observed statistically significant variations in power production efficiency (quantified by a power coefficient) upwards of 15% due to shear and veer. However, it is not yet clear how non-uniform inflow conditions alter rotor aerodynamics and drive these efficiency variations. In this study, we perform concurrent-precursor large-eddy simulations (LES) of an actuator disk-modeled wind turbine across stratified ABL conditions to demonstrate that shear and veer can reduce wind power efficiency by more than 20%. To support these ABL simulations, we perform simplified inflow LES where shear and veer are controlled independently. Using these controlled simulations, we demonstrate that shear and veer effects can be decomposed into: (1) geometric effects, due to changes in rotor-equivalent wind speed, and (2) inductive effects, which change the rotor aerodynamics and induced velocities. Inductive effects of wind shear modulate the power coefficient through changes to the local induction, while inductive effects of wind veer reduce the power coefficient by generating an adverse pressure gradient at the rotor scale. The geometric and inductive effects of shear and veer approximately linearly superimpose, with increasing losses as shear and veer magnitudes increase. Inductive effects account for a significant fraction of the observed losses, and the induction of a turbine is affected by shear, veer, and wall proximity through processes that are neglected in existing engineering models. Revealing the mechanisms through which shear and veer affect rotor performance establishes a framework that can enable improved power prediction in realistic ABL conditions.

We investigate how cooperative feedback shapes global oscillatory dynamics in a glycolysis model with product recycling and allosteric phosphofructokinase regulation. Using bifurcation theory and numerical continuation, we analyze the stability of equilibria and characterize Hopf and generalized Hopf bifurcations, using the Hill exponent as an effective measure of cooperativity. We show that a codimension-2 cusp-of-cycles point governs the creation and annihilation of detached branches of limit cycles (isolas) and, together with saddle-node bifurcations of limit cycles, organizes a regime map of six qualitatively distinct dynamical regions. In the birhythmic regime two stable oscillatory states coexist on connected branches; in the isola regime a stable oscillation exists on a fully disconnected branch, producing threshold-dependent onset of rhythmic activity. Time-domain simulations confirm coexistence of distinct rhythms and illustrate how the choice of initial condition determines which attractor is reached. Together, these results show how variations in cooperative feedback strength can generate isolated oscillatory modes and multistability in metabolic networks, highlighting isola dynamics as a general mechanism for rhythm selection and switching in nonlinear biological oscillators.

This work presents a comprehensive analysis of coupled stochastic van der Pol oscillators, a paradigm for understanding synchronization, bifurcations, and chaos in nonlinear systems subject to random fluctuations. The system comprises two or more oscillators with nonlinear damping, linear diffusive coupling, and additive Gaussian white noise. We develop a unified framework that systematically connects global bifurcations, synchronization phenomena, and chaotic dynamics within a single coherent stochastic model. We explore the stochastic dynamics of coupled van der Pol oscillators by seamlessly blending theoretical principles with in-depth numerical simulations. This integrated approach forms a robust framework for analysis, with essential phenomena clearly depicted in the accompanying figures. We then extend this framework to a comprehensive investigation of large networks, focusing on their continuum limit, emergent pattern formation, the role of noise, and the onset of collective chaos.

Hidden structures with well-defined predictability are uncovered in the evolution of a chaotic optomechanical system from the perspective of the $\epsilon$-machine. Tuning the frequency of the driving laser can switch off this predictability, and such behaviour corresponds to a phase transition that is deeply related to topological changes in phase space. The transition probabilities between causal states allow us to define an entropy (uncertainty) that serves as an effective order parameter. This phase transition can be readily demonstrated in currently available experiments by monitoring the quadrature of the optical mode. We hope that this work could fundamentally broaden the regimes of cavity micromechanics and nonlinear optics.

Dissipative solitons constitute a robust class of self-localized nonlinear states sustained by the dynamic balance between nonlinearity and gain-loss, possessing an intrinsic stability that stems from their fundamental attractor nature. When combined with lattice truncation, this balance gives rise to dissipative surface solitons (DSSs), whose existence and stability are jointly dictated by boundary-induced confinement and non-Hermitian dynamics. In two-dimensional truncated lattices with linear gain and loss, surface localization emerges within gap regimes, where families of DSSs bifurcate from linear surface localized gain modes as the nonlinearity increases. Increasing the number of waveguide rows at the interface enriches the diversity of supported surface modes in both linear and nonlinear regimes. Although multiple DSS families with distinct phase configurations may coexist within the same gap, their dynamical stability is strongly phase selective. These insights establish linear gain-loss engineering as a powerful mechanism for controlling nonlinear surface localization and provide practical guidelines for realizing robust nonlinear surface states in gain-loss-tailored photonic platforms.

We investigate the Thouless pumping dynamics of nonlinear gap solitons and attempt to realize topological Chern number switching by modulating nonlinear parameters and varying the ramping rate of the relative phase between periodic potentials. We find that gap solitons can undergo nonlinear instabilities accompanied by finite Bogoliubov excitations under near-adiabatic ramping. Such finite Bogoliubov excitations induce the particle loss of the solitons, leading to reversed propagation directions that signals the occurrence of Chern number switching with analyzing the correspondence between soliton chemical potential and Bloch topological energy band. Our findings offer a feasible strategy for manipulating the Thouless pump dynamics of gap solitons mediated by finite Bogoliubov excitations, with implications for topological quantum transport and quantum computing applications.

Extreme events in financial systems, often captured by indicators such as volatility, remain difficult to identify close to their onset. Volatility shares many statistical properties with other natural, complex systems which experience extreme events, which we explore in this manuscript. We extend the analogy between rogue waves in optical and hydrodynamical systems to financial volatility by identifying rogue-wave-like peaks with similar statistical properties. We use a Schrödinger equation where the potential follows the shape of a Kerr nonlinearity to examine the properties of financial volatility indices within a moving time window. We see evidence of Anderson localisation as a rogue peak approaches in the VIX, and show that the numerical gradient of the system's minimum eigenvalue reliably spikes at the onset of an extreme event. We adapt our methodology to simulate the real-time arrival of data, and show that all but one of the VIX's major peaks can be detected given a reasonable amount of history. We then perform two out-of-sample tests, one for the VXO index, and one for the VSTOXX index, and successfully replicate our initial results, identifying all but one major peak (87.5% or 7/8) in both cases. This method of analysis shows considerable promise as a tool for identifying potential financial crises, aiding in their mitigation.

Alzheimer's disease (AD) is characterized by the accumulation of Amyloid-$\beta$ ($A\beta$) plaques and hyperphosphorylated Tau proteins. However, many individuals exhibit substantial $A\beta$ and Tau pathology without developing dementia, suggesting that disease progression may depend not only on pathological burden but also on the spatial organization of these proteins. Motivated by this observation, we adapt Gray-Scott reaction-diffusion model to investigate pattern formation arising from the interactions between $A\beta$ and Tau. % To systematically identify stable spatial configurations, we employ a Companion-Based Multi-Level Finite Element Method (CBMFEM) on both two-dimensional domains and anatomically realistic cortical surface meshes. Numerical simulations reveal a rich landscape of multiple steady-state solutions, which are subsequently classified into representative pattern phenotypes using principal component analysis and clustering techniques. The results demonstrate that the coupled $A\beta$--Tau system admits numerous stable spatial patterns rather than a single pathological endpoint. % These findings provide a potential mathematical framework for understanding the heterogeneity of Alzheimer's disease and the existence of cognitively resilient individuals despite significant pathological burden. More broadly, the proposed framework suggests a pattern-based therapeutic paradigm in which disease dynamics are guided toward favorable stable states rather than solely targeting the elimination of pathological proteins.

The "new" Système international d'unités (SI), which became effective May 20, 2019, defines and is defined by a set of constants. These include the speed of light, the Planck constant, the Boltzmann constant, and the constant relating the elementary electric charge to the coulomb. Interpreting such constants as conversion factors organizes the units they relate into a unifying geometric framework. In this framework, units appear (perhaps raised to some power) either as rows/columns in a single conversion table or as entries in a list of dimensionless numbers. This organization clarifies the distinction between "fundamental" physical constants with values that are set by people, like those defined in the SI, and those with values that are set by nature. It also reveals geometry permeating our theories of physics that is normally hidden by a surplus of units.

Physical heterogeneities in the context of sliding friction, such as a human finger exploring an object, have been well studied, yet the behavior of chemical heterogeneities in mesoscale soft sliding remains underexplored, despite the similar prevalence of chemical and physical variations in real systems. Here, we experimentally characterized the friction of a planar soft elastic probe sliding across a single chemical heterogeneity that was formed at the interface of two silanes on silicon wafers. By constructing phase maps across multiple loads and velocities, we quantified the occurrence of several frictional phenomena at and around the chemical edge, including stiction spike formation, edge slope direction, baseline shifts, and baseline drift, and quantified their sliding direction-dependent formation. We found that chemical heterogeneities made by more disparate materials (butyl- and aminopropyl-terminated) exhibited several phenomena that were more often direction-independent compared to chemical heterogeneities formed from more similar materials (butyl- and hexyl-terminated). We attributed this directional asymmetry to elastic body effects. In subsequent human testing (n=36), we observed that humans also exhibited directional-dependent accuracy (66.7% versus 38.9%) on one pair (butyl- and hexyl-terminated) but not the other (77.8% versus 75%), which in the context of our phase maps, suggests that the slope of the friction force when sliding over a chemical edge is important for generating a clear edge of a tactile feature, rather than the differences in simple material properties or other friction phenomena.

Conventional materials derive their properties from microscopic composition and arrangement, whereas mechanical metamaterials are defined by mesoscopic structure rather than constituent material. Bridging these paradigms, using macroscopic geometric alterations to orchestrate microscopic degrees of freedom and program mechanics, remains a central challenge. Here, we demonstrate that cuts in anisotropic, responsive solids provide such a connection. Using liquid crystal elastomer (LCE) sheets with kirigami patterns, we reveal that engineering strain through cuts harnesses molecular anisotropy to control emergent mechanics. Similarly, the interplay between cut patterns and the molecular phase transition of LCEs enables soft robotics functionalities such as supersoft grippers with remote actuation and architectures that reversibly morph under temperature variations, behaviors inaccessible to conventional kirigami or LCE sheets alone. LCE kirigami thus establish a new class of multiscale metamaterials in which geometry governs access to microscopic degrees of freedom, to program macroscopic function.

Mechanical stresses are fundamental regulators in biological tissues, where the vertex model (VM) is pivotal for theoretical and force-inference studies. Yet, no uniform expression for the stress tensor exists for the VM. Here we provide a microscopic derivation of it, linking mesoscopic stresses to the VM forces. The stress field presents a freedom on how tensions are distributed across cells, which allows previous expressions to emerge as particular realizations of the field and suggests a link between mesoscopic stresses and cytoskeletal force-transmission architectures in real cells.

It is well known that growing tumors generate and respond to stress in their local microenvironment. Tissue re-arrangements can relax these mechanical stresses and make the tissue more fluid-like. Further, intricate coupling between mechanotransduction and biochemical signaling leads to complex patterns of growth. To predict the outcomes of these nonlinear interactions, we develop a phase-field model to simulate tumors growing into a surrounding medium taking into account their elastic and viscous properties as well as their compressibilities. We couple continuum modeling of the viscoelastic mechanics to the concentration of a diffusible growth-promoting nutrient in a mass conservative way. The phase-field method is a stable and flexible way to describe the dynamics of arbitrarily shaped tumors. We demonstrate convergence of the phase-field model to a sharp interface model in radially symmetric geometries and can observe progression to stationary tumors. However, our results show that these stationary symmetric tumors are subject to symmetry-breaking instabilities in 2D and 3D driven by two primary mechanisms: (i) elastic buckling instabiliies due to differential growth induced by the nutrient gradient and (ii) instabilities generated by apoptosis-related volumetric loss. Further, tissue fluidity and compressibility can lead to changes in tumor topologies. Our modeling framework provides a robust methodology for investigating how tissue mechanics and growth factor signaling influence the progression and invasive potential of solid tumors.

We investigate the emergence of flagellar beating in chains of magnetic self--propelled particles (MSPPs) built from centimeter--scale vibrating robots (Hexbugs) with embedded neodymium dipoles. When one end of the chain is anchored and self--propulsion is activated, longitudinal stress accumulates along the chain until it overcomes the magnetic bending stiffness, triggering a buckling instability that drives sustained flagellar beating. Using a combination of experiments and numerical simulations, we identify three distinct dynamical regimes straight chain, stable flagellar beating, and fission governed by the competition between active force, chain length, and magnetic bending stiffness. The onset of beating requires a seed misalignment set by the balance between magnetic torques and rotational noise, and we show that the transition corresponds to a supercritical Hopf bifurcation. A kinematic model reproduces the observed orientation dynamics with excellent agreement. The magnetic bending stiffness, which arises directly from dipole--dipole interactions, is fully tunable via dipole strength and chain length, offering independent experimental control over both activity and rigidity. Our results establish a macroscopic platform for studying force-induced buckling and self--oscillations in active filaments, with direct connections to flagellar motion in biological and synthetic microswimmers.

Shearing a packing of solid granular grains can be difficult, especially when the solid fraction is high and the boundary confinement is strong. It was recently shown that embedding voids in grains can make a packing easier to shear when such voids make the grains auxetic. Here, we use finite element simulation to show that auxeticity is not a necessary condition even in a seemingly very constrained setting: shearing dense and ordered granular packings under a constant solid fraction. More specifically, by controlling the geometry of a void embedded in a grain, we induce an apparent elastic anisotropy and softening of the grain under shear, which collectively leads to a significant reduction -- up to 90\% -- of the apparent shear modulus of a packing of these grains. Complementary analysis shows that this reduction correlates well with a decrease in contact-force anisotropy, and is insensitive to system size and contact friction variation. Our results highlight how grain-scale geometry, mediated by multi-body contact mechanics, modulates macroscopic system-scale elasticity, providing a minimal design mechanism towards targeted collective mechanical properties of soft granular metamaterials.

Clathrin assemblies in cells can persist as flat plaques, abort after partial invagination, or close into clathrin-coated vesicles, but the determinants of these different fates remain unresolved. To investigate the stochastic and complex dynamics of clathrin assemblies, we have developed a kinetic Monte Carlo simulation framework that couples individual clathrin agents to an adaptive continuum membrane. In this hybrid discrete-continuum description, the effective coat bending rigidity and the preferred coat curvature emerge during growth, rather than being prescribed as material parameters. Once connected, curved lattices stiffen from molecular bending modes to coat-level rigidities, because curvature changes require increased stretching or compression, while newly incorporated triskelia hardcode a history-dependent preferred curvature. An analytical theory for non-Euclidean elasticity identifies the relevant internal variables and predicts growth laws that are validated by the simulations. The same microscopic assembly rules yield flat, stalled, and closed coats through two sequential gates in the effective membrane-coat energy landscape. Comparisons with experimentally observed coat geometries and nanodissection-induced curvature changes agree with our theoretical predictions without any fitting parameters. The clathrin coat thus emerges as an adaptive assembly with prestress and memory, whose fate and material parameters reflect the environment in which it has been growing.

Experiments in multiphase flows are often limited in their ability to simultaneously obtain velocity measurements in different phases. At the same time, flow reconstruction from phase-limited measurements is a challenging problem due to the substantially different velocity statistics across the phases. We address this problem for buoyancy-driven bubbly flows in the pseudo-turbulence regime by using a guided diffusion model. We train the model using two-dimensional slices of the velocity field extracted from fully resolved three-dimensional direct numerical simulations. The model generates physically realistic velocity fields both unconditionally and when conditioned on the surrounding liquid flow. The reconstructed bubble-phase velocity field accurately reproduces key statistical features of the flow. We further show that a simple patching procedure for adjacent two-dimensional slices enables a reasonable reconstruction of the three-dimensional flow inside a bubble. These results establish the potential of diffusion models to serve as generative priors for three-dimensional turbulent multiphase flows, opening a route toward the reconstruction of unobserved or experimentally inaccessible velocity fields from sparse, partial, or phase-limited measurements.

We study stochastic models of a microscopic active heat engine, comprised of an overdamped Brownian particle trapped in a harmonic potential, and in simultaneous contact with thermal (passive) and athermal (active) baths. The interaction with the active bath is modeled as a stochastic force described by Poisson shot-noise (PSN) having a specified amplitude distribution. With analytical calculations and numerical simulations, we study the thermodynamic performance of the machine to quasistatic cyclic protocols analogous to those running two-stroke and Stirling-like engines. For specific parameter ranges, the thermodynamic behavior is that of a $\textit{hybrid machine}$, simultaneously operating as a heat engine with respect to the passive/active baths and as a refrigerator with respect to the passive/active baths. Focusing on the parameter region where the overall performance is such of an engine, we show that the average total extracted work per cycle divided by average total heat intake from the cold baths per cycle may surpass the Carnot efficiency associated with the temperature of the passive baths. Applying the second law for active heat engines, we focus on a bona fide efficiency (bounded by Carnot's efficiency) that incorporates an information-theoretic metric $\mathcal{I}-$ which we call $\textit{quasistatic divergence}-$ quantifying how distinguishable are the engine's statistics in the quasistatic limit with respect to a continually changing equilibrium distribution. We analyze, with theory and numerical simulations, how the PSN shot rate and the degree of non-Gaussianity in the particle position distribution influence the efficiency of the engine, and explore the correlation between non-Gaussianity and efficiency. Our findings reveal optimal PSN shot rates maximizing the engine's efficiency and an intriguing non-bijective relation between efficiency and kurtosis

Active fluids consisting of living cells or synthetic microswimmers display rich emergent behavior and nonequilibrium mechanical properties, which not only shed light on various biological processes but also inform the engineering of autonomous fluidics and self-driven materials. The individual behavior of microswimmers and their interaction with self-generated mesoscale solvent flows underlie the emergent properties of active fluids. Here we studied the microscopic dynamics in dense 3D bacterial active fluids by simultaneous imaging of cell body, flagella, and flow field. A surprising finding is that the polarity of cells was randomly distributed in mesoscale flow regimes, and yet the system displays mesoscale order in the self-generated solvent flows. Despite the apparent flow-polarity decoupling, the motion of cells relative to local solvent flows predominantly navigated upstream, with the self-advection speed universally enhanced by a flow-controlled constant. Numerical modeling with full hydrodynamic interactions reveals that the observed flow-polarity decoupling arises from the breakdown of the commonly held force-dipole assumption for anisotropic microswimmers: in the presence of flow gradient and near-field hydrodynamic interactions, the direction of total active forcing exerted by a swimming bacterium to the surrounding fluid no longer aligns with its polarity. The simulations suggest that near-field interactions serve as a new type of emergent, configuration-dependent active forcing, which profoundly impact self-organization and transport in dense bacterial suspensions. Taken together, our work establishes fundamental knowledge for faithfully understanding the collective behavior of dense polar active fluids.

We introduce a class of dynamic systems we call phase time crystals consisting of a binary assembly of particles with intermediate or long-range repulsive interactions that are subjected to a circular drive of uniform chirality in which each particle species is out of phase from the other by 180 degrees. As a function of the particle density and orbit radius, this system can organize into a rich variety of dynamical crystalline states, including one in which the out of phase particles form bound pairs that assemble into a triangular lattice. We also find stripe phases, overlapping packed crystals, disordered or phase glass states with no diffusion, mixed fluids, and different types of phase-separated states. We show that these states are robust against the addition of thermal fluctuations, and that the paired crystal can melt into a paired fluid. If the drive on each particle species is of opposite chirality, the system forms stripes and packed lattices, but no paired crystal is present. We demonstrate that by modifying the nature of the chiral driving, it is possible to realize numerous kinds of active molecular lattices, including dynamic square spin ice geometries and higher-order complex structures.

A recent pioneering experiment [Nat. Commun. 16, 10114 (2025)] demonstrated that a driven overdamped colloidal particle in a harmonic trap immersed in a viscoelastic fluid can recuperate energy dissipated into the surrounding bath and convert it into useful work. In this article we considerably extend the original predictions. In particular, we show that energy recuperation is a generic feature of non-Markovian systems both in and out of equilibrium, even as simple as a free Brownian particle. Moreover, we demonstrate that inertia alone, even in the strong damping regime, can lead to this effect despite the absence of any external forcing. These results suggest that energy recuperation can be ubiquitous in nature and it may be the modus operandi of various phenomena in setups with memory. We show that this novel mechanism of energy recovery is the source of memory-induced ultrafast directed transport of a particle in a periodic potential in which it almost attains its top speed corresponding to the system with no energy barriers. Our results may answer from the fundamental point of view the question why the cytosol, the intracellular fluid in biological cells, is viscoelastic.

We develop a theory for the electrophoresis of a spherical porous liquid droplet with prescribed uniform surface charge. The exterior electrokinetics is governed by the Poisson-Nernst-Planck-Stokes equations, while the internal liquid motion is described by the Brinkman-Debye-Bueche equation. A regular perturbation expansion in the applied electric field reduces the governing equations to coupled radial ordinary differential equations. In the Debye-Hückel regime, we derive a closed-form mobility expression valid for arbitrary Debye layer thickness. The analysis shows that the porous interior modifies clean-droplet electrophoresis through a single Brinkman-screened hydrodynamic resistance, yielding a continuous transition between clean-droplet and rigid-particle limits. Numerical solutions beyond the low-potential regime reveal a non-universal role of permeability: increasing the Darcy number can either suppress or enhance the mobility. This reversal is determined by the sign of the interfacial-velocity mode, which is governed by the competition between tangential Maxwell traction and hydrodynamic shear generated by electric-double-layer distortion. Dielectric polarization, surface charge and double-layer thickness can reverse the internal circulation, while the Darcy number controls how strongly this circulation is transmitted through the porous interior. This permeability sensitivity is especially pronounced for highly polarizable droplets in the thin-double-layer regime. The theory provides a basis for tuning electrokinetic transport of soft porous droplets in microfluidic and biomedical technologies.

Opposition control reduces skin-friction drag by opposing the wall-normal velocity on a near-wall detection plane, but the detection-plane velocity it requires is not available from wall-mounted sensors. Wall data can reconstruct inner-flow quantities accurately when assessed offline on a fixed flow state, and we ask whether such a reconstructed field can instead serve as a live surrogate sensor inside the feedback loop. We train a recurrent estimator to infer the detection-plane velocity from the two wall-shear-stress components in opposition-controlled turbulence. Offline it performs extremely well, reaching a correlation of 0.99 and near-unity coherence across the energetic scales; yet the same estimator fails in closed loop, decorrelating from the true field within a few viscous time units as the control collapses. The failure is not one of accuracy but of distribution shift induced by the controller itself: small closed-loop errors carry the flow off the attractor represented in the training data, while unresolved high-wavenumber errors enter through the wall boundary condition and return as out-of-distribution inputs. Standard remedies such as low-pass filtering and exponential averaging only delay numerical breakdown while accelerating decorrelation. Stable wall-only control is recovered by imposing spectral consistency on the deployed actuation and retraining the estimator on its own closed-loop data, giving a controller that holds much of the drag reduction of ideal opposition control from wall quantities alone. The obstacle is not whether the near-wall flow can be reconstructed offline, but whether that reconstruction stays dynamically consistent when allowed to modify the flow it senses.

We study the flow in a symmetric three-dimensional confined sudden expansion with lateral inflow at Reynolds number below 300 and varying lateral-to-central flow rate ratio, using experiments, linear stability analysis, weakly nonlinear theory, and direct numerical simulations. Three distinct flow regimes are identified. Outside an intermediate band of lateral-to-central flow rate ratio, the flow undergoes a steady symmetry-breaking bifurcation above a critical Reynolds number, deflecting the central jet toward one side wall; weakly nonlinear analysis shows this bifurcation to be supercritical, excepting a very narrow parametric range. Within the intermediate band, no such critical Reynolds number exists and direct numerical simulations confirm that residual velocity asymmetries reflect the imposed geometric imperfections rather than intrinsic amplification. Fluctuations observed experimentally in the intermediate band of lateral-to-central flow rate ratio remain unexplained and warrant further investigation.

Scale-resolving simulations of wall-bounded turbulent flows remain prohibitively expensive at high Reynolds numbers, owing to the stringent near-wall resolution requirements. High-order compact gas-kinetic schemes (CGKS) are accurate, robust, and efficient for compressible flows, making them an attractive foundation for reducing this cost. Building on the fifth-order scheme CGKS-5th, we develop a wall-modeled CGKS framework that alleviates the near-wall resolution burden through a pressure-gradient-based non-equilibrium wall model while preserving the resolving power of the outer solver. CGKS-5th resolves the outer flow and supplies the wall model with data at the exchange location. On coarse near-wall meshes, the wall model reconstructs the under-resolved viscous wall stress, while CGKS-5th provides the inviscid wall flux directly; the two combine to form the wall momentum flux. To capture non-equilibrium effects in adverse-pressure-gradient and separated regions, the wall model retains a pressure-gradient source term together with a pressure-gradient-corrected near-wall damping function. We assess the framework on two distinct flows: bluff-body separation past a circular cylinder, and a shock-induced separation bubble on the transonic RAE 2822 airfoil, using near-wall meshes far coarser than wall-resolved simulations require. For the RAE 2822 case, this corresponds to a twentyfold coarsening in the wallnormal direction, with comparable coarsening in other directions. In both cases, the wall-modeled CGKS-5th reproduces the separated flow structures and markedly improves near-wall predictions over its wall-model-free counterpart, most notably the skin-friction coefficient. The framework thus delivers accurate predictions of these separated flows at substantially reduced near-wall cost, while its lightweight coupling adds less than 1% runtime overhead in a multi-GPU implementation.

Near the liquid-vapor critical point, fluids become highly compressible, giving rise to a special, strongly coupled thermo-mechanical process: the piston effect. In this phenomenon, a thin thermal boundary layer develops near a heated wall; owing to strong thermal expansion, this layer acts like a piston, compressing the bulk fluid adiabatically and resulting in a seemingly accelerated thermal response. Although the piston effect is a thermo-acoustic process, the characteristic time scale of the boundary perturbation is typically orders of magnitude larger than the acoustic time scale of the setup. Consequently, rapid acoustic propagation can be neglected, justifying a post-acoustic approximation with a spatially uniform but time-dependent bulk pressure. Within the linear regime, the temporal evolution of pressure can be directly connected to the heat flux entering through the boundaries. As a result, the problem reduces to a diffusion equation governed by a spatially homogeneous source term that depends explicitly on the boundary conditions. Exact, closed-form analytical solutions are derived for effectively one-dimensional problems in both Cartesian and spherical coordinates, considering boundary conditions of the first and second kinds. Short-time asymptotic behavior and thermal penetration depth are analyzed for all four cases. By incorporating the heat capacity of a container via a homogeneous model, an effective boundary condition coupling the wall heat flux and the time derivative of the wall temperature is derived, allowing for a direct comparison with experimental data from the Spacelab D-2 mission. The analytical predictions show good agreement with the experimental results without relying on any numerical simulations.

Benefiting from the direct modeling of physical laws in a discretized space and the automatic decomposition of the gas distribution function into hydrodynamic waves and particles, the UGKWP method offers significant advantages for multiscale flows such as hypersonic flows, plasma transport, and radiation transport. In this study, the particle sampling accuracy in the UGKWP method is improved from first order to second order, so that the second-order spatial and temporal accuracy is preserved across the full scheme. Specifically, the modifications include second-order particle sampling based on local macroscopic gradients, a weighted least-squares gradient reconstruction that incorporates wall values, a revised Venkatakrishnan limiter for highly stretched cells, and conservation corrections after particle sampling. Moreover, the first-order Chapman--Enskog term is considered in the free-transport part of the hydrodynamic wave flux, enabling better recovery of the GKS in the near-continuum regime. Based on these improvements, the mesh-independence behavior of the UGKWP method is notably enhanced, which is more consistent with the performance of the UGKS, validated by a detailed hypersonic cylinder flow test case. Furthermore, systematic comparisons with the single-scale DSMC method are performed for two-dimensional hypersonic flow over a cylinder and three-dimensional flow over a blunt cone. Wall pressure, shear stress, and heat flux coefficients (CP, CF, and CQ) are examined in the cylinder case, while the overall aerodynamic coefficients (CL, CD, and L/D) are assessed in the cone case. The multiscale UGKWP method exhibits significantly better mesh-independence performance than DSMC for mesh-sensitive quantities such as CF, CQ, CD, and L/D, which are critical for aerodynamic and thermal protection design of near-space hypersonic vehicles.

In this paper, two novel data-driven models based on kriging and neural networks (NN) are proposed to predict pressure losses across perforated plates with circular perforations in turbulent flows. The models are developed using two sets of experimental data available in the literature. The predictive performance of the proposed models is assessed and compared against widely used empirical formulae. It is found that the proposed models consistently outperform existing empirical models for most perforated plate configurations contained in the experimental datasets. Besides, the predicted pressure losses generally show good agreement with experimental measurements, demonstrating that data-driven approaches based on kriging and NN provide a feasible framework for modelling pressure losses across perforated plates. Overall, both approaches are promising, despite being trained on a relatively limited amount of experimental data, owing to the scarcity of measurements reported in the literature. To demonstrate the applicability of the proposed models in numerical simulations, two-dimensional channel flows are simulated using the Reynolds-averaged Navier-Stokes (RANS) equations, in which the new pressure-loss models are implemented as a source term in the momentum equations. The RANS predictions are found to be in excellent agreement with the model predictions, confirming the suitability of the proposed approaches for practical computational fluid dynamics applications.

We propose a lattice Boltzmann model (LBM) on standard lattices for simulating multi-dimensional, weakly compressible, isothermal flows within and around isotropic heterogeneous porous media. The model incorporates Darcy-Forchheimer drag and a Brinkman-like effective viscous stress tensor. In the hydrodynamic limit, it recovers a generalized volume-averaged formulation valid in both free-fluid and porous-medium regions. By relying on a single kinetic equation and a monolithic LBM algorithm, the formulation provides a one-domain solver for free-fluid/porous-medium interactions. Unlike previous LBM formulations for porous media, the proposed model recovers the correct porosity scaling of both the pressure and convective terms, while preserving the isotropy, and hence the Galilean invariance, of the viscous stress tensor. Linear and nonlinear drag, variable-porosity corrections, and additional body forces are incorporated through a consistent generalized forcing scheme. The model allows the speed of sound to be specified independently thereby improving computational efficiency. In addition, it includes a freely tunable effective bulk viscosity that can be used to enhance numerical stability. Model performance was evaluated using 2D benchmark flow problems. The ability of the proposed LBM model to simulate transport between free-fluid and heterogeneous porous regions within a one-domain framework enables a broad range of applications, particularly in early-stage, device-scale design studies of engineered porous structures with spatially varying porosity.

This paper presents the derivation of closed-form expressions of the single-point statistical moments of a solution to a nonhomogeneous stochastic advection equation with a linear relaxation. While analytical solutions exist for homogeneous systems, nonhomogeneous cases have traditionally relied on intensive numerical simulations. Here, we provide an analytical framework for calculating single-point statistical moments by first obtaining the solution to the stochastic advection equation via the method of characteristics, from which the moments are derived. Explicit, closed-form expressions for the first four moments are derived as functions of the characteristic length scale of the stochastic velocity field and the spatial derivatives of time-mean profile of the field. The analytical results are validated against numerical simulations, demonstrating excellent agreement across a range of physical parameters. The resulting theory acts as a generalized ``equation-of-state" style approach for predicting variability and non-Gaussian statistical behavior directly from the macroscopic mean state, providing applicability across transport systems with a wide range of time and length scales, including geology, hydrology, and atmospheric sciences.

Premixed flames in stagnation point flows are traditionally described using Navier--Stokes equations where inertia and density variations play an important part in determining the flame structure. However, in porous media or Hele-Shaw configurations, Darcy's law replaces the momentum balance, shifting the governing physics to a balance between pressure and viscous forces. This study investigates non-adiabatic strained premixed flames under Darcy's law, pertinent in particular to confined flames in Hele-Shaw burners, accounting for non-unity Lewis numbers and volumetric heat losses. The flame is established in a planar counterflow formed by impinging a cold unburnt gas and a hot burnt gas maintained at the adiabatic flame temperature. We show that the jump in the strain rate across the flame is associated with a jump in viscosity, rather than, as in the classical Navier--Stokes case, a jump in density. Furthermore, the ratio of viscosity to the density-permeability product $\mu/\rho \kappa$, i.e., kinematic viscous resistance, is identified as a key coordinate stretching factor in the mathematical description of the flame structure. This ratio increases significantly across the flame. As a result: (1) the burnt gas acts as a strong viscous barrier, (2) for an increasing strain rate, flame migration towards the burnt gas is hindered, (3) for a decreasing strain rate, migration towards the unburnt gas is promoted, and (4) streamline refraction is augmented. By analysing the burning rate across varying strain rates and heat-loss parameters, we identify distinct extinction and ignition regimes that fundamentally differ from classical combustion theory, thereby providing new insights into flame stabilisation in friction-dominated environments and under confinement.

Boundary vorticity dynamics provides a rigorous theoretical foundation for understanding vorticity creation at boundaries, vorticity-boundary interactions, as well as the rational design of effective boundary flow control strategies. It cornerstone is the boundary vorticity flux (BVF), first introduced by Lighthill in 1963, which quantities the local rate of vorticity production at a boundary, and thereby serves as a mathematical measure of distributed vorticity source strength. By adopting a differential-geometric approach, we develop a general theory of the intrinsic decomposition of BVF for compressible Newtonian fluid interacting with an arbitrarily moving and deforming boundary surface. The analyses are further extended to the decomposition of boundary enstrophy dynamics, centered on the boundary enstrophy flux (BEF). Beyond the existing literature, the new theory explicitly identifies a complete set of boundary sources for the rigid-rotation and spin modes, as well as for various enstrophy constituents, arising from the interplay among external force, surface geometry and kinematics, and both longitudinal and transverse physical processes on a deformable boundary. It is noteworthy that introducing a conjugate curvature tensor pair consistently yields compact mathematical representations for all source terms, manifesting as bilinear (or quadratic-form-type) couplings between fundamental vortcity modes and the surface curvature tensors, irrespective of the complexity or generality of the boundary kinematics.

First introduced by Lighthill in 1963 for two-dimensional flows and later generalized by Jie-Zhi Wu to three-dimensional scenarios since 1986, the boundary vorticity flux (BVF) is the cornerstone of boundary vorticity dynamics, which quantifies the vorticity source strength on a solid boundary. Recent advances in vorticity and vortex dynamics have revealed both the rigid-rotation and spin modes of vorticity from multiple perspectives. In the present study, we propose a novel quadruple decomposition of the BVF on a stationary solid wall, which essentially uncovers the boundary creation rates of the elementary vorticity modes for both the tangential and wall-normal BVF components, respectively. The proposed framework is illustrated through skin-friction and surface-pressure measurements for flow over a hill model in a low-speed wind tunnel, revealing a set of intriguing BVF patterns for the first time. These theoretical results are expected to be valuable for global surface flow diagnostics when combined with experiments, as well as for understanding the formation mechanisms of near-wall coherent structures and flow-induced noise.

Bubble bursting is a major source of aerosol generation in a wide range of natural and industrial systems. While the resulting jet dynamics have been extensively studied in deep liquid pools, bubble bursting often occurs in shallow liquid layers where the influence of the nearby solid boundary remains poorly understood. Here, we show numerically that a shallow liquid layer produces smaller and more numerous jet drops, even when the initial bubble shape is unchanged. We identify a wall-induced viscous sticking effect that suppresses the upward motion of the cavity bottom, leading to a steeper cavity geometry during capillary-wave focusing. We further develop a semi-empirical scaling law that predicts the jet drop radius as a function of the Ohnesorge number and the initial bubble-wall distance. Our results establish geometric confinement as a governing factor in bubble bursting and provide a framework for predicting and controlling aerosol generation in shallow liquid environments.

We conduct 2D numerical simulations employing a widely used constitutive law for elasto-viscoplastic fluids to show that linear instability leads to spatio-temporal complexity in inertialess channel flow. Fluctuations in the final state are pronounced near and between the yield surfaces that border an unyielded plug spanning the centre of the channel. The instability and transition arise for Weissenberg numbers of order unity and higher.

Mean-flow-based linear analyses of turbulent flows, such as resolvent analysis, provide valuable insight about flow structures and their dynamics that has been widely leveraged to model, control and understand the underlying flow physics. However, these analyses are computationally expensive for flows over complex geometries and require the use of specialized codes that are typically only available in research environments. On the other hand, data-driven modal decompositions, such as the dynamic mode decomposition (DMD), identify turbulent flow structures that, although statistically relevant, do not provide insight into the physical mechanisms driving their dynamics. Here we introduce a novel data-driven method -- nonlinearity-subtracted DMD (NSDMD) -- that leverages knowledge of the structure of the Navier--Stokes equations to ensure that the learned operator is a low-rank approximation of the underlying mean-flow-linearized dynamics. Specifically, the method uses snapshots of the nonlinear terms in the perturbation equations to explicitly account for the contribution of the nonlinear forcing to the dynamics. We demonstrate the use of NSDMD to perform data-driven resolvent analysis on direct numerical simulation (DNS) and large-eddy simulation (LES) datasets, starting with a minimal channel flow and scaling up to the flow over a full aircraft model. As a result, NSDMD allows performing linear analyses of turbulent flows as a post-processing step on simulation data obtained with any available high-fidelity computational fluid dynamics (CFD) code.

Stars like our Sun expand as they exhaust their core hydrogen fuel, becoming red giants that eventually reach sizes up to 100 times their original radius. These giants have long presented a puzzle: they show systematic changes in their surface chemical composition that can only be explained by the transport of material from their nuclear-burning interior to their surface. The challenge is that this transport must somehow cross a stable layer that acts as a barrier between the star's outer convective envelope and its nuclear-burning interior. The convective motions in the envelope create internal waves that propagate through this barrier layer, but on their own these waves produce very little material transport. Here we show through high-resolution three-dimensional hydrodynamical simulations that stellar rotation dramatically amplifies how effectively these waves can mix material across this barrier. We find that the mixing rates can exceed those in non-rotating stars by over 100 times, increasing with faster rotation rates. This enhanced mixing provides a natural explanation for the observed chemical signatures in typical red giants. The amplification of wave-driven mixing by rotation may have implications beyond red giants to other types of stars.

We show convergence of solutions to a Navier--Stokes/Allen--Cahn system as the interfacial thickness $\varepsilon>0$ tends to zero for well-prepared initial data as long as the limit system possesses a sufficiently smooth solution. The limit system consists of a two-phase Navier--Stokes system separated by a sharp interface in the presence of surface tension coupled to a convective mean curvature flow equation. In comparison to previous results we obtain improved convergence estimates for higher-order norms. These enable us to prove convergence in the case of three space dimensions and non-constant viscosity, which was unknown before. The convergence results relies crucially on uniform higher-order estimates for the associated linearized Navier--Stokes/Allen--Cahn system in suitably weighted $L^2$-Sobolev spaces. Here a novel problem-adapted weight proportional to the sum of $\varepsilon$ and the distance to the sharp interface of the limit, which gives improved and sharp estimates, is an important new ingredient. This approach can be potentially adapted to other sharp interface limits as well.

We study the late-time relaxation of a neutral relativistic viscous fluid in $d+1$ dimensions. In the long-wavelength regime, linearized hydrodynamics predicts that the sound mode at momentum $nk$ decays as $e^{-n^2\omega_I t}$. However, nonlinear analysis gives a decay of $e^{-n\omega_I t}$. We derive a closed asymptotic attractor solution in which the frequency of the $n$-th harmonic locks to $n$ times the complex frequency of the fundamental mode. The amplitude envelopes for energy current $J$ obey a simple cascading relation, $J_n=\alpha_J^{\,n-1}J_1^n$, with $\alpha_J$ fixed by the equation of state, the longitudinal viscosity, and the fundamental wavenumber. For conformal fluids, $\alpha_J=1/(8\eta k)$, in agreement with the holographic result of arXiv:2512.07242 . The existence of the attractor shows that, even near equilibrium, field powers are not equivalent to amplitude order.

Extracting interpretable, localized physical mechanisms from complex spatiotemporal data is a foundational challenge across physics, biology, and engineering, but has remained out of reach on real measurements. The central obstacle is obtaining high-quality gradients of data via numerical differentiation, which amplifies noise, diverges for high-order equations, and falters on irregular geometries, limiting the scope of existing approaches to clean simulations of low-order systems. Here, we present weak dominant balance, a derivative-free framework that projects governing equations into a weak (integral) formulation, offloading differentiation onto smooth analytical test functions and leaving the data untouched. The method sustains accurate regime identification under severe noise where existing approaches categorically fail, delivers the first data-driven decomposition of a third-order partial differential equation applied to turbulent duct flow, and produces matching decompositions across direct numerical simulation and particle-image velocimetry measurements of a wavy channel flow, uncovering a previously uncharacterized dynamical regime. Weak dominant balance brings mechanism-level analysis out of simulation and onto measured data, and opens complex physical systems to direct, equation-grounded interpretation.

The rapid growth of energy-intensive technologies, including artificial intelligence, large-scale computing, and thermal management systems, has intensified global energy demand amid accelerating climate change. Meeting these demands requires innovative, low-carbon thermal management strategies that improve energy efficiency while minimizing environmental impact. This review revisits the underexplored phenomenon of bioconvection, a self-organized fluid motion generated by motile microorganisms, as a bio-inspired approach to sustainable heat transfer. Drawing on studies from natural ecosystems and laboratory experiments, we synthesize current knowledge of microorganism-induced hydrodynamics, pattern formation, and thermofluidic transport to assess the feasibility of harnessing bioconvection for thermal management. We further support this assessment through quantitative analyses of the thermal performance of bioconvective systems and discuss this in the framework of relevant non-dimensional numbers. By generating spontaneous convective plumes through density stratification, motile microorganisms enhance heat and mass transfer without external mechanical forcing. These self-organized flows provide a promising route toward hybrid bio-engineered cooling systems that reduce pumping energy, disrupt thermal boundary layers, and improve heat transfer efficiency. We conclude the review with the key challenges on the way to practical implementation, including microbial stability, material compatibility, controllability, scalability, as well as integration with existing cooling technologies. Finally, we identify critical research directions spanning heat transfer, microbiology, and nonlinear fluid mechanics within the broad context of sustainability, positioning bioconvection as a promising strategy for environmentally responsible thermal management in an era of rapidly increasing energy demand.

Inspired by nonequilibrium phenomena in game dynamics and behavioral evidence on the impact of extreme events on decision making, we investigate the nonlinear dynamics of a discrete-time multiagent learning rule in population congestion games under extreme events affecting one of the actions. The population state, following a risk-sensitive variant of the Multiplicative Weights Update (MWU), is coupled with a belief variable capturing the agents perceived risk and updated through an adaptive expectation rule. We perform a two-parameter bifurcation analysis with respect to the agents controlled parameters, identifying regions of qualitatively distinct behavior. Equilibria are studied first from both game-theoretic and dynamical perspectives. The resulting two-dimensional system exhibits complex behavior, including multi-stability among fixed points, invariant curves, periodic and chaotic attractors. Despite this complexity, the attractors can be grouped into distinct families, while the Cesàro averages of the trajectories are shown to converge to the stationary equilibrium. The incorporation of risk associated with the extreme event leads to new dynamical phenomena: attracting invariant curves arise and give rise to phase-locking Arnold tongues, within which the dynamics is qualitatively similar. In this setting, codimension-two resonances are identified as organizing centers, both within individual tongues and along the bifurcation curves associated with the fixed-point family. Chaotic attractors emerge and are destroyed through Feigenbaum cascades and forward or reverse boundary crises, with interior and merging crises also observed, along with transient chaos and narrow periodic windows. For each qualitatively distinct region, representative phase portraits and the associated basins of attraction are examined.

We report stable, ballistic cycler orbits in the circular restricted three-body problem: periodic trajectories that alternately undergo temporary capture about each primary. We construct continuous families of symmetric cyclers from intersections of the stable and unstable manifold tubes of the $L_1$ Lyapunov orbit and exhibit stable examples across more than two orders of magnitude in mass ratio, from the Sun--Jupiter regime to the equal-mass limit. Linear stability separates naturally into planar and out-of-plane components. The planar-stable branch of every computed family is created together with a hyperbolic branch in a saddle-center bifurcation of the return map at the family's maximal Jacobi constant, while out-of-plane instability occurs only through isolated parametric resonances. Every family examined contains a subfamily that is linearly stable to both planar and out-of-plane perturbations. We conjecture that saddle-center birth is universal among cycler families, implying that stable cyclers are a generic feature of the restricted three-body problem.

Training in artificial neural networks can be viewed as a trajectory evolving through a high-dimensional loss landscape. However, the large number of trainable parameters makes the direct analysis of these dynamics challenging. In this work, we treat such training trajectories as temporal networks and apply recently proposed strategies for the scalar embedding of temporal networks. We investigate whether such a scalar embedding provides a meaningful low-dimensional representation of neural network training dynamics. Using a multilayer perceptron trained on the MNIST classification task, we show that the embedding preserves the main dynamical features observed in the original parameter space, including the emergence of sensitivity to initial conditions for specific learning rate regimes and an accurate reconstruction of the network's maximum Lyapunov exponent. We then use the embedded scalar trajectory to define a characteristic time, analogous to a Lyapunov time, after which the exponential separation between initially close embedded trajectories saturates. This characteristic time captures the typical decorrelation time between initially close network trajectories in the original high-dimensional system. Finally, we investigate the statistical organization of asymptotic training states through a spacing observable defined in the embedded space. We find that the distributions of rescaled asymptotic spacings collapse onto a common form across initial conditions and are compatible with a skew lognormal distribution. Altogether, our results suggest that scalar low-dimensional embeddings provide a useful framework for studying and visualizing the dynamical properties of neural network optimization trajectories.

Extreme weather events are difficult to understand for the same reason that they are dangerous: they happen rarely, catching victims unprepared when they do occur and scientists unable to assess risks confidently, given such limited precedent to learn from in the real world and high computational expense to simulate more examples. Rare event sampling (RES) algorithms seek to reduce this expense by forcing simulations more directly towards the extremes and then compensating for that forcing in statistical analysis. But the performance of RES hinges on several hyperparameter choices which are ad hoc in practice, and must be better understood if RES is to be broadly useful. This paper addresses one particular parameter, the \emph{advance split time} (AST), which prescribes when to perturb a simulation to split off the most informative possible ensemble of alternative extreme event scenarios. We prescribe the optimal AST as the time it takes for an initial perturbation to amplify into the size (inverse rarity) of the extreme event being targeted. For the Logistic and Tent maps, two archetypal examples of one-dimensional chaos, we rigorously derive and express the rule as a simple log-ratio between perturbation size and event rarity. The pair of examples also illuminates where the rule breaks down, and subsequently, we generalize the rule into a maximum-entropy criterion that solidifies recent heuristic and empirical results. Despite the idealized setting, our results deliver theoretical clarity that can anchor future developments of principled RES methods applicable to real-world, high-impact weather and climate extremes.

The dynamical order of self-sustained oscillators is often characterized by phase synchronization, extensively studied within the framework of the Kuramoto model. It has recently been reported that strong coupling leads to further organization of coupled oscillators, termed waveform proportionality (WP), through amplitude dynamics that cannot be addressed using the Kuramoto model. A previous study [Phys. Rev. Lett. 134, 167202 (2025)] showed that, in coupled oscillator systems, synchronization induces Taylor's law (TL). Particularly, it demonstrated that strong coupling gives rise to WP, which leads to TL with an exponent 2. The findings suggested that WP requires the individual oscillators constituting the coupled system to possess sufficiently fast intrinsic frequencies. Here, we show that WP and TL with an exponent 2 can be induced by a pacemaker oscillator, regardless of the magnitude of the intrinsic frequencies of the individual oscillators in a population. Specifically, even in a population composed of oscillators with slow intrinsic frequencies, WP and TL with an exponent 2 can be induced by coupling the population to a fast pacemaker. Furthermore, we demonstrate that WP and TL can also be induced in a population of non-self-oscillatory units by coupling them to a pacemaker. These results indicate that WP and TL with an exponent 2 are more universal than previously thought, extending beyond oscillator populations with fast intrinsic dynamics.

We formulate a general system of kinetic equations for a non-stationary two-dimensional gas of elastically interacting line solitons and apply it to the description of a soliton gas governed by the Kadomtsev-Petviashvili II (KPII) equation. We then verify the predictions of the kinetic theory in two analytically tractable problems: the oblique interaction of a KPII line soliton with a one-dimensional soliton condensate of the Korteweg-de Vries equation, and the interaction of a trial KPII soliton with a monochromatic KPII soliton gas. In both cases, we compare the analytical results with direct numerical simulations obtained by constructing two-dimensional soliton gases via exact KPII $N$-soliton solutions for large $N$, using appropriately chosen random distributions of soliton parameters. The comparison demonstrates excellent agreement, thereby providing strong validation of the proposed kinetic theory of 2D non-equilibrium soliton gases.

In the present work we analyze traveling and dispersive shock waves of a two-dimensional Fermi-Pasta-Ulam-Tsingou lattice. In the first part of the paper, using variational techniques we prove the existence of both periodic and solitary traveling waves for convex potentials. In the case of unimodal profiles we are able to remove the assumption of convexity. The variational formulation also provides a natural algorithm for the numerical computation of traveling waves, which we use to explore both solitary and periodic traveling waves. The numerical computations are compared with analytical approximations based on the derivation of the KdV equation for quasi-one-dimensional propagation. In the second part of the paper, we focus on dispersive shock waves (DSWs), which are expanding modulated waves that connect states of different amplitude. In particular, we focus on line DSWs, which are constant along one direction and propagate in the direction orthogonal to which it is constant. Such solutions form when subject to quasi-one-dimensional jump initial data. We find that while the shape of the DSW depends on the direction of travel, properties such as the speed and amplitude do not. The systematic numerical study of the line~DSWs is then compared to those predicted by the KdV equation along the line of propagation. Key characteristics of the DSWs, such as the speeds of the trailing and leading edges, are investigated for various jump heights, yielding good agreement between simulation and KdV approximation in the limit of vanishing jump height. Finally, we apply the DSW fitting method to study the trailing and leading edge characteristics of the DSW, finding even better agreement to the numerics when compared to the KdV prediction. The KdV prediction and DSW fitting predictions agree in the limit of small jump height.

Nonlinear photonic time crystals (PTCs) can support solitons inside momentum k gaps, where the amplification of k gap modes is saturated by Kerr nonlinearity, forming spatially homogeneous but temporally localized excitations. Yet their quantum nature remains unclear. Here we quantize nonlinear k gap dynamics of PTCs and show that k gap solitons are represented by biphoton Fock ladder states. K gap amplification drives two-mode squeezing of the biphoton, while Kerr nonlinearity generates an anharmonic potential along the biphoton Fock ladder that balances this squeezing process, creating a finite biphoton number turning point and giving rise to quantum collapse and revival dynamics and nonclassical phase space interference. We further analyze how photon loss and dephasing reshape the biphoton statistics of quantized k gap solitons. Our results establish a biphoton Fock space description of k gap soliton quantization and provide a framework for studying quantum nonlinear excitations and entangled light generation in photonic time crystals.

Self-injection locking (SIL) of a diode laser to a high quality-factor microresonator has recently become increasingly important in hybrid integrated photonics, providing access to compact sub-Hz linewidth lasers. It was also shown to facilitate the access to dissipative Kerr solitons - the key to a low-noise coherent frequency comb on a photonic chip. However, the existence and stability ranges of SIL soliton states in experimentally controlled parameters are still not fully understood. Here we study the bifurcation structure of solutions in a model of soliton SIL in the weak-backscattering limit. We show that SIL produces soliton-number-dependent existence ranges of multi-soliton solutions in free-laser detuning and feedback phase parameters. We identify exclusive single-soliton existence regions and demonstrate dynamical access to single solitons in this region by direct numerical simulations using prescribed parameter sweeps.

Symmetries plays a significant role in understanding the conservation laws in Quantum field theories. Here, we attempted a quadratic type dimensionless gauge transformation to achieve the invariance in QFTs. We have shown the extensive study of invariance of complex scalar, Abelian and Non- Abelian theories and established the conservation laws. We included an explicit graphical analysis to invoke the invariance. This is studied in a physical context, where different field configurations correspond to the same physical state. The necessity of the covariant derivative is studied in detail, highlighting how it ensures consistent transformation under local symmetry operations. The meaning of covariance is clarified as the preservation of the form of physical laws under transformations.

We present an exact variational scheme for the physics of inhomogeneous classical fluids in thermal equilibrium. A joint metadensity minimization principle is proven for the one-body density and the global interparticle distance distribution. The theory bypasses the inhomogeneous two-body density and thus remains computationally simple. A universal excess entropy functional accounts for all many-body correlations in arbitrary pairwise interacting systems. The framework is relevant for neural functional machine learning, for soft matter design, and for predicting structural correlation functions via entropic test-particle and meta-Ornstein-Zernike routes.

Bubble coalescence phenomenon in electrolytic media finds applications in technologies from mineral flotation to electrochemical energy conversion. However, the underlying governing physics still remains unresolved, with longstanding disagreement over the extent to which Marangoni stresses affect the coalescence time by modulating the interfacial mobility. Here, we show that the thin film morphology governs drainage more strongly than the interfacial boundary conditions. We demonstrate experimentally that thin film drainage during bubble coalescence proceeds through three distinct regimes. An initial visco-capillary stage that exhibits a power-law thinning, followed by an exponential decrease in film thickness with time induced by rim stabilisation. The final regime is governed by disjoining pressure and is marked by an exponential relaxation of the film to the equilibrium thickness. We show that, irrespective of the electrolyte type and concentration, film evolution exhibits universal behavior by collapsing onto a single curve when rescaled with the characteristic film thickness and time scale, demonstrating that electrolyte effects act only to renormalize timescales rather than alter the underlying dynamics.

Fluid transport in deformable porous media is central to many biophysical and geophysical processes. While extensive studies exist, how porosity governs fluid behaviour in deformable systems during cyclic injection remains elusive. Here, we investigate gas-liquid multiphase flow in a quasi-2D Hele-Shaw cell packed with soft hydrogel particles at different initial porosities. Alternative gas and water injection experiments, combined with high-resolution imaging and continuous pressure monitoring, are used to quantify gas dynamics and pressure evolution. Results show that the gas entry pressure increases as porosity decreases, consistent with a Young-Laplace estimation based on effective pore-throat width. After entry, invasion shifts from cavity-dominated expansion in high porosity packings to localised pore invasion in low porosity packings, with a mixed cavity-fingering regime at intermediate porosity. Pressure fluctuations are linked to pore-scale gas escape and internal gas redistribution. Low porosity packings produce frequent small-amplitude pressure drops, whereas higher porosity packings produce more discrete pressure relaxations. Across cycles, the decreasing mean pressure suggests preferential-pathway reuse and reduced local capillary constraints. Residual gas saturation increases systematically with injection cycles and reaches higher terminal values as porosity decreases. Specific interfacial length increases as available pore space decreases and follows a power-law relationship with gas cluster size, with scaling exponent decreases as porosity decreases and cycling progresses. Together, these results demonstrate that gas trapping in deformable porous media depends on both initial packing structure and cyclically evolving gas-solid interactions. This study provides insights for interpreting porosity-dependent trapping and reinvasion during repeated gas injection.

We investigate Anderson localization in three-dimensional disordered systems by comparing scalar classical waves with mass and force-constant disorder to electronic tight-binding models with diagonal and off-diagonal disorder. We show that the commonly employed mapping between classical-wave localization and the electronic Anderson model with diagonal disorder is not mathematically justified. Instead, the correct modulus-type formulation reveals that classical-wave systems constitute a distinct constrained disorder class, in which the acoustic sum rule correlates diagonal and off-diagonal matrix elements and prevents any direct correspondence with the standard electronic disorder models. Within a unified eigenvalue framework, we determine localization phase diagrams for all four disorder classes using complementary spectral, eigenvector, and level-statistics diagnostics. We find that classical-wave systems share a key qualitative feature with electronic off-diagonal disorder: localized states occur only near a band edge, while extended states persist in the central part of the spectrum even at strong disorder. At the same time, the acoustic sum rule produces localization topologies that differ fundamentally from both diagonal- and off-diagonal-disorder electronic systems. In particular, for mass disorder we obtain a phase diagram that differs qualitatively from previous results based on the conventional potential-type approach and reveals an extended localized regime near the upper band edge. Our results establish a unified perspective on localization in quantum and classical wave systems and provide new insight into the conditions under which Anderson localization may occur in three-dimensional photonic and acoustic media.

Microbes in marine environments are often confined to thin near-surface layers while being advected by turbulent flows. Because such constrained advection generates an effectively compressible flow, reproduction and transport interact in a nontrivial way. Here, we focus on populations whose growth is governed by an Allee effect and show that sinks and sources, generated by the compressible flow, have dramatic consequences for the survival of such species. We derive analytical expressions for the carrying capacity as a function of the Allee strength in the limit of small and large Damköhler number, which measures the product of the large eddy turnover time and the organism growth rate. Numerical simulations reveal how these two limits connect. In the limit of small Damköhler number, we find a maximal Allee strength, set by the statistics of the compressible flow, that leads to species extinction in fully developed turbulence.

A multiscale sub-grid cavitation model is developed in which the bubble size distribution evolves as a linear stochastic process in radius space. Starting from the integrated Rayleigh--Plesset equation, the population balance is recast as a hyperbolic transport equation for the number density per radius, whose method-of-characteristics solution, projected onto a discrete histogram basis, yields a column-stochastic Markov chain governing the bubble counts per size bin. The transition matrix factors into a precomputable, mesh-only geometric part and a local, pressure-dependent shift, isolating the coupling to the surrounding flow into a single dimensionless vector per cell. The framework recovers classical homogeneous-mixture cavitation closures in the limit of a single representative scale.

Thermochemical non-equilibrium can alter the structure, loads, and time scales of hypersonic shock-wave/turbulent boundary-layer interactions, yet its role in fully turbulent configurations remains largely unquantified. The present work addresses this issue by performing three direct numerical simulations of an oblique shock impinging on a turbulent high-enthalpy boundary layer at edge Mach number $M_e=6.4$ and stagnation enthalpy $H_e=16.9$ MJ/kg. The simulations share identical geometry and freestream conditions, but employ a hierarchy of progressively simplified thermochemical descriptions: a finite-rate reactive case, a single-species thermally perfect gas model, and a single-species calorically perfect model. The reactive simulation shows that the shock-induced temperature rise substantially enhances chemical activity relative to the incoming boundary layer, with peak concentrations of dissociation products attained downstream of the interaction. Thus, the thermal and chemical responses are not synchronised: the composition lags the rapid thermal forcing imposed by the shock system, and turbulent Damköhler numbers reach values of order unity within the recirculation region, indicating non-negligible turbulence-chemistry interaction. The comparison among the three models shows that thermally and calorically perfect descriptions yield similar predictions, whereas finite-rate chemistry produces systematic differences: a smaller separation bubble, lower post-interaction wall heat flux, lower mean and fluctuating temperatures, and a less inclined reflected shock. In the present regime, the dominant modelling distinction is therefore between frozen and chemically reacting descriptions, with caloric-model effects playing only a secondary role.

In this study, a theoretical and graphical analysis is conducted to examine the effects of wall-velocity slip, anisotropic ratio, and porosity parameter on a two-dimensional, viscous, laminar, and incompressible flow through a wavy channel filled with anisotropic porous media. The flow is assumed to be steady and symmetric, with a constant volumetric flow rate imposed along the channel walls. The governing equations are described using the Darcy-Brinman model coupled with the continuity equation, while the tangential velocity at the wavy boundaries is represented through Navier slip conditions. An analytical solution is obtained using a perturbation approach under physically consistent boundary conditions. The effects of key parameters, including anisotropic ratio, Darcy number, and slip parameter, on flow characteristics such as axial velocity, pressure gradient, shear stress, and streamline patterns are examined in detail and presented graphically. The results indicate that wall velocity slip significantly reduces flow reversal, enhances near-wall velocity, and decreases the center-line velocity. For a fixed non-zero slip, a decrease in the Darcy number leads to a pronounced modification in the velocity profile, while increased slip further strengthens near-wall flow and weakens the core flow. Additionally, the streamline analysis reveals that velocity slip plays an important role in controlling flow separation near the crest of the wavy wall. In the case of isotropic porous media with a large amplitude wavy channel, flow separation can also be effectively regulated. Overall, the study demonstrates that velocity slip provides a powerful mechanism for controlling flow behavior by altering the shear distribution within the perturbed flow, with potential applications in technological, geophysical, and biophysical transport systems.

The stability of incompressible flow past a circular cylinder under collinear steady and oscillatory forcing is investigated within a two-dimensional Floquet framework. The flow is parameterised by the Keulegan-Carpenter number $KC \in [4,12]$, the steady-to-oscillatory velocity ratio $m \in [0,1]$, and the oscillatory Reynolds number $Re_m \in [20,100]$. The loci of the leading Floquet multipliers, and hence case-specific bifurcation modes, are examined by progressively reducing $Re_m$ to subcritical values for prescribed $m$. A steady current with $m > 0.5$ gives rise to a period-doubling subharmonic bifurcation that does not occur in purely oscillatory flow, where only synchronous and quasi-periodic modes arise. For $Re_m = 100$, three key features are discernible. First, the neutral stability curve in $(KC,m)$ space is strongly non-monotonic in $m$, separating intrinsically stable regions from those with single unstable modes; a sub-region of striking mode re-stabilisation appears beyond $m \approx 0.9$, where the flow recovers a $Z_2$-symmetric state at peak Reynolds number $\approx 190$, despite the steady and oscillatory components each being individually unstable. Second, a distinct regime supports the coexistence of two unstable modes of different types. Third, complementary direct numerical simulations show that, for a single unstable mode, the linear analysis successfully predicts the saturated nonlinear state even when $Re_m = 100$ substantially exceeds the critical Reynolds number, whereas under mode coexistence the quasi-periodic attractor tends to dominate the developed dynamics.

Based on the original Miller-Robert-Sommeria theory, we explicitly compute a statistical equilibrium of two-dimensional turbulent flow on a sphere for a generic initial vorticity field introduced in a previous study. The macroscopic vorticity field corresponding to the obtained statistical equilibrium has a quadrupole structure. The resulting quadrupole structure is topologically consistent with the final state of the long-term time integration of the vorticity equation. However, the statistical equilibrium does not predict the formation of concentrated vortices as seen in the time integration. We also calculate statistical equilibria for the initial vorticity field with a planetary vorticity term, and find a change of statistical equilibria from quadrupole states to zonally symmetric states as the angular velocity of the sphere increases. The quadrupole statistical equilibria show nearly linear relations between the macroscopic vorticity and the macroscopic stream function, implying that higher-order Casimir invariants are virtually ineffective even when all Casimir invariants are considered. The discrepancy between the equilibria and the time integration results emphasizes the importance of mixing barriers, which prevent the relaxation of the evolving vorticity field to the statistical equilibria and allow the point-vortex-like dynamics of coherent vortices to persist.

In this paper, we experimentally demonstrate the microscale direction control of thermoosmotic flows using a focused-laser heating. The key is the off-center laser irradiation on an immobilized light-absorbing microparticle, which generates a nonuniform, asymmetric heat source. The resulting thermo-osmotic flows are evaluated using the optically trapped particle tracking velocimetry (ot-PTV), presented in our preceding paper (T. Tsuji, et al., Physical Review Fluids 11, 034901 (2026)). It is shown that the flow characteristics can be modulated by the ionic strength of a sample solution and/or the surface molecular coating of the substrate. In particular, the significance of ionic strength on thermo-osmotic flows are discussed based on the surface potential of the substrate measured by frequency-modulated atomic force microscopy.

We design and implement a Microscale Topological Surgery (MTS) algorithm to detect and enforce topological transitions in two-dimensional tracked interfaces. The method combines classical Lagrangian tracking with an intermittent topological processor that: (i) constructs Eulerian snapshots from which an interface family with microscale-resolved topology is extracted, (ii) infers adjacency topology between dual Lagrangian and Eulerian interface families, and (iii) performs interface surgery to stitch the two families together across microscale defect regions. A novel long-time nonlinear alternating-shear flow is introduced, in which repeated stretching and folding generate rich multiscale interface dynamics with filamentation at microscales. Using the MTS algorithm and a posteriori geometric and material diagnostics, we compute and visualize microscale filament-breakup dynamics. Error analysis and scaling studies demonstrate second-order geometric convergence and optimal computational scaling of the MTS algorithm, with topology-processing costs comparable to those of the underlying Lagrangian evolution. Ensemble simulations generated by pseudo-random perturbations of the flow further reveal coherent droplet size distributions and statistically robust filament-breakup dynamics.

The Garrett-Munk (GM) spectrum has long provided a canonical model of the oceanic internal gravity wave field. However, it relies on hydrostatic assumptions and idealized stratification that limit its applicability where non-hydrostatic dynamics, vertical boundary effects, or non-monotonic stratification are important. Here we develop a generalized framework for the internal wave spectrum based on non-hydrostatic vertical modes formulated in horizontal wavenumber-vertical mode space. Energetic orthogonality among wave modes requires that such a formulation be cast in horizontal wavenumber space rather than frequency space. In this formulation, the deformation radius associated with each vertical mode provides a proxy for distinguishing hydrostatic and non-hydrostatic regimes. Vertical modes are obtained numerically from the fixed-K Sturm-Liouville problem, allowing arbitrary stratification and multiple turning depths. Combined with a generalized spectral function, the formulation yields expected distributions of horizontal kinetic, vertical kinetic, and potential energy as functions of depth, frequency, and horizontal wavenumber. Example applications illustrate departures from GM theory associated with boundary effects and non-hydrostatic dynamics, including improved representation of vertical variance and high-frequency vertical kinetic energy, while reproducing observed features of horizontal wavenumber spectra.

We introduce a two-dimensional non-hydrostatic model for shallow water wave dispersion. The model is based on a locally adapted application of a non-hydrostatic correction to the hydrostatic shallow water equations (SWE) in a predictor-corrector scheme. Applying the non-hydrostatic correction uniformly to the entire domain demands a high computational cost, since an elliptic system of equations needs to be solved for the correction terms. We demonstrate that by determining the area where the non-hydrostatic effects are significant, and applying the correction only locally, the computational effort can be reduced by approximately 40\% without sacrificing accuracy in tsunami-like scenarios. As indicators for the non-hydrostatic effect, we use the ratio between total water depth and surface elevation, as well as horizontal velocity norms. Results are shown for several well-known test cases, including wave trains over a semi-circular shoal, static, and moving bottom tsunami-like wave propagation.

The intermittency of the rate of turbulent energy dissipation ${\epsilon}$ is investigated experimentally, with special emphasis on its scale-similar facets. This is done using a general formulation in terms of multifractals, and by interpreting measurements in that light. The concept of multiplicative processes in turbulence is (heuristically) shown to lead to multifractal distributions, whose formalism is described in some detail. To prepare proper ground for the interpretation of experimental results, a variety of cascade models is reviewed and their physical contents are analysed qualitatively. Point-probe measurements of ${\epsilon}$ are made in several laboratory flows and in the atmospheric surface layer, using Taylor's frozen-flow hypothesis. The multifractal spectrum $f({\alpha})$ of ${\epsilon}$ is measured using different averaging techniques, and the results are shown to be in essential agreement among themselves and with our earlier ones. Also, long data sets obtained in two laboratory flows are used to obtain the latent part of the $f({\alpha})$ curve, confirming Mandelbrot's idea that it can in principle be obtained from linear cuts through a three-dimensional distribution. The tails of distributions of box-averaged dissipation are found to be of the square-root exponential type, and the implications of this finding for the $f({\alpha})$ distribution are discussed. A comparison of the results to a variety of cascade models shows that binomial models give the simplest possible mechanism that reproduces most of the observations. Generalizations to multinomial models are discussed.

We study the classical tree-level scattering amplitudes of deep-water surface gravity waves using the methods of high-energy physics. For scattering in one horizontal dimension and in the two-negative-wavenumber sector we obtain a closed formula for $n$-wave scattering. Up to a kinematic prefactor, the amplitude is the volume of a classic polytope -- a box sliced by a hyperplane, which we dub the hydrotope, whose purpose in life is simply to organize the sign patterns of the "chambers" characterizing all the different regions of the two-minus kinematic space. The general formula was discovered by Claude Opus 4.6 working under our guidance, beginning with our earlier discovery of a one-term expression valid in the "simplest" kinematic chamber. Our results resolve the puzzle raised by Y.V. Lvov's 1997 computation of the five-wave amplitudes, unifying and extending it to all multiplicities.

Accurate parameterizations of ocean wave spectra are necessary in a wide array of disciplines including coastal, ocean, and naval engineering as well as in the study of wave interactions and ocean-atmosphere momentum flux. Many such applications use spectrum parameterizations based on temporal data collected well over a half century ago. The development of spatial wave measurement techniques that can accurately capture a larger range of scales allows us to revisit the question of how best to represent an ocean wave spectrum in a variety of ocean wave conditions. We discuss two commonly used wave spectrum parameterizations through a comparison to data collected in field campaigns studying fetch-limited, fully-developed, and mixed sea conditions. We discuss a spectrum parameterization for fully-developed seas that has a $k^{-2.5}$ (or $\omega^{-4}$) dependence on the wavenumber (or angular frequency) in the tail as opposed to the $k^{-3}$ (or $\omega^{-5}$) dependence seen in other frequently-used parameterizations. With knowledge of the peak wavenumber $k_p$ and significant wave height $H_s$, alongside the wind speed, fully-developed conditions can be well-represented. We then compare the impact of using different wave spectrum parameterizations through a Large Eddy Simulation (LES) study of Marine Atmospheric Boundary Layers (MABLs) over the sea surface and find that changing the parameterization used results in variations in the equivalent roughness akin to significant changes in wave conditions.

We introduce a finite-element framework for simulating thermal fluctuations in compressible fluids governed by the fluctuating Navier-Stokes equations. The method is designed to preserve the fundamental fluctuation-dissipation balance at the discrete level. This is achieved by defining the stochastic forcing term in the weak formulation, ensuring its covariance is proportional to the discrete viscous dissipation operator. A nodal quadrature rule is employed to eliminate unphysical mesh-scale correlations. The time integration is performed using the Crank-Nicolson scheme to maintain numerical stability and accuracy. The proposed approach is numerically validated in one, two, and three spatial dimensions, demonstrating its capability to correctly capture equilibrium fluctuation statistics across various discretisation parameters.

The flow behavior and hydrodynamic characteristics of fluids in rotational viscometry systems are investigated using the Brookfield DV3TLV viscometer, with emphasis on measurement reliability and applicability limits of different measuring geometries. The results are compared and validated using the high-precision MCR 302 rheometer manufactured by the Austrian company Anton Paar. Both Newtonian (water and glycerol) and non-Newtonian fluids (guar-based gels), exhibiting fundamentally different viscosity-shear rate behavior, were included in the study. Based on the comparison of measurements obtained with the Brookfield DV3TLV viscometer and the MCR 302 rheometer, empirical coefficients were determined that relate the spindle rotational speed to the shear rate, taking into account the geometry of the measuring systems. Analysis of the Reynolds number range showed that laminar flow conditions were maintained for all measurement systems, which justifies the application of quasi-static models that neglect possible flow turbulence within them. Comparison with high-precision measurements performed on the MCR 302 rheometer showed that, with appropriate interpretation, the data obtained using the Brookfield instrument can be used to estimate the real viscosity of process fluids with an accuracy specific to each geometry and its operating conditions. The proposed methodology enables reliable characterization of flow properties in rotational systems and can be applied in engineering practice and laboratory analysis of complex fluids, especially at oil and food production facilities where high-end rheometers are unavailable or impractical to use. The study is formulated within the framework of experimental fluid mechanics and non-Newtonian flow characterization.

This paper investigates the stability and large post-critical dynamics of an inextensible spinning fluid-conveying pipe with pinned-roller supports. Replacing the pinned-pinned support of the extensible counterpart with a sliding support removes the axial-stretching restoring mechanism and fundamentally changes the governing equations of motion. Derived here for this configuration, these equations contain a different set of nonlinear terms -- arising from the inextensibility constraint and the bending curvatures rather than the single axial-stretching term -- that drives a post-critical regime with large deflections. The regime is analysed with two complementary methods. The first is a Galerkin discretisation in which the bending curvatures are Taylor-expanded to ninth order, shown to be the lowest order resolving the post-critical amplitude; the standard cubic truncation overestimates the deflection significantly by missing the geometric stiffening from inextensibility. The second is a modified Hencky bar-chain model with a global angular description: a closed, $n$-independent matrix framework with exact trigonometric kinematics, directly implementable in any standard programming environment with matrix routines and adaptable to both extensible and inextensible configurations through a single boundary-condition reduction. The linearised dynamics give an ellipse-like stability boundary in the flow-velocity--rotational-speed plane with semi-axes $U=\pi$ and $\Omega=\pi^{2}$; three damping regimes are identified, including a high-rotation instability driven by rotating damping. Close agreement between the two methods across linear-stability, bifurcation, and time-history comparisons confirms the ninth-order Galerkin truncation and establishes the modified Hencky bar-chain as a reliable general-purpose discrete framework for spinning fluid-conveying pipes.

Strongly dipolar gases, such as dysprosium, erbium and thulium, exhibit dense Feshbach spectra whose level statistics have been associated with quantum chaos arising from couplings among many molecular channels. Here, we combine a precise calibration of the Feshbach spectrum of $^{162}$Dy with spectroscopic measurements of the differential magnetic moments of bound states associated with more than 80 resonances between 0 and 30 G. These magnetic moments provide an eigenstate-sensitive probe of the molecular states underlying the resonance spectrum. We find that the level statistics are not uniform: resonances associated with states near the center of the magnetic-moment distribution display enhanced level repulsion, whereas those near the lower edge remain close to Poisson statistics. Our results reveal hidden structure within the chaotic dysprosium Feshbach spectrum and identify molecular-state composition as a key ingredient in the emergence of quantum chaos in strongly dipolar scattering.

In this work we develop an integrable perturbation theory for the defocusing modified Korteweg-de Vries kink solution based on the squared eigenfunction expansion associated with the underlying Zakharov-Shabat scattering problem. We derive the completeness relation for the squared eigenfunctions appropriate to the kink background, establish the adjoint structure needed to handle perturbations of both the continuous and discrete spectral components, and obtain explicit evolution equations for the perturbed kink parameters at leading order. The study of the first order correction shows that perturbations generically produce a radiative shelf in front of the kink. We also apply our results to certain physically relevant perturbations and show that the predictions are consistent with direct numerical simulations.

Conventional rheodielectric studies of dipolar suspensions primarily examine flow-induced variations in the principal permittivity components. In contrast, an asymptotic solution of the perturbed Fokker--Planck equation for orientable Brownian dipoles under weak flow predicts the emergence of off-diagonal permittivity components that are linear in the relative flow strength. For planar shear flow, these terms exceed the corresponding higher-order diagonal corrections, leading to a rotation of the principal dielectric axes. This previously unrecognized rheodielectric response suggests new possibilities for flow-controlled dielectric and electro-optical functionalities.

Phase separation organizes matter across scales, yet how it operates under sustained energy input remains poorly understood. Experimental approaches to driven phase separation have largely relied on chemically fueled systems, in which reaction fluxes are intrinsically coupled to fuel consumption and reaction-network complexity. Here we show that continuous molecular switching alone is sufficient to generate active phase behavior in a minimal two-phase system. Using light-responsive DNA-azobenzene coacervates confined in microfluidic droplets, we modulate intermolecular interactions with spatiotemporal precision and quantitatively track phase separation dynamics under illumination. Light-driven azobenzene isomerization controls both thermodynamics and kinetics, setting phase boundaries and regulating dissolution and nucleation rates. Under single-wavelength illumination that couples forward and backward isomerization into a dynamic photostationary state, coarsening is arrested and micron-sized coacervates are stabilized. When the two photoisomerization pathways are driven independently, spatially unbalanced reaction fluxes generate sustained interfacial instabilities, including surface undulations, budding, and division. These behaviors arise from a physical coupling between reaction kinetics and phase separation, without chemical fuels or biochemical regulation. Our results show that non-equilibrium phase behavior is governed by how opposing reaction fluxes are imposed, establishing reversible molecular switching as a minimal route to active materials from equilibrium building blocks.

Organic semiconductors are lightweight, solution-processable materials with strong potential for printed and flexible electronics, from deformable displays to wearable sensors. Despite significant advances in materials synthesis and manufacturing, controlling molecular and mesoscale alignment during deposition remains a central challenge, as film morphology critically governs charge transport and device performance. Here, we demonstrate that flows developing within the intrinsically confined volume of microliter vapor-guided droplets can be harnessed to produce highly aligned organic semiconductor films. As droplets move in response to an external vapor source, internal flows align organic semiconducting nanowires within the droplet prior to deposition, yielding films with pronounced directional order. Organic field-effect transistors fabricated with this approach exhibit approximately 40% enhancement in saturation current relative to spin-coated controls. Beyond improved device performance, the contactless and compact nature of our method enables the deposition and alignment of organic semiconductors on curved and flexible surfaces. More broadly, vapor-guided droplets offer a scalable framework for the confinement-induced alignment of functional soft materials, with potential for integration into existing additive manufacturing platforms for flexible electronics and beyond.

Understanding the dynamic behavior of complex biomolecules requires simplified models that not only make computations feasible but also reveal fundamental mechanisms. Coarse-graining (CG) achieves this by grouping atoms into beads, whose stochastic dynamics can be derived using the Mori-Zwanzig formalism, capturing both reversible and irreversible interactions. In liquid, the dissipative bead-bead interactions have so far been restricted to hydrodynamic couplings. However, friction does not only arises from the solvent but notably, from the internal degrees of freedom missing in the CG beads. This leads to an additional ''internal friction'' whose relevance is studied in this contribution. By comparing with all-atom molecular dynamics (MD), we neatly show that in order to accurately reproduce the dynamics of a globular protein in water using a coarse-grained (CG) model, not only a precise determination of elastic couplings and the Stokesian self-friction of each bead is required. Critically, the inclusion of internal friction between beads is also necessary for a faithful representation of protein dynamics. We propose to optimize the parameters of the CG model through a self-averaging method that integrates the CG dynamics with an evolution equation for the CG parameters. This approach ensures that selected quantities, such as the radial distribution function and the time correlation of bead velocities, match the corresponding MD values.

Cell shapes in confluent tissues range from nearly isotropic epithelial morphologies to highly elongated endothelial ones. In standard vertex models, tissue rigidity is controlled by a target shape index; increasing this index drives cell elongation and ultimate tissue fluidization. Here, we consider the case where cell elongation emerges autonomously by assigning an intrinsic, passive elastic preference for anisotropic shape. This distinction reverses the usual expectation: cell elongation does not fluidize the tissue, but drives a solid-to-solid transition from an ordered isotropic solid to a disordered anisotropic solid, with finite yield stress and shear rigidity on either side of the transition. These results decouple cell shape from tissue rheology and caution against inferring fluid-like mechanics from elongated cell morphologies alone.

The gelation transition, a process that transforms a flowable liquid into an elastic solid, is a present in variety of systems, from colloidal to polymeric. During the gelation transition, a system passes through a critical gel state characterized by scale-free power-law viscoelasticity. Interestingly, the fractional calculus provides a natural mathematical language for such power-law viscoelasticity. In this work, we develop physically constrained fractional viscoelastic models as well as those based on the three-parameter Mittag-Leffler-Prabhakar function for both, the pre-gel state and the post-gel regimes, ensuring consistency with the conventional scaling relations in each regime. While the fractional pre-gel model is observed to be valid only for a restricted subset of parameter values, the Prabhakar function-based model rigorously removes this limitation. We enforce continuity of the dynamic moduli and their derivatives across the critical gel point, which universally imposes a symmetry in the relaxation dynamics on either side of the critical gel state. Such enforcement further validates the hyper-scaling relation connecting the critical exponents, making it a theoretical necessity rather than an empirical coincidence. We validate the proposed models against time- and frequency-domain experimental data. A model-agnostic, frequency-independent rheological fingerprint of the critical gel state, uniquely determined by two critical exponents, is also identified.

We develop a thermodynamically consistent phase-field model for soluble surfactants in two-phase flows, incorporating both interfacial and solid surface adsorption. The model is derived via variational principles consistent with the second law of thermodynamics, resulting in modified free energies and boundary conditions that capture surfactant transport, adsorption, and wetting dynamics. A key contribution of this work is the inclusion of surfactant adsorption on solid walls, which leads to qualitative agreement with experimental observations: unlike prior numerical studies that predicted hydrophilic surfaces becoming more hydrophilic and hydrophobic surfaces more hydrophobic, our model shows a shift toward increased hydrophilicity across all contact angles-consistent with experimental trends. Our results establish that solid adsorption provides the missing mechanism required for predictive modelling of surfactant-laden contact line dynamics.

We present a comprehensive characterisation of dynamic heterogeneity in sodium silicate melts using molecular dynamics simulation with machine-learning potentials. By studying sodium disilicate, tetrasilicate, and hexasilicate melts across a range of temperatures, mean squared displacement and a time-correlation function computed up to the nanosecond timescale provide a detailed account of how spatial mobility disparities emerge in a realistic multicomponent oxide glass. Within these timescales, the self-part of the van Hove function for sodium displays a bimodality, demonstrating that alkali transport is mediated by discrete displacement events consistent with a hopping mechanism. This distinct hopping allows sodium ions to decouple from the sluggish relaxation of the silicate matrix. Furthermore, evaluation of the non-Gaussian parameter reveals that, although all constituent species exhibit dynamic heterogeneity, the non-Gaussian behaviour is most pronounced for oxygen atoms. This trend reflects the intermittency of structural rearrangements, where framework atoms undergo rare and stochastic events compared to the frequent displacements of mobile ions. Our findings elucidate the microscopic mechanism of ion transport and its connection to dynamic heterogeneity in silicate melts, offering a new avenue to study fundamental glassy physics in realistic vitreous materials.

Fluid-solid composite vesicles, comprising 2D solid domains integrated into a topologically-closed fluid bilayer membrane, exhibit complex morphologies arising from the geometric frustration between spherical closure of the membrane and 2D solid elasticity. This scenario is distinct from the better studied case of multi-fluid domain vesicles. Here, we study the elastic energies and shape equilibria of a closed vesicle membrane containing a single, flexible circular solid domain using discrete finite-element (Surface Evolver) simulations, determining the key physical and mechanical parameters to govern shape selection. While we find that the 2D solid (shear) elasticity has minimal impact on the highly-under inflated morphologies, the geometrically non-linear resistance of the solid to Gaussian curvature substantially impacts the shape and elastic patterns form for inflated vesicles, by an amount that it grows with ratio of vesicle size to the elastic thickness of solid. For sufficiently large (thin) vesicles we characterize a generic sequence of ground state patterns of solid shape with increasing inflation: from cylindrical rolls and isometric folds to spatially complex patterns of crumples and wrinkles and ultimately to smooth caps. This sequence of non-isometric patterns at high-inflation is shown to be governed by the same far-from-threshold mechanics used to describe similar shape transitions in microscopic sheets on curved liquid interfaces, establishing that inflated shapes are governed by two basic mechanical scales of membrane tension. We find our predictions for highly-anisotropic shape equilibria of fluid-solid composite vesicles closely match experimentally observed shapes of giant unilamellar vesicles of phase-separated DPPC and DOPC.

Odd diffusion is a hallmark of chiral active matter, generating currents transverse to density gradients. Existing theories rely on a linear antisymmetric transport coefficient that exists only in two dimensions, raising the question of whether odd diffusion can occur in isotropic three-dimensional systems. Here we show that such transport is possible through a nonlinear constitutive law. Symmetry considerations reveal that the three-dimensional Levi-Civita tensor permits a leading order isotropic odd current at second order in the density gradient expansion and only in multicomponent systems. The resulting transport generates boundary-driven rotational currents, finite vorticity, and enstrophy despite the absence of external torques or preferred directions. We show how such a constitutive law derives from a microscopic model of particles interacting through nonreciprocal three-body forces using the Dean--Kawasaki coarse-graining procedure. These results establish a minimal framework for odd transport in isotropic three dimensions.

We study a non-reciprocal XY model on a square lattice, in which spins interact with their nearest neighbors through vision-induced anisotropic interaction. Such anisotropy breaks rotational symmetry and leads to the pinning of the spin orientation along preferred lattice directions. We systematically characterize this phenomenon for different interaction kernels, including modulated, sinusoidal, von Mises, and hard vision-cone couplings, and for two classes of microscopic update rules: Glauber and Langevin dynamics. A central result of this work is the identification and detailed analysis of two distinct contributions that naturally arise in the Langevin formulation, which we refer to as the reactive and the proactive term. We derive the corresponding equations governing both local fluctuations and the global orientation, and use them to characterize the mechanisms responsible for directional pinning. We show that both reactive and proactive contributions can generate global pinning, whereas their role in determining local pinning depends on the specific interaction kernel and may differ qualitatively. Our analysis clarifies the distinction between local and global pinning, explains the emergence of preferred lattice directions in the different models considered, and reconciles apparent discrepancies reported in previous studies. More generally, it provides a microscopic framework for understanding lattice-induced orientational selection in non-reciprocal XY models.

We investigate a two-temperature Brownian dimer with odd mobility, characterized by antisymmetric transport coefficients, as a controlled paradigm for odd nonequilibrium dynamics. The system is made of two harmonically confined particles coupled by an elastic spring and connected to reservoirs at different temperatures. Odd mobility converts conservative forces into transverse motion, linking heat exchange to circulating probability currents without requiring external torques, spatial anisotropy, or nonconservative driving. Our exact solution shows that odd mobility creates handed correlations between the two particles while leaving the individual particle distributions isotropic. These correlations arise only when temperature imbalance, elastic coupling, and odd mobility act together, and their handedness reverses when the odd response is reversed. The steady probability current contains two distinct parts: the ordinary irreversible current of a two-temperature dimer and an additional handed contribution generated by odd mobility. When projected onto the motion of each particle, this handed contribution becomes a pair of counter-rotating circulating currents inside the traps. Based on the currents we compute the heat transfer and entropy production analytically. We show that odd mobility enhances thermal conductance between the reservoirs, while the net heat current and total dissipation remain unchanged under reversal of the odd handedness.

Collisional bouncing limits the growth of dust aggregates in protoplanetary disks, but its dependence on aggregate size, collision velocity, and filling factor remains poorly understood. Here we develop a semi-analytic model for the sticking probability of colliding dust aggregates. We divide each aggregate collision into two phases: a compression phase and a separation phase. The compression phase is described with an elastoplastic contact model, which determines the maximum contact radius and repulsive energy after compression. The separation phase is treated as fracture of a stochastic network of interparticle bonds, whose fracture energy is evaluated using weakest-link statistics. The model naturally predicts that larger aggregates bounce more readily because larger contact regions are more likely to contain weak bonds. Comparison with distinct element method simulations shows that the model reproduces the simulated sticking--bouncing boundary. Furthermore, applying the calibrated model to moderately porous aggregates inferred from ALMA observations of protoplanetary disks, we find that the predicted bouncing barrier passes through the observationally inferred size--velocity range. Thus, our semi-analytic model provides a useful framework for predicting the collisional evolution of protoplanetary dust aggregates.

Biomolecular condensates formed by phase separation often exhibit viscoelastic behavior, yet their shape recovery and fusion dynamics are frequently interpreted using purely viscous models. Here, we develop a unified theoretical and computational framework to quantify how viscoelasticity governs these two processes. We combine analytical theory for small-deformation shape recovery with axisymmetric finite-element simulations based on the Oldroyd-B constitutive model to systematically investigate both shape recovery and droplet fusion under comparable conditions. Our results show that, although both processes are driven by capillary forces, they are fundamentally distinct in their underlying physics. Shape recovery is governed by global viscocapillary relaxation of a single connected interface and follows single- or multi-exponential decay depending on the relative magnitude of the viscocapillary timescale and the stress relaxation time. In contrast, droplet fusion is intrinsically a multistage process involving localized curvature-driven neck formation, rapid bridge expansion, and a transition to global relaxation. We demonstrate that viscoelasticity introduces an additional intrinsic timescale that governs the competition between capillary driving and stress relaxation, characterized by the Deborah number. This leads to enhanced intermediate-stage fusion dynamics and modified relaxation behavior compared to Newtonian droplets. Furthermore, we show that the presence of an exterior fluid introduces additional hydrodynamic dissipation, significantly slowing the fusion process. Finally, we compare the computationally predicted droplet fusion in the Newtonian and viscoelastic cases with a stretched-exponential empirical formula. Deviations observed in viscoelastic regimes highlight the limitations of purely viscous descriptions and the need for models incorporating stress relaxation.

The spatiotemporal evolution of many physical, chemical, and biological systems is described by nonlinear partial differential equations (PDEs). Recently, deep neural network-based surrogate models have gained increasing interest as efficient alternatives to computationally expensive traditional numerical solvers. In this work, we propose an attention-based, physics-guided convolutional neural network as a surrogate model to learn the microstructural evolution of such systems. We train the model to accurately predict the full time-evolution of phase separation in binary mixtures governed by the Cahn-Hilliard equation. We show that predictions from our trained surrogate model remain stable and accurate over long-time rollouts for both critical and off-critical mixtures and preserve the mixture composition throughout evolution. We also show that our model accurately captures the growth of domain size and is consistent with the Lifshitz-Slyozov domain-growth law. The prediction results demonstrate the effectiveness of the proposed framework for modeling systems with conserved kinetics and can be extended to other complex dynamical systems.

Motivated by the chiral motility of microswimmers, we investigate how geometric asymmetry in a system of two self-propelled active Brownian robots coupled by a spring gives rise to rich collective dynamics. We demonstrate that asymmetry in the propulsion directions of the robots generates net torques that induce persistent rotational motion. Depending on the choice of propulsion angles $\alpha_1$ and $\alpha_2$, the system exhibits three distinct dynamical regimes -- run-and-tumble motion, circular trajectories, and spinning -- with the geometric configuration primarily determining the realized regime. We further show that spring stiffness and rotational noise act as additional tuning parameters governing the stability of these regimes. These results demonstrate how the interplay of mechanical coupling and activity produces diverse self-organized dynamics in simple robotic dimers, providing a bridge between artificial active systems and biological microswimmers such as bacteria, Chlamydomonas reinhardtii, and spermatozoa.

Active microrheology experiments, in which a probe is driven through a complex fluid, often exhibit nonlinear responses that cannot be captured by generalized Langevin equations. Models that couple the probe to a Gaussian field reproduce such nonlinear effects qualitatively, but their large number of parameters hinders direct comparison with experiments. Here, we restrict these models to a small number of field modes and demonstrate that this reduced description quantitatively reproduces a broad range of active microrheology experiments in a micellar solution using a single set of parameters. We further show that the same framework extends naturally to multi-probe systems, such as colloidal dumbbells.

Despite extensive studies of equilibrium conformations of colloidal clusters, little is known about their mechanical response. Here, we investigate the tensile behavior of a quasi-two-dimensional colloidal cluster subjected to uniaxial tension up to fracture. The sample is a ribbon-shaped assembly of 16 colloidal beads bound by short-range depletion attraction. Using multiple optical tweezers, we clamp the cluster at both ends and perform a tensile test along its long axis. Combining video microscopy with particle tracking, we measure the tensile stress, strain, and particle configurations during deformation. We observe diverse mechanical response behaviors, including elastic, plastic, and soft-mode deformation, with fracture occurring at a strain near 10\%. To explain these behaviors, we construct a spring-mass frame model with breakable elastic bonds. We perform canonical Monte Carlo simulations on the full model with 32 degrees of freedom and compute the statistical distributions of mechanical observables using a simplified model with only 7 degrees of freedom. Both the simulations and the theoretical calculations accurately reproduce the experimental stress--strain curves. Moreover, the configuration distributions predicted by the simplified model agree well with both experiment and simulation in the elastic and soft-mode regimes, with only minor discrepancies in the plastic regime. This work demonstrates that the simplified spring-mass model captures the essential physics governing the rich tensile response behavior of the colloidal cluster.

Particles and clusters moving across real-space periodic potentials can become locked to discrete directions or orientations due to competing symmetries. Here, we demonstrate an analogous locking phenomenon within a synthetic frequency space. We drive ring-shaped colloidal clusters using a circular optical tweezer array, where power modulation of the traps generates coexisting, distinct potential waves. Relative displacements between the cluster and these waves trace zigzag trajectories across a synthetic two-dimensional lattice, mirroring directionally locked motion in real-space periodic potentials. By tuning the relative wave amplitudes, both the cluster's direction in synthetic space and its velocity in real space exhibit discrete plateaus, both governed by square-lattice symmetry. Furthermore, the formation of superlattices between the particles and potential wave minima mirrors the characteristic features of kinetically locked two-dimensional clusters, demonstrating the capability to explore driven cluster dynamics within higher-dimensional potentials using lower-dimensional setups. Our findings establish new strategies for controlling transport of particle clusters via power-modulated laser tweezers.

We investigate the transport dynamics of an active Brownian particle (ABP) traversing a complex, non-Newtonian liquid crystal (LC) matrix. Employing the Generalized Lebwohl-Lasher (GLL) model, we systematically vary higher-order orientational interactions to stabilize three distinct host environments: isotropic, uniform nematic, and structurally frustrated canted phases. Modeling the coupled system via off-lattice over-damped Langevin dynamics, the resulting trajectories are characterized by evaluating their step-size distributions (SSDs), mean-square displacements (MSDs), and Hurst exponents. In the uniform nematic phase, the anisotropic matrix elastically channels the ABP, producing a left-skewed exponential SSD and persistent ballistic motion parallel to the director $\hat{\mathbf{n}}$. Similarly, transverse transport obeys a Rayleigh distribution and acquires a prominent $t \ln t$ super-diffusive correction-an explicit signature of the particle coupling to the host's gapless transverse Goldstone modes, as predicted by Toner et al. [Phys. Rev. E {\bf 93}, 062610 (2016)]. Crucially, we reveal that this active super-diffusion is systematically suppressed when the long-range Goldstone fluctuations are disrupted by topological defects. This breakdown manifests both macroscopically within the fractured, multi-domain canted phase due to a structural mass gap, and locally in the unfrustrated nematic phase through scattering by vortex disclination lines. Consequently, while the local SSDs qualitatively mirror the ideal nematic state, the transverse $t \ln t$ scaling vanishes in the presence of these structural constraints. Our findings demonstrate that tuning the background defect architecture of a complex fluid can fundamentally alter the transport universality class of active matter, offering a novel paradigm for controlling microscopic mobility.

We study the strict locked-orientation limit of hard spherocylinders on a sphere, in which the rod axes are rigidly locked to a prescribed tangential director field and cannot reorient. Because the bulk hard-rod phase diagram contains no smectic-C phase, any coherent tilt isolates a geometric curvature mechanism rather than a finite-stiffness equilibrium effect. A ratio-symmetric recognition cost fixes the layer spacing at the bulk close-contact value and yields a hierarchy of geometric statements: the lower edge of the smectic-area window at $45^\circ$ follows from reciprocal symmetry; the upper edge at $58.3^\circ$ is a falsifiable channel-saturation hypothesis; the smectic-A to smectic-C boundary is a closed-form prediction; and the rod tilt angle is set by the rod-to-radius ratio, modulated by a chirality envelope peaking near $24^\circ$. Locked-orientation Monte Carlo across fifteen geometries confirms these predictions with no fitted elastic constants: the smectic area peaks at $55^\circ$, and a coherent smectic-C window is detected.

The detection of hyperuniformity relies critically on accurate characterization of the small-wavenumber behavior of the static structure factor of the system. In practice, however, measurements are performed on finite subsystems or through incomplete observations that effectively mask portions of the underlying configuration. Inspired by a recent numerical study [Y. Liu, X. Li, J. Tian, X. Yan, G. Zhang, {\it J. Chem. Phys.} {\bf 164}, 094102 (2026)], we develop a unified theoretical framework that quantifies how finite windows and spatially correlated binary masks modify the observed structure factor. We show that the measured structure factor $S_{obs}(k)$ is the convolution of the intrinsic structure factor with the spectral density of the observation function, whether it is a compact window or an extended random mask. For generic hyperuniform systems with small-$k$ scaling $S(k)\sim k^{\alpha}$, finite observation window induces a universal quadratic leakage term at sufficiently small wavenumbers (i.e., $k \lesssim 1/L$), leading to an apparent $k^{2}$ scaling independent of the true exponent. The true hyperuniform exponent $\alpha$ can only be measured in the intermediate regime $1/L \ll k \ll q_c$. In stealthy hyperuniform systems, where the intrinsic structure factor possesses a spectral gap, all observed small-$k$ power arises entirely from this convolution mechanism. For spatially correlated masks, we derive the corresponding convolution relation in terms of the mask spectral density and identify conditions under which hyperuniform signatures are suppressed, preserved, or distorted. Our results establish quantitative criteria for reliably extracting intrinsic scaling exponents and distinguishing genuine hyperuniform order from measurement-induced artifacts.

Organic semiconductors, which include a diverse range of carbon-based small molecules and polymers with interesting optoelectronic properties, offer many advantages over conventional inorganic semiconductors such as silicon and are growing in importance in electronic applications. Although these materials are now the basis of a lucrative industry in electronic displays, many promising applications such as photovoltaics remain largely untapped. One major impediment to more rapid development and widespread adoption of organic semiconductor technologies is that device performance is not easily predicted from the chemical structure of the constituent molecules. Fundamentally, this is because organic semiconductor molecules, unlike inorganic materials, interact by weak non-covalent forces, resulting in significant structural disorder that can strongly impact electronic properties. Nevertheless, directional forces between generally anisotropic organic-semiconductor molecules, combined with translational symmetry breaking at interfaces, can be exploited to control supramolecular order and consequent electronic properties in these materials. This review surveys recent advances in understanding of supramolecular assembly at organic-semiconductor interfaces and its impact on device properties in a number of applications, including transistors, light-emitting diodes, and photovoltaics. Recent progress and challenges in computer simulations of supramolecular assembly and orientational anisotropy at these interfaces is also addressed.

We establish a self-consistent analytical model demonstrating that trapped non-wetting liquid phases in narrow capillary channels can be successfully unpinned via non-resonant, second-order acoustic streaming (acoustic wind) coupled with background static drive gradients. Moving away from boundary-guided or resonant mechanisms, our approach exploits the bulk acoustic-wind force density generated by the steady-state momentum flux of attenuated first-order linear wave interactions. By expanding the hydrodynamic equations up to second order, we determine the critical assisted acoustic wave amplitude required to break capillary pinning thresholds and derive an explicit formulation for steady transport velocity under viscous wall constraints. Furthermore, incorporating both boundary-layer wall effects and bulk core thermo-viscous dissipation reveals a natural mathematical optimum condition where the spatial absorption coefficient matches half the inverse distance to the target droplet ($\alpha = 1/2x_0$). This condition is then numerically validated and cross-correlated against legacy industrial frequency baselines, providing a fundamental theoretical framework for minimizing transducer power requirements while maximizing localized mobilization velocities in geological pore networks. Finally, we demonstrate that this optimal operational frequency scales inversely with the transmission distance, providing an analytical framework to optimize downhole acoustic tools according to the spatial damping constraints of the specific formation rather than relying on rigid hardware parameters.

Recently, Zhao & Dong (J. Fluid Mech. 2025, vol. 1013: A44) developed a high-efficiency, high-accuracy numerical framework, the shock-fitting harmonic linearised Navier-Stokes (SF-HLNS) approach, which enables a systematic study of the receptivity of non-modal perturbations in hypersonic blunt-body boundary layers over a wide parameter range. In this Part II, we employ a high-Reynolds-number asymptotic analysis to elucidate the physical mechanism of the receptivity process. A distinct slow-down convection mechanism is identified in the nose region, amplifying the perturbation streamwise vorticity from the post-shock position to the boundary layer around the stagnation point by a factor of O(\sqrt{R}), where R is the Reynolds number based on nose radius. Downstream, the lift-up mechanism further leads to a transient growth of the perturbation streamwise velocity up to an amplitude of O(R). Based on these mechanisms, a reduced model is developed to predict the downstream evolution of the non-modal perturbations initiated by receptivity, whose predictions agree well with SF-HLNS calculations. This model can also be used to investigate the effects of wall temperature and nose radius on non-modal receptivity efficiency, as will be detailed in Part III of this work series.

Premixed flames propagating in porous media or Hele-Shaw channels are governed by Darcy's law, which accounts for the strong frictional forces imposed by the solid matrix or confining walls. Prior theoretical studies of such flames have typically employed phenomenological Markstein-type corrections and have assumed unity Lewis numbers and adiabatic conditions. In this work, we develop a rigorous hydrodynamic theory for premixed flames under Darcy's law that incorporates nonunity Lewis numbers and heat losses. Using large activation-energy asymptotics and a systematic multiple-scale analysis, we derive the interfacial jump conditions across the flame from first principles. The conventional continuity requirements of mass flux and pressure at an interface under Darcy's law acquire corrections to the finite thickness of the flame. The adiabatic burning rate is shown to involve three distinct Markstein numbers, corresponding to curvature, tangential flow strain, and gravity-induced strain. The gravity term is unique to Darcy's law and has no counterpart in classical Navier--Stokes formulations. Moreover, the curvature Markstein number and the tangential strain Markstein number are found to be unequal, in contrast to the classical case where they coincide under constant transport properties. Explicit formulas for the Markstein numbers are provided, and the resulting new dispersion relation, linking the perturbation wave number $k$ to the growth rate $s$, takes the form $s = (a|k| - bk^2 - d|k|^3) / (1 + c|k|)$. This relation, applicable under Darcy's law, is to be compared to the classical Clavin--Garcia dispersion relation derived from the Navier--Stokes equations. The theory provides a rigorous foundation for flame dynamics in strongly confined environments, with direct applications to porous media combustion and Hele-Shaw cell experiments.

Numerical simulations of reactive hypersonic flows under thermochemical non-equilibrium conditions are presented for the FIRE II and Mars Pathfinder capsules. An 11-species chemical model is employed to simulate Earth's atmosphere, while an 8-species chemical model simulates Mars' atmosphere. The current formulation uses Park's two-temperature model to account for the non-equilibrium phenomena. The present work analyzes the impact of different sets of weight factors used in Park's model to calculate the control temperature. The code used to simulate the hypersonic flow addressed in this work solves the Navier-Stokes equations for reacting gas flows. The findings are depicted in terms of the Mach number, temperature modes, and mass fraction distributions along the stagnation streamline in a region closer to the shock wave. The study also includes results regarding the stagnation point convective heat flux. The results presented are encouraging and show that the weight factors significantly impact the FIRE II test cases while having little impact on the Mars Pathfinder flows. In all cases, it is possible to observe some effect of the weight factor selection on property distributions. In summary, the weight factors influence the flow behavior with varying intensities depending on the flow conditions.

Channel geometry strongly influences capillary-driven fluid transport in paper-based devices, yet systematic comparative studies correlating geometric design with flow behaviour and analyte confinement remain limited. The present study investigates five distinct channel geometries namely converging-diverging, diverging-converging, wide-to-narrow, circular, and rectangular that was fabricated on cellulose filter paper with a standardized area of 32.5 mm\textsuperscript{2} and analyzed using geometry-adapted extensions of the Lucas--Washburn equation. Pyrene and benz[{\alpha}]anthracene were employed as fluorescent model analytes to enable UV-based quantification of analyte confinement within each geometry. Flow transport times ranged from 23.1 s (circular, fastest) to 65.0 s (diverging-converging, slowest), with corresponding mean velocities of 0.571 and 0.284 mm/s for pyrene respectively, demonstrating that channel geometry strongly influences capillary transport in paper-based devices. Diverging-converging and wide-to-narrow designs produced the greatest analyte confinement by imposing flow retardation and sustained channel acceleration respectively, while circular and rectangular designs yielded relatively uniform velocity distributions and weaker confinement. Cyclodextrin-functionalized chitosan coatings served as a surface chemistry tool to anchor analyte retention at designated preconcentration zones, enabling geometric effects to be isolated and quantified. Computational fluid dynamics simulations, calibrated against experimental flow data and validated through a mesh independence study, reproduced the experimentally observed velocity magnitude distributions across all five geometries, showing semi-quantitative agreement with geometry-adapted Lucas--Washburn predictions.

We introduce a new energy-conserving, moist shallow water model with thermal stratification and rotation. The model is derived from a variational principle, using a Lagrangian expressed in terms of enthalpy. In this model, the latent heat from phase transitions modifies the buoyancy dynamics, which in turn feeds back to alter the vertically integrated hydrodynamic motion. Finally, we generalise this moisture parameterisation to non-hydrostatic Green-Naghdi equations.

Kolmogorov Arnold networks (KAN) have recently been introduced as a (deep) neural network architecture whose trainable parameters adapt the activation functions, instead of the coefficients of the affine transformations at the core of traditional architectures such as deep multilayer perceptrons (MLPs). This architecture builds on the Kolmogorov-Arnold theorem, which endows it with universal approximation properties. While the advent of KANs has been received with excitement, there is a current debate about the possible KAN supremacy over deep multilayer perceptrons (MLPs) for classic fields such as symbolic regression, generic-purpose machine learning, natural language processing or computer vision. Here we assess the performance of KANs --and its nuanced comparison against MLPs and graph neural networks (GNNs)-- in the realm of fluid dynamics surrogate modelling. To that aim, we consider the task of predicting the surface pressure distribution over subsonic and transonic airfoils, a canonical task in aerodynamics. Our results show that KAN models show good performance in predicting the whole pressure coefficients and is able to interpolate across Mach numbers and angles of attack, however its performance is comparable --marginally inferior-- to a suitably trained MLP, where best performance is achieved by a GNN at the expense or requiring lengthier training. While the optimal KAN model have typically much lower complexity than MLP and GNN --hence resulting in faster training--, we find that KANs suffer from training instabilities, and their performance is highly dependent on a proper hyperparameter optimisation.

In this paper we study the dynamics of relativistic detonation waves theoretically and numerically. The reaction is physically accounted for by an extra term in the definition of the total energy density and by an additional equation for the evolution of the mass fraction of the reactant, while leaving formally unmodified the equations of mass and energy-momentum conservation. In this way, the Rankine-Hugoniot relations maintain the same formal structure of the inert version. For the numerical solution we use a second order finite volume ALE scheme with TVD reconstruction, where the mesh velocity is chosen equal to the shock speed. We also adopt a locally implicit algorithm for the treatment of potentially stiff reaction source terms that arise in the equation of the reactant. We furthermore propose a particularly efficient algorithm for the conversion from the conserved to the primitive variables, which for the relativistic Euler equations is known to be nontrivial. Following this approach, we can successfully solve the Zel'dovich-von Neumann-Doering profile of a relativistsic detonation wave, up to Lorentz factors of the shock front $\gamma_S\sim 7$. Our analysis allowed us to highlight a new special relativistic effect, which has remained unnoticed so far. While in Newtonian detonations the Zel'dovich pressure jump decreases monotonically with the mass flux through the shock front, in the relativistic case it shows a minimum and then rises monotonically as a function of the mass flux. This may have interesting physical implications on the amount of energy that can be extracted from a relativistic detonation wave.

In this work, we present pyDOF, a Python-based software library which provides a domain-specific framework for the design of symmetric, physical-space, forward as well as inverse discrete filters. pyDOF is based on a constrained optimisation framework developed in our previous work [1, 2]. This framework allows the user to impose a wide range of constraints on the discrete filter transfer-function such as monotonicity, positivity, value-fixing, gradient-smoothing etc. amongst many others. pyDOF additionally includes an adaptive filter stencil selection option, and a van Cittert-based inverse-filter design with a user-controlled reconstruction order. The filter coefficients are computed automatically, and saved to a plain text file which can be readily parsed by any programming language. pyDOF can be used to design a wide range of low-pass, high-pass, multi band-pass/band-stop etc. discrete filters. In addition, due to its generality and abstraction, pyDOF can be used to design specific filters for user-defined target filter transfer functions. Although developed primarily for application to computational fluid dynamics simulations, pyDOF can be used to design discrete filters for a wide range of signal processing applications.

A general formulation of metriplectic dynamics is presented, where the metriplectic four-bracket is constructed by multiplying two skew-symmetric brackets. The new formulation is then used to introduce irreversibility in a generalized two-dimensional (2D) quasigeostrophic (QG) upper-ocean model involving advected quantities, with the thermal QG model as a special case. By construction, the resulting dynamics ensure the conservation of internal energy and the generation of entropy, in accordance with the first and second laws of thermodynamics. Our metriplectic dynamics formulation allows for a flexible specification of irreversibility, ranging from a type that results in nearly material conservation of potential vorticity to the representation of realistic forcing and dissipation in 2D QG ocean modeling with advected quantities.

The Collatz map is a simple deterministic transformation whose orbit structure remains highly nontrivial. A recent direction-phase decomposition partitions each orbit into upward and downward steps, and numerical observations indicate that the number of upward phases, $N_{\uparrow}$, follows an approximate Gamma distribution. In this work, we provide a mechanistic explanation for this statistical regularity by modeling the occurrence of upward phases in the odd-compressed, or Syracuse, version of the Collatz map as a homogeneous Poisson process. From the mean-field logarithmic balance and the geometric distribution of $2$-adic valuations, we derive closed-form expressions for the Gamma parameters: the scale parameter $\theta = 2/(2-\log_2 3)^2 \approx 11.61$ is constant, whereas the shape parameter $K$ grows logarithmically with the maximal initial value $X_0=2L+1$. We also analyze the closure conditions for periodic orbits, showing that nontrivial cycles are severely constrained, which supports the plausibility of the statistical framework. Numerical validation for $L$ ranging from $10^5$ to $10^{15}$ confirms the theory with relative errors below $3\%$, and a bias-corrected mean estimate reduces the error to $10^{-3}$--$10^{-2}\%$. These results establish a quantitative link between the arithmetic properties of the Collatz map and Gamma-type statistics, and suggest possible extensions to generalized Collatz-type problems.

Dynamical systems can exhibit complex responses when noise is injected. In particular, dynamics can be qualitatively altered by dynamic noise, a phenomenon known as noise-induced bifurcation. Predicting noise-induced bifurcations is a critical challenge in nonlinear physics. Recently, it has been reported that reservoir computing, a machine learning framework, can reconstruct the unseen global structure of a dynamical system, including bifurcations, from limited time series data. However, learning global structures in random dynamical systems has not yet been systematically addressed. In this study, we report that a simple reservoir computing framework can predict the noise-induced bifurcation structure from the time series at a single noise condition. We demonstrate dynamic noise cancellation and the reconstruction of entire noise-induced bifurcation structures, including noise-induced chaos and noise-induced order, in representative dynamical systems. Additionally, we provide a theoretical explanation for noise cancellation and demonstrate noise cancellation of a neuromorphic spintronics device. Our results provide significant insights into understanding and harnessing real-world noisy complex dynamics.

The notion of internal reliability in dynamical networks describes whether replicas of a particular unit follow the dynamics of the reference unit. Reliability and anti-reliability can be quantified by the transversal Lyapunov exponents. We study phase oscillators coupled via Kuramoto-Sakaguchi-type interactions. Already the simplest solvable system of two oscillators demonstrates nontrivial reliability properties. We present numerical evidence of reliability and anti-reliability in small networks with a uniform distribution of natural frequencies. The dynamics of an ensemble of replicas can be described within the Watanabe-Strogatz theory, which predicts symmetry of the transversal Lyapunov exponents for replica-attractor and replica-repeller.

Deep-learning emulators have emerged as a promising approach for reducing the computational cost of Earth System Models while potentially improving forecasting skill. Here, we demonstrate the successful emulation of a high-complexity marine biogeochemistry model within a simplified one-dimensional water-column framework. We explore two emulator architectures: Long Short-Term Memory (LSTM) neural networks that emulate a selected subset of variables at daily resolution, and physics-informed one-dimensional Convolutional Neural Networks (1D CNNs) that emulate the full pelagic system throughout the water column also at daily resolution. Using ocean physics simulator inputs, both emulators remain largely stable over multi-decadal timescales and accurately reproduce the parent model in both decadal climate projections and short-range (10-day) forecasting applications. The former includes the ability to predict the timing of phytoplankton Spring blooms several years in advance. When trained on reanalysis data, the emulators substantially outperform the parent model's forecast skill score for several key ecosystem variables, including phytoplankton and zooplankton. If similar performance can be achieved in three-dimensional regional applications, these emulators could provide substantially higher-quality predictions at a fraction of the computational cost. We further apply novel explainability techniques to identify key drivers of emulator behaviour and gain insights into emergent ecosystem dynamics. Performance is evaluated using a range of metrics, including the reproduction of daily variability and extreme events. These approaches have considerable potential for future applications in operational forecasting, climate-scale simulations, and marine autonomous systems.

When implementing the method of multiple scales, one is traditionally instructed to treat the slow and fast time scales as if they were independent. Despite the intuitive motivation and the effectiveness of this perturbation method, one cannot failt to notice that these two scales relate to the same unique variable, so independence can only be formal. How sensible is it, then, to split a variable asymptotically into two (or more) independent ones? In this paper, we elucidate this issue with Van der Pol's equation, one of the simplest weakly nonlinear oscillators, as well as a simple example of a Hopf bifurcation. The discussion involves carrying the multiple-scale analysis up to arbitrarily large order and dealing with the divergent character of the resulting asymptotic series. Using the technique of optimal truncation, we re-connect the two scales. Specifically, we show that an initial translation of the fast coordinate leads to a non-trivial, exponentially small, phase shift that depends on the slow coordinate. This phase shift breaks the independence of the slow and fast scales and is found to result from the nonlinearity. Numerical simulations confirm its existence, as well as the predicted scaling. The calculation is carried out in sufficient detail to provide confidence in the generality of our result, both in its essence and in its form. In particular, we find strong indications that a Hopf bifurcation with a quadratic nonlinearity would lead to the same phenomenon, but with a larger magnitude.

The process of excitation of degenerate optical parametric oscillations via bichromatic pump is studied numerically in normal-dispersion photonic-crystal microresonator. It is demonstrated that the photonic-crystal structure with two split modes placed symmetrically at the particular interval from the pumped modes provides significant reduction in pump power threshold for the considered process. The parameter range for this phenomenon is determined. Introduction of mode splitting at the signal mode located in the center between pumped modes leads to an increase in the generation threshold.

This work is devoted to data-driven identification of discrete breathers in numerical simulations of a two-dimensional crystal lattice using locally sampled wave data. Different lattice wave datasets are considered, with data collected from regions of different shapes and sizes defined by the lattice particles in mechanical equilibrium. Specifically, in addition to regions with a regular hexagonal shape, one- and quasi-one-dimensional regions reflecting the quasi-one-dimensionality of discrete breathers in two-dimensional hexagonal crystal lattices are proposed. To improve numerical efficiency, dataset dimensionality is reduced using Principal Component Analysis, and highly accurate Support Vector Machine classifiers are trained to distinguish between linear and nonlinear wave data. The obtained classifiers, together with the sliding window method, are applied to detect localization regions in two-dimensional hexagonal crystal lattice numerical simulations. High-precision algorithms for detected localization region segmentation and localized wave directionality estimation within the detected regions are further proposed, and their performance is evaluated. The presented methods are successfully applied to detect localized waves and their collision regions, as well as their directionality, performing a numerical study of stationary and traveling two-dimensional discrete breather interactions. Qualitatively better results are obtained when considering wave-data collection regions respecting the quasi-one-dimensional nature of two-dimensional discrete breathers in the hexagonal crystal lattice model.

We investigate kink antikink collisions in higher order scalar field theories described by the higher order models and their shifted periodic extensions. Both classes of models possess three degenerate vacuum states and support topological kink solutions with asymmetric profiles and algebraically decaying tails. By extending conventional polynomial potentials across multiple spatial sectors, we construct shifted periodic high order field theories and examine how this modification affects the scattering dynamics of topological defects. The primary objective of this study is to provide a comparative numerical analysis of kink collisions in the standard and shifted periodic versions of these higher order models. Using direct numerical simulations, we determine the critical velocities that separate capture from escape regimes and identify resonance structures associated with energy exchange between translational and internal vibrational degrees of freedom. Particular attention is devoted to the emergence of escape windows, quasi-fractal patterns, and the role of algebraic tails in shaping the collision outcomes. Our results demonstrate that, although the conventional and shifted periodic models exhibit similar kink antikink configurations, important quantitative differences arise in their critical velocities, resonance structures, and scattering characteristics. The findings further confirm that both classes of models support resonant energy transfer mechanisms analogous to those observed in lower order theories, while simultaneously exhibiting novel features associated with higher-order interactions and long range effects. These results contribute to the growing understanding of nonlinear excitations in scalar field theories and provide new insights into the dynamics of topological solitons in shifted periodic systems

Straight dark solitons in two-dimensional (2D) quantum fluids usually decay by transverse modulational instability, with no intrinsic suppression in contact-interacting Bose--Einstein condensates (BECs). We theoretically show that anisotropic long-range interactions in a quasi-2D dipolar BEC stabilize an embedded straight soliton, with spontaneous stripe order providing stronger pinning. The excitation spectra show that the lowest transverse solitonic branch remains gapped, while stripe-supersolid density modulation further hardens this branch and increases the soliton bending stiffness, penalizing transverse deformation. Accessible in current $^{166}$Er and $^{164}$Dy platforms, these results establish interaction-driven protection for straight dark solitons in structured quantum fluids.

The quantum geometry of electronic, photonic, and atomic lattice systems quantifies the distance in Hilbert space between Bloch states at neighboring lattice momenta. This quantity has profound implications for flat-band systems especially, characterizing surprising behavior such as superfluidity and superconductivity when the group velocity is zero and no transport would be expected for non-interacting particles. However, when the band is not flat, the effects of quantum geometry are often intertwined with and partly masked by the band dispersion. Here, we show that in weakly interacting bosonic systems in the critical dimension (i.e., two dimensions for Kerr nonlinearity), the deviation from critical behavior due to the presence of the lattice is governed by the quantum geometry, which is directly proportional to the fourth-order dispersion. Furthermore, we identify the family of continuous lattice potentials that saturates the bound on the quantum metric for a given effective mass tensor.

Thermohaline interfaces in the ocean are often treated through local double-diffusive favorability, yet finite interfaces can also inherit roughness from prior waves, stirring, intrusions, and earlier mixing events. Such inherited geometry can matter because salt fingering does not develop from a flat abstract surface in many geophysical settings. We use controlled three-dimensional direct simulations to test whether the spectral state of a finite rough interface changes the pathway by which salt-finger activity develops between adjacent layers. The density ratio, diffusivity ratio, Prandtl number, interface thickness, roughness amplitude, domain, resolution, and analysis window are held fixed; only the imposed roughness spectrum and, for one pair, the realization are changed. Broad low-mode memory produces the largest cumulative salt exchange and the earliest finite-depth contact. High-annulus memory remains localized and intermediate-scale dominated. Mixed memory produces delayed scale transfer and scalar-rich structure that is robust in integrated exchange and broad-memory measures across a second realization, while local plume timing and probe amplitudes remain realization-sensitive. The simulations therefore support treating interfacial spectral memory as an additional state variable for finite-depth double-diffusive exchange, complementary to local thermodynamic descriptors.

We introduce a Gaussian-based spatially weighted loss framework (G-PINNs) for physics-informed neural networks (PINNs) to improve the resolution of sharp discontinuities and shock waves. The proposed method dynamically prioritizes collocation points in high-gradient regions during optimization. Without requiring prior knowledge of the shock location or trajectory, the framework can autonomously detect and track moving discontinuities directly from the PDE residual landscape, making it broadly applicable to problems in which the position of shocks or discontinuities is unknown \textit{a priori}. The approach is validated using one-dimensional quasi-inviscid Burgers' problems exhibiting both stationary and moving shock waves. For the low-viscosity regime $(\nu = 0.0005)$, the proposed method achieves $L_2$ relative errors of approximately $13\%$ and $14\%$ for the stationary and moving shock cases, respectively, compared with $45\%$ and $33\%$ obtained when using standard PINNs.

Ammonia is a high-density hydrogen energy carrier and can be decomposed to produce hydrogen for use in fuel cells. However, a significant challenge in ammonia-decomposition-based fuel cell applications is the unavoidable presence of trace ammonia impurity, which can poison the fuel cell, but the poisoning mechanism remains unclear. To address this, a three-dimensional numerical model of proton exchange membrane (PEM) fuel cells with ammonia impurities is established to explore the transport process and underlying poisoning mechanism. The influences of key factors, including ammonia concentration, operating temperature, operating humidity, and membrane thickness, are studied. The poisoning mechanism is analyzed from the perspectives of the distributions of proton conductivity, current density, and dissolved water content. The results show that ammonia diminishes the cell performance by substantially reducing the proton conductivity of both the PEM and the anode catalyst layer. Higher operating temperatures and higher operating humidity can alleviate ammonia poisoning. Decreasing the membrane thickness can also help to mitigate ammonia poisoning, but may lead to less uniform current distribution.

Traditional particle-based kinetic methods, such as DSMC, suffer from prohibitive computational cost in low-signal flows, where the deviation from thermodynamic equilibrium is small and statistical noise overwhelms the signal of interest. The Variance-Reduced BGK-DSMC scheme is further advanced and implemented to support this class of flows in the open-source gas-kinetics framework PICLas. Modified versions of flow estimators and collision operators enhancing stability are developed. The Shakhov and Ellipsoidal Statistical models for BGK are demonstrated, along with entirely new features such as adaptive equilibria, variable particle weights and domain axisymmetry. The implementation is validated using synthetic benchmarks, 1D, 2D and axisymmetric simulations. Comparison of VRBGK to BGK simulations shows exact agreement of the models. A further comparison with an analytical solution of thermal transpiration in a microchannel showcases the low-signal efficiency of the method as well as newly proposed features.

The T-shaped mixer is widely used in fundamental studies of chemical engineering. Its transitional regime is well understood, whereas the turbulent dynamics has received scarce attention so far. Here we perform direct numerical simulations of the turbulent regime for Reynolds numbers up to $Re=2000$ at Schmidt number $Sc=1$. Our analysis reveals two distinct stages along the mixing channel prior to relaxation toward duct flow. Near the junction, a jet-like flow forms and exhibits the approximately self-similar behaviour of transitional planar jets. Subsequently, a decay region characterised by power-law decay of turbulent kinetic energy, dissipation and scalar variance emerges. For the velocity field, the observed exponents are consistent with those of decaying turbulence in bounded domains, whereas the scalar-variance exponent is consistent with that of unbounded turbulence. We argue that this apparent discrepancy is a consequence of the mixing process progressing from the center of the channel toward the side walls in the decay region, while turbulence already fills the channel cross-section entirely at the end of the jet this http URL time-averaged mixing state presents error-function profiles of the scalar in the transverse direction, similar to the laminar cases, and is quantified here through a stream-wise evolving effective diffusion coefficient.

Localized protrusions on hypersonic vehicles generate pressure, heat-transfer, and shear loads whose rarefied response can depend on gas beyond the immediate wall neighborhood. This work quantifies that bulk-to-wall dependence for triangular protrusions and tests whether coordinate-conditioned surrogates preserve it. Geometry-consistent surrogates are trained for direct simulation Monte Carlo (DSMC) velocity, temperature, pressure, and wall-load profiles over Mach numbers 4--8, Knudsen numbers (Kn) 0.1--0.8, and three protrusion orientations. The central analysis is performed on raw DSMC fields. Around each wall point, circular neighborhoods of increasing radius are summarized by weighted statistics, extrema, nearest-point values, and tangent-normal gradients of velocity, temperature, and pressure. A fixed region-to-point diagnostic predicts the pressure coefficient ($C_p$), heat-transfer coefficient ($C_q$), and shear-stress magnitude ($|\tau|$). We define $R_{95}$ as the smallest tested radius whose complete wall-profile error lies within 5\% of the full-domain descriptor error. The principal physical result is that rarefied surface loading has no single information length. Full-domain descriptors reduce errors from 45.5\% to 13.8\% for $C_p$ and from 72.6\% to 12.9\% for $C_q$, whereas shear improves only from 49.1\% to 31.9\%. Heat transfer exhibits the clearest order-$h_s$ nonlocal support, where $h_s$ is the protrusion-base length. Pressure is frequently right-censored beyond $3h_s$, and shear saturates at shorter radii but remains least identifiable. Ridge-regression and threshold controls preserve this hierarchy, while a closed-loop audit shows partial surrogate preservation, with the largest degradation in forward-facing heat transfer and shear.

Traditionally, the critical blast wave parameters used to characterize loading conditions are obtained through pressure gauge measurements. However, these instruments are costly, require careful calibration, provide discrete location measurements only, and must be deployed in hazardous environments. Recent events, such as the Beirut port explosion have demonstrated that video recordings, which provide time of arrival (ta) versus distance data, offers valuable information for post-event blast analysis. However, methodologies capable of predicting key blast parameters, such as positive phase duration and impulse, using video data alone remain limited. This work proposes and validates a novel methodology to predict positive phase duration and impulse for spherical, non-cased, free air bursts of ideal explosives using ta data only. The proposed methodology was evaluated using experimental datasets from the literature for bulk and cartridge PE4, PE7, Composition B, and PETN. The positive phase duration and impulse models achieved, respectively, mean absolute percentage errors of 5.3% and 5.3%, maximum deviations of 20% and 9.4%, absolute biases of zero and 3.1%, and confidence interval coverages of 86% and 83%. The predicted results achieve remarkable comparison to all reported experimental data, verifying the ability to capture positive phase blast loading for high speed video; a step-change in explosive characterisation through full spatial and temporal primary shock characteristics.

Volumetric particle tracking velocimetry (PTV) produces scattered Lagrangian tracks that must be reconstructed on an Eulerian grid before velocity gradients, pressure, or hydrodynamic loads can be evaluated. This step is usually performed on a domain treated as entirely fluid. When a solid body lies within the measurement volume, its surface kinematics are not imposed and the reconstruction is weakest in the steep-gradient region next to the body. We introduce LE-DM (Lagrangian-to-Eulerian reconstruction with Dynamic Masking), a constrained reconstruction framework for moving solid boundaries. A time-dependent signed-distance function classifies grid nodes as open fluid, boundary shell, or solid interior. The particle data, incompressibility constraint, prescribed surface velocity, and regularization terms are then assembled on the masked domain within a single solve. The method requires only a signed-distance field and a surface velocity, allowing stationary walls, translating, rotating, multiple, and deforming bodies to be represented in the same formulation. LE-DM is assessed using an analytical oscillating sphere, synthetic tracks from a CFD rising-sphere simulation, and a refractive-index-matched tomographic-PTV experiment on a freely rising sphere. The surface kinematics are enforced to solver tolerance, while the bulk reconstruction remains unchanged where no body is present. In the analytical case, the first-cell error is reduced from 14\% to 3\% of the body speed. In the experiment, LE-DM recovers the independently measured surface velocity, whereas an all-fluid reconstruction does not. The result is a divergence-free, boundary-consistent velocity field for pressure and force estimation.

Numerical simulation of deformable particle suspensions in Stokes flow is computationally expensive due to nonlinear fluid-structure interactions, evolving interfaces, and multiscale hydrodynamics. We present VesNet, a hybrid framework that accelerates two-dimensional vesicle suspension simulations by approximating vesicle self interactions, including background flow coupling and short-range lubrication forces, while retaining conventional modules for boundary reparameterization and far-field hydrodynamics. A GPU-accelerated implementation achieves over 100x speedup compared to a multithreaded MATLAB CPU boundary integral solver and about 5x relative to its GPU counterpart. VesNet accurately captures key dynamics, including single-vesicle phase behavior, pair interactions, and large-scale suspensions in Taylor-Green and Poiseuille flows, enabling efficient simulations of thousands of vesicles on modest computational resources.

This study investigates propeller hydrodynamics at intermediate Reynolds numbers (Re), crucial for small-scale robotic systems but still uncharted. Experiments on a propeller-driven underwater vehicle and numerical simulations reveal thrust reversal--a phenomenon where clockwise propeller rotation leads to backward motion--in the approximate range 1.3 < Re < 150 under specific conditions. Notably, counterclockwise rotation consistently results in backward motion. Simulations reveal that this behavior arises when centrifugal suction, an inward force along the axis caused by radial outward flow from the propeller's rotation, dominates over fluid backward acceleration, the primary thrust mechanism at high Re. These findings provide critical insights into the unique dynamics of the intermediate Re regime and inform the design of efficient propulsion systems for miniature aquatic robots.

Estimating past events in wall turbulence based solely on surface measurements and first principles is an ill-posed problem that is complicated by chaos. The sensitivity of a measurement to the earlier flow state is described by the adjoint Navier-Stokes equations, which are solved in reverse time starting from the measurement kernel at the sensing position and time. The resulting adjoint field is the spatio-temporal domain of dependence (DOD) of the sensor, which is a dual to the concept of the domain of influence (DOI) of an actuator in the linearized forward equations. In channel turbulence, the energy of each adjoint realization grows exponentially in backward time according to the Lyapunov exponent, even though the energy of the ensemble average should decay. We introduce a linear eddy-viscosity closure model in the ensemble-averaged adjoint equations, and directly compute the mean DOD and compare our prediction to the ensemble average. Furthermore, we demonstrate that the DOD of a wall-stress measurement and the DOI resulting from a wall-stress perturbation exhibit respective universal behaviors across Reynolds numbers. However, their spatio-temporal structures differ qualitatively, due to the time-asymmetry of the governing equations. The DOD field has a two-part structure: one component is associated with the Orr mechanism, characterized by rapid reorientation under mean shear, and the other is related to self-similar expanding streaky structures. These two components jointly define the sensitivity of the wall-stress measurement to past flow events.

A near-wall cavitation bubble is generally expected to acquire a wallward Kelvin-impulse bias and to rebound or jet toward the wall. Here we show that this canonical direction can be reversed by a wall-supported free sphere. High-speed imaging reveals a transition from away-from-wall to wallward rebound as the initial bubble--sphere separation is increased. By reconstructing the Kelvin impulse on a closed bubble boundary that includes both the visible free interface and the bubble-side contact closure, we find that the reversal is not governed primarily by the instantaneous velocity of the sphere. Instead, sphere displacement creates a contact closure on which the bubble-source contribution supplies an away-from-wall impulse. This contact-source impulse competes with a wallward background formed by the wall-image source and the quadrupolar component of the sphere-induced field. The resulting balance yields a calibrated geometric criterion, $\mathcal{M}_K$, and, in the comparable-size bubble--sphere regime, reduces to a contact number $a_z z_b/R_K^2$. These results identify a contact-geometric mechanism by which a movable particle can redirect the first-cycle jet and rebound bias of a near-wall cavitation bubble.

The channel flow of a liquid metal driven by a rapidly varying applied magnetic field is analyzed. The flow configuration, physical properties, and parameters correspond to a duct within a liquid-metal blanket of a nuclear fusion reactor under off-normal plasma conditions, such as plasma disruptions. The problem is solved numerically using a one-dimensional flow approximation. The longitudinal magnetic field, decaying at a typical rate on the order of 100 T/s, induces eddy currents that interact with a steady wall-normal magnetic field, generating the Lorentz force that drives the flow. Standing Alfvén waves are identified as the key mechanism controlling the liquid metal's response. These waves manifest as large-amplitude, gradually decaying oscillations of velocity, the induced magnetic field, and eddy currents. A parametric study predicts a severe response developing within the first few milliseconds of the event, with maximum flow velocities reaching several meters per second and Lorentz forces exceeding $10^9 \text{ N/m}^3$. Power-law approximations for the dependencies of the response characteristics on the flow parameters are developed. Finally, the effects of fluid compressibility and pressure waves are analyzed and found not to lead to a major modification of the flow evolution.

This review focuses on the liquid jet in crossflow (LJIC) configuration. LJIC is one of the most common strategies used for fuel injection in aerospace applications. It is popular due to its simplicity and efficient atomization characteristics. The aerodynamic force of the airflow is utilized to break liquid jet into small droplets. The objective of the present work is to give a basic overview of the physical processes involved in the breakup and penetration of LJIC. Breakup modes and underlying mechanisms are discussed in detail. Various modes are described and associated non-dimensional numbers are explained. Injector geometry which is often overlooked in literature is paid special attention. The mechanism of liquid jet instability getting triggered by velocity profile redistribution is explained using experimental and computational results. Surface waves on liquid jets are discussed. A theoretical model used to predict the wavelength of surface waves is described. DNS results are used to demonstrate the growth of surface instability on a liquid jet. Jet penetration and trajectory in the presence of crossflow are discussed. Various trajectory equations and the parameters used are discussed in detail. Progress in computational studies for LJIC is highlighted and challenges are discussed.

The drag and mobility of bodies in viscous (Stokes) flow govern problems in shape design, suspensions, or microorganism swimming. Classical solvers compute them accurately but expensively; purely learned surrogates are fast but unreliable off their training data. We combine both: a solver's exactness for the part of the solution operator known in closed form, and learning for the part that is not. For incompressible Stokes flow the elliptic-core kernel is already known: in free space the Leray projector is a single rotation-equivariant Stokeslet with no free parameters, and the boundary-integral solver built on it is exact to machine precision at $O(N)$. The one object with no closed form is the boundary correction. We split the operator: fix the core exactly and equivariantly, and learn only that correction, as a well-conditioned second-kind operator. On a Stokes testbed where the exact solve is ground truth, the split gives a working solver ($2 \times 10^{-3}$ end-to-end, $5$-$16\times$ more data-efficient than a black-box DeepONet) and overturns three expectations. (i) Conditioning is not the bottleneck: a $10^{16}$-conditioned first-kind and a bounded second-kind operator give the same error. (ii) Cross-shape generalization is governed by the descriptor's equivariance, not capacity: a noninvariant descriptor degrades by $>10^5\times$ under rotation, while canonicalization restores near-machine transfer. (iii) Coverage, not expressivity, is the lever; a local equivariant kernel removes the heavy out-of-distribution tail, cutting worst-case interior error from $O(10)$ to $\sim 10^{-7}$. We then open the central exterior problem in 3D: a completed double layer, made exact by quadrature by expansion, is second-kind well-conditioned and $SO(3)$-equivariant, reproduces the analytic drag of spheres and ellipsoids, and composes across bodies.

The time-averaged geomagnetic field provides crucial insights into deep Earth dynamics and thermal core-mantle interactions. Paleomagnetic observations and numerical dynamo simulations are equivocal regarding the longitudinal structure of the time-averaged field, though the latter have often considered a generic buoyancy source, which may obscure distinct signatures of thermal and chemical buoyancy that arise near the equator and poles, respectively. In this study, we present a new suite of top-heavy geodynamo simulations, varying the relative strengths of thermal and chemical driving and comparing the resultant magnetic signatures to observational field models spanning centuries to tens of thousands of years. None of the spatially-averaged measures of field morphology and variability we tested could robustly distinguish between different levels of chemical driving or the presence of heterogeneous outer boundary heat flux. On the other hand, observational constraints requiring longitudinal variations in time-averaged inclination anomaly are readily matched by simulations with heterogeneous outer boundary thermal forcing, in contrast to those with homogeneous mantle heat flux. Longitudinal field structures are reduced, but not erased, by elevated chemical driving, which also promotes the formation and deepening of polar minima in the radial magnetic field. Our simulations indicate that both the strong heat flux heterogeneity and chemical driving in Earth's core are likely to result in small but persistent departures from the geocentric axial dipole approximation.

Moment closures at odd truncation order present a fundamental difficulty: the standard Gramian closure saturates the realizability boundary, producing only weak hyperbolicity and failing to preserve Maxwellian equilibrium. We show that every odd-order closure for the one-dimensional kinetic equation admits a decomposition into a boundary term, given by the Schur complement of the Hankel moment matrix, and a positive margin above it. An exact polynomial identity connects this margin to the eigenvalues of the flux Jacobian, reducing hyperbolicity to a root-splitting problem. A dimensional argument proves that no margin depending only on density, velocity, and temperature can produce a hyperbolic system for $M \geq 5$. A one-parameter family $C_{\eta,n}$, $\eta \in [0,1]$, built from normalized Schur-complement ratios, reveals that the Morin-McDonald closure is the arithmetic endpoint. The weighted AM-GM inequality orders the family: the geometric endpoint ($\eta = 0$) is 2-4% more accurate on bimodal benchmarks, while the arithmetic endpoint ($\eta = 1$, Morin-McDonald) is the most robust. All members share the same equilibrium Jacobian, whose spectral radius is 13% ($M = 5$) to 29% ($M = 13$) smaller than Grad's closure, allowing larger CFL time steps. A linearized entropy exists for all $M$, and the BGK source dissipates it near equilibrium; a smooth nonlinear entropy exists for $M = 3$ but provably does not for $M \geq 5$. The closure is validated on bimodal and Mott-Smith benchmarks, achieving errors 10-40x smaller than the Gramian or Grad closures, and demonstrated in free-transport Riemann problems at $M = 5, 7, 9, 11$ and BGK Riemann problems at $M = 5$ and $9$.

We prove a three-dimensional positive-cone continuation criterion for the stress-diffusion-free Oldroyd-B system on the periodic torus. Writing the positive conformation tensor as A = exp(B), we show that finite-time breakdown of a strong H^s solution, s > 5/2, can occur only through loss of the logarithmic spectral envelope of A or divergence of the endpoint vorticity clock given by the time integral of the B^0_{infty,1} norm of curl u. The proof combines compact positive-cone envelopes, endpoint Biot-Savart estimates, and high-order logarithmic conformation estimates, without using stress diffusion. We also derive a positive-cone Reynolds admissibility criterion with an exact residual-work cost. The least L^2 conformation residual needed to pay positive pressure-free residual work is determined by the entropy-dual lever G = I - A^{-1}, and this cost degenerates quantitatively near the equilibrium A = I. Together, the two criteria identify the same positive-cone obstruction in the strong and relaxed regimes: before breakdown one must control the endpoint flow clock on a compact logarithmic cone, while after passage to a relaxed description positive residual work must be paid for by an exact entropy-dual conformation defect.

We prove sharp residual-work criteria for entropy-admissible Reynolds states in viscoelastic models whose elastic variables are constrained by a positive cone or by a finite-extensibility domain. The argument is formulated for an entropy-dual class of closures in which the entropy lever and the elastic stress satisfy a compatibility relation. For the stress-diffusion-free Oldroyd-B system, written in positive-cone variables A=e^B, we derive an exact defect-work identity and remove pressure and mean modes from the momentum residual. The resulting pressure-free admissibility condition is a signed work inequality coupling the conformation residual to the entropy-dual lever I-A^{-1}. The criterion gives the optimal pointwise cost, the unique aligned minimizing residual, a windowed three-channel alternative, and closed exclusion tests for structured families. We also prove the corresponding entropy-dual closure theorem and recover the FENE-P case as a finite-extensibility corollary. A concrete finite-thickness shear-layer construction shows that positive pressure-free work can outrun the available lever-residual-alignment budget, giving a gauge-invariant residual-level obstruction.

This paper presents a neural surrogate approach for improving the accuracy of natural convection problems simulated with a Boussinesq flow model (incompressible flow with heat transfer). Our approach, based on Fourier neural operators, uses training data consisting of matched pairs of simulations run under the computationally cheaper yet less accurate Boussinesq flow model and a more computationally expensive and more accurate compressible flow model. In both cases, we implement our parallelized simulation codes based on an implicit monolithic mixed finite element method (FEM) approach using the open-source FEniCSx framework. Our implementations are validated against a commercial software package, COMSOL, as well as standard test problems from the literature. We include a careful discussion and analysis of data set generation and present learning results in two and three spatial dimensions. Using compressible flow results as high-fidelity reference solutions, our learning approach, with a single model evaluation per simulation, substantially improves the per-channel accuracy of Boussinesq predictions, with structural similarity (SSIM) close to unity across all flow variables and test distributions and corresponding mean-squared error reductions of one to nearly three orders of magnitude. All code and data is released as open-source.

This paper proves geometric continuation criteria for two-dimensional stress-diffusion-free Oldroyd--B and FENE-P flows. In both models the conformation tensor is transported and stretched without spatial diffusion, while the elastic stress enters the viscous velocity equation through one derivative. The positive-cone geometry is encoded by the logarithmic variable B=Log C. For Oldroyd--B this leads to two possible continuation obstructions: loss of the endpoint velocity-gradient Besov modulus and concentration of logarithmic conformation. For FENE-P the state space is smaller, D_b={C in S_{++}^2: tr Cinfinity; at fixed b, however, the finite-extensibility barrier is an independent high-frequency obstruction.

We present a scalable time-based molecular dynamics (TBMD) framework for simulating single-bubble sonoluminescence within a hybrid continuum-MD formulation. Unlike prior event-based approaches, which model gas dynamics through instantaneous hard-sphere collisions, the present method integrates continuous Lennard-Jones and damped shifted force Coulomb interactions at each timestep, enabling self-consistent tracking of ionization state and long-range electrostatics throughout the collapse. To bridge the gap between the physical particle count ($N_\mathrm{real}\sim 10^{10}$) and computationally tractable ensemble sizes, we introduce an ensemble particle (EP) scaling formalism that preserves temperature, pressure, and ionization statistics while reducing the simulated particle count by up to four orders of magnitude. Applying the framework to argon under standard single-bubble sonoluminescence driving conditions, we perform a systematic sweep over the ionization model and thermal accommodation coefficient $\alpha_t$, with ensemble sizes up to $N_\mathrm{ensem} = 10^8$ particles. The results establish that ionization is the dominant regulator of peak temperature, reducing $T_\mathrm{max}$ by approximately a factor of two relative to the non-ionizing baseline, while $\alpha_t$ primarily controls the spatially averaged temperature at the collapse minimum. Scalar observables at $N_\mathrm{ensem} = 10^8$, including peak temperature, minimum bubble radius, and maximum wall velocity, are assessed against prior studies to help validate the EP scaling formalism and our hybrid continuum-MD framework.

Every Cartesian three-dimensional PDE solver hides a structural secret that production CFD codes have used for half a century and that graduate-level textbooks rarely state plainly. The derivative matrices, the compact Padé line solves, the Galerkin mass inversions, the alternating-direction-implicit substeps, and even the fast Poisson and Helmholtz diagonalization transforms all factor along the coordinate axes and collapse into repeated one-dimensional banded kernels executed along the grid lines. The three-dimensional operator exists only on paper; it is never assembled, factored, or stored. This paper is the manual for that collapse. We derive the Kronecker-product algebra that makes it exact, carry it cleanly through central differences, compact schemes, tensor-product Galerkin, B-spline and isogeometric methods, collocation, ADI time stepping, and direct Poisson and Helmholtz solves, and bring into the open the three production tricks that turn the reduction into hardware-conscious floating-point throughput on real machines: the multi-right-hand-side reshape that exposes a sweep as one batched line kernel (a dense BLAS-3 GEMM when the line factor is dense or element-local, a banded or stencil kernel when it is not), the sum factorization that rescues high-order Galerkin from the $O(p^{2d})$ quadrature trap, and the pencil decomposition that keeps every direction contiguous across an MPI cluster. For fixed stencil width or fixed polynomial degree, the compute cost stays $O(N)$ in the total number of unknowns $N = N_x N_y N_z$; the operator storage drops to $O(N_x + N_y + N_z)$ up to bandwidth constants; direct separable Poisson and Helmholtz solvers add the expected transform cost; the line kernels are embarrassingly parallel. These facts are familiar to practitioners but rarely assembled in one place; this paper collects them and shows how to use them.

Stellar toroidal magnetic fields are known to be unstable to the Tayler instability. Here we demonstrate the existence of a complementary current-driven instability of essentially arbitrary toroidal-field configurations in stably stratified nonrotating stars with the following properties: (i) in ideal magneto-hydrodynamics, it grows on the Alfvén timescale $\tau_{\rm A}$; (ii) under certain conditions, it may reveal itself by driving shellular differential rotation about an arbitrary axis perpendicular to the magnetic-field symmetry axis; (iii) it is large-scale in the angular directions $\theta$ and $\varphi$, and develops at radial wave-numbers $k \lesssim \mathcal{N}\tau_{\rm A}/R$, where $\mathcal{N}$ is the Brunt-Väisälä frequency and $R$ is the stellar radius. Thus, unlike the Tayler instability, the proposed instability is intrinsically global. Consequently, it may be less susceptible to dissipative suppression than the Tayler instability and can prevail over it in some regimes. This instability may have broad implications for magnetic field generation in stars and could modify scenarios of magnetic field amplification within the Tayler-Spruit dynamo, contributing to models of efficient angular-momentum transport and chemical mixing in stellar interiors.

In the three-rotor problem, three equally massive point particles move on a circle interacting via attractive pairwise cosine potentials. Rotors can represent superconducting phases of distinct metallic segments in a chain of coupled Josephson junctions. We propose a digitization of the classical dynamics that records successive pair and triple coincidences of rotors using four symbols. Rotor coincidences correspond to boundaries in a disjoint partition of the configuration torus into cells where the rotors are ordered clockwise and anticlockwise. It is shown that isolated rotor coincidences must be crossings. Despite being a rather coarse digitization, we find that replacing trajectories by coincidence symbol sequences captures significant qualitative features of the dynamics through word statistics. Word-complexity $C_n$ measures the diversity of $n$-letter words in the symbol sequence while topological entropy governs asymptotic exponential growth of $C_n$. Sequences from periodic orbits have a word-complexity that saturates at the period. Ultra-high-energy trajectories with irrational 'slope' are quasiperiodic. We show that they have zero entropy and $C_n = n+3$ by examining limiting slopes and by a mapping to Sturmian sequences. We examine their grammar rules and propose how their right-special words may be identified. On the other hand, numerical investigation of sequences from chaotic orbits in the band of global chaos leads us to conjecture an exponentially growing word-complexity $C_n = 3 \times 2^{n-1}$, corresponding to a topological entropy $\log 2$. We identify their grammar rules and model them by a subshift of finite type, unlike the quasiperiodic ultra-high-energy sequences which cannot be modeled as a topological Markov shift.

Takens' theorem is the gold standard for attractor reconstruction from time series, but it guarantees only topological equivalence and does not preserve metric or group properties such as symmetries. We show that switching from delay-coordinate space to jet space (signal and its derivatives) allows one to exactly preserve the symmetry group of the original system. This statement is rigorously justified by a theorem on the isomorphism of Lie algebras under jet prolongation. Numerical experiments on the Lorenz and Rössler systems confirm that jet-space reconstruction preserves geometry and symmetries, whereas Takens embedding distorts them. As quantitative metrics we use a variational elastic energy functional and the correlation dimension. It is shown that jet-space reconstruction not only outperforms Takens embedding but in some cases yields more accurate estimates of invariants than projections of the original system. The proposed approach provides a coordinate-invariant criterion for the classification of strange attractors and can serve as a basis for detecting hidden attractors.

In confined space, deviations from bulk structure and properties are expected due to additional thermodynamic variables. In particular, composition variations arising from surface interactions may lead to additional phases and altered phase transitions. Here, we introduce a non-invasive method for nanoscale composition mapping in confined liquids using the surface force balance (SFB). The method extends conventional SFB analysis from apex measurements to spatially resolved reconstruction of refractive index profiles within confined fluids. When multiple phases are present, the refractive index profiles provide direct access to the position and geometry of the nanoconfined fluid interfaces. We describe the interferogram analysis in detail and establish its range of validity through two model scenarios. First, measurements in air demonstrate the precision of the method and allow detection of a nanometric wetting capillary. Second, we analyse dynamic evaporation of a confined heptane droplet down to 0.1 pL volume. The method provides a time-resolved reconstruction of the meniscus geometry throughout the evaporation process. Although evaporation continuously drives the system out of equilibrium, the meniscus remains well described by a catenoidal geometry down to heights of approximately 80 nm. At smaller separations, systematic deviations from the catenoidal profile emerge, indicating a crossover from a surface tension-dominated regime to a confinement-dominated regime. Overall, we demonstrate composition profiling as a framework to analyse confinement-induced composition variations and to quantify interfacial thermodynamic effects at the nanoscale.

Vapor-deposited organic glasses can show enhanced kinetic stability relative to liquid-cooled glasses. When such stable glasses of model glassformers are annealed above the glass transition temperature Tg, they lose their thermal stability and transform into the supercooled liquid via constant velocity propagating fronts. In this work, we show that vapor-deposited glasses of an organic semiconductor, N,N-bis(3-methylphenyl)-N,N-diphenylbenzidine (TPD), also transform via propagating fronts. Using spectroscopic ellipsometry and a new high-throughput annealing protocol, we measure transformation front velocities for TPD glasses prepared with substrate temperatures (TSubstrate) from 0.63 to 0.96 Tg, at many different annealing temperatures. We observe that the front velocity varies by over an order of magnitude with TSubstrate, while the activation energy remains constant. Using dielectric spectroscopy, we measure the structural relaxation time of supercooled TPD. We find that the mobility of the liquid and the structure of the glass are independent factors in controlling the thermal stability of TPD films. In comparison to model glassformers, the transformation fronts of TPD have similar velocities and a similar dependence on TSubstrate, suggesting universal behavior. These results may aid in designing active layers in organic electronic devices with improved thermal stability.

Previous work has shown that vapor-deposition can prepare organic glasses with extremely high kinetic stabilities and other properties that would be expected from liquid-cooled glasses only after aging for thousands of years or more. However, recent reports have shown that some molecules form vapor-deposited glasses with only limited kinetic stability when prepared using conditions expected to yield a stable glass. In this work, we vapor deposit glasses of 2-ethyl-1-hexanol over a wide range of deposition rates and test several hypotheses for why this molecule does not form highly stable glasses under normal deposition conditions. The kinetic stability of 2-ethyl-1-hexanol glasses is found to be highly dependent on the deposition rate. For deposition at Tsubstrate = 0.90 Tg, the kinetic stability increases by 3 orders of magnitude (as measured by isothermal transformation times) when the deposition rate is decreased from 0.2 nm/s to 0.005 nm/s. We also find that, for the same preparation time, a vapor-deposited glass has much more kinetic stability than an aged liquid-cooled glass. Our results support the hypothesis that the formation of highly stable 2-ethyl-1-hexanol glasses is inhibited by limited surface mobility. We compare our deposition rate experiments to similar ones performed with ethylcyclohexane (which readily forms glasses of high kinetic stability); we estimate that the surface mobility of 2-ethyl-1-hexanol is more than 4 orders of magnitude less than that of ethylcyclohexane at 0.85 Tg.

The dynamics of flexible polymers and chains under follower activity is known to produce diverse nonequilibrium states. A prominent feature of such systems is the emergence of periodic motion arising from the coupling between internal activity and chain conformation. Recently, it has been shown that flexible and extensible chains of active particles exhibit rich dynamical patterns in the overdamped limit, where inertia is negligible. Here, we study the complex dynamics of a flexible and extensible chain of active particles under follower activity when inertia is significant. Using numerical simulations, we quantify the chain dynamics as a function of chain length ($N$), segment mass, and activity. To rationalize the numerical results, we develop theoretical descriptions in the limit of short chains ($N=3$) and long chains ($N \gg 1$). In both these limits, we derive approximate expressions for the bond lengths and bond angles along the contour, which show excellent agreement with the numerical results. In addition, for short chains, we derive the stability conditions for a periodic motion as a function of segment mass and activity. For long chains ($N\gg1$) we identify parameter regime in which the circular, periodic solution becomes structurally unstable. Our theoretical and numerical analysis provides insights into the emergence of ordered and periodic behaviour in active chains.

Hydrodynamic memory governs Brownian motion over a broad range of timescales, from acoustic wave propagation at short times to diffusive relaxation at long times. While confinement-induced corrections to Brownian diffusion are well established, how confinement modifies the full hydrodynamic response remains less explored. In this Letter, we use molecular-dynamics simulations of a neutrally buoyant colloidal particle in an explicit solvent to resolve the velocity autocorrelation function across a broad hydrodynamic spectrum. In the bulk, the simulations recover compressibility, added mass, the hydrodynamic long-time tail, and Stokes-Einstein diffusion without adjustable parameters. Near a rigid wall, the velocity correlations become anisotropic, their algebraic tails are modified, and the diffusion coefficients are reduced. Most importantly, the short-time dynamics reveals a pronounced enhancement of the effective added mass as the wall is approached. As such, the velocity autocorrelation function appears as a central quantity to bridge the zero-frequency mobility and the high-frequency inertial behaviour of a confined Brownian particle.

We computationally investigate how environmental sensitivity of active matter interacts with soft confinement to shape collective dynamics. In our model, the active constituents are represented as self-propelled particles (SPPs), implemented as nematic, disjoint ring polymers whose direction of motion can reverse without tumbling. Coarse-grained molecular dynamics simulations reveal that collective dynamics arise from a three-way feedback between active stresses, boundary elasticity, and particle-level memory. With increasing driving force, FD, this feedback generates a sequence of collective dynamical regimes. At low FD, SPP motion is dominated by thermal fluctuations. At intermediate FD, coherent vortical motion emerges with intermittent, noise-driven reversals. With further increase in FD, reversals are suppressed, yielding sustained unidirectional vortical motion. At sufficiently high FD, the system transitions to a polar state characterized by strong nematic ordering of the SPPs, symmetry breaking of the enclosure shape, and persistent polar collective motion. In this regime, the SPPs accumulate at the leading edge of the enclosure, driving sustained ballistic propulsion. These results demonstrate how environmental sensitivity and soft confinement jointly regulate emergent collective states and identify boundary elasticity as a control parameter governing the balance between vortical and ballistic dynamics.

Active filaments, ranging from motor-driven biopolymers to elongated bacteria and worms, are paradigmatic examples of deformable active matter. How filament flexibility interacts with environmental heterogeneity to control their transport in crowded environments, however, remains poorly understood. Here, we perform large-scale Brownian dynamics simulations of tangentially driven active polymers moving through ordered and disordered obstacle arrays to map the long-time diffusion as a function of obstacle density and filament flexibility. We find that flexibility can either enhance or hinder transport depending on the structure of the medium. In disordered environments, transport is optimized at intermediate filament flexibility, whereas both highly flexible and semiflexible filaments diffuse more slowly. In contrast, dense ordered arrays enhance the mobility of semiflexible filaments by promoting directed motion along periodic channels. We identify three distinct transport regimes: (i) tortuosity-controlled diffusion of highly flexible filaments, characterized by trapping-and-hopping dynamics; (ii) confinement-assisted transport of moderately flexible filaments, which enhances diffusion in dense media; and (iii) persistence-controlled transport of semiflexible filaments, which facilitates diffusion in dense ordered media, but suppresses it in disordered media. Combining theory and simulations, we show that long-time diffusion is governed by confinement-induced changes in filament conformation and reorientation dynamics. Our work uncovers general transport principles for deformable active agents in heterogeneous environments and provides a predictive framework for active-filament navigation in complex porous landscapes.

We compare two different soft matter models, a generalized Random Organization Model (ROM) describing the stroboscopic dynamics of cyclically sheared suspensions, and an elastoplastic model describing the mesoscale dynamics of a yield-stress fluid under imposed stress. Both show absorbing phase transitions, sharing a peculiar mechanism: activity induces an internal noise which is transmitted over large distances by long-ranged mediated interactions, either hydrodynamic or elastic, which results in non-local creation of activity. They also both show convex transitions (i.e., the exponent $\beta >1$), in stark contrast with usual absorbing phase transitions, like (Conserved) Directed Percolation, which are concave ($\beta <1$). We further compare the dependence of the critical properties (activity mean value and fluctuations, avalanche statistics, low-wavenumber structure factor) on the decay exponent $\alpha$ of long-range interactions in both models, finding a qualitatively similar scenario. A smooth crossover is observed as a function of $\alpha$ between a concave transition regime for short-range interactions, with diverging fluctuations and compact avalanches, and a convex transition regime, with vanishing fluctuations and non-compact avalanches, for longer-range interactions. Although for a given range exponent $\alpha$, the values of critical exponents for both models differ, a good agreement between the models is found by parametrically plotting the different critical exponents as a function of the exponent $\beta$ of the mean activity. In this parametric representation, the concave regime is consistent with the behavior of the Long-Range Conserved Directed Percolation class, while the convex regime can be accounted for by a mean-field-type scenario with anomalous diffusion close to an absorbing boundary, inspired by the Hébraud-Lequeux model for the yielding transition.

Intelligent active particles are characterized by self-propulsion, directional sensing of their environment, information processing, decision making and goal-oriented self-steering. This implies, in particular, the prevalence of non-reciprocal interactions, and the importance of information propagation through agent groups. Examples include biological systems (cells, insects, birds, fish, pedestrians) as well as engineered systems (nano- and microbots). As many agents move in an aqueous medium, hydrodynamic interactions strongly affect the dynamics. The emergent dynamics includes the formation of swarms and flocks, predator-prey behavior, and the navigation in complex environments.

Cryogenic phase-change phenomena play an important role in a wide range of engineering applications, including cryogenic cooling systems, superconducting technologies, and space propulsion systems. In particular, the three-phase contact line is recognized as a key region governing evaporation and heat transfer. However, direct measurements of temperature distributions near cryogenic three-phase contact lines remain limited because conventional infrared thermography becomes increasingly difficult at extremely low temperatures. In this study, a two-color temperature-sensitive paint (2C-TSP) technique was applied to visualize the temperature field around a liquid-nitrogen three-phase contact line. A temperature-sensitive dye and a temperature-insensitive reference dye were incorporated into a single coating, enabling robust temperature measurements based on luminescence intensity ratios by compensating for changes in optical intensity caused by refraction and reflection at the liquid-gas interface. Temperature distributions were measured under three heating conditions with heat fluxes of 110, 430, and 900 W/m2. The measured temperature fields revealed a localized temperature minimum at the observed three-phase contact line, suggesting localized cooling associated with phase change. Quantitative analysis showed that the average temperature in the liquid region remained nearly constant, whereas the temperature in the gas region increased with increasing heat flux. These observations reveal a non-uniform thermal structure around the cryogenic three-phase contact line. The present results demonstrate that 2C-TSP is a promising technique for direct visualization of temperature fields around cryogenic three-phase contact lines and provides new insights into phase-change phenomena in liquid nitrogen.

Fibre recruitment plays an important role in tendon and other biological soft tissue mechanics. Due to their large water content, a popular modelling approach for tendons is poroelasticity. Within this framework some tendon studies have included fibres, though none have included crimped fibre recruitment. We present a one dimensional poroelastic model in which the solid skeleton is composed of a soft neo-Hookean background matrix and crimped fibrils which do not bear load (FIB model). As the tissue is stretched, fibrils are straightened and contribute to load bearing. The fibre-reinforced tissue is compared to a tissue with a purely neo-Hookean (NH) skeleton in response to a uniaxial constant applied load (loading) and release of the load (unloading). The system dynamics are governed by a diffusion equation where the diffusion coefficient depends on stiffness. Within tendon parameter ranges, the FIB model is softer than the NH model, and so approaches steady state more slowly during loading. The presence of crimped fibrils allows the tendon to stretch further without excessively straining the fibrils or the NCM, providing a natural protection mechanism for the tendon's structural components to load, in agreement with experiments. During unloading, the FIB model is much slower to relax as the tissue softens due to fibril re-crimping. This asymmetry in loading and unloading manifests as a hysteresis loop in the stress-strain curve averaged over the tendon. The hysteresis is reduced with increasing applied load. The inclusion of fibrils allows for clearer biological interpretation and potential comparison to data. While the stress law employed in this study is bespoke for the application at hand by accounting for crimp and fibril recruitment, other fibril constitutive laws can readily be considered and incorporated into this framework.

Topological defects play a central role in the mechanical behavior of crystalline materials, yet their relevance to amorphous solids has only recently begun to emerge. Over the last few years, theoretical, computational, and experimental studies have revealed the presence of well-defined topological invariants in vibrational eigenmodes, non-affine displacement fields, and deformation-induced vector fields of glasses. These defects have been shown to correlate strongly with soft spots, localized plastic rearrangements, yielding, and shear-band formation, suggesting a new perspective on the microscopic origins of plasticity in disordered materials. In this review, we provide a comprehensive overview of recent developments in the rapidly growing field of topological defects in glasses. We discuss the underlying theoretical concepts, including Burgers vectors, non-affine plasticity, vibrational modes, and topological invariants, and review recent numerical and experimental advances. Finally, we assess the current achievements, limitations, and open questions, and discuss future directions toward a unified topological description of plasticity and mechanical failure in amorphous solids.

In 1966, Hohenberg, Mermin and Wagner proved that long-wavelength fluctuations destabilize the long-range order of continuous symmetry in two-dimensional (2D) systems. Later in the 1970s, Berezinskii, Kosterlitz and Thouless developed the BKT theory describing an unconventional phase transition between quasi-long-range and short-range order in 2D systems driven by the binding-unbinding of topological defects, which has become a fundamental topic in statistical mechanics, condensed matter physics, and soft matter physics. One of the most important applications of the BKT theory is the melting of 2D crystals, whose mechanisms are not yet fully understood. Recently, this topic has been extended to the area of active matter, where the non-equilibrium nature leads to novel phenomena that deviate from the Hohenberg-Mermin-Wagner theorem. In this review, we first focus on the recent theoretical and computational progress in the 2D melting problem in passive systems, and then summarize the inspiring results obtained from non-equilibrium systems. The review closes with comments on several promising directions for predicting 2D melting scenarios and for understanding the non-equilibrium nature in 2D active matter systems.

Physics-informed surrogate models can accelerate computational fluid dynamics simulations. However, many existing methods reproduce global flow patterns more reliably than localized multiscale structures. This study presents a physics-informed Fourier-wavelet transformer for next-step velocity-field reconstruction in real-world flow benchmarks. The proposed formulation combines hybrid Fourier-wavelet spectral encoding with physics-biased self-attention based on partial differential equation residual diagnostics. It also uses self-supervised pretraining through Masked Physics Prediction and Equation Consistency Prediction. The experiments are conducted on two real benchmark cases: cylinder-wake flow and fluid-structure interaction. All approaches are evaluated under a shared local protocol and compared with spectral, transformer-based, operator-learning, and physics-informed neural-network baselines. On the cylinder-wake benchmark, the proposed model achieves the best aggregate accuracy, with an all-channel normalized mean-squared error of 0.05875 and an all-channel Pearson correlation coefficient of 0.97019. On the fluid-structure-interaction benchmark, it gives the lowest all-channel normalized mean-squared error of $2.70 \times 10^{-4}$, compared with $4.02 \times 10^{-4}$ for the strongest baseline. Component-wise field comparisons and scale-separated diagnostics further show stronger recovery of localized wake structures, including near-body, wake-core, and far-wake features. The results demonstrate improved real-world flow reconstruction while maintaining a practical accuracy-cost tradeoff.

We investigate how the influence of a free surface is transported in turbulent open channel flow by analysing matched open- and closed-channel direct numerical simulations up to $Re_\mathrm{\tau} \approx 900$ in a domain large enough to accommodate very-large-scale motions (VLSMs). The turbulent kinetic energy (TKE) budget shows that the surface influence is communicated primarily through transport terms. Near the free surface, pressure transport supplies energy towards the interface, whereas turbulent transport and dissipation are reduced; the resulting energy surplus is exported away from the surface predominantly by viscous diffusion. The near-surface budget terms do not exhibit a single universal similarity scaling: viscous diffusion is organised over the near-surface viscous scale $\ell_\mathrm{V}$, dissipation over the Kolmogorov sublayer scale $\ell_\mathrm{K}$, and pressure-related terms require the mixed velocity scale $u_\mathrm{b} u_\mathrm{\tau}^2 /h$. The pressure-strain redistribution further reveals outer-inner coupling: although intense pressure-strain events remain small-scale, their magnitude and directional bias are organised by low-velocity VLSM streaks. The free-surface influence is therefore best understood as a coupled multi-scale process involving local kinematic constraints, Reynolds-number-dependent surface layers, and outer-layer coherent motions.

Turbulent fluxes in the atmospheric boundary layer (ABL) govern exchanges of momentum, heat, and mass between the surface and atmosphere, shaping boundary layer structure and influencing weather, climate, and engineering applications. Yet their representation in coarse resolution models remains challenging, particularly under unstable conditions with strongly nonlocal transport and stable conditions with intermittent turbulence. Here, we develop a data driven turbulent flux parameterization in which nondimensional fluxes are represented by a linearized convolution operator acting on nondimensional mean state profiles. We train and evaluate the closure using high resolution large eddy simulations (LES) of idealized flow over homogeneous surfaces spanning multiple stability regimes. Several first order closure variants are constructed from different combinations of mean temperature and velocity profiles to predict heat and momentum fluxes, and the best model is selected by minimizing mean squared error across training and unseen test cases. The resulting parameterization improves predictive skill relative to a standard K-profile closure while retaining an interpretable operator form. Its learned kernels expose the locality and nonlocality of turbulent transport across stability regimes, linking empirical performance to physically inspectable flux--profile relationships. In a posteriori single column simulations, the closure remains stable and produces state profiles that closely match LES, demonstrating its potential as an accurate and transparent ABL flux parameterization.

An analytical formulation of the fluid-structure interaction of a flexible foil driven by an oscillating force actuating on its elastically mounted leading edge, so that it can heave, pitch and deform passively with the hydrodynamic forces, is used to investigate the aquatic locomotion of a body, responsible for the whole drag and thrusted by the oscillating flexible foil. The small-amplitude theoretical model is validated with previous theoretical and experimental results for a body propelled by a rigid plate oscillating with a prescribed heaving motion and passive pitch. The inclusion of passive heave and deformation allows to expand the parametric ranges for optimal self-propulsion conditions in terms of length travelled by flapping cycle (stride length) and locomotion efficiency. In addition to the known optimal locomotion condition localized near the resonance of the torsional spring on which the foil is elastically mounted, which here is modulated by its coupling with the resonances of the translational spring and of the structural deformation of the foil, another even better local optimal locomotion condition is found near the translational spring branch of the elastic support resonance that occurs at lower stiffnesses of both springs. Unlike the local maximum of efficiency close to the natural frequency associated with the torsional spring branch, which increases with the stiffness of the foil, being the highest for a rigid foil, the larger local maximum associated with the translational spring branch increases as the stiffness of the foil decreases.

We compare two geometric stochastic frameworks for the two-dimensional Euler equations, being the circulation-preserving stochastic advection by Lie transport (SALT) and the energy-preserving stochastic forcing by Lie transport (SFLT) approaches. While preserving both circulation and energy is ideal, their simultaneous conservation restricts perturbations to a stochastic reparametrization of time. Consequently, a fundamental choice must be made between preserving structure or the kinetic energy. Analysis reveals that SALT is significantly more sensitive to high-frequency flow components, with noise effects scaling by $| \bk |^2$ relative to SFLT. This suggests that SALT acts as a localized perturbation sensitive to sharp gradients, while SFLT behaves as a more regularized global forcing. Numerical experiments on a traveling dipole, vortex merger, and forced-damped turbulence confirm that SALT introduces uncertainty localized near dynamically active vorticity gradients, whereas SFLT produces a more diffuse variance field spread across the domain. These results illustrate how the choice of geometric invariant fundamentally determines scale-sensitivity and spatial distribution of modeled uncertainty in vortex dynamics.

Traditional time-domain prediction of vessel motions in irregular waves usually relies on superposing responses from many regular-wave components, which is computationally expensive for long-duration simulation and real-time applications. This issue is particularly relevant to unmanned surface vehicles (USVs), for which efficient and realistic motion prediction is needed for seakeeping assessment, simulation-based testing, and control-system development. This study applies an impulse response function (IRF)-based time-domain framework to predict vessel motions in short-crested irregular waves. Froude-Krylov, diffraction, and radiation loads are obtained from frequency-domain analysis and transformed into the time domain. Instantaneous responses are then evaluated directly through convolution-based force reconstruction, reducing the need for repeated regular-wave simulations. Weak nonlinear restoring effects are included by instantaneous wetted-surface pressure integration, and directional wave spectra are used to represent realistic sea states. The framework is validated against model-test measurements of an offshore supply vessel in long-crested beam irregular waves and full-scale measurements of a USV operating in real sea conditions. Predicted significant amplitudes, mean zero-crossing periods, standard deviations, and motion time histories agree well with measurements. The effect of directional-spectrum discretization is also examined. Results show that motion amplitudes are moderately sensitive to directional resolution, whereas motion periods are relatively insensitive. A 30 deg directional interval provides a practical balance between prediction accuracy and computational cost. The proposed framework offers an efficient tool for high-fidelity time-domain prediction of USV motions in realistic directional irregular seas.

Diffusive-convective (DC) staircases in the ocean are observed across a wide range of settings, but their formation, structure, and persistence are not fully understood. Theories for DC staircases are reviewed to identify mechanisms governing their development and evolution. Staircase evolution through layer merging and possibly interface splitting, including the relationship to background turbulence, is assessed. Oceanographic examples illustrate the variety of settings in which DC staircases are found, and how they can persist under weak turbulence but are disrupted when turbulence becomes sufficiently strong. Key open questions are identified, highlighting the challenge of linking small-scale processes to the large-scale coherence and persistence of DC staircases in the ocean.

Skewed turbulent shear layers, formed by the interaction between two non-aligned turbulent boundary layers, are investigated using high-fidelity large eddy simulations in a temporally evolving framework. It is argued that a skewed shear layer of this form should be viewed, in the long-time limit, in a rotated reference frame as the superposition of a standard planar shear layer and an orthogonal jet-like component that decays in time. The skewed shear layer is found to have reduced vertical integral length scale, and the coherent pressure rollers characteristic of shear layers undergo transient realignment towards the direction orthogonal to mean shear, consistent with the long-time limiting planar shear layer. Numerical experiments using fictitious test cases indicate that these effects are primarily driven through misalignment in the mean flow, and that the two orthogonal flow components in the mean shear frame are only weakly coupled.

Droplet impact on solid surfaces is a complex fluid dynamics problem with applications in spray cooling, inkjet printing, and pharmaceutical processing. Although numerical simulations are widely used to investigate these dynamics, their computational cost becomes significant when multiple parametric variations are considered. In this work, we investigate the use of a Video Vision Transformer (ViViT) architecture to predict the temporal evolution of viscoelastic droplets impacting solid surfaces using volume fraction fields obtained from the Volume of Fluid (VOF) method. In Newtonian fluids, impact dynamics are mainly characterized by the Reynolds number $Re$, representing the ratio of inertial to viscous forces, and the Weber number $We$, representing the ratio of inertial to surface tension forces. For viscoelastic fluids, additional parameters are required to account for elastic effects, namely the solvent viscosity ratio $\beta$ and the Weissenberg number $Wi$, increasing simulation complexity and cost. Instead of simulating the entire droplet dynamics, the proposed approach uses only the initial 10% to 20% of the simulation to predict the remaining evolution. Depending on the prediction configuration, this strategy reduces computational cost by approximately 80% to 90% compared to full numerical simulations. The ViViT produces physically consistent predictions across different parameters and prediction horizons, successfully capturing both spreading and bouncing regimes while preserving geometric features and structural similarity. Since volume fraction fields can also be extracted from experimental videos, the proposed framework could be extended to incorporate experimental data during training, potentially improving the physical fidelity of the predicted dynamics.

The proposed study is motivated by experimental evidence, dating back to 1985, demonstrating the possibility of deflagration-to-detonation transition (DDT) in a fuel-air cloud. The detonation is initiated by a flame jet developed in a thin open-ended tube inserted into the cloud. Despite the experimental data, a first-principle understanding of the mechanism controlling the transition is still missing. The current research is aimed at resolution of this issue through a simple 2D formulation involving minimum physical ingredients.

Data-driven reproduction of chaotic dynamics under partial observation remains a challenge despite its practical importance. Reservoir computing (RC) and other data-driven approaches often succeed in short-term prediction, yet they are sensitive to hyperparameters and fail to reproduce the long-term statistical properties of the system. We identify one cause of this failure: the reconstructed attractor set is placed in a transversally unstable region of the representation space. We therefore propose a design principle for RC that introduces a few slow modes into its evolution rule in advance, so that a designated attracting low-dimensional subspace retains the history of the input series. We show that this achieves attractor reconstruction in attracting subspaces (ARAS) and, without relying on a posteriori performance-based tuning, enables robust prediction and reproduction of chaos under partial observation.

We study the diatomic FPUT lattice with cubic anharmonic potential, and analyze the recurrent behaviour of its solutions. We find that two distinct types of recurrence occur. One type is the classic FPUT recurrence; for such recurrence, we find that the relation between recurrence period and nonlinear strength is similar to that in the monatomic case. The other type, which cannot exist in the monatomic lattice, is the recurrence due to the interactions between modes in the two branches of the dispersion relation. Indeed, we prove the existence of the optical-acoustical-acoustical resonant interaction between three Fourier modes for which a recurrent behavior in the distribution of the energy is observed. In addition, we develop a reduced Fourier-space dynamical model that reproduces the same recurrent behavior. We assess the robustness of our results through numerical simulations of the diatomic Toda lattice and the diatomic granular chain; in both cases, the same recursive behavior is observed. Finally, in the continuous limit, we derive from the diatomic model a system of three coupled PDEs which are known to be integrable.

Multi-dimensional chaos refers to processes described by erratic functions of several dynamical variables. In this letter we analyze the string scattering amplitudes of highly-excited states and ground states. We show that the amplitudes, which depend on a scattering angle and a polarization angle, are characterized by two sets of non-intersecting curves associated with the vanishing of the derivatives with respect to the angles. We introduce the notion of the "area eigenvalue" $A_n$ associated with the $n$-th curve. We compute the spacings $\delta_{n}= A_{n+1}-A_n$ and their ratios $r_{n}=\frac{\delta_{n+1}}{\delta_n}$. We show that the distributions of the spacing ratios take the form of the RMT Gaussian $\beta$-ensembles. The curves associated with the scattering angle tend to converge to the Gaussian Orthogonal Ensemble value of $\beta=1$ and those related to the polarization angle to the Gaussian Unitary Ensemble $\beta=2$. We also compute the ``areas form factor" associated with the areas and discover the regions of decline, ramp and plateau which characterize chaotic processes. The slope of the ramp seems to agree with the $\beta$ values extracted from the distribution of the spacing ratios.

Consider a smooth one-parameter family of vector fields defined over some smooth manifold transitions from order into chaos. Inspired by the Second law of Thermodynamics, one is led to ask: can we find a flow whose dynamics realize this transition? To answer this question, motivated by the Mallet-Yorke Orbit Index theory, the Arnold-Khesin scheme for hydrodynamics and a heuristic argument by Rene Thom, we introduce a construction that transforms any one-parameter family of vector fields into a new object: the "Entropy flow". The Entropy flow is a flow defined on the product of the phase space with the parameter space and is best thought of as a flow generated by the original one-parameter family together with a drift in the parameter space, that pushes the trajectory of a given initial condition into a disordered, more complex state. To exemplify, for the Period Doubling, the Ruelle-Takens-Newhouse and the Intermittency routes to chaos the Entropy flow behaves exactly as expected - that is, it truly pushes trajectories into more complex states. In addition, in the spirit of Forcing Theory, in the paper we use the Conley index to discuss how one can use the Entropy flow to study the connection between topology and bifurcations. Moreover, drawing on the numerical and analytic evidence, we will analyze how the Entropy flow behaves in several examples of famous flows, including the Lorenz system, the Rössler attractor, and the breakup of the Shilnikov homoclinic scenario.

We discuss phenomenology associated with turbulent hydrodynamics in quantum fluids from a condensed-matter perspective. We begin with weakly-interacting superfluids, often modeled by a mean-field theory governed by the Gross-Pitaevskii equation. Considering the effect of quantum fluctuations beyond the mean-field approximation, we propose a study of many-body quantum effects in turbulent hydrodynamics, especially near zero temperature. We motivate examples of quantum many-body systems where such effects may be uncovered. These include bosons confined in a periodic potential in low spatial dimensions (one and two), and the associated quantum critical point of the superfluid-insulator transition, realized in present-day ultracold-atom and quantum computing platforms. We conclude by listing a set of (open) questions that may be answered using modern quantum many-body techniques. This article is part of the theme issue 'Frontiers of turbulence and statistical physics'.

We propose a unified perspective on classical and quantum chaos based on the stability of a system's stationary states under slow driving. We probe this sensitivity via the system's susceptibility to the average protocol speed, which we call the ``speed-Fisher information," and relate it to irreversible entropy production in the system. We show that chaotic dynamics manifests as a divergence of the speed-Fisher information with the protocol time, and that this response is controlled by the perturbation's low-frequency spectral weight. This approach to chaos applies to both classical and quantum Hamiltonian systems, and naturally extends to non-Hamiltonian classical flows. We illustrate this framework with simple classical and quantum examples, along with a non-Hamiltonian flow that qualitatively exhibits analogous low-frequency spectral behavior.

We introduce the Quantum Split-Step Fourier (QSSF) algorithm for nonlinear optical waveguides, a numerical framework that combines split-step propagation of the nonlinear Schrödinger equation with a commutator-preserving Bogoliubov evolution of Gaussian quantum fluctuations. The method propagates the classical mean field together with the Bogoliubov matrices $U$ and $V$, from which reduced second moments, covariance matrices, symplectic eigenvalues, and entropic measures are constructed for arbitrary spectral windows. Applied to soliton-driven resonant radiation, QSSF shows that the selected radiation band acquires a steadily increasing von Neumann entropy and a corresponding loss of purity, quantifying its entanglement with the rest of the spectrum in the lossless Gaussian setting. The analysis also reveals a surprisingly pronounced low-dimensional structure: although the radiation occupies many Fourier bins, its reduced Gaussian state is dominated by only a few Williamson modes. QSSF therefore provides a practical information-theoretic diagnostic for quantum correlations in nonlinear frequency conversion, supercontinuum generation, and multimode squeezed-light formation in ultrafast waveguide platforms.

Demographic noise generates stochastic Turing patterns even when reaction-diffusion systems are deterministically stable. We show analytically and verify numerically in the Levin-Segel model that temporal integration of configurations reveals emergent large-scale organization. The intensive number variance in a window of size $R \gg 1$ approaches a finite reaction-kinetic floor as $1/R$, over a spatial range growing by orders of magnitude near the Turing instability. This yields an effectively hyperuniform, fine-tuning-free regime previously unidentified in non-conserved multispecies stochastic systems.

A variational minimum principle for linear elastodynamics of a possibly heterogeneous material without a stored energy function is developed. It involves a change of variables to dual fields, and results in a degenerate elliptic Euler-Lagrange system, even when the primal elastodynamics is hyperbolic. Uniqueness assertions for the dual dynamic and static problems and implications of the degenerate ellipticity are sketched. Some implications pertaining to heterogeneous materials and ones with indefinite elastic moduli are discussed.

This work addresses the problem of identifying colloidal monolayer assemblies using particles of various shapes (two-dimensional coatings): spheres, ellipsoids, cuboids, and rods. The following classification of assemblies is considered: isolated particles, dimers, chains, clusters, and loops. The YOLO model was chosen as the identification method. Synthetic datasets were prepared for each of the four particle shapes to train the models. The paper discusses the application of models trained on synthetic data to experimental images. An analysis was carried out on the feasibility of using such models for recognizing configurations in real images. While recognition on artificial images is nearly perfect, tests on experimental images showed a significant deviation. The average error across all particle types was 43.1%, but a considerable spread in values is observed: from 20% for spheres to 58.5% for cuboids, indicating the algorithm's selective sensitivity to object geometry. The created datasets and trained models are freely available for use. The corresponding modules have been integrated into the previously developed information system ( this https URL ). To further improve prediction results, it is necessary to prepare datasets based on experimental images.

We report classical molecular dynamics simulations of NaCl association and dissociation in supercritical aqueous fluids over a wide range of salt concentrations, from moderate salinity to highly concentrated H2O-NaCl mixtures attainable at high temperatures. The degree of dissociation a and the corresponding ideal dissociation constant Kd, derived directly from a, were calculated as functions of the stoichiometric NaCl mole fraction at selected pressure-temperature (PT) conditions from 673.15 to 1273.15 K and from 0.1 to 2 GPa. At moderate salinity corresponding to a molality of approximately 1 mol/kg, NaCl remains largely dissociated a = 0.3-0.7 depending on pressure and temperature). In contrast, when the mole fraction of NaCl increases up to xNaCl = 0.333 (27.8 mol/kg), the degree of dissociation tends towards zero, and most ions form Na$^+$Cl$^-$ contact pairs and multi-ion clusters. As a result of these competing trends, the mole fraction of structurally dissociated Na$^+$ and Cl$^-$ ions is a non-monotonic function of the stoichiometric NaCl concentration and typically reaches a maximum at xNaCl = 0.06-0.10. This result shows that increasing salinity does not necessarily increase the abundance of structurally available chloride ions in supercritical aqueous fluids. Additional fixed density simulations at 1 and 7 mol/kg extend the analysis up to 1673.15 K and separate the effects of temperature and density on the associate/dissociate state of the ions. The obtained concentration dependences provide molecular-level constraints for thermodynamic descriptions of concentrated supercritical electrolytes and for evaluating chloride availability in high-temperature aqueous fluids.

Granular flows in ambient fluids exhibit grain-size-dependent segregation, which is difficult to capture efficiently with existing models, especially in large-scale systems involving more than a million grains. We develop a two-way coupled framework that integrates heterarchical granular dynamics (HGD) with a fluid-fraction-weighted incompressible Navier-Stokes solver. This heterarchical granular-fluid dynamics (HGFD) model extends a previous HGD model for quasi-static deformations by introducing inertial, force-balance-driven particle velocities and consistent fluid-solid momentum exchange. The coupling between the inertial HGD and the fluid solver is performed using a staggered explicit sequential scheme and co-located Eulerian fields. The framework is evaluated against experimental data of (i) single-particle settling to verify inertial relaxation, (ii) hindered settling to reproduce concentration-dependent settling and vertical size stratification, and (iii) representative cases covering three reported segregation types to assess regime sensitivity. These results establish HGFD as an efficient and consistent approach for simulating fluid-coupled granular segregation dynamics.

The collective behavior of passive particles within chiral active matter has emerged as a significant area of soft matter research. However, most existing studies focus on systems where chirality is imposed by external torques rather than intrinsic activity. In this work, we study emergent dynamics in a suspension of active spinners and passive colloids by computing many-body hydrodynamic interactions via Ewald summation. By systematically exploring a broad range of area fractions and rotational velocities, we identify distinct phase-separation regimes sensitive to the system's kinematic parameters. Specifically, we report the emergence of unique structural morphologies, including the formation of passive particle vortices surrounding phase-separated active spinners and the development of large-scale active-passive bands. We characterize the underlying dynamics by analyzing the temporal evolution of characteristic length scales and the non-equilibrium velocity distributions of the passive particles. Our findings provide new insights into the role of long-range hydrodynamic couplings in governing the self-organization of non-equilibrium condensed matter.

Granular materials dissipate energy efficiently through intergranular interactions, yet their disordered, dense nature precludes precise control and integration into lightweight systems. Architected materials offer tunable mechanical responses at low densities but tend to localize stress, limiting dissipation efficiency. Here, we introduce hierarchical granular metamaterials that reconcile these trade-offs through three levels of design: lightweight architected grains engineered with hollow elliptical inclusions, crystal-inspired grain packings, and functional gradients and defects within grain tessellations. These metamaterials exhibit simultaneous increases in impact energy absorption per unit mass and reductions in transmitted peak force at low densities, outperforming conventional architected materials. In situ nanomechanical experiments and nonlinear computational models reveal that enhanced lateral grain expansion drives recruitment of neighboring grains, amplifying plastic and frictional dissipation. Multiscale impact experiments confirm that these mechanisms persist across length scales, constituent materials, and dimensionalities. Beyond mechanical performance, we demonstrate that spatially programmable inter-grain contact networks enable deterministic routing of deformation, which extends to electrical transport pathways independently of packing geometry. By combining granular principles with architected material design, this work establishes a paradigm for multifunctional metamaterials whose contact topology, mechanical response, and transport properties can be programmed independently.

Higher-order topological insulators (HOTIs) have revolutionized our understanding of wave localization, extending the bulk-boundary correspondence to lower-dimensional hinges and corners. Thus far, the realization of mechanical HOTIs has relied exclusively on discretely engineered metamaterials or periodic phononic lattices. Here, we report a fundamental paradigm shift by demonstrating that continuous, homogeneous hyperelastic manifolds undergoing finite multiaxial deformations naturally harbor intrinsic higher-order topological phases. By extending the generalized Stroh-Lie impedance formalism into a fully coupled 3D finite-strain framework, we map the highly nonlinear orthotropic geometric frustration onto a four-band effective Dirac Hamiltonian spanned by Clifford $\Gamma$-matrices. We reveal that macroscopic orthogonal stretches act precisely as competing Dirac mass terms, driving the continuous spatial transitions of topological domain walls and triggering a breakdown of $C_{4v}$ spatial symmetry. Remarkably, we analytically prove that beyond classical 2D surface wrinkling (1st-order topology), concurrent multiaxial extreme compression unconditionally triggers the emergence of 1D hinge states (2nd-order) and completely localized 0D zero-energy corner states (3rd-order). We further extend this static bifurcation framework into the elastodynamic regime, proving the existence of mid-gap localized vibrational modes. The theoretically derived topological phase diagram, nested Wilson loops, and fractional corner charges are comprehensively verified. Finally, we propose a concrete experimental realization using electro-active dielectric elastomers, enabling the dynamic programming of 0D topological singularities.

We conduct a comprehensive dynamical analysis of quasi-two-dimensional (Q2D) dispersions of Brownian particles with competing short-range attractive (SA) and long-range repulsive (LR) interactions using Langevin dynamics (LD) and multiparticle collision dynamics (MPC). As the attractive interaction is strengthened, self-diffusion is significantly suppressed, and clustering gives rise to pronounced subdiffusive behavior. We find that cluster lifetimes are influenced more strongly by attraction strength than by particle concentration. Two dynamical criteria for the transition from non-clustered to clustered phases are identified in terms of the mean cluster lifetime and the relaxation time of local hexagonal order, respectively. Moreover, clustered Q2D-SALR systems exhibit pronounced non-Gaussian dynamics. In particular, the self-van Hove function in the equilibrium-cluster phase displays an approximately exponential form, consistent with an underlying diffusing-diffusivity mechanism. Importantly, MPC simulations reveal the critical role of hydrodynamic interactions (HIs) in collective dynamics. We observe that the anomalously enhanced large-scale collective diffusion characteristic of hydrodynamically interacting Q2D systems is qualitatively preserved in Q2D-SALR dispersions. However, this enhancement suppresses the intermediate-range-order peak in the hydrodynamic function compared to its three-dimensional counterpart. Furthermore, by analyzing the time-dependent evolution of hydrodynamic function and the sound mode in hydrodynamic correlations, we find that clustering in Q2D-SALR systems leads to an earlier onset of HIs than in Q2D hard-sphere reference systems, implying HIs become relevant already on inertial timescales.

This work presents an elastic model to study the interplay between entropic and energetic networks in confined hydrogel particles. We consider a quasi-two-dimensional system composed of spherical hydrogel beads confined in a circular container, where particle growth occurs through hydration. Based on experimental observations, an elastic potential is introduced to model interactions between particles and between particles and the confining wall. Computational simulations based on energy minimization identify the lowest-energy configurations adopted during growth. Analysis of the resulting energy landscapes reveals emergent self-organization, adaptability, and cooperativity arising from the competition between entropic and energetic networks.

Remembering here the work of two pioneers of the statistical physics of Coulomb systems, Günter Kelbg, and Ihor Yukhnovskii, we analyze their methods and give some new applications to ionic solutions and quantum plasmas. In particular, we develop applications of the theory to strong electrolytes and to thermal high-temperature plasmas at $T > 0^5$ K using the exponential interaction model. We show the strong structural similarity of these two classes of Coulomb systems, which physics is determined mostly by contributions proportional to $e^4$ and $e^6$. We predict at higher densities a structural transition to oscillating correlations. The thermodynamic functions show a smooth transition from a quadratic root increase to a slower increase like $n_i^{1/4}$ which observes the Onsager bound. Effects of asymmetries in charges and masses are studied with applications to ionic systems with multiple charges and to high-temperature plasmas, in particular, to plasmas with He$^{2+}$-ions.

We study pressure pulse generation and propagation in lipid monolayers by an experimental approach employing rapid photoisomerization of photoswitchable lipids (azoPC). This allows us to generate longitudinal surface pressure pulses by optical flash excitation in both free and constrained layer geometries. We compare the observed pulse shapes with a theoretical approach based on a nonlinear fractional wave equation for a surface displacement field, where a fractional time derivative term captures the hydrodynamics of the monolayer subphase. We explore channel geometries of different lengths and widths and find quantitative agreement between theory and experiment regarding pulse speed and pulse shapes. For narrow channels, we employ a one-dimensional version of the fractional wave equation to study pulse propagation without any fit parameters by using the pressure signal at a close pressure sensor as boundary condition to predict the pressure signal at a second far sensor. A full two-dimensional description can capture all effects arising from the channel geometry for wider channels using one common set of fit parameters for the pulse excitation that can be applied to all geometries. The nonlinearity in the fractional wave equation plays no role in explaining the observed pulse shapes because pulse amplitudes generated by azoPC photoswitching remain very small.

We study saturation in two-dimensional binary mixtures of fixed-orientation regular polygons deposited by random sequential adsorption (RSA). Polygons with (n\in{3,\dots,23}) are considered under an equal-area constraint, isolating shape effects from size effects. Saturated configurations are generated using an adaptive split-voxel RSA algorithm with exact overlap detection based on the Separating Axis Theorem, allowing a systematic exploration of all distinct binary shape combinations. Jamming coverage depends strongly on polygon geometry despite identical particle area. Triangle-containing mixtures yield the lowest coverages, whereas axis-aligned squares achieve the maximum observed value, (\phi_{\rm sat}\approx0.5646). Even-sided polygons consistently outperform neighboring odd-sided polygons, revealing a parity effect associated with centrosymmetry. For odd (n), the pure-species saturation approaches the disk RSA limit (\phi_{\rm disk}\approx0.547) from below according to (\phi_{\rm sat}(n)=\phi_{\rm disk}-c/n^\alpha), with (\alpha\approx2.41\pm0.06), close to the (1/n^2) scaling expected from isoperimetric arguments. Even-sided polygons instead converge from above, indicating a symmetry-driven packing advantage that disappears only in the circular limit. These trends are explained through the excluded area (E_{AB}=\mathrm{Area}(P_A\oplus(-P_B))), computed analytically via Minkowski sums. Centrosymmetry fixes (E_{AA}=4A_0) for even (n), whereas odd polygons have a larger excluded area that decreases monotonically toward the same limit as (n\to\infty). Saturation coverage is negatively correlated with excluded area, consistent with a mean-field RSA description and directly linking geometric symmetry to jamming efficiency.

Accurate initialization of polymer architectures remains a critical yet underappreciated determinant of reliability in molecular dynamics simulations of soft matter systems. Errors in coordinate generation and connectivity assignment frequently introduce artificial stresses, topological inconsistencies, and numerical instabilities that propagate throughout simulation trajectories. Here, we present a topology-preserving Python framework for generating star and cyclic polymer architectures with deterministic bond connectivity, exact ring closure, excluded volume enforcement, and spatial-hashing-based overlap detection. The algorithm produces LAMMPS-compatible data files under atom style full without reliance on third-party libraries. We demonstrate that the generated structures exhibit mechanical stability at initialization, suppressed artificial energy spikes, and consistent thermodynamic behavior during equilibration. Benchmark comparisons against naive random placement schemes reveal significant reductions in overlap-induced instabilities and improved reproducibility of structural and dynamical observables. The presented framework establishes initialization as a controlled physical boundary condition rather than a stochastic preprocessing step, thereby enhancing the reliability and reproducibility of polymer molecular dynamics simulations.

This article describes recent progress in understanding highly stable glasses prepared by physical vapor deposition and provides perspective on further research directions for the field. For a given molecule, vapor-deposited glasses can have higher density and lower enthalpy than any glass that can be prepared by the more traditional route of cooling a liquid, and such glasses also exhibit greatly enhanced kinetic stability. Because vapor-deposited glasses can approach the bottom of the amorphous part of the potential energy landscape, they provide insights into the properties expected for the ideal glass. Connections between vapor-deposited glasses, liquid-cooled glasses, and deeply supercooled liquids are explored. The generality of stable glass formation for organic molecules is discussed along with the prospects for stable glasses of other types of materials.

Colloidal smectics -- layered structures formed in dense suspensions of rod-like particles -- often exhibit grain boundaries, across which the layer orientation changes by $90^{\circ}$. Motivated by this feature, we develop a layer-based topological framework that treats orthogonal grain boundaries as constituents of the ground state rather than as exceptional defect structures. Extending the layer-based approach for ordinary smectics, we reduce the smectic structure to layers, half-layers, and domain walls. We classify the topology of defects and their combination rules based on this structure. In two dimensions, point defects are described by semi-directed cycle graphs. Although the disclination charge remains a valid topological invariant, it does not uniquely classify defects, as distinct graphs may share the same charge. In three dimensions, line defects are classified by their transverse graph structure, while point defects exhibit qualitatively different behavior. In particular, we show that the hedgehog disclination charge is not a topological invariant, but instead varies continuously under smooth deformations of the layer structure.

Matter can organize not only through forces, but also through the information its constituents acquire from their surroundings. Here we use perceptive Brownian particles as a minimal model to isolate nonlocal sensing as an organizing principle for nonequilibrium matter. The particles undergo purely Brownian motion, with no mechanical interactions, self-propulsion, alignment, or auxiliary fields. Their only coupling is informational, through diffusivity regulated by density measured over a finite perception zone. Whereas local sensing, when unstable, produces conventional long-wavelength demixing, nonlocal perception restructures the instability spectrum, introducing finite-wavelength patterning and nonlinear bubbling instabilities. More fundamentally, it reshapes the ordering pathway by assembling a cascade of instabilities: macroscopic demixing creates dense domains, finite-wavelength modes pattern them internally, and nonlinear feedback hollows them into void bubbles. This produces hybrid phase separation, where a macroscopic dense phase coexists with a dilute background while retaining ordered internal microstructure, whose symmetry, anisotropy, and length scales are selected by the perception kernel. These results establish information acquisition as a constitutive principle of nonequilibrium matter, capable of governing both phase stability and the dynamical pathways through which order emerges.

Signal-driven motion is widespread in natural and artificial systems, yet quantitative characterization of how transient chemo-hydrodynamic waves are converted into mechanical driving forces remains limited. Here, we investigate the self-propulsion of a MXene sheet asymmetrically coated with catalase in hydrogen peroxide solution. By combining dual-view particle image velocimetry experiments and numerical simulations reveal that active motion of the sheet is driven by chemo-hydrodynamic waves and exhibits direct-wave motion, the driving force of which is analyzed in terms of the shear stress on the sheet surface caused by chemo-hydrodynamic waves. This work suggests theoretical principles for designing and controlling hydrodynamically driven active motion.

Ferroelectric nematic (NF) liquid crystals exhibit polar symmetry and large polarization, giving rise to phenomena absent in conventional apolar nematics. We investigate NF liquid crystals confined to free-floating spherical shells with tangential boundary conditions, enforcing a total topological defect charge of +2. We conjecture that ferroelectric nematics avoid splayed configurations with half-integer defects, common in apolar nematic shells, instead concentrating the topological charge into escaped azimuthal +1 defects requiring only bend and twist. Indeed, at room temperature in the NF phase, our thin RM734+DIO shells with inner and outer aqueous poly(vinyl alcohol) solutions develop an azimuthal director field around two antipodal +1 bend-twist defects. The non-centrosymmetric nature and the azimuthal director configuration of the shells in the NF phase are confirmed also through second-harmonic generation microscopy. At intermediate temperature the antiferroelectric Nx phase generates a new exotic texture rife in zigzag lines in the shells. In the regular N phase at high temperature, the shells develop the usual four +1/2 disclinations located near the thinnest point. Our study highlights the rich platform offered by spherical shells to study the behavior of exotic liquid crystals subject to topological constraints, possibly opening new paths to apply the highly responsive ferroelectric nematic phase

Internally heated LCST thermo-responsive gels can show self-sustained swelling and collapse oscillations through feedback between temperature-induced collapse and collapse-suppressed heating. In this work, a minimal two-variable model is developed by coupling gel swelling dynamics with a lumped thermal balance. The analysis shows that stable large-amplitude oscillations are mainly controlled by global bifurcations of limit cycles, rather than by the local Hopf bifurcation. The Hopf bifurcation is subcritical in the studied parameter range, leading to a broad coexistence region where a stable fixed point and a stable limit cycle are both possible. The oscillatory behavior remains robust for different heating-gate functions, indicating that local linear instability is neither necessary nor sufficient for self-oscillation. Fast-slow analysis further shows that the oscillation period is mainly governed by the cooling rate, while the amplitude is determined by the geometry of the swelling equilibrium manifold. These results clarify the bifurcation mechanism of thermo-responsive gel oscillations and provide guidance for controlling their period, amplitude, and waveform.

Attractive three-body interactions have been reported for like-charged colloids in low-salt suspensions, based on both finite-element Poisson-Boltzmann calculations and direct experimental measurements, and have been proposed as a mechanism to drive colloidal clustering. However, these Poisson-Boltzmann calculations typically neglect charge regulation and higher-order many-body effects. Here, we construct machine-learned (ML) many-body interaction potentials for charge-regulating colloids, trained on finite-element Poisson-Boltzmann calculations, to accurately capture three-body and higher-order contributions. We find that the three-body contribution to the many-body potential as obtained from Poisson-Boltzmann calculations on isolated colloid triplets is strongly attractive, consistent with previous work, whereas the four-body contribution for an equilateral pyramid configuration of four colloids is repulsive. We then construct ML many-body potentials for charged colloids using finite-element Poisson-Boltzmann calculations on clusters of 13 colloids, and find that the incorporation of higher-body interactions weakens the cohesive nature of the interactions. We identify a parameter regime exhibiting gas-liquid or gas-solid phase separation using the ML potentials in molecular dynamics simulations. However, when we include clusters of 48 colloids in the training data, the cohesion diminishes further, and molecular dynamics simulations using these potentials no longer include broad phase separation in aqueous dispersions of charged colloids. Finally, we compute the potential of mean force of pairs and triplets of colloids using primitive model simulations. We find that the resulting potentials are in good agreement with those obtained from the Poisson-Boltzmann calculations, thereby supporting the validity of the Poisson-Boltzmann approach for determining many-body interactions.

Segregated states based on particle size emerge in granular materials from the competition between segregation and diffusive remixing. Here, we show that quantum coherence can enhance segregation beyond this classical limit. We introduce an open quantum cellular automaton for bidisperse mixtures that combines coherent transport and dissipative segregation. The automaton reproduces experimental and continuum-theory segregation dynamics, with segregation degrees collapsing onto a theoretical Péclet-dependent relationship. However, weakly decohering systems exhibit a coherence-driven transport regime that produces more strongly segregated steady states than classical predictions. Across a broad parameter range, the steady-state degree of segregation collapses onto two dimensionless numbers governing the competition between segregation, diffusion, and decoherence. These results identify quantum coherence as a mechanism for enhancing particle-size segregation and establish a framework for studying transport phenomena in open many-body systems.

We study the polar director structure in thin planar cells filled with bent-core liquid crystals in the ferroelectric smectic-A phase (SmAP$_\text{F}$). We analyze a continuum phenomenological model proposed in the physics literature and present rigorous proofs of the existence and uniqueness of the equilibrium solutions. We further investigate the qualitative properties of nontrivial solutions and examine the effects of a bias electric field, surface anchoring, and cell thickness on the polar director configuration. Our results are consistent with previous experimental and numerical simulations reported in the physics literature. In addition, our analysis reveals new parameter-dependent behaviors supported by our numerical simulations and extends results reported from previous literature.

Geometric phase quantifies net locomotion in dissipative media via gauge theory, but linking this theoretical quantity to noisy, sparse, and weakly periodic biological shape data is challenging. We develop a theory-guided, data-driven Koopman autoencoder to recover the limit cycle embedded in imperfect cyclic data and extract shape gaits and geometric phase from sperm and nematode data. We introduce a geometric phase sensitivity function that quantifies responses to shape perturbations and reveals mechanical information using only gauge-theoretic structure, without assuming mechanical laws.

Disordered stealthy hyperuniform materials combine liquid-like statistical isotropy with crystal-like homogeneity, suppressed density fluctuations at large length scales, bounded holes, and an isotropic structure factor that vanishes for a finite range of wavevectors. This combination yields unusual physical properties, including optical transparency, effective delocalization, ultrafast spreadability, optimal conductivity, and complete isotropic photonic bandgaps. Gyromorphs, point patterns whose structure factor includes rings of Bragg-like peaks arranged with discrete $G$-fold rotational symmetry, were recently introduced as counterexamples: disordered media that can somehow achieve the same physical properties, in some cases with higher performance, without stealthiness or hyperuniformity. In this paper, we resolve the puzzle of how gyromorphs fit consistently with the stealthy hyperuniform studies. We first show that gyromorphs are actually hyperuniform and, in the large-$G$ limit where they become nearly isotropic, belong to the weakest form of hyperuniformity, known as Class III. Thus, gyromorphs should have comparatively degraded physical properties compared to stealthy hyperuniform media, which belong to the strongest form of hyperuniformity, known as Class I. We verify this expectation using the rigorous spectral Green's matrix method for the calculation of the density of states (DOS) and Purcell factors in large arrays of electric dipoles. We find that gyromorphs display size-dependent pseudogaps richly populated by localized states rather than smooth band gaps like those found for highly stealthy hyperuniform materials or in deterministic structures such as Vogel spiral and triangular lattices. Furthermore, we predict similar disorder-induced degradation relative to stealthy hyperuniformity with regard to transparency, spreadability and diffusion properties.

Techniques from glass art and fabrication provide a controllable physical platform for studying tissue mechanics in simple organisms. Here, we use glass-based physical models to investigate tissue deformation in the marine organism Trichoplax adhaerens. Previous studies have shown that the epithelial tissues in T. adhaerens undergo large deformations and form fracture holes under mechanical loading, exhibiting a ductile-to-brittle transition at fast loading rates. To model these behaviors in a tunable and experimentally accessible system, glass is shaped into tissue-like monolayers in a glass studio, heated to its specific process temperature, and subjected to controlled stretching. Rapid cooling arrests the deformed configurations, providing snapshots of tissue-like strain states under load. Under lateral and radial stretching, we quantify changes in the area and eccentricity of individual "cells" in the glass models, and found that eccentricity increases after stretching. We further use tensegrity-based models to quantify deformations in the cellular geometry of the glass tissues, enabling direct comparison between experiments and simulations. The model captures the principal experimental deformation patterns, but underestimates the magnitude of the observed eccentricity changes. Our results demonstrate that glass-based physical models provide an experimentally accessible platform for studying tissue-scale deformation and mechanical behavior, while supporting interdisciplinary approaches that connect methods in the arts and sciences.

The viscoelastic instability of cross-slot flow was first observed experimentally almost half a century ago and reproduced numerically two decades ago, yet its physical origin remains unresolved. We revisit this problem for two-dimensional creeping flow of Oldroyd-B fluid by combining direct numerical simulations, global stability analysis, structural sensitivity analysis, and energy-budget analysis. Our simulations reproduce the canonical pitchfork bifurcation, and the stability analysis consistently predicts the threshold and perturbation growth rates. The leading eigenmode consists of a chiral velocity--stress perturbation that tilts and rotates the birefringent strand generated by the extensional flow. Structural sensitivity and energy-budget analyses identify narrow high-extension-rate ridges within the extensional flow as both the spatial core and energetic source of the instability. In these ridges, the stress-based wavemaker co-localizes with large positive disturbance polymeric stress power density, indicating localized transfer of stored elastic energy to the disturbance flow. Analyses of cross-slot variants with rounded corners and with a centered cylinder further reveal that neither sharp corners nor a free central stagnation point is the essential destabilizing ingredient; rather, the instability originates from elastic-energy release in extension-dominated regions characteristic of cross-slot flow.

The scaling patch approach is applied to analyze the turbulent kinetic energy (TKE) budget equation in wall-bounded turbulent flows. The balance of the TKE equation is divided into several distinct regions, or scaling patches, each characterized by a dominant balance among the governing terms and its own appropriate scaling parameters. In the near-wall viscous sublayer, the TKE balance is primarily between viscous diffusion and dissipation, and the characteristic scales are set by the kinematic viscosity and the wall dissipation rate. The thickness of this sublayer is on the order of the Kolmogorov length scale. Moving away from the wall, the peak TKE production provides a natural reference scale for the inner layer, yielding the traditional inner scaling. Grouping the viscous diffusion and dissipation terms in the inner layer enhances the collapse across different Reynolds numbers. In the outer region, Prandtl's mixing-length model is used to derive a characteristic scale for TKE production. A new meso-scaling is further introduced to describe the intermediate region, ensuring a smooth transition between the inner and outer layers. The scaling patch framework offers a unified interpretation of the structure and scaling behavior of the TKE budget across all regions of wall-bounded turbulence.

Generalised Lagrangian Mean (or Hybrid Euler-Lagrange) theory aims to describe the joint evolution of the mean flow and its perturbations. This paper considers related forms of continuity equations (CEs) and clarifies the conditions of their validity. We do not consider equations of motion; therefore, we use only exact formulae and general notions of fluid dynamics and operate only with the most general statements for CEs. The tools used are Lagrangian X, Eulerian x, averaged Eulerian x' coordinates of fluid particles, and ensemble-based averaging. The targeted forms of CEs are expressed in terms of function x(x',t). Our first step is to present the actual velocity divergence div u via div'u', where u and u' are the actual and average fluid velocities. Then we introduce three versions of exact CEs and demonstrate that each is mathematically incomplete. The third step is to restore their completeness by introducing the compatibility equations required for their validity in general fluid flows. As a basic reference, we present two versions of the McIntyre-Andrews Transformation (MAT) for CEs. The original MAT introduces an auxiliary function that satisfies an auxiliary PDE and special initial conditions. Therefore, it works for a special class of fluid flows. The presented generalisation of MAT makes CEs applicable to arbitrary fluid motion. Both versions require compatibility equations, which we compare with ours. Finally, we consider average flows with small perturbations, thereby linking our exposition to the classical GLM theory.

Far away from solid boundaries, energy can be transferred between different flow scales due to the non-linear self-advection of velocity. This energy transfer can be quantified using well-established Fourier diagnostics or filtering methods. However, these diagnostic tools fail to provide a physical representation of the linear energy transfer that may occur during the formation of oceanic boundary layers or Rossby wave reflections. In this document, I outline a novel filtering methodology that is able to quantify this linear energy transfer by combining coarse-graining with volume-penalization. Its utility is illustrated by quantifying the down-scale energy transfer occuring during a Rossby wave reflection off a western boundary. The conceptual framework developed here is thought to be broadly applicable to the study of multi-scale energetics of bounded geophysical fluid flows.

Recent studies Vorticity packing effects on long time turbulent transport in decaying two dimensional incompressible Navier Stokes fluids, Phys. Fluids 38, 045159 (2026) demonstrated that, at a fixed high Reynolds number (Re), the initial vorticity packing fraction (VPF) governs the coupled Eulerian flow evolution and Lagrangian tracer particle transport in decaying two dimensional incompressible Navier Stokes fluids, revealing a strong Eulerian Lagrangian relationship during the nonequilibrium inverse cascade regime and a direct Eulerian Lagrangian correspondence in the late time coherent vortex quasi equilibrium regime, wherein increasing VPF drives transitions from point vortex to patch vortex equilibria and from subdiffusive to superdiffusive transport. In the present work, we investigate how these Eulerian Lagrangian connections evolve across a broad (VPF, Re) parameter space. The results show that the Eulerian Lagrangian relationship remains largely preserved during the nonequilibrium inverse-cascade regime, where transport increases systematically with VPF and remains primarily controlled by VPF despite secondary Re dependent oscillatory modulation. In contrast, the late-time coherent-vortex quasi-equilibrium regime exhibits Eulerian statistical equilibria that remain largely insensitive to Re, while the corresponding tracer-particle transport displays a strong Re dependence characterized by strong oscillatory and nonmonotonic variations across the (VPF, Re) parameter space, substantially weakening the VPF-ordered transport hierarchy observed in the inverse-cascade regime. Consequently, for the parameter range, spatial resolutions, and integration times explored in the present study, the direct Eulerian Lagrangian correspondence identified at fixed high Re is not universally maintained across the broader (VPF, Re) parameter space.

We adopt the Bayesian inference framework to solve an inverse Reynolds-Averaged Navier-Stokes (RANS) problem for the approximate posterior probability distribution of the turbulence model parameters and inlet boundary conditions of a confined turbulent jet. The data are noisy 3D flow MRI measurements of a Newtonian fluid flowing through the Food and Drug Administration (FDA) nozzle geometry. We assimilate this into RANS using two algebraic turbulence models based on the mean shear rate magnitude and the turbulence kinetic energy. We demonstrate that the inferred models are able to reconstruct the measured mean flow velocities without overfitting and we provide uncertainty estimates for the model parameters. The methodology can readily be extended to more complex RANS models, provided that they remain differentiable.

Predicting the transition of turbulence in pipe flow remains a fundamental problem in fluid dynamics. We use a variational approach to compute nonlinear optimal perturbations to the laminar flow at Reynolds number $Re\leq 5000$. As $Re$ increases, optimal perturbations remain structurally similar, but increasingly localize while their thickness scales as $\delta_r \propto Re^{-1/3}$. They grow via the Orr mechanism, followed by a phase of strong nonlinear interaction of oblique waves and a lift-up phase. The energy gain during the Orr phase increases linearly with $Re$ and is independent of the initial perturbation energy, $E_0$. The energy gain during the oblique and lift-up phases is governed by nonlinearities and scales as $\propto Re^2$. We find that regardless of the Reynolds number, transition occurs if the energy of the perturbation exceeds a constant threshold. As a result, the minimum perturbation energy required to cause transition in pipe flow scales as $\mathcal{O}(Re^{-3})$.

Non-normality can induce large transient growth in linearly stable systems. Determining whether this growth triggers a transition in the underlying nonlinear system, however, requires understanding the interaction between non-normality and nonlinearity. Here, we develop a weakly nonlinear theory for linearly-stable, non-normal systems subject to harmonic forcing, enabling a systematic analysis of this interaction. Following Ducimetière et al. (J. Fluid Mech., vol. 947, 2022, A43), we define a formal small parameter $\varepsilon$ as the reciprocal of the system's maximum linear amplification. However, we ensure asymptotic consistency by providing a framework that naturally adapts to the underlying structure of the system. The approach is applied to a harmonically forced channel flow and to a two-dimensional model mimicking the structure of the Orr-Sommerfeld-Squire equations. Unlike classical weakly nonlinear analysis near bifurcation points, the resulting amplitude equations are non-universal. In fact, a single linear mode amplified by the non-normality can nonlinearly excite a multi-modal and multi-frequency response at leading-order, which is system- or even regime-specific. Nevertheless, the method yields asymptotically consistent amplitude equations that capture this complexity provided a limit in which $\varepsilon\rightarrow0$ can be identified. As the forcing amplitude increases, the reduced equations capture stable nonlinear states emerging from the laminar flow, their subsequent bifurcations, and their eventual collision with the boundary of their basin of attraction. Thus, the amplitude equations can capture subcritical transitions driven by forcing and varied initial conditions and enable the identification of critical parameters beyond which no stable weakly nonlinear state exists.

Several recent experimental studies have revealed non-monotonic variations in elastic turbulence-induced chaotic flow behaviour and pressure drop during the flow of viscoelastic fluids through a microporous medium. The present numerical study aims to investigate and hypothesise about the physical mechanisms governing these complex flow behaviours in an ordered microporous medium consisting of cylindrical micropillars arranged in a staggered configuration. We propose that birefringent strands of high elastic stress, generated by the stretching and alignment of polymer molecules within the porous structure, play the dominant role in controlling the non-monotonic variations in chaos and pressure drop. At low Weissenberg numbers, these stress strands develop gradually, mainly downstream of the micropillars, whereas beyond a critical Weissenberg number, they begin to fluctuate strongly, leading to chaotic flow dynamics. However, at even higher Weissenberg numbers, the strands become larger and stronger, eventually interconnecting between neighbouring micropillars, causing the flow to reorganise into a nearly steady, ordered state similar to that observed at low Weissenberg numbers. On the other hand, the pressure drop in the system consists of a mean contribution, obtained from statistically stationary flow quantities, and a fluctuating contribution. While the mean component increases monotonically with the Weissenberg number, the fluctuating component varies non-monotonically, leading to a similar trend in the total pressure drop. Moreover, the non-monotonic chaotic behaviour strongly depends on the solid volume fraction of the porous medium, which alters both the critical Weissenberg number for instability onset and the range over which the non-monotonic behaviour persists.

This paper presents a conservative high-order discontinuous Galerkin (DG) method featuring time-accurate local time stepping for simulating low-Mach-number unsteady flows, based on a weakly compressible formulation. In this model, pressure is defined solely as a function of density, eliminating the need for a global pressure Poisson equation typical of incompressible solvers while preserving the locality and conservation of compressible schemes. This makes it suitable for low-speed unsteady flows and aeroacoustics. The spatial discretization uses a strong-form nodal DG spectral element method (DGSEM) on Gauss-Lobatto-Legendre points. Inviscid fluxes are handled by numerical fluxes tailored to the weakly compressible system; specifically, a two-rarefaction approximate Riemann solver is developed for the constant-sound-speed barotropic equation of state. Viscous terms employ the incomplete interior penalty Galerkin (IIPG) method. For time integration, a continuous extension Runge-Kutta (CERK) scheme constructs cell-local predictor polynomials for continuous-in-time volume reconstructions. Face fluxes are split into interior and common contributions: the former matches the volume quadrature, while the latter uses piecewise Gaussian quadrature from continuous predictors. This split preserves discrete summation-by-parts cancellation and ensures conservative inter-element flux exchange.

A methodology for passive mitigation of vortex-induced vibrations (VIVs) in subsea dynamic power cables is developed using optimized, strongly nonlinear bi-stable mass-spring-damper attachments, termed bi-stable nonlinear energy sinks (BNESs), within the open-source MoorDyn library. A fully three-dimensional time-domain framework captures cable dynamics, Morison-type hydrodynamic forcing, nonlinear vibration-mitigation mechanisms, and spatially and temporally varying currents. The BNESs are consistently integrated into the cable model, allowing treatment of highly non-stationary VIVs. A data-driven optimization study samples the BNES design space across multiple current profiles and shows that properly tuned configurations substantially reduce peak-to-peak cable vibration amplitudes. The BNESs also produce significant and robust reductions in cumulative VIV-induced energy intake from the surrounding flow and in drag energy. To the authors' knowledge, passive nonlinear attachments are shown for the first time to reduce both energy intake and drag amplification in a subsea cable, with potential benefits for short- and long-term fatigue. Time-frequency wavelet analysis reveals targeted nonlinear energy transfers and scattering from dominant high-amplitude, low-frequency cable modes to lower-amplitude, higher-frequency modes. This modal redistribution promotes rapid dissipation through hydrodynamic damping and internal structural losses, explaining the simultaneous reductions in vibration amplitude and cumulative energy intake. The results demonstrate that BNESs can provide effective and robust VIV mitigation for subsea power cables under realistic unsteady operating conditions and motivate future studies involving combined current-wave loading, platform-induced motion, and fatigue-life assessment.

Characterizing the complete wall-pressure spectrum in turbulent wall-bounded flows requires simultaneous access to the viscous-scale high-wavenumber content and the outer-layer low-wavenumber content -- a requirement that neither short-domain direct numerical simulation (DNS) nor sparse experimental measurements alone can satisfy. We propose Patched Flow Matching (Patched FM), a generative framework that fuses these two complementary sources by learning a patch-local prior over inner-scaled wall-pressure statistics from short-domain DNS and assimilating sparse sensor measurements at inference time through training-free posterior sampling. The patch-additive decomposition of the flow matching vector field decouples the generative prior from the global domain size, enabling reconstruction on domains arbitrarily larger than the training configuration. By expressing the patch prior in inner-scaled coordinates, where high-wavenumber wall-pressure statistics are approximately Reynolds-number invariant, the framework extends to higher Reynolds numbers through hierarchical transfer learning with as few as $500$ short-domain snapshots ($2.5\%$ of the base training data) at a fraction of the scratch-training cost. Applied to compressible channel-flow DNS at $Re_\tau = 180$, $500$, and $1000$, Patched FM reconstructs full-resolution wall-pressure fields on a domain four times larger than the training configuration ($L_x^L = 16\pi\delta$ versus $L_x^S = 4\pi\delta$) from sensor coverage as low as $0.25\%$, recovering the low-wavenumber spectral content inaccessible to short-domain DNS with high fidelity in both streamwise and spanwise directions. Zero-shot generalization to unseen Reynolds numbers and ablation studies further confirm the role of inner scaling as a physical prerequisite for data-efficient Reynolds-number transfer.

Despite their widespread use, mesoscopic models for non-ideal fluids have rarely been systematically validated against microscopic simulations. In this work, molecular dynamics (MD) simulations of confined fluids are mapped onto a mesoscopic framework, enabling direct comparison with lattice Boltzmann (LBM) formulations. By analyzing the moments of the distribution function, we identify a force formulation that consistently reproduces the microscopic statistics and macroscopic force balance. The results show that a hybrid formulation combining pseudo-potential and free-energy approaches provides the most consistent description. These findings establish a direct link between microscopic particle dynamics and mesoscopic modeling, offering practical guidance for the development and selection of LBM models for non-ideal and multiphase flows.

Spanwise wall oscillation can enhance convective heat transfer disproportionately to its drag penalty, a departure from the Reynolds analogy termed dissimilar heat transfer (DHT). The companion study of Gu'erin et al. (2026) established that an optimised quasi-plateau waveform attains an analogy factor $\overline{A}n \approx 1.09$ at $Pr = 1$ and attributed this preferential thermal enhancement to the absence of a pressure-strain redistribution channel in the temperature variance equation, but the mechanism had not been quantitatively verified. The present study addresses this gap through phase-resolved variance transport budget analysis from direct numerical simulation of turbulent channel flow at $Re\tau = 200$, $Pr = 1$. Two complementary pressure-mediated mechanisms are identified. At the Stokes-strain reversal, the pressure-strain redistribution $\Pi_{uu}$ imposes a pronounced drain on the streamwise velocity variance with no counterpart in the temperature variance equation: the divergence-free constraint redistributes momentum variance among velocity components but has no scalar analogue. During the quasi-steady plateau phases, the pressure-temperature-gradient correlation $\Pi_{v\theta}$ preferentially enhances the wall-normal scalar flux relative to the momentum flux. The concentration of both mechanisms within the reversal and plateau phases, rather than at the Stokes-layer penetration maxima, identifies the duration of the quasi-steady phases as the controlling parameter for DHT enhancement, resolving the paradox whereby increased penetration depth does not produce increased dissimilarity.

High-resolution turbulence modeling is essential for scientific computing, but remains constrained by the cost of direct numerical simulation and the scarcity of full-resolution data. Existing scientific compressors reduce storage but typically operate on per-frame representations, whereas learned compressors yield compact latents that are often resolution-dependent and weakly aligned with the physics of turbulence. This raises the need for a compression framework that reduces data size, preserves physical diagnostics, and transfers from low-resolution training fields to high-resolution test fields without retraining. In this paper, we propose Physics-Preserving Latent Compression (PPLC), a patch-local latent compressor for three-dimensional turbulence. Motivated by inertial-range scale similarity, PPLC treats fixed-size patches as transferable units and applies a shared variational autoencoder independently of the global grid size. It combines exact mean preservation, zero-mean fluctuation encoding, an invertible Haar wavelet front-end, shift-consistency regularization, and overlap-aware reconstruction. Instantiated on forced isotropic turbulence, PPLC is trained only on stride-downsampled 256^3 fields and transfers zero-shot to 1024^3 fields. Experiments show that PPLC improves the balance between reconstruction accuracy and physical fidelity over classical and learned baselines, keeping diagnostics such as dissipation, enstrophy, energy spectra, and incompressibility closer to the ground truth. Beyond turbulence compression, PPLC offers a general strategy for physics-preserving latent representations that support data-efficient scientific surrogate modeling.

Motivated by the need to extrapolate the results from ground-based experiments to the conditions of high-speed flight, we present the Lie equivalence symmetry analysis of the hypersonic stagnation-point boundary layers. We demonstrate the application of the equivalence symmetry on the set of coupled ODEs which are physically relevant in hypersonics. By allowing the property laws to transform along with the independent and dependent variables, the invariants derived within the similarity-reduced stagnation-point ODE formulation, identify families of non-linear maps that can be used to extrapolate the laboratory-scale predictions to flight. In practice, implementing these maps requires the laboratory-scale ODE solution together with the lab- and flight-side thermochemical property data, which are generally available from existing databases. The maps are derived for the similarity-reduced non-dimensional temperature across the boundary layer and are shown to {collapse with independently computed flight solutions} for a range of relevant cases.

The receptivity of the inviscid flow on the stagnation streamline of a blunt body in supersonic flow is investigated theoretically for incoming freestream disturbances. The wave transmission and coupling are quantified by solving the linearized shock-fitting problem with a spectral method, whereas the steady base flow is obtained using a nonlinear shock-fitting spectral solver. Revisiting previous theoretical work, we identify and correct an error in a key coefficient in the analysis by Morkovin (J. Appl. Mech., 27, 1960), overturning the prior conclusion of body-induced damping and revealing amplification instead. The post-shock entropy disturbances display singular behavior near the stagnation point, which is treated analytically. Acoustic disturbances dominate pressure and velocity responses, while density is affected by both acoustic and entropy modes. The base flow pressure gradient introduces weak coupling between the acoustic and entropic components of the response. The actual stagnation-line base flow amplifies all disturbances more than the simplified model of uniform post-shock flow; as well as a shock without a body, and the differences are quantified for a range of Mach numbers. The responses to entropy, fast acoustic, and slow acoustic waves are compared as functions of the freestream Mach number.

For centuries, the intrinsic chaos of unsteady fluid motion has stood as a formidable barrier to long-term forecasting. While machine learning (ML) has recently emerged as a transformative paradigm for predicting flow evolution, it encounters a pervasive yet unexplained "performance wall": an inevitable deterioration in accuracy as the forecast horizon extends. Here, we demonstrate that this deterioration is not a deficiency of model architecture, no matter how state-of-the-art, but a fundamental constraint imposed by the underlying system, which can be understood through turbulence theory established decades ago. In the setting of bluff body flow, a canonical phenomenon for spatiotemporal complexity in fluid mechanics, we reveal a scaling law governing the deterioration of ML predictability, derived from a Kolmogorov-inspired framework and validated through high-fidelity simulations. Our findings establish a closed loop between the predictability ceiling and its interpretation, bridging the gap between transparent physical theories and modern black-box inference. More broadly, this work provides a theoretical compass for constructing trustworthy ML in complex dynamical systems across the physical sciences.

We numerically verify multifractal theory (Frisch and Parisi 1985) for turbulence using simulation data at a high Reynolds number. First, we propose a simple method to directly estimate the multifractal dimension $D(h)$ of vortical structures with a given Hölder exponent $h$. Thus measured $D(h)$ is in good agreement with indirectly measured experimental data. Then, we demonstrate that these structures for $h\ll1/3$ form the hierarchy of coherent eddies, while those for $h\gg1/3$ are featureless.

Heat transport in fractured media is governed by coupled thermal-hydraulic (TH) processes. This study evaluates TH processes at fracture intersections, focusing on T-intersections where one horizontal fracture is subjected to a pressure gradient while the other forms a vertical dead-end fracture. Using numerical simulations, we investigate the influence of the inlet velocity, thermal Péclet, and Rayleigh numbers, and the impact of a pressure gradient along the T-intersection, on the resulting heat transport. The model domain consists of a fluid and a solid region. Fluid flow and heat transport in the fractures are described by the conservation equations for mass, momentum, and energy. The rock matrix is considered impermeable, therefore, it is governed by heat conduction. The simulations consistently show that heat transfer from the fluid to the matrix is enhanced when fluid flow occurs within the dead-end fracture, since such fluid flow maintains a higher temperature difference between the matrix and the fluid. This flow arises either from buoyancy-driven natural convection due to temperature-dependent fluid density or from a pressure gradient imposed by the orientation of the dead-end fracture with respect to the flow direction in the horizontal fracture. Natural convection dominates at high flow rate, Rayleigh, and Péclet numbers, whereas pressure-driven flow becomes the controlling mechanism for an increasing deviation from the orthogonal configuration of the two fracture planes and under higher flow rates. At low flow rates, Péclet, or Rayleigh numbers, no flow develops in the dead-end fracture, and heat transport in the dead-end fracture becomes conduction-dominated.

Two factors that influence the oscillation mechanism of a sonic fluidic oscillator are investigated: the geometry of the feedback channel connections (control ports) and the influence of flow restrictions in the oscillator outlets. Phase-averaged planar PIV measurements are performed inside the oscillator, synchronised with unsteady pressure measurements, and analysed using space-only proper orthogonal decomposition (POD). The POD analysis reveals two coupled modes: a Sweeping Mode capturing lateral jet displacement and a Bending Mode capturing jet curvature during switching, the latter being the primary driver of outlet mass flux modulation. Flow separation at the control port entrances is shown to throttle the feedback flow and progressively limit oscillation strength at higher inlet flow rates. Restrictive outlet paths induce a differential back pressure that is shown to cause the jet to separate from its attachment wall and bend towards the splitter tip (`secondary separation'). The secondary separation reduces the differential outlet mass flux and introduces a flow curvature that limits the upstream propagation of the back pressure and thus shields the primary jet attachment. The consequence of these effects is that strong oscillations are sustained down to the smallest outlet apertures investigated. The principal contribution is to demonstrate that the assumed coupling between upstream jet attachment and outlet flow split is broken when the outlet aperture is reduced, with significant implications for the design of fluidic oscillators operating with downstream flow impedances.

Salt fingering drives diapycnal scalar exchange across thermohaline interfaces that are statically stable but double-diffusively unstable. Oceanic interfaces are finite-depth structures and may carry roughness inherited from waves, shear, intrusions, or prior mixing. We test how the horizontal spectrum of that roughness controls the route from a two-layer interface to a finite-depth salt-finger plume forest. Direct simulations of the modeled Boussinesq equations are performed at $\mathrm{Pr}=7$, $\tau=0.01$, and $\mathrm{R}_\rho=1.2$, with matched domain, grid, amplitude, boundary treatment, and analysis measures. The imposed spectra are high-annulus, low-mode, and mixed; a second mixed realization tests robustness. The imposed spectrum selects distinct routes to vertical exchange. High-annulus roughness remains compact and branch-locked through $t=60$, without a tracked broad-branch transition. Low-mode roughness begins on the broad branch, produces the strongest salinity transport at $t=45$, and reaches the finite-depth boundary region first. Mixed roughness follows a velocity-led pathway: vertical velocity selects the broad branch before salinity, while salinity develops the richest planform spectral population. At $t=45$, the mixed salinity effective mode count is $86.66$, compared with $3.26$ for high-annulus forcing and $5.46$ for low-mode forcing. Angular and signed-branch measures show branch-dependent diagonal organization, and probe/volume measures show that local plume-passage asymmetry does not imply large global upper/lower imbalance. The replicate preserves the mixed route with shifted transition times. Thus a finite-depth thermohaline interface can retain spectral memory, controlling whether salt-finger mixing remains localized, penetrates rapidly, or forms a scalar-rich plume forest through delayed modal handoff.

Large-scale intermittency in the vertical velocity (LSI) has received significant attention in studies of coherent structures and their detection using data-driven approaches. However, a theory that predicts the origin of LSI from the Navier-Stokes equations or some approximated version of them at very high Reynolds numbers is yet to be achieved. This letter proposes such a theory for a neutrally stratified wall-bounded turbulent flow based on a dominant balance between inertial and pressure forces. Using multiple flume and wind tunnel experiments, it is shown that the flatness factor ($FF_w$) measuring LSI collapses to a universal trend for all flow configurations within the inertial sublayer (ISL) before reaching a common minimum value above the ISL. A theory that predicts $FF_w$ using second-order statistics and explicitly accommodates large-scale energy anisotropy is tested against a wide range of Reynolds numbers from laboratory to field settings with varied surface roughness conditions. The theory also demonstrates why $FF_w$ cannot be described using down-gradient closure approximations routinely employed in large-scale meteorological and climate models.

Turbulence closure models are essential for solving the equations of motion in realistic systems, where fully resolving all relevant scales of motion is computationally infeasible. Developing turbulence closures remains one of the most challenging problems in fluid dynamics. Specifically, the Navier-Stokes equations, when filtered to isolate large-scale motions, introduce new terms representing the influence of subgrid-scale turbulent stresses. These terms, which can only be computed directly by resolving the turbulence itself, therefore lead to the closure problem: we must add new equations or introduce assumptions to relate the unresolved scales of motions to the resolved flow. Here we consider the closure problem for oceanic flows, i.e., stratified, Boussinesq, incompressible, in a rotating frame of reference. In particular, we focus on a closure for ocean mesoscale eddies, which have horizontal scales of 10-100km and are key to the redistribution of momentum, energy, and tracers in the ocean. In particular, mesoscale eddies can reinject energy and momentum into the large-scale flow through an inverse energy cascade. Here, we explore a range of theoretical and data-driven ocean mesoscale closures and examine their connections using analytical and data-driven methods. This note aims to bridge the gap between novel methods from artificial intelligence (AI) and machine learning and theoretical fluid dynamics to address significant challenges in the physics of turbulence.

We examine receptivity and biorthogonal decomposition in a reacting temporal mixing layer using direct and adjoint eigenmodes of a finite-thickness compressible linearized operator built from the mean reacting base state. The analysis focuses on the Kelvin--Helmholtz branch and asks how the reacting base state modifies the selected temporal instability, where localized forcing most efficiently excites it, and how strongly the associated modal family is represented in time-resolved planar simulation data. Receptivity maps are constructed for mass, momentum, thermal, and mixture-fraction forcing channels using an energy-weighted adjoint projection, with biorthogonality enforced by the corresponding direct--adjoint inner product. A complementary biorthogonal decomposition provides modal amplitudes and cumulative few-mode reconstructions at the fundamental streamwise wavenumber. The finite-thickness branch is interpreted against a compressible vortex-sheet reference built from the outer-stream states. The reacting layer supports an unstable finite-thickness Kelvin--Helmholtz family over low-to-moderate wavenumbers even though the discontinuous reference is essentially neutral. Mass forcing leads the raw localized receptivity maps, mixture-fraction forcing follows through composition-pressure coupling, and chemistry-weighted thermal forcing identifies the strongest thermochemical support of the same family. The results show how distributed reacting thermodynamics reorganize compressible shear-layer instability and how that reorganized branch remains embedded in the nonlinear flow.

Convection remains one of the main uncertain links between multidimensional hydrodynamics and one-dimensional stellar evolution. In particular, transition regions such as near-surface layers or convective boundaries require mean-field descriptions that remain connected to the underlying dynamics rather than to a prescribed mixing length. We describe the flow as a distribution of mesoscopic fluid particles in position-velocity space. A conservation law for this distribution defines the average and yields the Reynolds-Favre mean-field equations as velocity-space moments. Under standard interior conditions, the same dynamics can be written in Liouvillian form, which extends the Hamiltonian structure to stratified and dissipative media. The Liouvillian formulation identifies the phase-space divergence, $\{s, T\}$, as a local measure of contraction or expansion of nearby trajectories. In the quasi-adiabatic limit, its sign reduces to the classical Schwarzschild stability criterion. Away from this limit, the diagnostic remains velocity-resolved and can distinguish different parts of the convective population within the same layer, for example in surface and penetration regions. Appendices show how rotation, magnetic fields, and composition changes can be incorporated through modifications of the phase-space structure. Phase-space averaging provides a dynamically grounded route from hydrodynamics to mean-field stellar convection equations. It also supplies a local trajectory-based stability diagnostic and a natural starting point for the maximum-entropy closures constructed in the companion paper.

An improved formulation of the recently developed cell-centered nodal integral method (MCCNIM) is proposed for the numerical solution of the nonlinear Burgers' equation. The improved scheme, referred to as RCCNIM, reformulates the nonlinear convection term prior to discretization by evaluating the convective velocity using cell-averaged values from the previous time level, rather than the present-time approximation used in the original MCCNIM formulation. This reformulation leads to a fully algebraic system whose coefficients depend only on known quantities and are therefore evaluated once per time step. As a result, the proposed method significantly reduces computational cost while retaining the accuracy of the original MCCNIM. The performance of RCCNIM is assessed through systematic numerical comparisons with MCCNIM for the nonlinear Burgers' equation. The results demonstrate that RCCNIM achieves comparable accuracy with improved computational efficiency, indicating its potential for extension to more complex nonlinear fluid flow problems.

Convection in icy moon oceans is strongly influenced by rotation, organizing into slantwise columnar structures aligned with the planetary rotation axis. They generate significant meridional heat transport, which can affect the ice shell topography, a primary observable of these moons. However, global ocean simulations cannot resolve convection under realistic icy moon conditions, and traditional convection schemes cannot represent slantwise convection. Here, we develop a slantwise convection scheme and implement it in a global ocean model. We perform benchmark tests in a global spherical shell by comparing parameterized fluxes with convection-resolving simulations. The scheme reproduces the meridional heat transport inside the tangent cylinder, where slantwise convection dominates. The resulting meridional heat transport significantly modifies the surface heat flux, producing variations comparable to the imposed bottom heating magnitude. Although the simulations with parameterized convection cannot fully reproduce the temperature structure, likely due to an inability to reproduce the temperature gradients near the boundaries, they capture the bulk interior vertical temperature gradient. The new scheme allows unresolved slantwise convection to be represented in global ocean simulations for icy moons. It is also applicable to other rapidly rotating oceans with small natural Rossby number ($\mathrm{Ro}^* \ll 1$), including deep ocean worlds on exoplanets.

Comprehensive characterization of numerical dissipation is essential for high-fidelity simulations of magnetohydrodynamic (MHD) turbulence. In this work, we present an a posteriori framework for directly estimating numerical dissipation in MHD turbulence from simulation data without invoking a priori assumptions. Implemented in the open-source Python package PyMHD, the framework is applied to simulations of Alfvénic turbulence, turbulent small-scale dynamos, and MRI-driven turbulence, yielding a systematic characterization of the anisotropy and spectral properties of numerical dissipation across these regimes. The results indicate that numerical dissipation primarily dissipates energy transferred by the turbulent cascade at small scales, consistent with the conventional interpretation. However, its spectral properties are distinct from those of physical viscosity and resistivity, such that it cannot simply be represented by effective dissipation coefficients. In addition, numerical dissipation inherits the anisotropy of the underlying turbulence, and can even exhibit anomalous anti-dissipative behavior under certain circumstances. Moreover, this framework enables identification of the conditions under which physical dissipation dominates numerical dissipation across all scales, thereby providing practical guidance for achieving high-fidelity simulations of astrophysical MHD turbulence.

We are concerned with the geometric structures of pseudo-sonic curves in two-dimensional self-similar solutions for the Euler equations for potential flow, allowing for non-uniform supersonic states. Mathematically, the governing second-order potential flow equation is of mixed hyperbolic-elliptic type, with degeneracy occurring along the pseudo-sonic curve. In this paper, we develop rigorous analytical approaches to analyze the geometric structures of pseudo-sonic curves in such self-similar solutions. We first show that the pseudo-sonic curve is necessarily a circle if the pseudo-velocity at each point is a normal to the curve. We then analyze the general case in which the pseudo-velocity on the pseudo-sonic point is not a normal to the curve, and study the geometric properties of streamlines in a neighborhood of the pseudo-sonic curve. Next, we establish two theorems that provide sufficient conditions ensuring that the pseudo-velocity at a pseudo-sonic point is normal to the curve, under natural assumptions on the local behavior of the solution. These results yield a precise characterization of the geometry of pseudo-sonic curves. Finally, we apply the developed theory to the shock reflection-diffraction problem with non-uniform incoming flow. We prove that the pseudo-sonic curve must be an arc if the solution is a $C^2$-small perturbation, either in the pseudo-supersonic or pseudo-subsonic region, of a solution with uniform incoming flow. In particular, the density and velocity must be constant, corresponding to the radius and the center of the pseudo-sonic arc, respectively. Moreover, we prove that the solution is $C^{2,\alpha}$-regular in the pseudo-subsonic region up to the sonic arc (except at point $P_1$). The techniques and ideas developed in this paper are expected to be applicable to other nonlinear problems involving similar mixed-type degeneracies.

Resolving the impact of magnetic field instabilities in triggering small scale turbulent flow and the associated rearrangement of the field is of critical importance in understanding multimessenger observables in binary neutron star mergers, and angular momentum transport in neutron stars and accretion disks. Direct simulation of these instabilities are unfeasible, however large-eddy simulations can incorporate the impact of this turbulence with a subgrid model. We present the first machine-learning-based subgrid model for special relativistic magnetohydrodynamics, trained using a neural network. We demonstrate its performance in online simulations of the 3D Kelvin-Helmholtz instability through both a priori and a posteriori tests. Evaluated in a low resolution simulation, our model captures magnetic field amplification of a simulation at 4 times the resolution with a speed-up of a factor 44. This demonstrates the applicability of such methods in general relativistic simulations of neutron star mergers and other scenarios.

In recent years a weak but robust response of mean midlatitude circulation to Arctic amplification (AA) has emerged from modeling experiments. However, open questions remain about the mechanisms linking such circulation differences to weather extremes in the midlatitudes. In this study we investigate such mechanisms and the importance of zonal asymmetries in shaping the atmospheric blocking response to AA. We perform idealized aquaplanet simulations in two configurations: a zonally symmetric setup and a zonally asymmetric experiment featuring a localized midlatitude storm track. For each configuration, we examine the response to AA by imposing an anomalous surface heating in the polar region. In the zonally symmetric configuration atmospheric blocking increases uniformly with AA from mid to high latitudes. In the asymmetric configuration, the response is more complex; instead of a zonally uniform response, we observe an upstream displacement of the blocking maximum, which sits at the exit of the localized storm track. We interpret these changes through the lens of the Traffic Jam theory by diagnosing the carrying capacity of the midlatitude flow. In both configurations, the zonally averaged increase in blocking is primarily driven by a weakening of the zonal winds, which reduces the Doppler-shifted Rossby wave group velocity and, in turn, decreases the flow carrying capacity. While the reduction in carrying capacity has similar characteristics in the two configurations, in the asymmetric case it leads to an upstream shift of blocking frequency as a direct consequence of the threshold behavior of blocking onset that lies at the core of the Traffic Jam theory. This mechanism, which has received limited attention so far, highlights the importance of mean circulation characteristics in shaping the blocking response to external forcing such as Arctic warming.

Purpose: Physics-Informed Neural Networks (PINNs) struggle with stiff, regime-changing transport equations due to instability, loss imbalance, and violations of physical consistency. This paper investigates these failures through the Marshak wave equations - a canonical benchmark from radiative transport - where initial and boundary conditions differ by up to 12 orders of magnitude, and proposes targeted modifications to the standard PINN framework to overcome them. Design/methodology/approach: Three modifications are introduced: (1) a ScaledSigmoid final activation enforcing physical bounds and positivity of the unknowns; (2) a logarithmic MSE loss replacing the standard quadratic loss for initial and boundary conditions, enabling training across extreme scale disparities; and (3) explicit enforcement of global conservation laws derived from the governing equations as an additional physics loss term. Monte Carlo sampling with exponential time weighting is used throughout. Findings: The proposed framework successfully recovers the Marshak wave dynamics - including the hot, cold, and wave-front regions - in agreement with a reference Implicit Monte Carlo solution, with run times under 30 minutes. Ablation studies confirm that each ingredient is essential: linear activation, absence of the logarithmic loss, or removal of the PDE term each independently cause the method to fail qualitatively. Originality/value: This work identifies and resolves three concrete failure modes of standard PINNs on stiff hyperbolic systems with nonlinear coupling. The combination of bounded activations, scale-aware loss functions, and conservation law enforcement constitutes a novel and practically validated framework, with applicability to radiative transport and other coupled stiff PDE systems in engineering.

Sums of independent exponential random variables lead to the Erlang distribution, providing a direct probabilistic route from exponential waiting times to the integer-shape gamma law. This paper investigates how this classical construction changes when the exponential waiting-time density is replaced by the $q$-exponential density of nonextensive statistics. Our main result is an analytical asymptotic expression for the outflow of a mass-conserving cascade of reservoirs driven by a $q$-exponential waiting-time kernel. In the critical case $q=5/3$, the large-cascade flow rate converges to a stable Lévy density whose time argument is shifted by a Galilean-type transformation. This shifted Lévy law gives the asymptotic hydrograph of the cascade. We also found that for the entire regime $1

In a recent paper [ arXiv:2604.24783 (2026)], we have proposed a general approach to treat systems with inherent non-Boltzmann-Gibbsian behaviour. Given the extremely high accuracy of our approach, we have adopted the term hyperstatistics. We have applied such a statistical mechanics approach, i.e., hyperstatistics, to the discharge of a capacitor in a RC series circuit, pumping of $^4$He of a closed cycle cryostat, midrapidity data of $p$-Pb collisions at the LHC, as well as for the distribution of accelerations in turbulent systems. Here, we discuss into more details the ground of hyperstatistics. We demonstrate the versatility of hyperstatistics upon applying it to the velocity autocorrelation function in Brownian motion and also regarding its potential to describe brain dynamics.

Physics-informed and data-driven surrogates are increasingly used to approximate mechanics-governed flow fields, but the target quantities assigned to such models are not always identifiable from the input variables available at prediction time. We introduce an input-schema identifiability certificate for computational surrogates. Starting from a reduced physical model, the certificate decomposes a target field into components that are measurable from geometry, components that require boundary-condition information, and components identifiable only up to a symmetry quotient. This yields a pre-training audit: it predicts which oracle-channel interventions should reduce error, which should fail, and which ambiguity cannot be removed by changing the architecture, loss, optimizer, or sample size. We instantiate the framework for incompressible tubular flow using a Cosserat-rod reduction, where lumen velocity separates into a mesh-measurable tangent direction, a boundary-condition-dependent magnitude, and a signed-orientation ambiguity. Controlled experiments on patient-specific aortic CFD geometries, analytic Womersley flows, and an advection-diffusion transfer problem confirm the predicted pattern: supplying signed direction collapses angular error to the oracle regime, whereas supplying magnitude without orientation leaves the predicted sign ambiguity and yields 16-33 percent per-node sign flips. The results provide a mechanics-based diagnostic for deciding whether a surrogate modelling task is physically identifiable before training, and expose failure modes that aggregate error metrics can hide.

Finite-strain hyperelasticity on curved embedded domains poses a geometric challenge for lattice Boltzmann methods. After streaming across an embedded material surface, the missing population is recovered at the physical cut-link point, where the lattice direction, surface normal, and tangential deformation directions are generally distinct. We develop a total-Lagrangian vectorial lattice Boltzmann method that resolves this geometric mismatch for two- and three-dimensional hyperelastic dynamics. The continuum equations are written as a conservative first-order system for material velocity and deformation gradient. Vector-valued populations are chosen so that their moments recover the state and the material-coordinate Piola fluxes, giving D2Q4\(\times\)6 and D3Q6\(\times\)12 schemes from one \(D\)-dimensional construction. Curved boundaries are embedded by a level set and closed link by link through opposite-population moment identities, cut-link interpolation, and local geometric information at the boundary point. The reconstruction is coupled to a compatibility projection that keeps the recovered displacement aligned with the evolved deformation gradient on embedded active-node graphs. The resulting method extends the previous grid-aligned two-dimensional formulation to curved domains and three-dimensional lattices while retaining explicit collide-stream updates on Cartesian grids. Benchmarks in two and three dimensions show agreement with exact finite-strain fields, nonlinear radial boundary-value problems, and finite-element references.

An efficient implementation of quantum algorithms is often hindered by the lack of efficient primitives for operators and state preparation. This limits both the ability of near-term quantum hardware to simulate complex problems and the potential of fault-tolerant algorithms to achieve practical quantum advantage. To address this, we propose a full-stack variational framework that transforms arbitrary operators to compact quantum circuits. The resulting variational circuits can be tailored to the connectivity and long-range interaction of the target hardware. The learning process employs backpropagation together with a cost function that efficiently optimizes unitary operators and non-unitary -- dense or sparse -- operators using only a single ancilla qubit for block encoding. Additionally, we introduce a regularization term that reduces the approximation error. The approach is validated for both quantum mechanical and engineering applications. In the former case, we learn propagators that arise in native quantum problems -- such as quantum simulation and quantum chemistry -- and achieve improved resource scaling in comparison to standard Suzuki-Trotter expansions. In the latter case, we demonstrate the approach's ability to implement the second-order central finite difference approximation of the Laplace operator -- relevant for solving partial differential equations -- while improving upon current error metrics. The final example deals with learning a dense, non-unitary operator that arises in the analysis of inviscid potential flow around an airfoil. This universality of the framework opens the door for solving general problems beyond prototypical engineering and quantum applications.

Stickiness in mixed Hamiltonian systems causes chaotic trajectories to remain temporarily trapped near regular structures, making it difficult to distinguish regular, weakly chaotic, and strongly chaotic motion over finite times. We show that the recurrence time entropy (RTE), previously used in discrete maps, also characterizes weak chaos in Hamiltonian flows. In the Hénon-Heiles system, the RTE reproduces the phase space structures identified by the largest Lyapunov exponent: low values in regular islands, higher values in chaotic regions, and intermediate values in sticky layers. The proportion of chaotic trajectories identified by the RTE is consistent with that obtained from the smaller alignment index (SALI). The finite-time RTE series identify low-entropy episodes near regular islands, associated with temporary trapping. The duration of these episodes displays algebraic decay, while high-entropy episodes display exponential statistics. These results establish the RTE as an effective diagnostic of weak chaos and stickiness in Hamiltonian flows.

Antiferromagnets offer ultrafast, stray-field-free dynamics that are attractive for neuromorphic spintronic devices. Here we analyze an antiferromagnetic spin-Hall nano-oscillator in the overdamped regime and derive a reduced set of equations for the Néel-vector dynamics constrained to the unit sphere. For spin polarization along the easy axis, the model reduces to an asymmetric rotator, for which analytic solutions and the associated spin-pumping signal are obtained in selected limits. We further show that near a suitable operating point, the projected dynamics can be transformed into a local FitzHugh-Nagumo normal form. The resulting mapping identifies the effective fast variable, recovery variable, bias current, and Hopf condition in terms of magnetic material parameters. We finally extend the reduced model to an Itô stochastic FitzHugh-Nagumo equation driven by spin-pumping input and additive thermal or electronic fluctuations. The stochastic phase portrait shows that the deterministic nullcline geometry organizes noisy spike cycles and produces controlled spike-time variability. These results provide a minimal analytic framework for AFM-based spiking-neuron elements and suggest design criteria for future neuromorphic spintronic devices.

Stochastic fluctuations are inherent to thermoacoustic systems operating under turbulent combustion. Heat release and flow disturbances continuously perturb the acoustic field. In this study, we examine the influence of colored noise on amplitude death (AD) in coupled thermoacoustic systems. AD corresponds to the complete suppression of self-sustained thermoacoustic oscillations. The system consists of two coupled horizontal Rijke tube oscillators with time-delay and dissipative coupling. Stochastic forcing is modeled using an Ornstein-Uhlenbeck process, allowing independent control of noise intensity and correlation time. We find that increasing noise intensity gradually smooths the transition from limit cycle oscillations (LCO) to AD. It also reduces the extent of the AD regions. In contrast, the qualitative bifurcation structure remains largely unaffected by the correlation time of the colored noise. From coherence factor analysis, we find both white and colored noise induced coherence near bifurcation thresholds. The maximum coherence occurs when the correlation time is comparable to the acoustic time scale. For both shorter and longer correlation times, the coherence is reduced. These results highlights the robustness of coupling induced AD under realistic noisy conditions for effective control of thermoacoustic instabilities. Further, the coherence factor can serve as a potential early warning indicator of thermoacoustic instability in coupled thermoacoustic systems.

Synaptic transmission delays are ubiquitous in neural circuits and can alter the dynamical repertoire of coupled oscillators quantitatively and qualitatively. Here, we demonstrate that delayed coupling in inhibitory networks introduces an effective slow-fast structure in the phase-difference dynamics, generating low-frequency components that are not due to intrinsic cellular properties, and we show that this behavior is not specific to a particular model structure. The origin of this generic phenomenon is analyzed by numerical continuation and bifurcation analysis, which provides a systematic approach to find such delay-induced slow modulating rhythms. We employ phase reduction based on phase response curves to derive a phase-difference model with delay for mutually inhibitory coupled oscillators, where the individual units are given by the FitzHugh-Nagumo model, the Morris-Lecar model, or a next-generation neural mass model derived from quadratic integrate-and-fire neurons. We use phase planes to study multistability and limit cycles, which correspond to slow modulation of fast oscillations in the full model. Treating the synaptic delay as a bifurcation parameter, we apply numerical continuation to construct delay-dependent bifurcation diagrams. The analysis reveals Hopf, heteroclinic, and saddle-node-of-periodics bifurcations that cause and organize slow rhythmic behavior. Our analysis provides a systematic approach to the search for limit cycles in phase-reduction models corresponding to delay-induced slow rhythms in the original model.

Predicting the behavior of dynamical systems (DS) beyond the dynamical and parameter regimes observed in training is a pivotal and essentially unresolved problem in scientific ML. It is central to any good scientific theory, which we expect to be able to make predictions about regimes not covered by currently available data. Recent hierarchical and hyper-network guided approaches for DS reconstruction (DSR) enable training on many DS simultaneously, and revealed that extracted latent features are often related to crucial control parameters of the underlying DS that varied across the training corpus. However, true out-of-domain forecasting abilities of these models, e.g., across tipping points, remain limited, and fine-tuning, or even full model retraining, on time series from the new dynamical regime is usually required. Here, we mathematically analyze the root of these limitations in previous model formulations and identify three core shortcomings rooted in a mismatch between structural assumptions of the reconstruction model and typical properties of physical systems. We propose a combination of remedies for these shortcomings, most importantly feature splitting, and furthermore derive a closed-form bound on the reliable extrapolation range. We demonstrate empirically that our techniques allow for accurate zero-shot prediction into new dynamical regimes, outside the observed training regime, as, e.g., encountered across tipping points.

Biological systems maintain function in fluctuating environments by transforming past stimulation into internal dynamical states that support future-oriented responses. Reservoir computing provides a computational analogue, but standard formulations often treat the recurrent substrate as a fixed random network and train only the readout. Here we ask how the substrate itself changes when reservoir architecture is placed under evolutionary selection for prediction. Using the Kuramoto--Sivashinsky equation as a testbed for spatiotemporal chaos, we evolved reservoirs over five construction hyperparameters: size, connectivity degree, spectral radius, input scaling, and readout regularization. Evolution reduced prediction error at the population level, extended the low-error forecast horizon, and organized the design space along a diminishing-return size--efficiency frontier. Structural analyses showed that evolved reservoirs remained within a conserved stochastic-block-model-like spectral envelope while refining low-eigenvalue modes, locking modularity to an intermediate band, and pruning connection cost within that band. Pareto analysis showed that elite reservoirs occupied a horizontal floor in the cost--modularity plane, indicating that accuracy and efficiency were achieved jointly rather than through a simple trade-off. These findings show that evolutionary optimization does not merely improve prediction, but exposes interpretable structural constraints on the recurrent substrate: it stabilizes a task-suitable dynamical class and refines the architectural degrees of freedom most relevant for prediction. Evolutionary reservoir computing therefore provides a bio-inspired framework for studying how predictive demands shape adaptive dynamical networks.

The atmospheric tropical belt is believed to be more predictable than the extratropics. This question is revisited here by exploring the emergence of chaos in reduced-order model versions of the vorticity equation under the weak temperature gradient hypothesis, which provides a good description of the large-scale tropical atmosphere. The analysis reveals that under fairly realistic divergence forcing amplitudes, chaos may emerge, sometimes with Lyapunov time scales of less than a day. This result contrasts with the idea of a predictable tropical atmosphere, and opens important questions on the effective origin of predictability in the Tropics.

Detecting when a nonlinear dynamical system departs from its normal regime is a recurring problem across the sciences, from cardiology to climate and energy systems. We show that a very simple Kolmogorov--Smirnov test on the output weights of a reservoir computer is highly sensitive to regime changes in nonlinear dynamical systems, including those invisible to both classical nonlinear measures and modern deep-learning detectors. The core idea of our algorithm is to treat the readout layer of a reservoir computer as a representation of the input dynamics. Since the input mapping and the reservoir itself are random and fixed, the trained output weights are the only object encoding the system at hand. We summarize this fingerprint by the empirical cumulative distribution function of the readout weights and compare it to a reference band built from the training data. This unsupervised, online detector distinguishes two visually indistinguishable butterfly-shaped attractors, resolves parameter drifts seven times smaller than the strongest deep-learning baseline, flags noise four orders of magnitude below the signal, and identifies ventricular flutter in a clinical ECG recording. More broadly, we aim to establish a perspective on reservoir computers in which the trained output weights are treated as a representation of the learned system in their own right, rather than merely as a means to forecasting.

Frequency combs are discrete, equally spaced, phase-coherent spectral lines that emerge from nonlinear mode coupling in physical systems. We show that the incommensurate fractional-order financial model of Huang, Li, Ma, and Chen, whose Caputo derivatives encode macroeconomic long-range memory, generates an analogous structure in its steady-state spectrum. The comb appears only over specific values and ranges of the saving amount $a$, the investment cost $b$, and the demand elasticity $c$, outside which the spectral lines lose their equal spacing. It persists across extended parameter regimes and stays invariant to perturbations in the initial interest rate $x_0$ and investment demand $y_0$, while distinct spectral regimes appear at different initial price levels $z_0$. The comb is generated only when the fractional-order exponents $q_1$, $q_2$, and $q_3$ associated with interest rate, investment demand, and price index are above the critical threshold values. At even higher values of these exponents, the frequency comb transitions into chaos. These findings show that the long-run cyclic structure of a memory-bearing financial economy organises into a discrete, deterministic spectral fingerprint rather than a stochastic continuum.

Nonlocal optical nonlinearities arising from the thermorefractive effect provide a long-range material response determined by heat diffusion and absorption. In graded-index media, this nonlocality fundamentally alters modal interactions, yet its accurate modeling remains computationally demanding when starting from the full spatial nonlinear Schrödinger equation. In this work, inspired by the nonpolynomial Schrödinger equation (NPSE) framework, we extend the dimensional reduction techniques to incorporate thermally mediated nonlocal nonlinearities. By coupling the optical field to an equation for the temperature-induced refractive index change, and employing a variational ansatz based on Laguerre--Gauss modes of the annular kind, of arbitrary azimuthal order, we derive explicit analytic expressions for the variational equations. The resulting effective model captures the dependence of the nonlinear interaction on mode order and degree of nonlocality, providing a tractable reduced description of the dynamics in thermal nonlocal media.

In the focusing Manakov system, multiple modulation instability (MI) branches coexist on the same plane wave background, so the usual weak periodic modulation cannot selectively excite a single vector Akhmediev breather (AB). Here we propose an eigenvector-based initial perturbation scheme that constructs the initial condition as a plane wave plus Fourier modes whose coefficients follow the perturbation eigenvector of a selected MI branch, enabling controllable high-fidelity excitation of desired vector ABs. Numerical simulations show near-100\% fidelity with the exact AB solution. The underlying mechanism is eigenvector-controlled mode selection. The initial seeding of the target MI branch through the chosen eigenvector, together with the non-Hermitian coupling inherent in the linearized MI dynamics, ensures that the targeted unstable mode dominates the early linear stage and thereby dictates the breather type. This eigenvector-based control succeeds in gain-balanced regimes and when the targeted branch has a sufficient gain advantage. The proposed method provides a simple and robust framework for controllable generation of vector ABs over a broad parameter range, highlighting the key role of eigenvector selectivity in multi-component nonlinear systems.

We show that compartmentalizing a single molecular species into intracellular and extracellular fields, and coupling them through membrane transport or nonlinear basal production rates, can produce diffusion-driven (Turing) instabilities. By linearizing the two-field system, we derive the corresponding Turing conditions under which such instabilities may arise. We present three biologically motivated examples that satisfy these conditions and demonstrate the resulting spatial patterns through numerical simulations. These results indicate that tissue compartmentalization alone might enable pattern formation traditionally attributed to multi-species systems.

We show that an oscillon can be understood as a localized discrete resonant (non-normalizable) mode. Specifically, oscillon in the vacuum arises from the threshold mode, which because of nonlinearity gets localized. Following this idea, we find {\it wobblerons} - nonlinear excitations of kinks, that is, oscillons-kink bound state. Now, the oscillon can also originate in an antibound mode, i.e., a discrete, positive energy but non-normalizable mode.

Recent advances in the work with ultracold condensates of polar molecules have enabled the realization of highly tunable self-bound quantum droplets (QDs), with the help of dual microwave fields dressig the dipole-dipole interactions (DDIs) It has been reported that symmetry properties and the equilibrium phase diagram of such QDs can be controlled by parameters of the two microwave fields. However, the effect of these fields on the formation and dynamics of the QD has not yet been systematically explored. Here we address self-bound QDs in a regime dominated by non-axisymmetric DDIs and governed by the extended Gross-Pitaevskii equation with the Lee-Huang-Yang corrections. Within this framework, we identify the existence region of the self-bound QDs and characterize their chemical potential, total energy, effective volume, peak density, and geometric anisotropy. The results reveal a pronounced nonmonotonous dependence on the non-axisymmetric DDI strength, whereas the increase of the number of particles in the condensate leads to tighter bound and more anisotropic QDs. Furthermore, reducing the s-wave scattering length drives a transition from stable self-bound states to the collapse. Collisions between QDs moving along different directions reveal a strong directional dependence, with outcomes ranging from quasi-elastic rebound and merger to fragmentation.

We revisit the topic of false vacuum decay in field theory. We focus on a toy model of a real massive scalar field with an unstable quartic potential. This model has a false vacuum, and decay out of the false vacuum can be described via the method of constrained instantons, which work by introducing a constraint on the path integral. We identify and develop three different asymptotic limits which enable analytic construction of approximate {constrained} solutions. The first, in which the constrained solution is small compared to the inverse mass of the scalar field, is an application of the perturbative methods of Affleck, although we re-derive the main results and identify several terms which were previously neglected. Second, for very large constrained solutions we adapt the thin-wall approximation of Coleman. However, we find that the large instanton limit does not always exist. In this case we identify another useful limit, in which the Lagrange multiplier used to implement the constraint is large. In this limit, the solution's scaling with the parameters may be found via dimensional analysis and an exact solution is obtained with a single numerical computation.

The transition-matrix ($T$-matrix) method has established itself as a prominent technique for computing the scattering response from spatially localized objects. The suitability becomes apparent particularly when considering not just isolated objects but also large ensembles of aperiodically or even periodically arranged objects. A versatile implementation of the method is provided by the treams program, which efficiently computes the electromagnetic response of scatterers in various arrangements [Comput. Phys. Commun. 297, p. 109076 (2024)]. Here, we rely on this framework and present a new program, acoustotreams, dedicated to simulating the acoustic scattering of pressure waves by clusters of particles, both with and without periodic boundary conditions. The computations are performed using the $T$-matrix method with scalar spherical and cylindrical waves as basis sets, and the scattering matrix ($S$-matrix) method in the basis of scalar plane waves for stratified media. The underlying theory is presented alongside the program structure and illustrative examples. The code is open-source and available on the Python Package Index for Linux, Windows, and macOS. Version control is maintained through GitHub, where we also provide automated tests, documentation, and detailed examples. We expect this work to contribute to the field of numerical methods for multiple-scattering problems by offering a computational framework capable of a comprehensive description of pressure-acoustic scattering in artificial media, including well-established metamaterials and metasurfaces.

The present research presents potentials and complementary potentials used in the one-dimensional nonlocal integral formulations. The pure stress and the pure strain nonlocal formulations were considered. While the potential used in the strain driven formulation is well known, the complementary potential has not yet been presented in the literature. The same applies to the stress driven formulation. The equivalent formulations are obtained by resorting to the Legendre transformation, and their equivalence is proved. It is also shown that these results can be used to postulate a novel potential, i.e. a kind of mixed stress-strain potential, which is, however, as ill-conditioned as the pure strain-driven formulation. Finally, an example is given that practically confirms that the stress-driven formulations resulting from the potential and the complementary potential are equivalent.

When a wine glass is dragged on a table along a circular path, a spontaneous rotation about its vertical axis can develop even if the applied hand force does not directly introduce a yaw torque. This document provides a structured formal derivation of the governing equations that are responsible for this behavior. The analysis shows that the mechanism responsible for this effect is the redistribution of pressure onto the table when applying the force with your hand. This causes an uneven frictional force distribution which exerts a torque on the glass, causing it to spin.

We consider localized oscillation of an Euler--Bernoulli beam on a visco-elastic foundation coupled to a damped discrete oscillator. All parameters of the system independently vary in time in a slow manner. For the conservative case, we use three various analytic approaches. Namely, these are asymptotics, the method based on the adiabatic invariance of the action of a trapped wave, and the consideration of the equivalent Hamiltonian system. All approaches result in the same formula for the amplitude of oscillation. In the dissipative case, we obtain the amplitude of oscillation only utilizing the asymptotic approach.

We study the problem of cooking the yolk and albumen of a hen's egg to their respective optimal temperatures of $T_Y^* = 65^\circ$C and $T_W^* = 85^\circ$C, subject to the requirement that neither temperature ever exceed its target at any time during cooking, since temporary overshoot still overcooks the egg even if the final reading is correct. We model the egg as a two-domain sphere with distinct thermal diffusivities, and take the Laplace transform of the heat equation in each domain, reducing the problem to a $3 \times 3$ linear system in the transform variable $s$ with hyperbolic-trigonometric solutions. The resulting transform is inverted numerically via Talbot's method and validated against a finite-difference solver. A single boiling phase cannot satisfy the no-overshoot requirement: the thin outer albumen heats far faster than the insulated yolk and necessarily overshoots $T_W^*$ before the yolk approaches $T_Y^*$. We show that a three-phase protocol resolves this: a sous-vide pre-soak at exactly $65^\circ$C (which cannot overshoot since the bath temperature equals the target), a short boil to bring the albumen toward $T_W^*$, and an ice-water bath that arrests the albumen's residual overshoot while residual heat continues raising the yolk to its target. Optimizing the phase durations gives $17.26$ minutes of sous-vide, $66$ seconds of boiling, and an ice bath, achieving both targets at $T^* \approx 20.67$ minutes with neither constraint violated at any time. This compares favorably with the periodic protocol of Di Lorenzo et al. (2025), which requires 32 minutes and misses both targets substantially.

In this paper, we study the statistical field-theoretic renormalization of active flocks via the MSRDJ action formulation for stochastic systems, focusing on the Toner-Tu theory of `Malthusian flocks', or polar-ordered, momentum non-conserving active fluids where relaxation times for density fluctuations are so short that they can be eliminated as a hydrodynamic variable. Working in the limit of isotropic diffusion in two spatial dimensions, we compute the renormalization of the couplings and their anomalous dimensions to all orders, facilitated by a non-linear realization of a generalized \textit{Galileon} symmetry and its associated Ward identities. We find a range of behavior depending on the parameters of the theory. If $\kappa$ is the diffusion coefficient and $\Delta$ is the variance of the noise, we find a line of fixed points and a marginal vertex instability at $\Delta/\kappa = 2\pi$. This instability separates Gaussian, and strongly interacting, symmetry-protected gapless phases, realizing non-equilibrium critical behavior beyond conventional Wilson--Fisher criticality. The existence of gapless excitations in both phases can be traced to the soft (Adler zero) theorems associated with the generalized Galileon symmetry, and implies the persistence of long range order when $\Delta/\kappa$ is below the critical value. We revisit and contextualize various claims and counter-claims in the literature in light of our findings, and discuss extensions of our analysis to anisotropic diffusion, and towards flocks where density fluctuations are reintroduced.

Many industrial applications and biological scenarios involve the interdiffusion of two polymeric species. Motivated by biological subcellular source-driven processes, we study polymer-polymer interdiffusion problems in the absence or the presence of a polymeric source, for both unentangled and entangled scenarios. Utilizing a two-fluid formalism, we arrive at scaling relations, self-similar reductions, and analytical solutions, which are confirmed with one- and two-dimensional numerical simulations. The introduction of a source term breaks the self-similar structure, modifying the boundary conditions and the domain of integration. Nevertheless, we show that the front characteristics of the diffusing droplet exhibit similar spatial structures as in the absence of a source. Our results allow deeper understanding of polymer-polymer interdiffusion and nonlinear transport, especially in the presence of a source.

We study single-file transport of driven overdamped colloidal particles on a periodic path with deep potential wells. In the small trap limit (i.e., trap size smaller than particle size), the particle current transitions from zero to finite as the number of particles on the path exceeds a critical number $n_c$. Beyond this threshold, $n_c$ particles cluster behind the trap, demonstrating collective correlated motion. The remaining `extra' particles circulate, giving a finite current. We study this phenomenon numerically using overdamped Brownian dynamics simulations, and present an experimental realization of this behaviour for micron-scale colloidal particles driven in an optical vortex. Using our experimental observations, we present results characterizing potential wells as deep as several hundred $k_BT$.

We investigate shells of active oriented solid, materials in which orientationally ordered active particles are embedded in a deformable elastic surface. Focusing on cylindrical geometries, we show that active stresses drive a new class of buckling instabilities and nonlinear patterns absent in passive shells. Linear stability analysis reveals that the unstable buckling mode is selected by the nematic orientation and activity sign, leading to axial, circumferential, and helical deformations. Remarkably, circumferential modes become unstable at arbitrarily small activity due to the absence of stretching costs. The results of the linear stability analysis are corroborated by full nonlinear simulations, which further uncover steady diamond shaped patterns and persistent dynamical states including oscillations, traveling domain walls, and propagating waves. Our results establish fundamental buckling modes and emergent patterns in shells of active oriented solid materials, with potential relevance to active biological tissues and engineered responsive materials.

We study directed transport in a two-dimensional suspension of repulsively interacting colloids driven by a stochastic asymmetric piecewise-linear flashing ratchet using large-scale molecular dynamics simulations. The driving frequency and the ratchet asymmetry offer two independent ways of controlling the particle current, but they affect the suspension differently. At fixed asymmetry, the current shows a resonance with ratcheting frequency that is set by the collective relaxation dynamics of the interacting particles. The resulting increase in transport is accompanied by defect-mediated structural changes, showing density-dependent hexatic and solid-like states, with larger currents generally associated with weaker ordering. By contrast, at fixed frequency, changing the ratchet asymmetry mainly alters the strength of the directed bias and can significantly enhance the current while leaving the hexatic order largely unchanged. Near the equilibrium hexatic-melting regime, this makes it possible to generate substantial directed currents without strongly disrupting sixfold orientational order. These results show that frequency tuning couples transport to structural reorganization, whereas asymmetry tuning primarily controls transport leaving the structure largely unaltered, providing distinct and complementary routes for manipulating transport and order in driven colloidal suspensions.

Bacteria often swim in complex environments where surfaces are ubiquitous and rarely flat. Surface topography and curvature can strongly affect bacterial motility, with important consequences for surface exploration, adhesion, and biofilm formation. Here, we investigate the swimming of a non-tumbling \textit{Escherichia coli} bacterium near an undulating no-slip surface using hydrodynamic simulations of a detailed model bacterium. The latter is described by a rigid spherocylindrical cell body and flexible flagella modeled with the Kirchhoff rod theory, while the surrounding fluid is simulated using the method of multi-particle collision dynamics. At low curvatures of the sinusoidal surface modulations, the bacterium exhibits persistent near-surface swimming and clockwise trajectories, consistent with the known behavior near flat no-slip walls. As the curvature increases, bacteria swimming toward a ridge can escape from the surface, which we use to estimate a critical curvature where surface detachment is more likely. At larger curvatures, we find that the surface geometry promotes oscillatory swimming along the groove direction, which reduces escape opportunities and, therefore, enhances bacterial trapping. Indeed, the confinement around the groove reverses the swimming of the bacterium from clockwise to counter-clockwise, as we demonstrate by two minimal models. Thus our work highlights the importance of the three-dimensional surface topography in bacterial surface exploration.

We develop a molecularly motivated description of the nonlinear index (NLI) in oscillatory shear deformation of entangled polymers. The central assumption is that the shear component of the tube-orientation tensor cannot grow without bound. Convective constraint release (CCR), chain stretch, and tube dilation progressively reduce the number and lifetime of orientational constraints, but the maximum shear alignment of a tube segment is geometrically limited by $S_{xy}\leq 1/2$. This motivates a constraint-limited orientation closure in which the NLI first grows approximately with strain amplitude and then approaches the limiting value $\mathrm{NLI}_{\max}=3$ asymptotically rather than through an artificial cutoff. The same framework yields a molecular expression for the characteristic half-saturation strain $\gamma_s$, defined by $\mathrm{NLI}(\gamma_s)=3/2$, in terms of the entanglement number, oscillation frequency, and a critical number of remaining orientational constraints. We further derive architecture-dependent expressions for the nonlinear onset strain $\gamma_c$ for linear, sparsely long-chain-branched, and more regularly branched polymers. The resulting framework provides a compact bridge between Fourier harmonic analysis, CCR-based tube dynamics, and the progressive loss of orientational memory in highly deformed entangled polymer liquids.

We formulate a thermodynamic model of a nano-reactor containing charge-regulated macroions within an electrolyte-permeable enclosure. The model is then formalized within the Poisson-Boltzmann electrostatics augmented by the consistent inclusion of the charge dissociation of molecular groups residing on the surface of the entrapped macroions via charge regulation formalism. By solving the basic equilibrium equations in the linearized Debye-Hückel type approximation, we analyze the salient features of the inhomogeneous electrolyte distribution and macroion charge. We found that the surface charge asymmetry/symmetry of the macroions strongly affects the spatial profile of electrostatic potential. The effective screening length shows the non-monotonic behavior, arising from the complex interplay between the bathing external solution and macroion effective charges, which govern charge regulation equilibria. The total pressure at the nano-reactor enclosure boundary decreases monotonically as the enclosure radius and the ionic bulk salt concentration increase. Also, the resulting pressure is strongly influenced by the surface charge densities of the nano-reactor and the number of confined macroions.

Recent experiments combining electrophoresis with pressure-driven flows in microchannels have revealed that microparticles undergo lateral migration perpendicular to the applied electric field. Although fluid inertia has been proposed as a possible explanation, inertial effects are negligibly small in these regimes, leaving the underlying physical mechanism an open question. In this study, we address these observations by extending previous theoretical work on concentration polarization,i.e., the external-field-induced modification of the ionic concentration field surrounding a dielectric object. We consider a dielectric particle with surface conductance subjected simultaneously to an external electric field and a shear flow. We show that the shear flow breaks the symmetry of the ionic concentration around the particle in the direction perpendicular to the applied field, thereby driving lateral migration. We demonstrate that the resulting migration velocity comprises two distinct contributions: an electrophoretic and a diffusiophoretic component. Our theory yields an explicit expression for the velocity magnitude as a function of the zeta potential and the Dukhin number, predicting typical speeds on the order of $\mathrm{\mu}$m/s for representative experimental parameters. Notably, the model also predicts a reversal in the migration direction for Dukhin numbers of order unity.

We introduce a shape-based polar order parameter that captures the structural asymmetry of cells within epithelial monolayers. By combining bright-field imaging and traction force microscopy, we demonstrate that shape polarity serves as a unifying biomechanical metric, integrating the physical information encoded by nematic directors, principal stresses, and cellular motion. Furthermore, we show that the tissue organizes into a mixed polar-nematic phase, characterized by the coexistence of integer ($\pm 1$) and half-integer ($\pm 1/2$) defects. Through mechanical perturbations, we demonstrate that both substrate stiffness and cell-cell adhesion modulate the density of these excitations and the length of domain walls binding like-signed positive half-integer defects. Using a minimal continuum model of polar-nematic active matter, we establish that this mixed phase is fundamentally driven by the interplay of active stresses and polar-nematic elasticity. These findings provide a direct experimental evidence that epithelial monolayers behave as nematopolar matter, in which coupled polar and nematic elastic interactions jointly shape the active state

We study the collective dynamics of self-propelled spherocylinders carrying magnetic dipole moments in two dimensions. Magnetic interactions are modeled as two opposite monopoles $\pm Q$ separated by a distance $\ell$ along the particle director, a dumbbell model that remains well-defined at short range and introduces an explicit geometric lever arm for the magnetic torque. This approach, combined with the elongated particle geometry, produces a torque that competes with steric alignment in a manner inaccessible to point-dipole or disk models. By independently varying monopole separation and dipole strength (parameters that map directly onto the geometry and magnetization of cylindrical magnets) we show that the system navigates a rich landscape of collective states: gas, polar flock, chain, vortex-alignment, and locked-dimer phases. Our results establish that particle elongation and distributed magnetic charge together provide a minimal, experimentally accessible set of tuning knobs for controlling coherent states in magnetic active matter, with direct implications for the design of self-organized magnetic microswimmers and active colloidal assemblies.

Predicting detailed atomistic structures of self-assembling systems remains a challenge for all-atom molecular dynamics simulations. Replica exchange with solute tempering (REST) has been used to study those systems by accelerating all monomers in a global and uniform manner. While such a global approach can in principle predict any morphology of the system, it has computational drawbacks such as inefficient replica traversal due to order-disorder transitions and the growing number of replicas with system size. To address these issues, here we propose an alternative, stepwise construction approach to modeling supramolecular polymers under the assumption of one-dimensional polymerization. Specifically, we generate polymer structures by adding new monomers one by one to the system and applying REST to the new monomers to find their optimal binding positions based on an energy-based scoring function. The monomer addition and enhanced sampling are repeated sequentially until a polymer of desired length is obtained. We test the above procedure using a model supramolecular polymer in explicit solvent, and show that it can generate a polymer structure with characteristic H-bonding patterns at reduced computational costs, while also improving the efficiency of replica traversal significantly. We thus expect that the sequential REST will be useful for modeling supramolecular polymers, particularly for cases where global REST simulations are too demanding computationally.

Cellular automata are discrete dynamical systems defined on a lattice, in which each site carries a finite set of states that evolve in time according to local deterministic rules. An important application of cellular automata is in lattice gas models of fluids, where the cellular automaton framework provides a particle-based microscopic description of hydrodynamic behavior. The macroscopic fluid equations emerge after coarse-graining over many lattice sites and time steps, offering a bottom-up route to hydrodynamics. A celebrated example is the Frisch-Hasslacher-Pomeau (FHP) model, an automaton defined on a two-dimensional triangular lattice that yields the two-dimensional Navier-Stokes equations upon coarse-graining. In this work, we construct a parity-breaking generalization of the FHP model through two modifications: introducing chiral two-body collision rules and systematically rotating particle velocities to mimic the effect of a background magnetic field. We show that this automaton yields a hydrodynamic model with odd viscosity, a transverse transport coefficient that is a hallmark of odd fluids. We verify the analytical transport coefficients using Poiseuille-flow simulations of the chiral FHP automaton. Our results demonstrate that the chiral automaton introduced here provides a bridge between microscopic parity-breaking scattering processes and macroscopic odd-fluid hydrodynamics.

In this work, we develop a state estimation framework for two-dimensional Rayleigh-Bénard (RB) convection that combines a stable Galerkin reduced-order model (ROM) with an extended Kalman filter (EKF). The ROM, constructed from controllability modes of the linearised Boussinesq equations, provides the nonlinear dynamical model for the filter prediction step. Direct numerical simulations (DNS) are used to generate synthetic measurements for data assimilation. We assess filter performance across periodic, quasiperiodic, and chaotic regimes, demonstrating that the filter tracks the most energetic modes with high fidelity and achieves time-averaged reconstruction errors below $14\%$ for velocity and $9\%$ for temperature. We apply the ROM-based EKF to a hybrid simulation scenario where the system state is assimilated from coarse PIV-like velocity measurements. It is shown that velocity observations alone suffice to reconstruct the state, including the temperature field. Finally, we exploit the Kalman gain matrix to develop a greedy sensor placement strategy that progressively removes the least informative sensors. The algorithm reveals a clear hierarchy among sensor types and can be used to derive skeletal observation configurations. It also provides guidance on which measurement variables and spatial locations are most informative for state correction. The present framework is general, and may be applied to other quadratic Galerkin ROMs for state estimation.

We analyze planar Lagrangian transport and scalar-gradient organization in a supersonic, reacting hydrogen-air temporal mixing layer using time-resolved mid-plane data from a three-dimensional direct numerical simulation. The analysis combines forward/backward finite-time Lyapunov exponent (FTLE) fields, operational FTLE-ridge skeletons, Cauchy-Green deformation measures, shear-LCS metrics, and planar hyperbolic geodesic-LCS extraction to examine how finite-time stretching structures the reacting shear layer. The time-resolved FTLE ridges identify repelling and attracting finite-time transport skeletons in the constrained two-dimensional slice, from which ridge geometry, intersection occupancy, persistence, and scalar-conditioned transport are quantified. Hyperbolic geodesic LCS are extracted from Cauchy-Green tensors reconstructed from planar flow maps as strainlines seeded at high-$\lambda_{\max}$ normal maxima, providing a variational counterpart to the operational FTLE-ridge skeleton. We then relate the transport skeleton to temperature, mixture fraction, and a reaction intermediate. The results show localized forward/backward ridge overlap, strong scalar-gradient enrichment, finite-time geodesic LCS that occupy the same high-strain transport skeleton, residual direction-dependent separation from a time- and cross-stream-stratified null model, and scalar-response lags that remain compact relative to decorrelation and FTLE-integration scales. Together, these results provide a transport-oriented characterization of coherent structures and their role in mid-plane mixing within a compressible reacting shear flow.

Recent evidence on the sustainment of wall-normal-velocity bursts in wall-bounded turbulence challenges the classical streak-dependent picture, suggesting that the problem should be approached relying on no a priori knowledge regarding other flow structures. This paper discusses the restarts of bursts in a log-minimal channel within the framework of a linearised Navier-Stokes system with forcing terms encapsulating the nonlinear effects of all other structures. Two generic issues are addressed. The first concerns the conditions for burst-restart-like solutions for the forced linearised system itself. We formulate optimisation problems to understand the 'minimal requirements' for burst restarting. The solutions illustrate three conceptual periods in a typical restarting process, distinguished by the behaviour of spanwise vorticity structures: breakup, counter-rotating catch-up, and co-rotating catch-up. External forces promote this process by breaking up forward-inclined vortices and merging co-rotating, catching-up vortices. A quantity termed linearly available energy (LAE) is accordingly proposed to parameterise the restarting process. The second issue concerns the contributory features to the observed burst restarts in real turbulence. We show that an essential role of nonlinearity in restarting a burst is to increase a decaying state's LAE to a level sufficient for the onset of the subsequent burst. Flow patterns extracted during the restarting stage exhibit breakup and merging effects, both facilitated by nonlinearity. This suggests that the two effects observed in both the linearised models and real turbulence are manifestations of real flow structures that cause burst restarts.

The accurate prediction of laminar-to-turbulent transition is critical for the design of aerodynamic and turbomachinery systems, yet widely used experimental benchmarks, such as the ERCOFTAC T3 series, lack the full-field, three-dimensional, and time-resolved data required for modern model development. To address these limitations, this study presents a high-fidelity numerical database of bypass transition in boundary layers, generated using wall-resolved implicit Large Eddy Simulations (iLES) to rigorously mimic the ERCOFTAC T3 flat-plate experiments. Computations are performed using a high-order compressible Navier-Stokes solver across multiple configurations, encompassing a range of freestream turbulence intensities and both zero and varying pressure gradients. The numerical results demonstrate satisfactory agreement with legacy experimental data for skin friction, mean velocity, and fluctuation profiles. Finally, the resulting database is utilized to evaluate the predictive capabilities of standard Reynolds-Averaged Navier-Stokes (RANS) transition models (SA-BCM and $k-\omega-\gamma$), revealing systemic flaws in predicting transition onset and length. This highlights the dataset's value as a foundational resource for the calibration, assessment, and development of next-generation, physics-informed machine learning transition closures.

Viscous fingering instabilities during fluid displacement in porous media can compromise the efficiency of applications such as enhanced oil recovery, CO2 sequestration, and groundwater remediation. While extensive research exists on linear stability analysis for fully immiscible and fully miscible displacements, the intermediate case of partially miscible flow with limited mass transfer between phases remains largely unexplored. This study extends linear stability analysis to a two-phase, two-component system that accounts for gravity effects, fractional flow, capillary forces, mechanical dispersion, and interphase mass transfer, focusing on the case where a partially miscible gaseous fluid displaces a liquid. We formulate an eigenvalue problem to characterize instability growth rates and cutoff wavenumbers. The resulting ordinary differential equations have discontinuous coefficients at the transition from two-phase to pure-liquid flow, resulting in discontinuous eigenfunction derivatives. We derive jump conditions for the derivatives at this transition, and solve the eigenvalue problem using the matched initial value problem method. Results demonstrate that mass transfer has a pre-dominantly stabilizing effect by reducing viscosity contrast and altering shock properties at the displacement front. This stabilizing influence is particularly pronounced for high viscosity contrasts and dampens gravity-induced instability in upward displacements. Mass transfer most significantly affects the perturbation growth rate, while its effect on the cutoff wavenumber is less pronounced. We identify a critical value for the dimensionless longitudinal dispersion coefficient where both growth rate and cutoff wavenumber are maximized, suggesting complex interactions between capillary forces and mechanical dispersion.

Velocity slip at the solid--fluid (SF) interface plays a key role in fluid transport at the nanoscale, and the SF friction coefficient has been extensively studied because it indicates the degree of slippage. Owing to the scale of this phenomenon, molecular dynamics (MD) simulations are commonly employed using two major approaches: the Green-Kubo integral method in equilibrium MD (EMD), and the direct calculation of friction force and slip velocity in non-equilibrium MD (NEMD) systems under shear. Regarding the latter, a strict definition of the slip velocity is missing due to the nonzero thickness of the boundary at the microscale, and the average velocity of the first adsorption layer or the velocity at the boundary obtained by extrapolation or interpolation is often used. In this study, we propose an alternative description of the slip velocity based on a thermal perspective from the two different scales, i.e., at the macroscale, frictional heat is defined as the product of the friction force and slip velocity, whereas at the microscale, it can be expressed as the sum of the works exerted on the fluid and solid by each other. By combining the two different scales, we defined the slip velocity based on the dissipation induced at the SF interface under shear, which avoids the arbitrariness in the slip velocity at the microscale.

We present a forcing-informed (FI) resolvent analysis framework to identify input-output relations for statistically stationary self-sustained unsteady flows. The central idea of this method is to inform the resolvent operator about the spatiotemporal structures of the nonlinear terms that act as exogenous forcing with respect to the mean flow. To construct the FI resolvent operator, we estimate the basis vectors for the input subspace spanned by forcing snapshots and, similarly, for the output subspace, from simulation data. The extracted FI response and forcing modes are expressed through the estimated bases of the output and input subspaces, respectively, and the singular values of the FI resolvent operator correspond to the actual output amplitudes. These properties ensure that the extracted modes are consistent with the actual self-sustained flow fields. Additionally, the forcing snapshots can be used to construct the linear operator, enabling a fully data-driven FI resolvent analysis. The proposed framework is validated using the Stuart-Landau oscillator and demonstrated for a two-dimensional cylinder wake and a three-dimensional transitional boundary layer. We successfully identify the gains and the corresponding pairs of forcing and response modes, even at frequencies where the nonlinear amplification mechanism is crucial. Furthermore, leveraging the balance between the time-averaged energy amplification/attenuation by the linear operator and nonlinear forcing, we introduce a nonlinear energy transfer map that identifies the spatial domains where the extracted forcing mode injects or removes fluctuation energy, thereby providing key physical insight into the self-sustaining mechanisms.

Laminar-to-turbulent transition delay is a key challenge in hypersonic boundary-layer flows. Unstable disturbances-most prominently the first and second modes-trigger the onset of turbulence and pose a fundamental technological barrier to hypersonic transport. While existing control strategies target the second mode, simultaneous mitigation of the first mode has long appeared physically impossible. A new flow-control concept is introduced in which phase relations between wall pressure and velocity fluctuations are tailored using subsurface phonon engineering to control both modes concurrently. The outcome is substantial drag reduction and alleviation of the extreme thermal loads associated with turbulence.

This experimental work explores the flow field around a three-dimensional expansion-compression geometry on a slender cone at Mach 5 and 8 using high-frequency pressure sensors, high-framerate schlieren, temperature-sensitive paint, shear-stress measurements and oil-flow visualizations. The $7^\circ$ cone geometry has a hyperbolic slice acting as an expansion corner which is then followed by a $30^\circ$ finite-span compression ramp. The freestream Reynolds number was varied so that the boundary layer approaching the expansion corner was either laminar, transitional or turbulent. At laminar or early transitional conditions, the separation shock locks onto the expansion corner and the separation region encompasses most of the slice, with the separation shear layer flapping at a preferred frequency. As Reynolds number is increased, the separation shock moves downstream onto the slice, the separation bubble shrinks, and the shear layer flapping frequency increases while its amplitude drops. In all cases, large-scale low-frequency breathing motions are observed. The strong relaminarization across the expansion corner at Mach 8 prevents the shock/boundary-layer interaction from reaching truly turbulent conditions and fundamentally changes its behavior on this non-canonical geometry.

Increased upper-ocean stratification is an unavoidable consequence of global warming and will strongly impact the structure of ocean currents. Using a high-resolution ocean model, we show that intensification of stratification leads to the loss of coherence of the Gulf Stream Extension, replacing its steady eastward path with vigorous, chaotic meanders. This regime shift persists independently of changes in the Atlantic Meridional Overturning Circulation and surface wind forcing. Enhanced meandering under intensified stratification also proves to be a robust feature across both idealized and realistic ocean models that resolve mesoscale eddies, but is not captured by coarse-resolution models that parameterize eddies. The presented findings therefore highlight the need for improved representations of oceanic turbulence in climate projections.

This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations. Such systems, found in applications like turbidity currents and thermal convection, feature strong nonlinear coupling and multiscale behavior that make high-fidelity simulations computationally expensive. To address this, the chapter surveys state-of-the-art SciML methods for building efficient surrogate models, including linear reduced-order techniques based on Singular Value Decomposition (such as Dynamic Mode Decomposition) and nonlinear neural network approaches like Physics-Informed Neural Networks (PINNs) and $\beta$-Variational Autoencoders ($\beta$-VAEs). It first covers the authors' work combining these models with High Performance Computing strategies, including Adaptive Mesh Refinement/Coarsening (AMR/C) and scientific floating-point data compression. It then presents two new contributions: surrogate modeling of turbidity currents via PINNs, and the extraction of disentangled nonlinear modes from thermal flows using $\beta$-VAEs. Governing equations and representative benchmarks, including lock-exchange flows and Rayleigh-Bénard convection, illustrate these methodologies. The chapter is intentionally long, covering both the mathematical and physical foundations of coupled fluid flow and the computational aspects of state-of-the-art modeling. Overall, it demonstrates how SciML enables fast, accurate approximations of complex coupled systems within the specific data regimes and modeling assumptions considered, while substantially reducing computational cost relative to full-order simulations. Broader capabilities such as real-time prediction and uncertainty quantification remain active research directions whose feasibility depends strongly on the problem at hand.

Kerr frequency combs have recently emerged as an exciting new photonic technology, with applications across science and engineering. Their formation within driven optical resonators that possess a Kerr nonlinearity is enabled through the rich landscape of localized nonlinear dissipative structures intrinsic to these systems. This article offers a comprehensive review of the physics that underpins these nonlinear comb-generating structures. Particular attention is placed on bright temporal cavity solitons and nonlinear switching waves -- the canonical stable comb-generating states in the anomalous and normal dispersion regimes, respectively. Written as both a review and tutorial, the article also includes an in-depth treatment of the numerical methods required to simulate driven Kerr resonators, alongside a comprehensive discussion of the laboratory techniques used to experimentally realize and characterize Kerr combs.

We formulate reheating as a constrained variational problem in the space of equation-of-state histories, rather than attempting to describe it through microscopic models. We introduce a regularized functional framework that identifies reheating histories which extremize a given cosmological observable under minimal physical assumptions. As illustrative applications, we consider prompt gravitational waves, induced gravitational waves, and primordial black holes. We find that different observables select qualitatively different regions of reheating-history space. These examples demonstrate that cosmological observables define distinct extremal directions in reheating-history space and can therefore be used to systematically explore the space of post-inflationary expansion histories.

The structure of a porous material, and in particular its spatial variability, is known to control the intrinsic permeability of the system. We investigate how dead-end pores influence the intrinsic permeability of a porous medium beyond their contribution to total pore volume. Dead-end pores are ubiquitous in porous media, yet they are often treated as hydraulically inactive regions whose influence is assumed to be negligible or absorbed into effective-porosity descriptions. We perform pore-scale flow simulations across different dead-end pore structures, including heterogeneous arrangements, controlled granular assemblies, and a minimal single-channel model to study their impact on the system macroscopic permeability. This strategy allows us to isolate the effects of dead-end pore density, depth, and orientation while preserving the transmitting network. We find that dead-end pores can influence intrinsic permeability: increasing the density of dead-end pores along percolating flow paths enhances permeability, whereas pore depth and junction orientation have negligible effects. The observed permeability enhancement originates from localized hydrodynamic interactions at junctions between transmitting and dead-end pores. Based on these results, we propose an effective formulation that relates the density and spatial organization of dead-end pores relative to the transmitting network to macroscopic permeability. Our findings show that dead-end pore architecture provides an additional geometric control on intrinsic permeability beyond porosity and pore-size statistics.

Sphere packings in circular cylinders have attracted substantial research interest, among which the discovery of chiral helical structures is the most iconic. However, recent experimental results on zebrafish do not match the known packing structures in circular cylinders. To account for the inherent imperfections of biological tubes, we take elliptic cylinders as the canonical deformation of circular cylinders and investigate the densest packings of hard spheres in them using simulation, theory, and experiments. Starting from the chiral structures in circular cylinders, we demonstrate that even a weak cross-sectional deformation can trigger entirely new phases, including ones that either eliminate global chirality or significantly complicate the chiral structures. This reveals the significant effect of cylindrical anisotropy. The new helical phases under anisotropic confinement remain chiral and develop hierarchical periodic structures, which are difficult to obtain by simulations but are predicted by our newly developed theory for helical phases in elliptic cylinders. The theory also predicts double oscillated-chain phases without chirality, which perfectly match the simulations. Our work offers fresh insights into understanding packings in anisotropic cylinders, which will help researchers to design new materials and to understand many living systems.

Red blood cells (RBCs) are essential for oxygen transport, and their remarkable ability to undergo significant deformations during flow is a crucial feature for their physiological function. At intermediate shear rates typical of the microcirculation, RBCs can adopt complex, multi-lobed shapes, signifying a dynamic instability. Here we adopt a perturbative theoretical framework of a quasi-spherical RBC under external shear flow to study such shape instabilities. To better capture RBC maturation and enucleation, we first extend the framework to explicitly account for different excess areas between the stress-free and current membrane shapes. We revisit the reduced equations of motion obtained for an ellipsoidally-shaped RBC, and demonstrate the effect of different excess areas and initial orientation on the dynamical trajectories. Then, we introduce additional spatial modes and show that an emerging instability critically depends on the RBC's shear and bending moduli, the internal to external viscosity ratio, and the excess area, mainly through the RBC's membrane tension. We also study the instability-induced saturation of the membrane tension, and the resulting excess area redistribution at long times. The theoretical framework and the emerging picture of the different instabilities provide insights into the emergence of stomatocyte and trilobe shapes exhibited by RBCs under external flow.

The origin of some mesophases of the ferroelectric nematic realm is not yet well understood. In this work we study the highly polar liquid crystal MIO, a close structural analogue of the prototypical ferroelectric nematogen DIO, which exhibits a ferroelectric smectic A to ferroelectric smectic C (SmAF-SmCF) phase transition. Calorimetric, dielectric and light-scattering experiments reveal that it is a second-order phase transition with mean-field behavior, and is driven by the softening of the tilt elastic constant accompanied by the divergence of the amplitude of the associated dielectric mode.

We present a method to compute Ewald summation for the irreducible components of flow around active particles to study hydrodynamic interactions in active colloidal suspensions. An active particle is modeled as a colloidal sphere with a surface slip velocity. Using this model, we obtain an irreducible representation of the fluid flow produced by an active particle in periodic geometry of Stokes flow for an arbitrary surface slip. The solution of the active flow is obtained in terms of lattice sum of the Oseen tensor and their derivatives. The lattice sum is accelerated using the Ewald summation technique. We apply the method to compute explicit expression for rigid body motion of hydrodynamically interacting active particles. Our method presents a way for dynamic simulation of active particles due to arbitrary mode of active slip in periodic geometry of Stokes flow.

By assuming reversible H-bonding association and dissociation, this work provides a description of the supramolecular structure and dynamics of monohydroxy alcohols (MAs) within the framework of a recently proposed living chain model (LCM). Structurally, reversible H-bonding leads to a single exponential distribution of the molar concentration of the supramolecular chain with length N. Dynamically, reversible H-bonding enables supramolecular chain breakage and recombination, which modifies the relaxation time of the supramolecular chains. In addition to the structural relaxation, tau_a, and the Debye relaxation, tau_D, two other relaxation times are revealed: the chain breakage time, tau_B, and the H-bonding lifetime, tau_H. The interplay among these four-time scales defines five distinct dynamics regimes. In Regimes I and V, no supramolecular chains form. In Regimes II and IV, supramolecular chains form and give a Debye relaxation. The characteristic chain length scales as Nc~tau_D/tau_a. In these two regimes, the H-bonding lifetime controls the Debye process. In Regime III, large supramolecular chains form. In all regimes with supramolecular chain formation, the Debye relaxation comes from the overall chain end-to-end dipole reorientation and scales with Nc. Excellent agreements between experiments and LCM have been observed, leading to quantitative descriptions of the dielectric and linear viscoelastic properties of MAs. These results thus establish a theoretical framework linking reversible H-bonding interactions to supramolecular structures, dynamics, and macroscopic properties of MAs.

Classical nucleation theory (CNT) describes the formation of a stable phase from a metastable one. In equilibrium systems, it quantifies the free-energy competition between a favorable bulk gain and an unfavorable interfacial cost. For systems without detailed balance, the corresponding nonequilibrium nucleation theory (NNT) was so far developed only for cases with a conserved order parameter, such as active fluid-fluid phase separation. Here we construct the NNT for systems with a (single, scalar) nonconserved order parameter. Unlike in the conserved case, the nucleation barrier controlling (noise-driven) droplet growth is profoundly altered by deviations in the interfacial density profile from the one arising during (deterministic) droplet relaxation. The barrier can nonetheless be analysed by carefully defining the reaction coordinate (droplet radius) to project out those deviations. We give explicit NNT predictions for models drawn from population dynamics and active matter, finding excellent agreement with numerical studies.

The macroscopic instability of soft materials undergoing extreme deformations is traditionally viewed as a pure structural or mechanical failure. Driven by the quest to uncover universal principles across disparate physical systems, we bridge two vibrant yet seemingly disconnected research frontiers: macroscopic finite-strain solid mechanics and quantum-like topological physics. Here, we demonstrate that the classical elastic surface instability of a deformed hyperelastic manifold is not merely a mechanical bifurcation, but fundamentally a topological phase transition. By incorporating Lie group metric evolution into a generalized Stroh formalism, we map the highly nonlinear geometric frustration onto an algebraic surface impedance matrix $\mathbf{H}$. For a semi-infinite hyperelastic half-space under finite compression, we analytically map the system to a one-dimensional Dirac Hamiltonian, where the macroscopic mechanical stretch acts as a tunable knob for the Dirac mass. We reveal that the onset of surface wrinkles marks a topological transition from a trivial to a non-trivial phase characterized by a quantized step in the winding number, naturally giving rise to a robust, macroscopically localized zero-energy edge state. This fundamental linkage unifies macroscopic symmetry breaking with the topological paradigm, opening a new theoretical pathway for programmable smart soft matter.

Twisting layered materials produces moiré superlattices, but prescribed twist angles are usually obtained by demanding assembly procedures. Here we show that montmorillonite, an abundant swelling clay, forms tunable moiré superlattices naturally. Focal-series high-resolution transmission electron microscopy, geometric phase analysis, and molecular dynamics simulation reveal that its apparent rotational disorder is biased toward low-angle misorientations inherited from discrete hydration states. Multilayer stacks preferentially adopt twists near 1-2°, 4°, and 10°, producing long-wavelength moirés without long-range rotational order. We define this kinetically trapped state as a moiré glass, distinct from featureless turbostratic stacking. Simulations indicate that lattice-charge disorder stabilizes the angular preferences, whereas charge ordering promotes random stacking. Hydration screens interlayer interactions and lubricates twist, while dehydration arrests the resulting configurations in discrete steps. These results establish dynamic hydration as a macroscopic handle for programming twist in layered matter.

The biomechanics of pulsed-jet propulsion in aquatic animals, including squids and jellyfish, provide valuable insights into energy-efficient locomotion. In these organisms, flexible funnel deformation enables rapid acceleration and maneuverability while minimizing energy use. Drawing inspiration from these biological systems, this study investigates performance trade-offs between rigid and flexible nozzle geometries in pulsed-jet propulsion systems. A multi-objective Bayesian optimization framework integrated with three-dimensional fluid-structure interaction (FSI) simulations identifies nozzle designs that maximize hydrodynamic impulse and minimize jet energy input. The optimization reveals fundamentally distinct performance characteristics for rigid and flexible nozzles. Rigid nozzles achieve the highest impulse amplification, up to 5 times that of a baseline cylindrical nozzle, but at substantially increased energy expenditure. In contrast, flexible nozzles yield lower peak impulse enhancement of about 2.5 times while achieving significantly greater propulsion efficiency. The maximum normalized impulse-to-energy ratio for flexible nozzles is about 1.8 times higher than that of rigid configurations, indicating more effective conversion of input energy into useful propulsive output. Analysis of the flow physics shows that optimized rigid nozzles enhance performance through geometry-induced internal entrainment, secondary vortex formation, and contraction-driven jet acceleration. This results in stronger vortex circulation and downstream convection. Flexible nozzles use traveling expansion-contraction deformation waves that promote additional entrainment during expansion and accelerate the internally entrained fluid during contraction to improve pressure recovery, reduce pressure-energy expenditure, and mitigate negative pressure impulse contributions.

We consider stratified steady water waves in a two dimensional channel. Our subject is branches of Stokes waves, bifurcating from laminar flows. We assume that the mass flux and the Bernoulli constant are fixed and consider the period of the wave as a parameter, which can change its value along the branch. A new class of density and Bernoulli functions is presented, for which laminar flows generate global bifurcation branches. The laminar flows are not necessary unidirectional and we show that the bifurcation branch can bifurcate from the laminar flow with arbitrary large period.

Intermittency is one of the central features of turbulent transfer: the multi-scale energy cascade is mediated by rare and intense fluctuations. We investigate this phenomenon in a multi-branch shell model, which combines quasi-local triadic nonlinear interactions with a branching structure that mimics the growth of degrees of freedom toward small scales. Comparison with the standard Sabra model shows that branching enhances intermittency, as measured by anomalous scaling exponents of energy-flux structure functions. We further use multiplier statistics and large deviation estimates to characterize the multiplicative nature of the cascade. Our results suggest that reduced descriptions of turbulent intermittency should retain both nonlinear dynamics and geometrical organization. Implications on Navier-Stokes turbulence are discussed.

The exascale computing era, driven by heterogeneous GPU architectures, requires a fundamental redesign of traditional CFD solvers to fully leverage those heterogeneous systems. The discontinuous Galerkin spectral element method (DGSEM) provides an ideal foundation for this transition due to its high-order accuracy and local computational stencil. This work presents recent advances in the development and application of the architecture-agnostic DGSEM framework GALÆXI by linking hardware optimization, software implementation, and physical validation. The performance of GALÆXI on the AMD MI300A Accelerated Processing Units (APUs) featured on the Hunter supercomputer is analyzed. Specifically, evaluations of the strong and weak scaling performance and the impact of the compute partitioning modes available on the AMD MI300As are performed. Second, the strategy used to integrate the algorithms necessary for wall-modeled large eddy simulations into the GPU-accelerated framework is outlined. Validation of those algorithms is presented in the form of a plane turbulent channel testcase. Finally, the solver is applied to a demanding flow problem in the form of a wall-resolved large eddy simulation of a transonic compressor cascade. The results from this investigation demonstrate the capabilities of GALÆXI to accurately capture complex shock-wave/turbulent boundary-layer interactions.

We investigate the driving mechanism of low-frequency unsteadiness in bow shock-turbulent boundary layer interactions due to protuberances. Wind tunnel experiments are conducted at a freestream Mach number of 2.87 with protuberances of different shapes and sizes. From time-resolved surface pressure measurements and schlieren imaging, the unsteadiness is characterized by low-frequency shock oscillations, with a Strouhal number of $St_{\delta}\sim 0.01$ based on the boundary layer thickness ($\delta$), while the separated region exhibits predominantly mid-frequency pressure oscillations, with $St_{\delta} \sim 0.1$. Mid-span separation length, $L_{sep}$, is identified as a key parameter in determining time and length scales of shock oscillations. Further details of the interaction are examined through compressible adaptive detached eddy simulations for one particular case, viz.,the cubical protuberance of side 15 mm. A detailed modal analysis using proper orthogonal decomposition (POD) is performed with the 3-D data from computations. Flapping of shock-foot about mid-span was apparent, over and above the coherent to-and-fro oscillations, with the dominance of anti-symmetric mode in the POD of wall pressure fluctuations. The motion of the shock foot is initiated near mid-span, while the shock foot at other spanwise locations lags behind. The flap and asymmetries are related to the spanwise extent of reverse flow. From the reconstructed 3-D flow field using low-frequency modes, along with corroborating observations from the two-point correlations, it is inferred that the imbalance and time lag between the mass injected into the separated region at reattachment and the mass leaving spanwise at the horseshoe vortex core govern the observed shock motion.

We study the reflection of a weak planar shock from a rigid wall in the joint limit of weak shock strength and nearly glancing incidence. In the distinguished scaling (M=1+\lambda\alpha^2), where (M) is the incident-shock Mach number and (\alpha) is the glancing angle, the inner reflection region is governed by the unsteady transonic small-disturbance (UTSD) equation. The corresponding canonical shock-reflection problem is controlled by the single parameter[a=\frac{\alpha}{\sqrt{2(M^2-1)}}=\frac{1}{2\sqrt{\lambda}}+O(\alpha^2),]so the limiting inner parameter (a_0=1/(2\sqrt{\lambda})) is independent of (\gamma). Consequently, the detachment value (a_d=\sqrt2) maps to the physical scaling threshold (\lambda_d=1/8), with Guderley--Mach reflection for (\lambda>1/8). The physical trajectory angle is obtained from the canonical UTSD trajectory function (g(a)) by the Mach-number strength scale[\chi_{\rm phys}\sqrt{2(M^2-1)},g(a)+O(M^2-1) 2\sqrt{\lambda},\alpha,g(a_0)+O(\alpha^3).]We derive the self-similar UTSD reduction, the sonic parabola, the UTSD shock polar and its regular-reflection cubic, recovering (a_d=\sqrt2) directly. We also give the local linearisation and formal adjoint solvability condition defining the first correction (H(a;\gamma)), without claiming a computed correction curve. Finally, a time-marching solver for the full leading-order canonical UTSD system is benchmarked against the Hunter--Tesdall (a_0=0.5) triple point: once transverse compression (u>1) behind the Mach stem is retained, the computed (u=0.5) contour passes through ((\xi,\eta)=(1.007,0.514)), compared with the published ((1.008,0.514)).

The dynamic response of a zero-pressure gradient turbulent boundary layer (TBL) to a large-scale perturbation in the outer region was investigated experimentally. The baseline TBL had a moderate Reynolds number such that there was no naturally occurring energetic large-scale structure (LSS) present. An active plasma-based actuator was then placed in the outer region of the TBL to introduce a periodic, spanwise-uniform, synthetic LSS. This novel actuation scheme provides a new tool by which to experimentally examine the `top-down' view of TBL dynamics/interactions. The TBL response to this synthetic structure was investigated using a combination of planar particle imaging velocimetry and spanwise offset hot-wires, over a large streamwise extent downstream of the actuator device. Phase-locked analysis was implemented to isolate and measure the streamwise development of large-scale motions and changes in turbulence amplitude induced by this synthetic LSS. A strong correlation was observed between large-scale motions near the wall, linearly superimposed from the synthetic LSS, and a periodic modulation of turbulence amplitudes. This periodic modulation was found to be linked to phase-dependent changes in both the production and transport of turbulence driven by the induced large-scale motions. The phase speed of these induced large-scale motions, coupled with intermittent changes to spanwise coherence near the wall, revealed an additional, but transient, effect of the synthetic LSS on near-wall cycle dynamics. Overall, these results characterize the influences, and limitations, of top-down interactions on global TBL dynamics.

This study presents a comparative investigation of Physics-Informed Neural Networks (PINNs) and data-driven Deep Operator Networks (DeepONets) for predicting the evolution of plane Newtonian Couette flow with dynamic wall slip. While traditional numerical methods, such as the Crank-Nicolson scheme, offer high accuracy, their computational demand poses challenges in real-time applications. To address this, we first implement a PINN framework to solve the governing equations for specific physical parameters. Subsequently, we develop a data-driven DeepONet, trained on high-fidelity numerical data, to learn the continuous solution operator across a broad range of slip boundary conditions and upper wall velocities. Our results indicate that while the PINN achieved superior point-wise precision with a relative L_2 error of 0.083%, it remains constrained by the requirement for instance-specific retraining. In contrast, the DeepONet demonstrates robust generalization on unseen and out-of-distribution signals with a mean relative error of 0.36% and 0.88%, respectively. Most notably, it provides near-instantaneous inference, achieving a speedup factor of approximately 540X over the numerical solver and 30.5% over the PINN. This work demonstrates the synergy between physics-based and data-driven architectures and establishes DeepONet as a highly efficient surrogate model for rapid parametric exploration and real-time fluid dynamics forecasting.

Solving the pressure-Poisson equation remains the primary computational bottleneck in incompressible unstructured flow solvers primarily due to the inherent sensitivity of traditional linear solvers to mesh irregularities. This work introduces a data-driven algebraic multigrid (AMG) smoother that uses a modified graph convolutional isomorphism network (GCIN). The graph neural network predicts optimal polynomial coefficients to construct a sparse pseudo-inverse operator across diverse grid topologies. The coefficients are optimized to reduce the residual after each V-cycle iteration. By directly capturing the algebraic structure of the system from the sparse coefficient matrix, the proposed method maintains the solver's linearity while adapting to local anisotropies in unstructured grids. Our framework demonstrates significant performance gains by reducing the number of V-cycles required for a given tolerance and delivering wall-clock speedups from 4% to 37% across diverse benchmarks. Notably, the model exhibits robust generalization by maintaining efficiency on meshes up to 128 times larger than those seen in training, and by accelerating the solver's convergence on unseen industry-relevant problems such as the AirfRANS dataset.

We study the propagation of coupled surface and internal equatorial internal waves. A model of two vertically stratified fluid layers with different constant densities is employed. Taking Coriolis forces into account, we derive explicit solutions to the linearized governing equations which assumes irrotational fluid motion in both layers separately, and further obtain the dispersion relation which determines the phase speeds of propagating surface and internal waves. We prove a result on solutions to the dispersion relations which greatly simplifies our subsequent analysis of the nonlinear dynamical systems which describe the motion of the fluid in the upper layer. Phase portraits for all possible streamlines in both fluid layers are presented, while furthermore a Lagrangian description of the fluid flow is obtained, and the particle trajectories of the fluid particles are determined.

This paper explores the effectiveness of various novel deterministic and traditional stochastic data assimilation (DA) and parameter recovery (PR) algorithms given noisy data from chaotic systems. We use semi-analytic methods to numerically construct synthetic data from the Lorenz '63 and multiscale Lorenz '96 chaotic dynamical systems, adding white noise. Our findings show that, for different noise levels, deterministic PR algorithms paired with deterministic DA algorithms are shown computationally to be overall more accurate and stable than stochastic PR algorithms. Additionally, deterministic PR methods have demonstrated greater speed and efficiency, requiring less computational power than stochastic PR methods. This suggests that future work should consider exploring the full potential of deterministic PR algorithms in the presence of noise.

In equilibrium physics, topological defect insertions in quantum and classical partition functions provide non-perturbative probes of phase transitions beyond local observables. In non-equilibrium physics, the spectral form factor provides a minimal probe of universal quantum dynamics, and admits a representation as a product of two partition functions at imaginary inverse temperature. We define the topological spectral form factor (TopSFF) by inserting topological defects acting non-trivially on the doubled partition functions, producing mismatched spacetime world-sheet topologies. For the minimal $\mathbb{Z}_2$ spatially extended defect, implemented by the global swap operator, we derive an exact mapping of the TopSFF of a generic 1D many-body chaotic system to an emergent $(3+1)$D non-Hermitian single-particle problem describing a temporal domain wall (tDW). We show analytically that the effective tDW dynamics undergoes a $\mathcal{PT}$ symmetry breaking transition at a finite interaction strength $\epsilon_{\mathrm{EP}}$: below $\epsilon_{\mathrm{EP}}$, the leading modes are polarized into Gaussian or non-Gaussian tDW sectors and the TopSFF varies monotonically and exponentially with system size; above $\epsilon_{\mathrm{EP}}$, the tDW sectors hybridize and the TopSFF oscillates with system size; at the exceptional point $\epsilon_{\mathrm{EP}}$, Jordan non-diagonality produces a linear-in-system-size enhancement. For temporally extended topological defects, we derive exact universal scaling forms for the TopSFF free energy in systems with time reversal or time translation symmetry, and verify them numerically in independent models.

Out-of-time-ordered correlators (OTOCs) have emerged as a diagnostic of information scrambling and quantum chaos in many-body systems. We investigate the imprints of chaos in the dynamics of OTOCs in the Heisenberg spin-$1/2$ chain with random fields. The system is parameterized to exhibit a crossover from integrable to chaotic dynamics. We demonstrate numerically that the approach to saturation of the OTOC can distinguish between integrable and chaotic regimes, with a power-law $(1/t)$ relaxation for integrable systems and a higher-degree power-law decay $(1/t^\alpha; \alpha \ge 1)$ followed by an exponential relaxation for the chaotic regime. We further show that long-range spectral statistics, such as the number variance, are more effective in characterizing quantum chaos in the regime near saturation of OTOC. We also demonstrate that the relaxation and initial scrambling regimes exhibit distinct and universal features, with the former being sensitive and the latter being robust against different realizations of random-fields. The long-time saturation of OTOC also fluctuates with different realizations, and its exact expression is derived through the Eigenstate Thermalization Hypothesis.

The effect of a large environment on a finite-size quantum mechanical system is two-fold: It brings dissipation, but also fluctuations of thermal and quantum origin. While dissipation tends to stabilize the dynamics, we question if and how environmental quantum fluctuations can generate chaos in an otherwise classically non-chaotic system. We work out a paradigmatic model of quantum optics: the dissipative Dicke model, where a large spin interacts with a dissipative harmonic mode. We dial in the classical/quantum correspondence by working in the semiclassical regime at large but finite spin. We demonstrate that, starting from a classically regular phase space in the superradiant regime, quantum noise can generate a strange attractor with fractal dimension and a positive Lyapunov exponent. We unveil the deep connection with shear-induced chaos that was recently developed in the mathematical community.

Supratransmission is examined in nonlinear lattices with purely nonlinear coupling, extending the phenomenon to systems that lack a linear pass band. In contrast to standard lattices with mixed linear-nonlinear interactions, the present model has no linear spectrum, so energy propagation arises entirely from nonlinear effects. Asymptotic analysis yields a discrete $p$-Schrödinger (DpS) equation that {provides an accurate description in the weak- and intermediate-coupling regimes and offers qualitative insight in the strong-coupling regime}. Perturbation provides analytical approximations for the critical driving amplitude, explicitly showing its dependence on the driving frequency, coupling strength, and the nonlinearity exponent $p$. The analysis identifies a non-trivial dependence of the critical amplitude on $p$, with distinct trends in different coupling regimes. Numerical continuation and direct simulations {validate the theory in regimes where the asymptotic reduction is applicable and show good agreement across a wide range of parameters}. The results establish supratransmission in fully nonlinear lattices and clarify the associated energy-transport mechanisms, with relevance to mechanical lattices, tunable metamaterials, and nonlinear optical arrays.

In the present work, we present a number of localized wave patterns that are theoretically analyzed and numerically illustrated to be observable within the widely applicable paradigm of the FPUT lattice. In particular, we derive a modified KdV equation from the FPUT lattice, which admits a variety of localized waves including these exact rational solutions representing rogue-wave profiles, solitons and breathers on the top of not only homogeneous, but also periodic elliptic function traveling-wave background. We utilize these exact solutions of the modified KdV reduction to construct consistent initial conditions for the FPUT lattice and perform time stepping of the latter. Relevant comparisons between these numerical solutions of the FPUT lattice and their associated analytical counterparts have been conducted to demonstrate good performance of the derived modified KdV reduction in approximating distinct localized wave structures from the FPUT lattice. This approach paves the way for importing a number of quasi-continuum waveforms to the FPUT lattice and the potential associated physical experiments, including recent ones in mechanical metamaterials.

We assess the dynamical properties of liquid water predicted by several density functionals using machine-learning interatomic potentials. MACE models were trained for SCAN, RPBE-D3/zd, revPBE-D3/zd, revPBE0-D3/BJ, PBE0-D3/zd, and PBE0-D3/BJ using previously reported ab initio datasets. We compare translational, rotational, and viscous dynamics through time-correlation functions, which resolve relaxation processes across different timescales, and through the corresponding long-time kinetic coefficients. The diffusion coefficient, second-rank orientational relaxation time, and shear viscosity reveal systematic differences among functionals. Part of these differences can be rationalized as shifts along the phase diagram, as comparisons relative to each functionals melting temperature reduce the spread in the dynamical observables. Among the functionals considered, RPBE-D3/zd provides the best overall agreement with experiment. We therefore perform a broader validation of RPBE-D3/zd using a Behler--Parrinello neural-network potential over a wide range of temperatures, densities, and pressures. The model reproduces the magnitude and anomalous pressure dependence of the diffusion coefficient, gives generally good viscosities, and captures the temperature dependence of the rotational relaxation time.

Relaxation dynamics of supercooled liquids approaching glassy arrest remain a central challenge in integrated electronic architectures, where conventional rheometry becomes incompatible. Here, we demonstrate that an ambipolar PdSe$_2$ field-effect transistor functions as an electrical probe capable of resolving ion-specific relaxation dynamics in fragile ionic glass formers and semiquantitatively inferring rheological parameters within an operating device environment. Temperature evolution of the transfer curve hysteresis and time-resolved current transients under ionic-gate pulse reveal a non-Arrhenius fragile slowdown. We track the continuous reduction of dynamically equilibrated liquid regions approaching the glass transition through an electrically accessible quantity $p_\text{eq}(T)$, quantifying the fraction of the mobile ions able to relax within the experimental timescale. Upon cooling, $p_\text{eq}$ collapses sharply as mobile regions fragment into percolating fractal clusters, consistent with a reduction of configurational entropy predicted for fragile glass formers. This approach enables temperature-dependent scaling of viscosity and extraction of characteristic temperatures marking the ergodic-to-nonergodic crossover, within a solid-state device architecture where conventional rheological characterization is inapplicable. Further, polymer confinement of the ionic liquid shifts these characteristic temperatures upward, demonstrating the sensitivity of this method to structural constraints imposed by the polymer matrix.

The internal architecture of poly(N-isopropylacrylamide) (PNIPAM) microgels, which switches from fuzzy-sphere to star-like when the standard N,N'-methylenebis(acrylamide) (BIS) crosslinker is replaced with ethylene glycol dimethacrylate (EGDMA), critically determines their interactions and swelling behavior. Here, we systematically investigate the role of the surfactant and crosslinker content in modulating the internal structure of the microgels using Dynamic Light Scattering, Small-angle X-ray Scattering and monomer-resolved numerical simulations. We reveal that the presence of the surfactant is crucial for obtaining the star-like architecture, and that the transition from the star-like regime to a more core-dominated structure occurs above a threshold EGDMA concentration. Monomer-resolved simulations capture how the role of surfactant differs between EGDMA-crosslinked and BIS-crosslinked microgels. Our findings establish a direct synthesis-structure relationship, providing a clear guidance for the rational design of soft, star-like microgels with ultra-soft interactions, strenghtening the connection between microgels and model star polymers.

Collective stress generation in cellular monolayers is a key phenomenological process governing coordinated migration and emergent multicellular dynamics. We employ a generic active nematics model to investigate stress generation and its associated properties. By analyzing the maximal principal stress and its correlation with the nematic director across different activity strengths, we find that the principal stress aligns perpendicular (parallel) to the nematic director for extensile (contractile) activity. In the turbulent regime, we identify a distinct isoline derived from anisotropic stress components along which all $\pm 1/2$ defects (both nematic and stress) are localized. This feature is robust and remains unchanged with variations in both the magnitude and nature (extensile or contractile) of activity. Our findings provide a new route to probe the mechanical and rheological properties of confluent cell layers, where stress measurements are more accessible than detailed cell shape or size characterization.

Collective behaviour such as flocking (the collective motion of a spontaneously formed group along a common direction) or aster formation (the binding of opposing flocks, inhibiting each others motion) are intriguing emergent phenomena in active systems with local alignment rules. Until recently, their occurrence was mainly studied for classical systems, a prime example being the active Ising model (AIM), which translates the main ingredients of flocking and aster formation (i.e., alignment and self-propulsion) to a lattice framework. Here we introduce and study a one-dimensional (1D) quantum lattice variant of the AIM, based on ideal bosons with a spin degree of freedom. We find that both the collective behaviours of the 1D classical model, flocking and aster formation, are markedly enhanced by the bosonic quantum statistics. This contrasts with a recent quantum generalization of the AIM based onto hard-core bosons [Khasseh et al., Phys. Rev. Lett. 135, 248302 (2025)], where flocking, but neither its quantum-statistical stabilization nor aster states were observed as a consequence of interactions. Moreover, we investigate the competition of this quantum statistical stabilization of collective phases with their suppression by the quantum fluctuations induced by a transverse external magnetic field.

We derive an effective orbital-lattice model with quantum $S=1$ degrees of freedom for transition-metal compounds, providing a microscopic understanding of cluster formation driven by the cooperative interplay of spin, orbital, and lattice degrees of freedom. Motivated by the trimerized phases observed in LiVS$_2$ and LiVO$_2$, we consider a triangular-lattice three-orbital system with two electrons per site occupying the threefold-degenerate $t_{2g}$ manifold. Starting from a multiorbital Kanamori-Hubbard Hamiltonian, we project the low-energy sector onto the local $S=1$ triplet manifold, in which two electrons occupy different orbitals according to Hund's coupling. The resulting effective model exhibits exchange networks whose geometry is determined by the orbital configuration. However, the orbital-driven exchange interactions alone do not stabilize the experimentally observed trimer phase. We find that by incorporating ionic lattice displacements that modulate transfer integrals and induce bond-dependent exchange couplings on shortened and elongated bonds, the phase competition is qualitatively altered, leading to the robust stabilization of a trimerized ground state within a fully quantum-mechanical framework. We further show that a simplified orbital-lattice model, in which the spin-exchange energy is replaced by effective bond energies, faithfully reproduces the essential ground-state properties of the microscopic model. This reduced description enables large-scale finite-temperature simulations and reveals a rich sequence of thermal phase transitions, including first-order, second-order, and Kosterlitz-Thouless transitions into distinct spin-, orbital-, and lattice-ordered phases.

The optical binding of gold nanoparticles has conventionally been explored within the Rayleigh limit using dipole approximations. But the field is increasingly focusing on the Mie regime for particles in the 100-500 nm range, where the dipole approximation is insufficient, and a complex landscape of multipolar resonances must be considered. This can be leveraged to engineer more complex forms of optical matter. To this end, we computationally study the optical binding force landscapes experienced by a pair of AuNPs using generalized multiparticle Mie theory. We calculate the total optical binding forces and mechanical trap stiffness values ($dF_i/di$) at the specific resonance wavelengths where the electric dipole, quadrupole, or octupole modes reach their respective scattering peaks and dominate the mechanical response. We demonstrate that the plasmonic mode symmetry greatly influences the spatial distribution of zero-force nodes and the rigidity of the optically bound dimer. By aligning these multipolar phenomena with standard experimental configurations, this work provides a mechanical framework for programmable metafluids and reconfigurable micromachines, bridging the gap between fundamental electrodynamics and reconfigurable nanomanipulation.

Recent studies on Brownian gyration (BG) have focused primarily on spherically symmetric particles under overdamped conditions. To explore BG in the underdamped regime with a spherically asymmetric particle, we investigate the inertial dynamics of a microscopic ellipsoid in a dissipative medium. The particle is confined in a spherically asymmetric trap and simultaneously coupled to two distinct thermal reservoirs. This configuration drives the system into a nonequilibrium steady state (NESS) characterised by BG, which is quantified by the mean and fluctuation of the particle's specific angular momentum. Using inertial Langevin dynamics, we systematically analyze how this microscopic gyration depends not merely on the trap asymmetry and temperature difference, but also on the particle's intrinsic physical properties like shape and axial orientation, besides inertia. Our study uncovers fundamental differences between the gyration of spherical and non-spherical particles in overdamped as well as underdamped conditions, at microscopic scales. These findings provide key insights for optimizing Brownian gyration across a broader landscape of experimentally tuneable parameters.

A fluid system is 'globally stable' if all initial conditions eventually converge to the same state. Since Reynolds (1895) and Orr (1907), the standard way to show global stability has been the energy method, which uses the fluctuation energy as a Lyapunov function. However, the energy method fails whenever transient energy growth is possible, so it often yields overly strict stability criteria. The first broadly applicable alternative has recently been introduced (Goulart & Chernyshenko 2012; Fuentes et al. 2022), using polynomial optimization to construct non-quadratic Lyapunov functions. Unlike the energy method, however, this approach is highly technical, computationally expensive, and hard to interpret physically. Moreover, it treats only one set of parameters at a time; in particular, if it verifies global stability at a certain Reynolds number, it does not imply the same for smaller values. The present work makes progress by connecting this numerical program with new analytical and physical insights. We show how to exploit symmetries of shear flows via convenient complex variable representations, greatly reducing the problem size. We then refine key inequalities, replace several expensive computational steps with simpler analytical alternatives, and show how to prove global stability over a range of Reynolds numbers. Our analysis identifies the simplest class of non-quadratic Lyapunov functions for two-dimensional parallel shear flows: a three-parameter family of quartic polynomials. Using these Lyapunov functions, we verify global stability of 2-D plane Couette flow and plane Poiseuille flow up to higher Reynolds numbers than possible with the energy method. Our work takes a step towards an analytical theory of global fluid stability beyond the energy method, and offers structural insights that should significantly improve future numerical investigations of global stability.

Physics-informed neural networks (PINNs) offer a promising framework for inverse hydrodynamic modeling by combining sparse observations with governing physical constraints. However, their reliability for estimating hydraulic parameters under data limitations remains insufficiently characterized. This study benchmarks inverse PINN recovery of the Manning friction coefficient in the shallow water equations under controlled variations in observation sparsity, noise, and observed variable type. Two cases are considered: a one-dimensional MacDonald subcritical channel with an analytical steady reference solution, and a two-dimensional sloped channel with a parabolic transverse bed generated using a balanced finite-volume solver. The Manning coefficient is treated as a trainable positive scalar and recovered jointly with the flow field using a two-phase strategy that first fits observations and then incorporates the physics residual. Results show that the two-dimensional case achieves robust friction recovery, with errors below 5% when at least 10 depth and velocity observations are available and noise is at or below 10% of the field standard deviation. Recovery remains stable up to 20% noise with 50 observations, but becomes unreliable with only five observations. In contrast, the one-dimensional case shows a persistent positive bias of about 15% that is largely insensitive to observation count and noise, indicating a structural identifiability limitation rather than a data-density limitation. Observation-type ablation shows that recovery degrades substantially when only depth or velocity is observed, demonstrating that joint depth-velocity information is essential for reliable inverse identification. Overall, the results provide a reproducible benchmark for assessing when inverse PINNs can and cannot reliably estimate Manning friction from sparse and noisy shallow-water observations.

The dynamic Leidenfrost effect LFE and behaviour of impinging colloidal droplets is strongly influenced by the impact and spreading paradigms. LFE actuated rebound and levitation occurs due to enhanced spreading and near-frictionless recoil over the intervening vapour layer, providing opportunities for external field stimulus aided modulation and control of impact outcomes, and the resulting boiling-LFE behaviour. Magnetic field modulated LFE onset, dynamics and boiling transport of stable aqueous nano Fe2O3 based ferrofluid droplets was studied using high speed imaging. The interplay between magnetic, inertia, and viscocapillary forces on droplet spreading, magneto LFE-driven rebound conditions, residence time, and post-impact regimes was analysed using dimensionless parameters maximum spread factor, Weber number, and magnetic Bond number. We report a purely new phenomenon, namely magneto Leidenfrost effect MLFE, wherein magnetic field induces LFE aided onset of droplet rebound at substrate temperatures Ts below the zero-field dynamic Leidenfrost temperature LFT. The critical for the onset of MLFE decreases with increasing . Increasing the nanoparticle concentration permits the onset even at considerably lower . At elevated Ts , the residence time is noted as dependent. At much higher Ts, increasing promotes formation of radial filamentous structures, leading to complete droplet fragmentation. We also propose a theoretical framework that explains magnetic field driven spreading enhancement and rebound, and predicts of MLFE droplets in agreement with experiments. Our findings provide valuable insights into the novel realm of field dictated LFE, and hold significant implications towards the design of frictionless, rapid colloid droplet transport systems, and targeted droplet manipulation or activation for advanced thermal management.

The evolution of an axisymmetric vortex column in a weakly compressible supercritical fluid is analysed. A thermal layer is imposed to radially stratify the fluid and uncover effects of the large fluid property variations across the pseudo-boiling line. A multi-dimensional flow solver based on a low-Mach approximation is employed. Using supercritical carbon dioxide as the fluid, we examine axisymmetric configurations at low Reynolds number with the vortex core hotter or colder than the surrounding fluid and for different thermodynamic pressures close to the critical pressure. Vorticity evolution depends strongly on the core temperature and ambient pressure, differing substantially from the classical Oseen solution during the thermal mixing process under highly varying fluid properties. Viscous effects dominate the vorticity evolution. Beyond diffusion, three additional viscous mechanisms are identified, which become significant across the pseudo-boiling line: (1) a vorticity stretching term, (2) an alignment of vorticity and viscosity/density gradients, and (3) a vorticity source due to the interaction between the fluid swirl and the viscosity and density gradients. The first two mechanisms alter existing vorticity, while the latter injects new vorticity. In fact, the third mechanism can generate reverse vorticity, locally increasing circulation and substantially modifying the temporal evolution of the vortex.

Kirigami, the art of cutting flat sheets into deployable 3D structures, has recently inspired a new class of parachutes which can deploy into a naturally stable inverted canopy. However, the dynamic mechanism, fluid forces, and geometrical parameters that grant this stability have not yet been clearly identified. In this paper, we use a novel Biot-Savart far-field boundary condition to perform prescribed acceleration and free-falling simulations in effectively infinite domains, tracking the descent of a parameterized kirigami parachute. The far-field velocity is reconstructed from the interior vorticity, resulting in less than 0.1% variation in the predicted dynamics as the domain size is doubled. We first show the linear forces drop 2-5 times as the parachute is deployed due to increased permeability, whereas the moments increase due the counterbalancing effect of the increased lever-arm. Next, we find that the kirigami parachute achieves stable flight for deployment heights as small as half its radius, quickly damping out applied perturbations. For smaller deployments, the parachute tumbles due to side-slip and rotational coupling, as in falling disks. These effectively unbounded simulations identify that deployments approximately equal to the radius offer high drag forces with strong dynamic stability, providing a simple design rule for deployable parachutes.

Submesoscale fronts, occurring at intermediate scales between mesoscale eddies and boundary layer turbulence, play a crucial role in driving vertical transport from the ocean surface into the interior. Their dynamics involve complex interactions between submesoscale currents and turbulence. However, the mechanisms by which these multiscale processes combine to transport tracers such as pollutants or nutrients remain less well understood. This study uses large-eddy simulation to investigate passive tracer transport associated with submesoscale fronts. Intense turbulence develops during frontogenesis, leading to strong diapycnal tracer transport into the ocean interior. While part of this transport arises from the direct turbulent flux, represented by the covariance between turbulent velocity and tracer concentration fluctuations, a substantial portion is due to an advective diapycnal flux driven by the mean diapycnal velocity. The mean diapycnal velocity results from the evolving secondary circulation in the presence of turbulent density mixing. These findings reveal an underexplored diapycnal transport pathway in submesoscale frontal zones, with implications for improved representation of vertical exchange in ocean models.

This paper presents a non-dissipative, high-order, moving overset method for curvilinear grids to simulate unsteady compressible flows in complex geometries with moving components. Centered finite-difference schemes that are up to sixth-order accurate in the interior are used with a weak moving overset interface treatment. The novel aspects of the proposed approach compared to conventional overset methods are: (i) instead of overwriting all conservative or primitive variables at the interface (or fringe) points with the interpolated values, a characteristic decomposition is performed and only the incoming characteristic variables are imposed for inviscid flows, consistent with the hyperbolic character of the Euler equations; for viscous flows, the viscous fluxes are imposed in addition to the incoming characteristics variables, (ii) instead of using multiple layers of fringe points at the interface, the proposed approach ensures high-order accuracy and stability with a single layer, thus minimizing the parallel communication costs at each timestep, and (iii) the proposed approach ensures long time stability with non-dissipative schemes without introducing artificial dissipation explicitly (using numerical filters) or implicitly (using upwind schemes). The stability is demonstrated by an eigenvalue analysis of the time-dependent (semi-discrete) system matrix for moving grids, proving the eigenvalue spectra remains confined to the left half of the complex plane with grid motion. The proposed approach is validated over a range of canonical and practical unsteady flow problems involving moving grids: 1-D scalar advection, 2-D isentropic vortex convection, flow past rotating 2-D circular cylinder, pitching 2-D and 3-D airfoil/wing flow, and flow past 2-D and 3-D oscillating circular cylinder, demonstrating high-order accuracy and long time stability for inviscid/viscous flows.

Vortex stretching is a fundamental aspect of Navier-Stokes turbulence and is commonly understood in analogy to the stretching of infinitesimal material lines. However, the parallel alignment of material lines and vorticity cannot be maintained due to the role of viscosity in the directional realignment of vorticity. In Navier-Stokes turbulence, the result is relatively modest quantitative differences in the alignment and stretching rates of vorticity compared to material lines. In this study, the qualitative effect of viscous tilting of vorticity is demonstrated directly by surgically removing it from direct numerical simulations of isotropic turbulence. The result is a drastic change to the fundamental structure of the flow, including a substantial deviation from the -5/3 inertial range scaling of the energy spectrum brought about by the infiltration and prevalence of viscous effects beyond the smallest scales. These observations demonstrate that the viscous tilting of vorticity is an essential characteristic of fluid turbulence. By extension, the same may be said of the difference in orientation and stretching rates for vorticity and infinitesimal material lines.

Supergranular flows organize transport in the solar photosphere over spatial and temporal scales much larger than granulation. While coherent vortical motions have been identified using objective Lagrangian diagnostics such as the Lagrangian-averaged vorticity deviation (LAVD), rotational coherence captures only one aspect of coherent flow organization. Here we introduce finite-time rotationally coherent sets (FTRCS) by combining the inflated dynamic Laplacian (IDL), which identifies finite-time quasi-material coherent regions, with LAVD-based rotational diagnostics. The IDL extracts coherent structures with finite lifetimes, while LAVD identifies those exhibiting enhanced intrinsic rotation. Application to photospheric velocity fields shows that instantaneous vortical features do not necessarily correspond to finite-time rotationally coherent structures. The analysis also illustrates the effect of compressibility: coherent sets may form through persistent contraction associated with convergent transport, rather than through the persistence of rotating material regions. The combined IDL--LAVD approach separates finite-time transport coherence from intrinsic rotational organization in time-dependent flows.

Highly accurate stability boundary values for the ADER-DG method are obtained for arbitrary degrees $N$ of basis polynomials. In the linear case, stability is violated precisely when one of the matrix eigenvalues reaches $\lambda = -1$, regardless of the phase $\theta$. A rigorous mathematical framework for the stability is developed. The stability condition is significantly simplified, reducing it to the problem of calculating the roots of polynomials in the Courant number $\mathrm{CFL}$. The maximum of the Courant numbers $\mathrm{CFL}_{\rm max}(N)$ are calculated. These results are new and very convenient for practical use. A comparison of the obtained results with existing results reveals differences that may be significant for the selection of calculation parameters, especially for high degrees $N$. It is shown that widely used existing estimates $\mathrm{CFL}_{\rm max}(N) \propto 1/(2N+1)$ are overestimated. An interesting qualitative asymptotic $\mathrm{CFL}_{\rm max}(N) \propto (N+1)^{2}$ is obtained. A rigorous direct proof of the approximation is presented. Approximation orders $p = N+1$ for arbitrary degrees $N$ are rigorously derived. A set of numerical experiments is carried out to apply the ADER-DG method to solving both a linear advection equation and an Euler system of equations. The results obtained in these calculations confirm the theoretical results well. In particular, an excess of the Courant number over the $\mathrm{CFL}_{\rm max}(N)$ by even 1% in the linear case immediately leads to significant instability of the numerical solution. The obtained estimates of the boundary Courant number in the nonlinear case are somewhat underestimated -- by no more than 5%, which is due to the diffusivity and stability of the approximate Riemann solver. Empirical convergence orders are obtained, which are in good agreement with the theoretical results.

Thin wall treatments modify high-speed boundary-layer instability through the pressure they admit or absorb at the wall. This paper develops a unified admittance formulation for such effects on trapped compressible Rayleigh modes. For a simple rigid-wall eigenpair, we prove the spectral sensitivity law \[ c(A)=c_0+KA+\mathcal O(|A|^2), \qquad \delta\sigma=\alpha\Imag(KA)+\mathcal O(|A|^2), \] where \(A\) is the wall admittance and \(K\) is an explicit functional of the rigid-wall eigenfunction. The formula separates wall physics from outer-mode physics and yields a phase criterion for stabilisation. Matched asymptotics show that viscous and thermal wall layers, blind-pore coatings and shallow non-separating roughness all reduce to this same boundary condition, with additive leading admittances. Mach-4.5 computations validate the sensitivity coefficient and demonstrate porous damping, viscous-wall damping and sign-changing reactive roughness effects.

We propose using Transonic Flow Focusing (TFF) to produce 2D and 0D nanomaterials. This technique focuses liquid suspensions into high-speed micrometer-scale jets, combining extremely high shear and elongational stresses in a confined, contact-free zone. For the Graphene Nanoplatelets suspensions and TFF operating conditions investigated here, the process promoted exfoliation without added surfactants or oxidative chemistry. Both graphene monolayer flakes ($\sim 300-400$ nm in lateral size) and monolayer graphene nanofragments with lateral sizes compatible with quantum dots ($\sim 10-15$ nm) were obtained in a single TFF step using isopropanol and pure water. Our theoretical analysis reveals that, during microsecond residence times at the meniscus-jet transition, shear and extensional stresses of the order of $10^6$ s$^{-1}$ act on the suspended particles, yielding viscous power densities of the order of $10^{10}$ $\mathrm{W/m^{3}}$. High-resolution transmission electron microscopy and atomic force microscopy show that the monolayer fraction exceeded 99\% for isopropanol and 92.9\% for water. These results suggest that TFF can combine solvent versatility with a high monolayer fraction in a purely mechanical top-down process.

The understanding and modeling of high-energy particles transport in turbulent magnetic fields is an important open question in space- and astrophysics. The multiscale, nonlinear nature of turbulence, and the high variability of turbulence properties across different environments, make it particularly challenging to reach a full understanding of the interactions between particles and turbulent fluctuations. Using synthetic, realistically looking turbulent magnetic field realizations generated by the BxC toolkit, we investigate how the scattering of particles is affected by anisotropic fluctuations in strongly turbulent fields. We find evidence that, in the absence of a uniform background or guide magnetic field, the scattering process is not governed by the turbulence correlation length. We then further verify this hypothesis by studying particle transport in the presence of a guide field. We find evidence of a different scattering mechanism than the usual pitch-angle diffusion used to describe scattering in strong-guide-field settings.

This study investigates Thermal-Large Eddy Simulations (T-LES) of anisothermal and turbulent channel flows under physical conditions representative of solar receivers. Solving the low-Mach number Navier-Stokes equations, T-LES results are evaluated a posteriori against Direct Numerical Simulation (DNS) data. We assess 12 subgrid-scale models. All models are based on the Anisotropic Minimum Dissipation (AMD) model. After computing a global error rate to evaluate all models, we select four for a detailed analysis regarding the effects of mesh resolution, numerical schemes, and model formulations. Results demonstrate that a two-layered mixed model combining the AMD/AMD-scalar with the Gradient model yields the best agreement with DNS.

This study investigates supervised machine learning techniques for identifying ship hydrodynamic coefficients from CFD-generated data from free-running simulations. Specifically, ordinary least squares and regularized regression methods are applied to Abkowitz-type manoeuvring models. Training and validation datasets are derived from URANS simulations of zig-zag and turning circle manoeuvres, which are validated against experimental benchmark data. The analysis evaluates the effects of coefficient set size, minimum training length required for predictive model training, and manoeuvre combinations on model performance. Results demonstrate the suitability of large-angle zig-zag manoeuvres for hydrodynamic system identification, provided that multicollinearity is addressed through appropriate coefficient selection, regression models, or input data variability. Larger coefficient sets offer greater model flexibility for variable conditions but are more prone to multicollinearity. Regularized regression techniques effectively mitigate multicollinearity and notably enhance prediction accuracy, as does incorporating more diverse manoeuvring data. Among tested models, Ridge regression provided the best compromise between computational efficiency and prediction accuracy.

This study focuses on the complex coupling between discharge and flow properties in a ns-pulsed He micrometer scale atmospheric pressure plasma jet ($\mu$APPJ). This is investigated by integrating electrical measurements, schlieren photography, ICCD imaging, and space-resolved Optical Emission Spectroscopy (OES) with Computational Fluid Dynamics (CFD) simulations. In the flow rate range QV=0.1-1 slm, a critical threshold emerges at 0.3 slm, where the discharge consumes the highest energy overall, achieving maximum propagation length and remarkable collimation. Below 0.3 slm, insufficient momentum renders the jet susceptible to buoyancy and air entrainment, leading to shorter effluents, while higher flow rates enhance shear layer instabilities. CFD simulations reproduce the schlieren flow profiles to quantify the axial helium mass fraction (YHe) confirming a stable helium-rich core at 0.3 slm (YHe=90%), not seen in other flow rates. Furthermore, lower and higher flow rates promote stochastic branching which is more pronounced at QV>0.3 slm. Numerous lateral branches are clearly distinguished and quantified via single-shot ICCD imaging for the first time in a He $\mu$APPJ. The increase of voltage amplitude (VP) in the range 4-9.5 kV, amplifies their activity in the effluent tip at 0.3 slm. At VP=9.5 kV, their number increases for QV<0.3 slm compared to QV=0.3 slm, while for QV>0.3 slm they occur much closer to the nozzle exit and intensify farther downstream. Timeresolved imaging reveals a distinct peak in ionization wave velocities (up to $\approx$600 km/s at 0.3 slm/9.5 kV) just after the nozzle exit, followed by a progressive decay which becomes more abrupt at the higher flow rates. This correlates spatially with a surge and subsequent axial drop in N2 + (FNS) emission intensity, indicating Penning ionization as a key mechanism behind this acceleration. Average gas temperature estimations (TGas$\approx$350 K) suggest that localised thermal expansion could contribute to the instabilities observed, possibly combined with a sudden rise in the average electrohydrodynamic force at the nozzle exit for QV$\ne$0.3 slm. Finally, the device geometry also plays a decisive role in internal vortex formation, especially at higher flow rates, affecting effluent stability. These results provide a unique framework for optimizing $\mu$APPJs for high-precision applications such as in analytical chemistry and surface processing.

High performance computers produce extreme-scale data sets that require sampling or compression if they are to be used to their full potential. Existing data compression techniques typically exploit features such as sparsity in the data, homogeneity in the data, or {\it a priori} knowledge of what subsets of data are of most interest. Fluid dynamics data in general do not exhibit these features and so are attractive test beds for generic compression techniques that are objective, robust, and tuneable with respect to information lost due to compression. Presented here is a method based on tensor networks, specifically matrix product states or tensor trains, that meets these requirements. The method is demonstrated for compression in one-dimension and is extensible to higher dimensionality. Lossless compression is demonstrated for random Fourier series for sufficiently high bond dimension of the tensor network, with the memory required to store the tensor network scaling directly proportional to the bond dimension. The lossy compression exhibited at lower bond dimension can be well within the relative error of many fluid simulations. The compression algorithm is tested for the time evolution of Burger's equation with excellent results. We additionally demonstrate the capability to perform computations in the compressed form through a tensor network periodic convolution that can be orders of magnitude faster than using fast Fourier transforms and the convolution theorem. In addition to being an attractive method for working with data sets generated by existing computers, the tensor network methods utilised are directly translatable to the emerging paradigm of quantum computing.

This paper proposes a framework for energy localization in nonlinear oscillator chains operating in non-fundamental resonance, with emphasis on superharmonic regimes. The system is modeled as a metastructure composed of Duffing oscillators with both linear and nonlinear coupling, incorporating disorder-induced periodicity breaking. Under the assumption of strong excitation, the method of multiple scales is employed to derive the governing equations for soliton dynamics. At first-order perturbation, the classical form of the Nonlinear Schrödinger Equation emerges, whereas second-order analysis yields a previously unreported equation arising from the restitution of time scales. Analytical and numerical results demonstrate the nucleation of solitons in both hardening and softening regimes, based on two approaches: direct time-domain simulations from initially motionless states and numerical continuation in the frequency domain. A key finding is the distinct role of phase in superharmonic resonances compared to the primary resonance; specifically, the coexistence of multiple frequency components in the steady-state response precludes interpreting the soliton directly as a displacement envelope. Instead, the resulting secular terms captures the soliton associated with the resonant contribution, while transient components remain present under superharmonic excitation. Furthermore, robustness against disorder uncertainty is assessed by determining the tolerance levels that preserve the phenomenon. These results support the development of vibration control strategies aimed at mitigating the increase in resonant frequencies associated with the geometric downscaling of mechanical systems.

Among the most intriguing properties of honeycomb lattices is the presence of Dirac points that typically emerge in pairs, which can be destroyed by physical effects breaking certain symmetries of the system and leading to nontrivial band topology. We propose a nonlinear microcavity system supporting condensate of exciton-polaritons, where simultaneous breakup of inversion and time-reversal symmetries results in unusual spectrum with unpaired Dirac cones, profoundly affecting the properties of unidirectional edge states. Realized as an array of microcavity pillars, the inversion symmetry is broken by fission of pillar belonging to one of sublattices of honeycomb array into three pillars, while time-reversal symmetry is broken due to interplay of Zeeman splitting in the external magnetic field and spin-orbit coupling. Despite the absence of complete spectral gap, unidirectional edge states may still emerge that can circumvent array corners. Resonant optical pumping leads to reach bistability effects and allow selective excitation of the edge states. We obtain first example of stable localized dissipative edge soliton that circulates along the periphery of insulator over indefinitely long times without radiation. Our results suggest a new platform for nonlinear topological photonics and reveal nontrivial interplay between unpaired Dirac cones and nonlinear effects.

Starting from a spectral problem posed in a Clifford algebra with $d$ generators and Euclidean signature, we study an integrable, coupled system of PDEs that can be viewed as a vector perturbation of the Camassa--Holm equation with residual orthogonal symmetry. In the two-component case $d=2$, we show that the travelling wave solutions correspond to a Liouville integrable Hamiltonian system with two degrees of freedom, making use of a reciprocal transformation linking the coupled PDEs to a symmetry of the Hirota--Satsuma system. We also present a symmetry classification of all integrable two-component perturbations of Camassa--Holm, and find that besides the $d=2$ system analyzed here, the coupled 2CH system studied by Olver and Rosenau (as well as by Chen, Liu and Zhang, and Falqui), and equations related to either of those systems by Miura transformations, we also obtain a new system that (to the best of our knowledge) has not been reported previously. For the case of an arbitrary number of components $d$, we additionally investigate the short-pulse (high-frequency) regime, in which the limiting dynamics are governed by a vector-valued Hunter-Saxton type system. Furthermore, we provide a detailed analysis of the corresponding measure-valued (weak) solutions associated with this system.

The crack closure effect of a low-alloyed steel subjected to low-cycle fatigue loading has been characterized at two different imposed strain amplitudes. Two techniques (non-continuous DIC H-DIC and DCPD) have been employed in this aim, leading to similar conclusions. Thus, it is shown that the crack does not remain completely closed during a part of the compressive portion of the fatigue cycle for both applied loadings. The crack opening strains, combined with the cyclic stress-strain curve of the material allowed to determine an equivalent cyclic opening stress. This confirmed that the crack opening stresses decrease with the applied maximum stress when subjected to tension-compression loading, as commonly found in the literature.

We describe version 5.0 of the Bottom-up Open-source Coarse-graining Software (BOCS) package. BOCS employs the force-matching variational principle to parameterize potentials for coarse-grained (CG) models directly from atomically detailed simulations. BOCS version 5.0 significantly extends previous versions by treating potentials that depend upon the local density (LD) around each particle, as well as potentials that depend upon the square gradient (SG) of this local density. We also describe a new package, PKG-BOCS, for simulating these potentials in LAMMPS. This software treats complex molecular topologies and provides considerable flexibility for defining the local density, as well as the LD and SG potentials. We present numerical calculations that provide physical insight into these potentials and demonstrate the accuracy of our implementation. Finally, we demonstrate that LD potentials can significantly improve the structural fidelity, thermodynamic properties, and transferability of CG models for water.

The propulsion of active colloids is governed by their symmetry and shape, yet a systematic investigation of how small geometric effects influence the locomotion of anisotropic active colloids is lacking. In this paper, we study the effect of a cone shape by combining high-resolution two-photon polymerization 3D printing with AC electric field experiments to study anisotropic Janus micro swimmers. We fabricate a series of Janus colloids with different shapes, ranging from a sphere to a hemisphere with a cone-protrusion, but containing similar hemispherical gold-coatings. Under an applied alternating current (AC) electric field, all particles exhibit active, ballistic motion. We find a shape and size dependence on the propulsion velocity, with the spherical Janus particle moving fastest, followed by a small cone and a large cone protrusion, while surprisingly a printed sphere with a flat side moves slowest. In addition, a reversal in the direction of motion for all shapes was triggered, a phenomenon governed by a transition from induced-charge electrophoresis (ICEP) at low frequencies to self-dielectrophoresis (sDEP) at high frequencies. We reveal a distinct shape influence, with the large cone-protrusion increasing their velocity in the sDEP regime. Our results provide insight into the link between active particle geometry and their propulsion velocity that are important for understanding biological micro swimmers and designing optimized microrobots.

Hybrid lipid block copolymer membranes are promising for many applications in drug delivery, single molecule detection, in-membrane protein folding, and synthetic cells. However, rational design is difficult due to the many design parameters which determine the nano- and micron-scale morphology and properties. In this work, we propose a physically-informed framework which incorporates chemical immiscibility, hydrophobic thickness mismatch and geometric constraints to predict the morphology of hybrid membranes. For this purpose, we extend existing theory for amphiphilic monolayers to model the thickness of diblock copolymer bilayers, demonstrating that both the hydrophobic and hydrophilic block lengths determine the thickness. We identify and rationalize the four primary membrane morphologies observed: mixed, laterally phase-separated, unzipped (thick-thin coexistence), and polymer-rich. Specifically, chemical immiscibility differentiates mixed membranes from laterally phase separated membranes, and hydrophobic mismatch drives transitions to unzipped or polymer-rich morphologies. Areal density, finally, determines the crossover between unzipped and polymer-rich states. We validate our theoretical predictions using coarse-grained molecular dynamics across a broad parameter space, including multiple lipid species (DOPC, DPPC), polymer species (1,4 PBD-b-PEO, 1,2 PBD-b-PEO, PE-b-PEO), block lengths, temperatures, and compositions. The resulting phase maps unify previously reported experimental and simulation observations and enable a generic and mechanistic understanding for the effect of system parameters on the nanoscale morphology.

Block copolymers self-assemble into ordered nanostructures whose geometry is governed by a competition between interfacial energy and chain conformational entropy. While this competition produces a rich sequence of morphologies, topologically complex ``frustrated'' phases such as the primitive cubic ($Im\bar{3}m$) network incur severe packing penalties and are difficult to access in neutral systems. Here we show that ions functionalized at the termini of one block in an AB diblock copolymer melt introduce a qualitatively new stabilization mechanism. Strong ion correlations drive chain-end association and generate a curvature preference toward the charged domain; the resulting tendency of end-localized ion clusters to adopt compact, curved geometries selectively favors the highly frustrated $Im\bar{3}m$ single-network over the classical phases, in a region of parameter space lying below the order-disorder transition of the neutral system. Free energy decomposition reveals that the electrostatic energy, arising almost entirely from beyond-mean-field ion correlations, becomes increasingly negative with increasing interfacial curvature. In the primitive cubic network, pronounced local segregation of ions into the cylindrical struts generates compact curved clusters whose correlation energy gain more than offsets the enhanced packing frustration, so the very geometry that is the source of packing frustration in neutral systems becomes the source of its stability here. Increasing ion size weakens correlations and suppresses the $Im\bar{3}m$ phase, consistent with experimental observations. Our results establish curvature-selective end-group association as a general principle for accessing frustrated topologies in block copolymer systems.

We propose a heuristic model of underscreening phenomenon in high density Coulomb systems, such as strong electrolytes and electron hole conglomerates under ultra high dose rate (UHDR) radiation in biological tissues. It explains the data on screening length $L$ increasing with charge particle concentration and offers additional insights in understanding the conductivity and reduction potential of concentrated electrolytes. Also, it validates our current understanding of the FLASH radiation treatment of tumors (FLASH-RT) perceived as an analogous system. The underlying physics is that mutual binding creates diffusion barriers which suppress the concentration of mobile particles thus increasing the screening length. Also, they slow down the rates of chemical reactions responsible for generation of biologically active radicals which explains the sparing effect observed under UHDR.

Linker-mediated aggregation plays an important role in modern nanoscience. We demonstrate that it departs sharply from classical Smoluchowski kinetics because cluster reactivity evolves during growth. Combining theory with DNA-linked gold-nanoparticle experiments, we establish kinetic critical point controlled by linker abundance. Below threshold, active linkers are depleted and growth arrests; above threshold, clusters accumulate reactive sites, self-accelerate, and cross over to diffusion-limited coarsening. Experiments verify the predicted arrest, accelerated growth, and scaling collapse.

Liquid crystal elastomers (LCEs) exhibit unique viscoelastic behavior arising from reversible liquid-crystalline ordering, making them attractive candidates for switchable pressure-sensitive adhesives (PSAs). However, methacrylate-based LCEs are typically highly crosslinked, leading to elevated glass-transition temperatures ($T_g$) and storage moduli ($E'$) that limit adhesive performance. Here, we demonstrate that catalytic chain-transfer polymerization provides an effective strategy for engineering soft methacrylate nematic elastomers through systematic control of network architecture. Incorporation of parts-per-million concentrations of bis(boron difluorodimethylglyoximate)cobalt(II) (CoBF) during photopolymerization reduced the effective crosslink density and increased the molecular weight between crosslinks, producing substantial decreases in $T_g$ and $E'$ while preserving nematic order. Dynamic mechanical analysis revealed that increasing CoBF concentration enhanced viscoelastic dissipation and broadened the accessible nematic temperature window. To further optimize rheological properties for pressure-sensitive adhesion, monofunctional methacrylates and flexible poly(ethylene glycol) dimethacrylate (PEGDMA) were incorporated into the network. The optimized formulation exhibited a $T_g$ near 0~$^\circ$C, a room-temperature storage modulus of approximately 0.3 MPa, and high damping behavior, approaching the Dahlquist criterion for pressure-sensitive adhesion. As a result, the resulting nematic elastomers displayed strong tack, peel, and lap-shear adhesion in the nematic state, together with rapid, reversible, and residue-free debonding upon heating above the nematic-to-isotropic transition temperature.

Localization in finite elastic structures is often studied using infinite-domain solutions, which avoid the explicit treatment of boundaries and admit simpler analytical descriptions. Yet it remains poorly understood when finite-domain localized states can be accurately approximated by their infinite-domain counterparts. In this work, we show that the accuracy is controlled by an intrinsic decay length. Using a prototypical localization model, we show that finite-domain localized solutions converge exponentially to the corresponding infinite-domain localized solution once the structural length exceeds the intrinsic decay length. The intrinsic decay length also explains the markedly different validity regimes of finite- and infinite-domain weakly nonlinear approximations. It further has important implications for numerical computation, since once the structural length exceeds the intrinsic decay length, localized solutions corresponding to different domain lengths differ only by exponentially small quantities, making them increasingly difficult to distinguish numerically. The theoretical predictions are validated using two representative localization problems: bulging in membrane tubes and localized helical buckling in twisted rods. The present work provides a unified geometric framework for understanding localization transition, asymptotic validity, and numerical computation in elastic localization.

This paper is a specialization of a broad and complicated continuum theory [ arXiv:2403.07582 ] to a relatively simple and useful case so that it is more reader friendly. A continuum theory of the flow of charged particles in an elastic solid is presented. It can describe the behavior of soft solid electrolytes and elastic semiconductors. It is nonlinear and is valid for large deformation and strong fields. The theory is derived from a three-continuum mixture model including a charged lattice continuum, a bound charge continuum for electric polarization, and an ideal fluid for the flow of mobile charges. The basic electromechanical laws are applied systematically to the model. The electric fields are quasistatic and are in SI units.

Biological tissues must dynamically transition between rigid and fluid-like states during processes like morphogenesis and collective migration, often while simultaneously resisting physiological shear stresses. It remains unclear whether these tissue dynamics are governed by the same non-equilibrium critical phenomena that control conventional disordered matter. Here we show that model cell monolayers under constant stress display a rich phase diagram of nonlinear rheology. In rigid regimes, small internal fluctuations maintain a solid-like state up to a finite yield stress, above which the tissue shear-thins; conversely, fluid-like regimes exhibit robust continuous and discontinuous shear thickening, culminating in structural arrest via shear jamming. This space-filling shear-jamming transition is accompanied by structural changes including the formation of system-spanning force chains and the emergence of orientational ordering. We demonstrate that the macroscopic viscosity across these disparate regimes is described by universal scaling behavior controlled by the same underlying physical parameters. These results establish confluent tissues as a distinct class of disordered matter, demonstrating that universal jamming phenomena can emerge entirely through shape-driven topological constraints to regulate biological mechanics.

Supraparticles (SPs) are assemblies of colloidal particles whose properties can be tuned by modifying the chemistry, shape, and size of the colloidal particles as well as their arrangement in the SP. SPs with internal porosity are of particular interest for catalysis, photonics, and adsorption applications because of their high surface area and tunable pore size distribution. SPs are often fabricated by droplet drying, and the nonequilibrium nature of drying processes may provide an additional handle to control particle arrangement within the SP. Here, we use mesoscale particle-based simulations to explore the drying-induced assembly of SPs made from rod-shaped and spherical colloidal particles. We selectively remove one type of particle after drying and characterize the structure of the resulting porous SP. We find that the remaining particles form connected networks for most compositions, with rods percolating at lower volume fractions than spheres. Most of the resulting void volume forms a single contiguous space whose surface area closely follows the total surface area of the remaining component. The pore-size distribution, however, depends strongly on sphere size and on the removed component, reflecting differences in sphere-clustering and rod-bundling before removal. This work provides new insight into how particle size and shape, as well as processing conditions, might be used to manipulate porosity in SPs.

Particles governed by many-body interactions exhibit remarkably complex structures and dynamics. We experimentally investigate a monolayer of pentagon particles subjected to an up-lifting air flow which induces many-body aerodynamic interactions and stochastic motion akin to a thermal bath. To minimize air flow resistance, particles move collectively with interactions dictated by their geometry: hollow particles exhibit effective attraction, whereas solid particles repel each other. Under sufficiently large air flow, sparsely packed hollow pentagons overcome substrate friction and undergo long-time diffusive motion. Under lower air flow, we see a coexistence of isolated, static pentagons and densely packed, "active" clusters, whose particles display super-diffusivity. This "emergent activity" arises collectively when locally disordered structures interact with the air flow, resulting in correlated motion across broad temporal and spatial scales. Using Langevin dynamics simulations of two-dimensional attractive active pentagons, whose activity is an effective result of the local packing density, we further unravel the basic features of this emergent activity.

Aggregation processes play a central role in systems ranging from aerosol coagulation and cloud formation to dust growth in protoplanetary disks and granular materials. These processes are traditionally described by Smoluchowski's coagulation equation, which provides a mean-field account of growth through binary collisions. However, incorporation of granular physics-dissipative interactions, spatial heterogeneity, and force transmission through contact networks-reveals important limitations of this framework. In this review, we show how such effects lead to the breakdown of mean-field assumptions and motivate a view of aggregation as a multi-scale process shaped by the interplay between interactions, structure, and collective dynamics. Phenomena such as segregation, jamming, and clogging further highlight the role of mechanical constraints and spatial organization in limiting or redirecting growth. By integrating insights from granular physics, aerosol science, and astrophysics, we outline a unified perspective on coagulation in non-equilibrium particulate systems. This paper is part of the thematic issue "Sand, silos and asteroids: clustering challenges in granular materials research".

Dynamic Light Scattering (DLS) analyzes particle dynamics from the autocorrelation functions of scattered light intensity, yet extracting accurate relaxation time distributions from noisy data is challenging. We develop an inverse problem approach to recover this distribution by inverting the Laplace transform with physics-based regularization, called the CONTIN method. We improve it to use it on noisy data, across a wide range of time scales, with a selection of the regularization strength through a data-driven L-curve criterion. Our approach enhances robustness under high noise and reveals multi-scale dynamics in complex systems. Validation is performed on simulated data, compared to the Cramér-Rao bound and to parametric methods, and on experimental data from Carbopol microgels. It demonstrates superior accuracy over parametric methods, especially for broad time distributions. The algorithm's logarithmic discretization and variance-reduced correlation estimation enhance performance, offering a powerful tool for non-parametric DLS analysis and deeper insights into soft matter dynamics.

We present a rigorous analysis of the mathematical boundaries and kinematic consistency of a recently proposed rate-dependent relaxation time framework intended to unify pre- and post-yield dynamics in yield-stress fluids. By evaluating the governing constitutive equations under an idealized transient creep protocol from a state of physical rest, we show that the model encounters an unavoidable boundary paradox. To avoid predicting perfectly rigid solid behavior or falling into a division-by-zero mathematical singularity under a constant applied stress below the yield threshold ($\sigma \le \sigma_y$), the framework requires an unphysical, instantaneous velocity or strain-rate step at $t = 0^+$. We show that assuming a non-zero initial strain rate explicitly violates momentum conservation and fluid inertia. Consequently, the framework preserves the piecewise, discontinuous drawbacks of classic viscoplastic models.

The amplitudes of light modes in a homogeneous interface layer are investigated around the critical conditions (CC) in a total reflection geometry. CC occur when the normal wave vector vanishes; the resulting divergence upon variation of the angle of incidence is characterized by a critical exponent -0.5. Absorption replaces the divergence with a finite peak whose width and height are derived analytically. The high relevance of the amplification for Evanescent Wave Dynamic Light Scattering (EWDLS) is demonstrated using published experimental data. The relation to surface plasmon resonance (SPR) is briefly discussed. An outlook connects the amplitude divergence to a critical analysis of the Distorted Wave Born Approximation (DWBA) presented in a companion paper.

Living cells utilize condensates to spatially concentrate molecules in response to dynamic signals. For instance, nuclear condensates respond to oscillations in transcription factor levels in the nucleoplasm, including those involved in repairing multiple DNA breaks. To understand how oscillating signals affect condensates, we analyze a theoretical model using numerical simulations and analytical theory. While passive dynamics would drive all molecules into a single condensate, we find that sufficiently fast oscillations stabilize multiple droplets, allowing control of their sizes. We thus reveal a new behavior of chemically active droplets, which could be exploited in synthetic applications.

Self-organized critical systems often exhibit three macroscopic features simultaneously: nonextensive thermodynamics (quantified by the Tsallis index $q$), structural fractality (measured by the Hausdorff dimension $D$), and non-Markovian dynamics (characterized by the memory exponent $\alpha$). Historically, these parameters have been treated as independent, to be empirically fitted case by case. Here we demonstrate that phase-space self-consistency imposes a unique algebraic closure: $\alpha=D/(2D-1)$. This relation, together with $q=1+1/D$ derived from the extensivity of Tsallis entropy on fractal supports, yields the known result $\alpha=1/(3-q)$ as a consequence, not as an independent assumption. The closure contains no free parameters and satisfies the physical boundary conditions $\alpha(1)=1$ (ballistic transport in Euclidean spaces) and $\alpha\to1/2$ as $D\to\infty$ (maximally subdiffusive regime). We validate the Troika relation across eight independent experimental systems, including seismicity, electromagnetic precursors, EEG, urban networks, botanical architectures, and space plasma. All measured values fall within error bars of the theoretical prediction, establishing the universality of the closure.

Designing spray nozzles requires predicting how geometry shapes transient two-phase breakup, but high-fidelity volume-of-fluid (VOF) simulations with adaptive mesh refinement (AMR) are too expensive for iterative design exploration. Standard surrogate models are also challenged by this setting because both the liquid--gas interface and the underlying adaptive discretization evolve across time and geometries. We introduce a geometry-conditioned latent surrogate trained on 797 two-phase nozzle simulations that addresses this by encoding the AMR cell-density field, rather than the full multi-channel flow state, as a compact proxy for where the solver concentrates resolution. From this representation, the model reconstructs transient density evolution and nozzle geometry, and a lightweight second stage recovers the remaining flow variables. On held-out simulations, the method accurately captures key interface dynamics while reducing inference time to 0.045 seconds per trajectory, corresponding to a speed-up of more than $6\times10^4$ relative to Basilisk CFD. These results suggest that AMR refinement structure can serve as a compact and learnable representation for geometry-conditioned surrogate modeling of transient two-phase flows.

This study investigates the influence of representative engine positions on contrail evolution during the vortex and dissipation regimes, using three-dimensional simulations of a realistic aircraft geometry. Large Eddy Simulations are employed, coupled with an Eulerian microphysical bulk model, and initialized using fields obtained from prior Reynolds-Averaged Navier-Stokes simulations. This approach enables a consistent transition from near-field jet-vortex interactions to far-field wake dynamics. Three engine placements are examined under two atmospheric stratifications and two relative humidity conditions. The results reveal that engine position influences the onset and evolution of vortex instabilities, alters the descent of the vortex pair, and leads to slight changes in the distribution of particles within the wake. Despite these aerodynamic differences, the microphysical properties of the contrails tend to converge over time for the parameters and configurations covered in this study. From a broader perspective, engine placement strongly influences initial contrail formation and early vortex-regime dynamics. At later stages, these differences largely disappear, as vortex dynamics and atmospheric conditions dominate over the initial dilution changes induced by engine position.

We present a quantum-enhanced Markov chain Monte Carlo (QE-MCMC) method to sample turbulent acceleration vectors from a joint target distribution that depends on all three components and height to model the transport and dispersion of massless Lagrangian tracer particles in two turbulent shear flows. A homogeneous shear flow, characterized by a uniform shear rate S, is considered as the starting point. Secondly, a turbulent boundary layer, which forms in both halves of a plane turbulent channel flow at friction Reynolds number Re_tau = 1000, is considered, where the mean shear rate S(y) varies with distance from the wall y. In this hybrid quantum-classical method, the proposal distribution Q for the first of two Metropolis-Hastings sampling substeps is constructed by a parametric quantum circuit. The algorithm generates synthetic tracer particle tracks. The resulting scaling laws for tracer-particle pair dispersion, a central quantity to probe turbulent mixing from a Lagrangian perspective, agree with a stochastic transport model consisting of coupled Langevin equations and with the classical MCMC counterpart. Differently from the classical sampling method, QE-MCMC uses a tempered target distribution. Due to the height dependence of the tracer dynamics in turbulent channel flow, an effective height-weighted spectral gap between the first and second eigenvalue of the Markov-chain transition matrix is introduced. The latter is found to significantly exceed the one of classical MCMC when sampling from a multivariate distribution with cross-correlations at the highest qubit numbers and thus resolutions. Consequently, our results support the applicability of this one-shot algorithm as a generative Lagrangian quantum-computing module, possibly embedded in a complex fluid-flow problem. Our module is found to work reliably for a relatively small number of qubits per spatial dimension of Nq <= 6.

Biofouling -- the occupation of microplastic (MP) surfaces by marine microbes -- alters particles' buoyancy and transport, yet its effect on the global distribution of MPs has not been well quantified. We present the first three-dimensional global Eulerian model to fully couple MP transport with biofouling, by augmenting the concentration field with an extra dimension representing the biomass attachment density on MP surfaces. This approach embeds time-dependent particle properties directly into the Eulerian concentration field, overcoming a fundamental challenge of tracking property evolution in grid-based models. Idealized simulations show that biofouling significantly reshapes the vertical distribution of MPs when two conditions are met: the particles must be sufficiently buoyant when they are clean to remain near the sea surface, and the local plankton growth rate must exceed the decay rate. In three-dimensional global simulations, biofouling substantially alters the distribution of large MPs ($\gtrsim 10$ $\mu$m): biofouled particles are transported below the mixed layer to 500 m depth, and the subtropical surface garbage patches become more dispersed with reduced peak concentrations. This dispersion is due to a subsurface transport route, where biofouled particles sink into layers with reversed current and are carried outward from the gyre centers before regaining buoyancy. Small particles ($\lesssim 1$ $\mu$m) remain unaffected as they stay effectively neutrally buoyant even when biofouled. A comparison with a global trawler dataset shows that incorporating biofouling reduces the fraction of outlying model-observation data points from 25\% to 13\%, demonstrating a meaningful improvement in model skill.

This study investigates the capability of linear modeling to characterize the transitional dynamics in an axisymmetric stenosis and attempts a low-order representation of the turbulent stresses. The transition to turbulence in stenotic flows generates wall shear stress fluctuations that strongly influence the progression of cardiovascular diseases and the risk of plaque rupture. A description of the linear mechanisms driving the forced dynamics at Reynolds number beyond transition is currently missing. Linear modeling of coherent structures is leveraged to identify the flow amplification mechanisms using the mean field from a LES at Re=4000. Global linear stability analysis reveals an unstable and sinuous stationary eigenmode that is known to destabilize the flow at lower Reynolds numbers through a weak Coanda-type wall attachment. At intermediate frequencies, resolvent analysis identifies a second amplification region within the shear-layer where the most amplified fluctuations are axisymmetric, in contrast to findings from studies at lower Reynolds numbers. The linear model is validated against SPOD. At intermediate frequencies, the optimal resolvent response mode demonstrates both high gain separation and strong alignment with the leading SPOD mode. The low-rank nature of the resolvent operator is leveraged to reconstruct the turbulent kinetic energy (TKE) and turbulent wall shear stress (tWSS) from the optimal response mode. In the immediate post-stenotic zone, axisymmetric fluctuations dominate the tWSS and exhibit low-rank dynamics. Our findings highlight that linear mechanisms effectively capture the complex post-stenotic dynamics. The successful reconstruction of turbulent quantities from mean flow data alone opens new predictive possibilities of key turbulent quantities.

We explore the movement of a thin, circular quantum vortex filament within an infinite cylindrical pipe. The fluid surrounding the vortex ring moves through the pipe at a non-zero velocity denoted by $v$. Our study examines the energy spectrum $E = E(p)$, where $p$ represents the total momentum of a vortex ring. We have demonstrated that the function $E(p)$ significantly depends on the velocity $v$. The discovered spectrum $E(p)$ reveals the existence of states with both negative and extremely large effective masses. We also explored the hypothesis regarding the existence of coupled vortex pairs possessing finite summary effective masses. Every pair consists of vortices that possess both positive and negative masses, with the magnitude of these masses being unrestricted. In our model, the criterion for the appearance of these states is based on comparing two numbers. The first is seen as a quantum counterpart to the Reynolds number, while the second represents its critical value for a flow with a single vortex. We also explore how this studied effect might contribute to the emergence of quantum turbulence. This study discusses a method for determining the critical Reynolds number in quantum turbulence, using the proposed model as a framework. Here, we use a new quantization technique for classical closed vortex filaments developed by the author earlier.

Compression and heat release interact intermittently in high-speed reacting shear layers, and whole-field averages can obscure their coupling. We examine this coupling in a supersonic reacting hydrogen--air temporal mixing layer using time-resolved mid-plane slices from a three-dimensional direct numerical simulation. A fixed dilatation threshold identifies connected compression events, and exothermic heat release and mixture-fraction-gradient activity are then conditioned on the evolving event population. The record separates into startup ($t^*<5$), transition ($5\le t^*<20$), and developed ($t^*\ge 20$) regimes, with the developed regime carrying the persistent compression--chemistry interaction. In this regime, compression appears as a population of intermittent events with no single structure dominating the field. Stronger exothermic response is associated with larger maximum-event area, larger event count, greater compression--heat-release overlap, and smaller distance from compression to the most exothermic regions. Scalar-gradient amplification peaks near zero lag relative to compression-area excursions, whereas the strongest exothermic response precedes peak compression coverage by $\Delta t^*\approx -0.85$. These results show that compression organizes chemistry most clearly through event population, overlap, proximity, and lag, providing an event-level description of compression--chemistry coupling in an open supersonic reacting shear layer.

Compressibility and chemical reactions in reacting flows provide source mechanisms for pressure fluctuations whose signatures depend on the flow, source distribution, and acoustic environment. Bounded flows can sustain strong feedback and narrowband tones, whereas boundary-free flows more often exhibit broadband source activity distributed across frequency. Near-field combustion-noise source dynamics are examined in a supersonic reacting hydrogen-air temporal mixing layer using high-fidelity time-resolved direct numerical simulation data. Pressure, heat-release, and dilatation fields are used to identify how localized reacting structures, compressive disturbances, broadband spectral content, and burst-driven temporal organization interact. The results show weak pressure--heat-release coherence concentrated within selected low-frequency bands, with no collapse onto a single dominant mode. Combustion intermittency modulates the near-field pressure response within these bands and is accompanied by burst-driven amplitude modulation and transient trajectory sensitivity, while the overall dynamics remain broadband and bounded. A planar source-radiation-potential projection further shows moderate low-frequency angular bias associated with the heat-release source distribution. Information-theoretic measures indicate that pressure fluctuations share more statistical structure with heat release than with dilatation. The analysis characterizes source-side organization and near-field pressure response in the sampled DNS of a reacting shear layer, providing a basis for subsequent observer-based or acoustic-analogy radiation calculations.

In this work, we extend the method of averaged Lagrangian to the study of the general second-order (non-conservative) extended Korteweg--de Vries equation, known as the eKdV equation. Building on the framework introduced in [18], we construct a master (augmented) Lagrangian, modeled on Luke's Lagrangian, that incorporates the governing constraints at the appropriate asymptotic orders via the method of Lagrange multipliers. Averaging the resulting Euler-Lagrange equations in the traveling wave setting yields the existence of a (single) solitary wave solution with a $\operatorname{sech}^2$ profile. Explicit second-order formulas are obtained for the height of the solitary wave, together with the solitary wave velocity and inverse width, in terms of a fixed amplitude parameter. A key feature of the derived expressions is their asymptotic reduction to the classical KdV results when the first-order terms are retained. To assess the robustness and utility of the variational solitonic solutions, the derived formulas are subsequently applied, via the dispersive shock equal amplitude approximation method, to estimate the height and velocity of the leading solitary wave edge of dispersive shock waves governed by the eKdV Riemann problem. Theoretical predictions for the relevant wave parameters in both the eKdV solitary wave and dispersive shock wave problems are compared with direct numerical simulations and found to be in strong agreement.

Characterizing the Marine Atmospheric Boundary Layer (MABL) requires understanding the coupling between ocean waves and the turbulent atmospheric boundary layer above them. This coupling controls momentum exchange between the atmosphere and the ocean; it is of practical importance in the global climate, flow of ocean currents, ocean engineering, and offshore wind energy. Computational study of the MABL is complex because it must resolve the coupled physics of waves and turbulence over a wide range of spatial and temporal scales. This study expands on approaches for representing dynamic, local waves in Large Eddy Simulations (LES) of the MABL by developing a subfilter wave drag model to be local and scale-invariant. It explores the effects of different wave parameters (significant wave height and peak frequency of the wave energy spectrum) on the resulting momentum flux beyond monotonic relationships between surface stress through friction velocity $u_\ast$ and wind velocity above the surface $U_{10}$. Results are compared to field data and in a discussion on how representation of the MABL and associated momentum flux need to account for both wind and wave effects.

Spatial filtering is examined in time-resolved mid-plane DNS fields of a supersonic reacting shear layer using a sequence of box filters. The analysis tracks a nondimensional entropy-like scalar $s^\ast$, its in-plane material derivative $D s^\ast / D t^\ast$, a residual $\Pi_s^\ast$, and viscous and conductive entropy-production diagnostics, $\sigma_\mu^\ast$ and $\sigma_k^\ast$. Filtering changes $s^\ast$ only weakly, attenuates $D s^\ast / D t^\ast$ and the strongest tails of $\sigma_\mu^\ast$ and $\sigma_k^\ast$, but broadens the residual distribution and increases the residual RMS with filter width. The residual remains concentrated in the layer core that carries the largest mechanical and thermal activity. Conditional statistics show that $|\Pi_s^\ast|$ rises with both entropy-production intensity and entropy-gradient strength. Spectral and structural diagnostics show that increasing filter width removes high-wavenumber content and simplifies the geometry of the high-$|\Pi_s^\ast|$ sets. Coarser filtering therefore increasingly distorts entropy transport preferentially through the most dynamically and thermally active structures, rather than uniformly across the plane.

Accurate prediction of hydrodynamic performance is central to ship design, yet high-fidelity computational fluid dynamics remains prohibitively expensive for large-scale parametric exploration. This motivates the development of data-driven surrogate models that provide rapid approximations to hydrodynamic predictions at substantially reduced cost. We present ShipNet, a geometric deep-learning surrogate that predicts both hull-surface pressure distributions and far-field free-surface wave patterns directly from hull geometry and speed. The network employs a regularized dynamic graph convolutional backbone on hull point clouds, with a multi-head decoder for simultaneous near-body pressure and free-surface elevation outputs. Training data consist of 420 inviscid free-surface simulations generated using a potential-flow panel method for two parent yacht hulls, each parameterized into 70 variants and evaluated at three speeds. ShipNet predicts per-point pressure coefficient and two-dimensional wave elevation map using a composite loss that combines point-wise regression and image-structure terms. On a geometry-held-out test set, ShipNet achieves R^2=0.98 for hull pressure and R^2=0.91 for wave fields. Inference requires approximately 0.15s per case, yielding over a 550x speedup relative to the potential-flow solver on conventional hardware. Limitations include the restricted geometry and speed ranges and the inviscid training data, while future work will extend the model to high-fidelity viscous simulations with physics-informed regularization.

We investigate the settling behavior of suspensions of highly porous and permeable particles in the viscous regime using particle-resolved direct numerical simulations (DNS). The simulations employ a coupled Euler-Lagrange framework that accounts for particle permeability. The results show that the settling behavior of permeable particles follows the classical power-law relationship of Richardson-Zaki in terms of their settling velocity, but particles with higher permeability settle faster as the particle volume fraction increases. At a particle volume fraction of 30 percent, the difference in settling speed is up to 106 percent between the least and most permeable particles investigated in this study. We explain this effect by the alteration of counter flows induced by the fluid displacement of settling particles. Quantitative analysis of the mean vertical fluid velocity confirms that suspensions composed of more permeable particles generate weaker counterflows, posing less resistance to the settling motion. We furthermore show how velocity fluctuations and self-diffusivity depend on the permeability of the porous particles and the particle volume fraction. Both quantities increase with volume fraction and are largest for the least permeable particles, except at the highest volume fraction, where reduced settling velocities reverse this trend. The influence of particle permeability also reveals two effects in the particle microstructure. First, the analysis showed that particle clustering decreases with increasing permeability. Second, the overall probability of finding a neighbor within the lubrication range is lowest for the least permeable particles. We attribute this to the weakening of repulsive pressure forces between tumbling particles with increased permeability.

The present study provides a detailed vorticity-dynamical analysis of shock-driven hydrodynamic physics in canonical Richtmyer-Meshkov instability (RMI) flows: shock interaction with a single-mode perturbed interface, and a cylindrical air bubble immersed in Krypton. These findings provide insights into vortical flow physics beyond the conventional vorticity paradigm, and the DVD approach holds promise for the diagnosis of practical instability-induced flows.

We propose a multiscale probabilistic reconstruction framework for hypersonic Couette flow, where near-wall states are inferred from limited top-wall observations using conditional diffusion model. The boundary layer is divided into overlapping wall-normal subdomains, and a single height- and Mach-conditioned Elucidating Diffusion Model (EDM) is trained jointly for M=6,7,8 to sample velocity, density, pressure, and temperature fields conditioned on a top-wall boundary slice. A soft overlap inpainting strategy assembles subdomain predictions into full-volume reconstructions while maintaining inter-subdomain continuity and small-scale variability. To improve the spectral fidelity of the generated fields, we introduce a novel bounded binned spectral power (BSP) loss that preserves high-wavenumber content while remaining numerically stable across the diffusion noise schedule. Validation against direct numerical simulation data shows that the model recovers instantaneous structures, spectra, statistical profiles, correlations, and wall quantities across all training Mach numbers, while providing spatially structured uncertainty estimates. The reconstructed Mach-conditioned profiles also collapse under the Trettel-Larsson transformation, indicating consistency with compressibility scaling. These results establish the domain decomposed conditional diffusion model with a bounded binned spectral loss as an effective probabilistic surrogate for near-wall reconstruction in hypersonic wall-bounded turbulence.

We introduce a Mori--Zwanzig graph neural network (MZ--GNN) framework for learning reduced-order Lagrangian dynamics of tracer particles in homogeneous isotropic turbulence. The model represents particle acceleration as a finite-memory expansion over present and delayed particle-neighborhood graphs, with each memory contribution parameterized by an equivariant message-passing graph neural network. By construction, the architecture respects the relevant physical symmetries of the problem, including permutation equivariance, Galilean invariance, and equivariance under rotations and reflections. Trained on direct numerical simulation data, the model is rolled out autoregressively and evaluated on observables that are not imposed during training. We show that memory is essential for recovering the intermittent, heavy-tailed acceleration statistics, and that the learned dynamics accurately reproduce single-particle dispersion, pair-dispersion statistics, and four-particle tetrad geometry. Our results establish a physically structured, scalable route to data-driven multi-particle simulation of turbulent transport, and a template for learning reduced dynamics of correlated, symmetry-rich particle systems.

Evaluating neural operators for 3D turbulent flow requires validated datasets with physical benchmarks. We present a reproducible pipeline generating training data for 3D channel flows around generated geometries at Re=1,000-10,000. Our lattice Boltzmann solver with cumulant collision operators is rigorously verified against experimental measurements (Strouhal number, drag coefficients, turbulent fluctuations) with comprehensive grid convergence studies at resolution 1024x512x512. Building upon an established framework, this validated pipeline enables standardized surrogate model comparison. We outline planned systematic evaluation of Fourier Neural Operator and U-Net variants on forecasting, super-resolution, and error correction tasks, using physics-informed metrics to assess turbulent energy cascade representation. Future work will compare computational efficiency between numerical solvers and neural surrogates, exploring practical application. We seek community feedback on our validation approach, planned benchmark methodology, and evaluation priorities for neural operators in turbulent flows.

A fully quantum algorithm for solving the one-dimensional linear advection-diffusion equation using the Lattice Boltzmann method as a numerical procedure is presented in this work. We start by presenting a state of the art of the current usage of quantum algorithms for solving ordinary and partial differential equations. We then describe two algorithms for the one-dimensional Lattice Boltzmann method with two degrees of freedom. The first one is an existing hybrid quantum-classical algorithm with measurements at each time step, and the second one is our improved version, viz. a fully quantum algorithm where only one measurement is needed at the end of the algorithm. The fully quantum algorithm is first executed on a quantum simulator and then compared with a classical approach. Subsequently, the fully quantum algorithm is run on a quantum system with 133 qubits to investigate the effect of noise and the depth of the circuit on the output state. We find fluctuations in the final result due to the decoherence noise of the qubits.

Earth's magnetic field is generated by fluid motion in the liquid-metal core and has been active for billions of year. However, prior to the onset of inner-core growth, the sources of mechanical power that drove the geodynamo remain uncertain. During this period, the core may have been overlain by a basal magma ocean (BMO), creating two immiscible fluid layers separated by a density interface, beneath the solid mantle. We develop a theory for lunar tides in this core--BMO system, in which the tidal potential acts on the density contrast between the two layers rather than through deformation of a bounding envelope. The resulting dynamics differ fundamentally from previous models of tidally driven core flow. In the inviscid limit, the response transitions from an equilibrium tide to an inertia--self-gravity wave as forcing frequency increases. The two regimes are separated by a resonance that occurs when the forcing frequency matches the natural frequency of the interfacial mode. The inviscid core flow is formally identical to the canonical elliptical vortex, linking the problem to the theory of elliptical instability. Finite viscosity regularises the resonance, introduces phase lag and generates oscillatory boundary layers. Combined with parameterised models of lunar recession and BMO crystallisation, the theory predicts enhanced core-boundary ellipticity, core-flow speed, magnetic Reynolds number and instability metrics, particularly near resonance. These results identify a previously unexplored mechanism for tidally driven flow in differentiated planetary bodies and show that a BMO can enhance tidal coupling to the core, potentially contributing to dynamo action.

Particle-based Fokker--Planck (FP) models provide an efficient kinetic alternative to direct simulation Monte Carlo (DSMC) in slip and early transitional gas flow regimes, but advanced cubic-FP closures require repeated cell-wise moment evaluation and small dense linear solves. This work develops and validates a GPU-native neural surrogate that replaces the deterministic cubic-FP closure calculation inside the particle simulation loop. The trained weights are evaluated directly with batched \texttt{CuPy} operations, avoiding CPU--GPU transfers during online deployment. The validation emphasizes quantitative evidence: component-level runtime profiles, break-even cost analysis including offline costs, conservation and stability diagnostics, particle-per-cell sensitivity, a direct time-averaged coefficient audit, and covariance-based entropy-proxy fidelity checks. The Couette case is retained as a compact, dimensionless verification problem, while the main internal-flow validation is a 2D lid-driven cavity tested by complete simulation conditions, including unseen moderately rarefied cases at nominal $Kn=0.5$ and $Kn=1.0$. For the hypersonic cylinder, a particle-moment covariance-based entropy-fidelity audit is performed on the front stagnation line and in the cell-centered near-wall gas layer. The same deployed neural $C/\Gamma$ closure used for the cylinder flow fields closely reproduces the equilibrium and Gaussian kinetic entropy profiles over the reported front-line and near-wall gas bins; these profiles are used as a relatively exact-FP/ML-FP audit. The study establishes GPU-native learned closure as a practical route to accelerating cubic-FP rarefied-flow solvers, delivering substantial online speedups while retaining the macroscopic, high-order, and entropy-proxy structure of the reference kinetic model.

The turbulence driving parameter ($b \equiv \sigma_{\rho/\langle \rho \rangle}/\mathcal{M}$; the ratio of the density to velocity fluctuations) is widely used to infer the dominant mode of energy injection in interstellar turbulence. Numerical simulations of turbulence using Fourier Space Driving (FSD) establish a mapping from $b\approx 1/3$ for purely solenoidal to $b\approx 1$ for purely compressive driving. We test the robustness of this calibration by comparing FSD against Point Source Driving (PSD), which stochastically injects radial momentum at random locations mimicking supernovae. Using isothermal hydrodynamic simulations in a periodic box with AthenaK, we run a suite of carefully curated simulations to match Mach numbers between the two driving methods and compare morphology, probability density functions, and power spectra of density and velocity. Despite injecting purely compressive motions, the PSD models yield $b=0.33$ to $0.49$, values that the FSD calibration would associate with more solenoidal driving. With mass-weighted mean Mach number, excluding high-velocity bubble interiors, $b_M=0.74$ to $0.79$ still does not recover the expected $b\approx 1$ for volume-filling, purely compressive driving. More broadly, the PSD models show density and velocity statistics closer to solenoidal and compressive FSD models, respectively, and exhibit unique features, including non-Gaussian velocity tails and a positive density-Mach number correlation at high densities. Within the FSD framework itself, varying the forcing correlation time changes $b$ by a factor of more than 3 for compressive driving. These results demonstrate that $b$ is degenerate with both the spatial locality and the temporal correlation of the driving, limiting its utility as a standalone diagnostic of the energy injection mode.

Turbulent combustion simulations are crucial for many scientific and engineering systems. However, the high cost to fully resolve the complex multiscale and multiphysics behavior makes direct simulation typically infeasible. The equivalent reactor network (ERN) approach attempts to improve computational efficiency by replacing a multidimensional turbulent simulation with a series of much cheaper 0-D and 1-D chemical reactors, providing a surrogate model that retains detailed chemistry at the cost of simplified flow physics. However, their development remains a challenge, often requiring either expert analysis, or automated approaches that sacrifice accuracy. In this work, we develop an automated machine-learning-assisted framework for constructing ERNs of the Sandia-D turbulent methane/air flame. Principal component analysis is first used to reduce high-dimensional thermochemical computational fluid dynamics (CFD) data to a low-dimensional latent space, where k-means clustering identifies physically interpretable flame regions used to initialize a reactor-network graph. This initialization is then refined using finite-difference gradient descent wrapped around non-differentiable Cantera reactor simulations. Across 30 RANS simulations spanning a range of pilot temperatures and inlet methane compositions, the optimized 7-reactor ERN achieves a maximum-temperature $R^2$ score of 0.7945 while preserving a $\sim6000\times$ speedup over the CFD solver. Outlet CO prediction remains more challenging, with a final $R^2$ score of $-0.4183$, but improves substantially from the unoptimized clustering initialization. These results show that unsupervised thermochemical feature extraction can provide effective physics-informed initializations for ERN construction, while gradient-based refinement can significantly improve predictive accuracy without manual reactor-network design.

State-space models (SSMs) are the standard formalism for Bayesian treatment of dynamical systems, with natural applications in statistics, signal processing, and machine learning. Despite their importance in both theory and application, dynamical systems have proven difficult to incorporate in modern probabilistic programming languages (PPLs), making state-of-the-art methods less accessible to practitioners and introducing friction in following the "Bayesian workflow." We introduce dynestyx, a probabilistic programming library with first-class support for SSMs, including state-of-the-art methods in the estimation of both states and parameters. Through a single, unified interface, users may specify arbitrary priors for discrete-time or continuous-time dynamical systems, perform inference over mixed-effect data, and make state and parameter estimates with principled uncertainty quantification.

Chaotic quantum systems can retain spatial memory through scarred eigenstates, but whether these static structures control scrambling remains unclear. This work establishes a morphology-resolved connection between scarred eigenstates and eigenstate-resolved OTOCs in a peanut-shaped quantum billiard. Scalar localisation diagnostics, including differential entropy and continuum participation ratios, detect anomalous concentration but discard spatial architecture. A scale-normalised density overlap, in contrast, directly compares probability density profiles, revealing families of orthogonal eigenstates with nearly identical spatial morphology. Comparing the complete OTOC time traces of these orthogonal eigenstates reveals that morphological recurrence has dynamical content: moderate density overlap yields no universal prediction, whereas strongly recurring morphologies exhibit nearly identical OTOC growth and saturation. Thus, scarred structures act as spatial templates for operator growth, not merely static violations of ergodicity. This morphology-resolved framework turns eigenstate shape into a quantitative predictor of scrambling and provides a scale-controlled diagnostic of weak ergodicity breaking in quantum chaos.

Random non-hermitian matrix ensembles with double-sided rotation invariance obey, in the limit of large matrix size, the Single Ring Theorem, which states that the support of the mean eigenvalue distribution in the complex plane is either a disk or an annulus. In contrast, rotational-invariant random normal matrix ensembles can have mean eigenvalue densities supported over any number of concentric annuli in the complex plane. In this paper we introduce and investigate, both analytically and numerically, a non-hermitian matrix model which flows from a generic matrix distribution obeying the Single Ring Theorem to a distribution of normal matrices by tuning a parameter which penalizes non-normality. We observe numerically breakdown of the Single Ring Theorem as the model flows towards normality, and determine the critical value of the parameter at which the transition occurs. We also study in detail the behavior of the singular values of these matrices under the flow. These singular values form a Fermi gas confined to the positive half-line. In particular, we find that at small values of the flow parameter, the interparticle spacings in the gas exhibit Wigner-Dyson repulsion, whereas for asymptotically large values of the flow parameter, at the normal matrix endpoint of the flow, the spacing statistics is Poissonian. The flow interpolates continuously between these two types of statistics. However, this change in statistics is not related directly to breaking of the Single Ring Theorem, which occurs very early-on along the flow, in the regime of Wigner-Dyson statistics. Finally, we introduce a certain ensemble of random permutations associated with the gas, and make a conjecture on how to use it in order to reconstruct approximately the average density of complex eigenvalues from that of the singular values in the large-$N$ limit.

Discovering the governing equations of a physical system from data is a central goal across the sciences, yet in most experiments only a few states are accessible while the rest stay hidden. Existing approaches treat this partial observability as an obstacle to be removed by first reconstructing the hidden state -- a step that is ill-posed under noise and that discards the physical constraints, such as energy conservation, that the true dynamics obey. We show that for conservative (Hamiltonian) systems no reconstruction is needed: projecting the dynamics onto the measured coordinates yields a memory kernel that we prove to be a lossless positive-real rational matrix, whose poles are the hidden natural frequencies and whose positive-semidefinite residues encode the couplings. The governing equation -- and the underlying Hamiltonian -- can therefore be read directly from the autocorrelation of the measured signal, with guarantees of uniqueness and physical passivity, and without neural networks. We validate the approach on linear, nonlinear, and chaotic systems under realistic noise. By recovering interpretable equations of motion that conserve energy by construction from partial measurements, the method offers a common tool for problems spanning mechanics, fluid and plasma physics, and beyond.

In the present work we explore a prototypical three-dimensional (3d) lattice possessing a flat band in the form of a pyrochlore lattice in the context of a dispersive nonlinear dynamical model, namely the discrete nonlinear Schrödinger (DNLS) equation. We set up the corresponding steady state and dynamical problems and discuss the linear spectrum of the relevant model before delving into a more detailed analysis of the nonlinear equilibria of the system. For the latter, we analyze the more well-established -- at the DNLS level -- fundamental discrete soliton states, as well as vortex structures. For the fundamental solitary waves, we connect their existence and stability with how they approach the linear bands. In the vortex case, we identify their stability features for vortices of topological charge $S=1$ and $S=2$ with those of the honeycomb and triangular lattices. An arguably even more intriguing feature of the pyrochlore lattice concerns the compactly supported nonlinear eigenstates stemming from the flat band of the linear spectrum. These compact localized modes are found to possess oscillatory instabilities for a range of propagation constants in the focusing case, although they can be stable in the latter, while they are found to be subject to symmetry-breaking instabilities in the defocusing nonlinearity case. These results offer a glimpse at the nexus of topology, flat band systems and dispersive nonlinear lattices in three spatial dimensions and as such may be a starting point toward a deeper exploration of such an intriguing interplay.

We study topological edge solitons in a nonlinear Su--Schrieffer--Heeger (SSH) lattice subject to parametric driving and linear damping. Starting from a vertically driven pendulum chain, we derive an effective driven--damped nonlinear SSH model and investigate its stationary edge-localized states. Analytical calculations reveal the existence of two phase-locked dissipative edge-soliton families that emerge from the nonlinear continuation of the topological edge mode. Using numerical continuation and spectral stability analysis, we construct the corresponding nonlinear branches and determine their stability properties. We show that parametric driving and damping fundamentally modify the conservative edge-state family by generating two dissipative branches with markedly different stability characteristics: one branch remains predominantly unstable, whereas the other develops substantially larger stability regions and significantly weaker instability growth rates. Direct numerical simulations further demonstrate that the robust branch can remain strongly localized over long time intervals even when weakly unstable. Simulations of the full driven--damped Klein--Gordon pendulum chain confirm the persistence of the edge-localized dynamics predicted by the reduced model. These results identify parametric driving and damping as an effective mechanism for enhancing the robustness and persistence of nonlinear topological localization in active lattice systems.

We investigate the propagation of cylindrical waves in a square network of acoustic waveguides. We establish, both theoretically and experimentally, the anisotropic dispersion relation governing wave propagation in the network, and demonstrate excellent agreement between experimental measurements and theoretical predictions. Owing to this anisotropic band structure, each propagation direction exhibits distinct dispersive properties. Consequently, the network supports anisotropic cylindrical waves at both low- and high-amplitudes, with waveforms that vary markedly with direction: from nearly dispersionless pulses to Airy-like wave packets in the linear regime, and from sharp shock-like fronts to smooth solitary-like profiles in the nonlinear regime. The theoretical results are further corroborated by numerical simulations based on the two-dimensional Westervelt equation.

In the present work we revisit a ponderomotive nonlinearity model used to examine self-trapped laser beams in plasma. Upon briefly considering the exact stationary 1D solutions of the model, we extend considerations to two spatial dimensions where we find both solitonic and vortical structures. The solitary waves localized in both directions are found to be spectrally stable. However, all other structures that we consider in this model, including line solitons -- which are homogeneous 2D extensions of 1D solitons -- and vortices of topological charge S=1 and S=2 are found to be spectrally unstable. The focal point of our studies then turns to the examination of the collisions of the stable two-dimensional solitary waves for which we map a two-parameter space of soliton speeds and frequencies, in terms of the potential outcomes. While the standard scenarios of merger, inelastic collision leading to separation, separation that leaves behind a localized pulse are all possible, the intriguing outcome that we highlight here is that of a longitudinal collision yielding a transverse spliting of the solitons, either with or without a localized pulse remnant.

A generalized long-wave limit method that introduces spectral perturbations into the long-wave limit framework is proposed for constructing higher-order lump solutions. Within a unified small-parameter framework, the method simultaneously accounts for the degeneracy of spectral parameters, different vanishing rates of wave numbers, and higher-order modulations of the phase parameters. By tuning the phase parameters to push the leading term of the auxiliary function expansion to a prescribed order, the resulting solutions support a controllable number of lump waves and exhibit rich anomalous scattering behavior. Applied to the Kadomtsev--Petviashvili-I equation, second- and third-order lump solutions are systematically derived, and the degeneration of lump chains into higher-order lumps is transparently revealed in the long-wave limit. The method can generate degenerate solutions with up to \(M(M+1)/2\) lumps from an \(M\)-lump chain. Moreover, compared with the previously proposed improved long-wave limit method, the present approach is capable of producing higher-order lump solutions whose long-time asymptotic behavior is independent of the Yablonskii--Vorob'ev polynomials. Its extension to hybrid higher-order lump solutions with distinct spectral parameters is also discussed.

A (2+1)-dimensional hyperbolic system of four quasi-linear partial differential equations is derived that describes the modulations of lump solutions of the Kadomtsev-Petviashvili I (KPI) equation in the presence of a mean field. The system is then shown to satisfy the necessary conditions for integrability of hydrodynamic chains. Moreover, a suitable reduction of the resulting modulation system is applied to study the interactions between lumps and a rarefaction wave for the mean field. Precise conditions are derived that describe how the lump parameters change as a result of the interaction, and which in particular determine whether the lump is transmitted through or trapped inside the rarefaction wave. The theoretical predictions are compared to direct numerical simulations of the KPI equation, showing excellent agreement.

Internal water waves arise when there is a change in density stratification in a fluid, which may occur in an oceanographical context due to variations in temperature, salinity, or other fluctuations in the equations of state. We present a derivation of nonlinear integrable models for the propagation of interfacial internal waves arising between two fluid layers of different densities (at the so called pycnocline). We examine the integrable Benjamin-Ono (BO) equation as an internal wave model, incorporating underlying currents by permitting a sheared current in both fluid layers. The BO equation arises for a specific small-amplitude asymptotic regime. We show that the BO soliton characteristics are strongly affected by the shear current parameters.

Partial differential equations (PDEs) regulate the behaviour of countless spatiotemporal systems in the physical and life sciences. In many cases, they encode the coupling between the system's degrees of freedom, leading to nonlinear equations whose solution space is challenging to explore exhaustively. Systematic approaches to PDE model exploration are a holy grail of computational science. In this article, we formulate a criterion for increasing the diversity of a search campaign, based on the PDE residual behaviour under solution deformation. We develop a practical formalism to compute this property and illustrate its role in a few cases of interest.

Pattern formation in reaction-diffusion systems is traditionally analyzed under isothermal assumptions, overlooking the dynamical role of temperature in systems where reactions generate and dissipate heat. Here, we investigate non-isothermal reaction-diffusion dynamics by coupling activator-inhibitor kinetics to a dynamically evolving temperature field that modulates reaction rates through Arrhenius-type dependencies. This coupling introduces an additional feedback mechanism that influences stability and pattern selection. Through analytical and numerical analysis of the Cholrine dioxide-Iodine-Malonic acid (CDIMA) and Schnakenberg models, we demonstrate that thermal feedback modifies dispersion relations by enhancing instability growth rates and shifting pattern selection toward shorter wavelengths. Beyond these intrinsic effects, we identify a boundary-mediated mechanism in which thermal constraints qualitatively alter global dynamics. In particular, fixed-temperature boundaries induce nonstationary behavior in the CDIMA system, whereas the Schnakenberg model exhibits robust stationary patterns. These results establish thermal-kinetic coupling as a general mechanism for controlling pattern formation and highlight the role of boundary-mediated heat exchange as a tunable parameter for spatiotemporal organization.

We study the dichotomy between compact satellite and ring formation in proto-planetary disks. Specifically, we examine the behavior of a model system of $N$ identical particles locked into circular, gravitationally-bound orbits around a central body. We treat interactions as dominated by inter-particle collisions, and extract an effective two-particle interaction function based on both theory and simulations. We then demonstrate that the expected dynamics are equivalent to a variant of the Kuramoto model, which undergoes a phase transition as parameters vary. This offers a novel potential explanation for the transition between formation of rings versus moons.

The article is devoted to the problem of decay of initial stationary state for the Volterra lattice with zero boundary condition. We show that this process is asymptotically self-similar and calculate the propagation velocity of the decay wave, the leading terms of the asymptotics and corrections, in the main and transition sectors of the wave.

Three-dimensional (3D) optical solitons bear far stronger relevance to multi-dimensional nonlinear dynamics prevalent in complex physical, chemical and biological systems than conventional 1D solitons, and they support far richer and more intricate phenomena arising from their spatiotemporal degrees of freedom. However, real-time recording of 3D soliton evolution with simultaneous spatiotemporal resolution remains a critical challenging. Here, we demonstrate long-term real-time visualization of 3D soliton dynamics with spatiotemporal resolution using high-speed photodetectors combined with joint space- and time-division multiplexing. We visually capture complex transient behaviors of 3D solitons in a multimode fiber laser and, by integrating our method with the time-stretch technique, simultaneously record pulse-resolved beam and spectral evolutions. We observe that during the birth of 3D solitons, the highly multimode beam stabilizes for a substantial interval prior to spectral broadening, indicating that a large number of transverse modes have already locked before longitudinal mode proliferation. These findings highlight the critical importance of real-time spatiotemporal visualization for advancing ultrafast multimode laser design and delivering new insights into high-dimensional nonlinear dynamics.

We investigate energy supratransmission in a boundary-driven two-dimensional nonlinear Schrödinger equation with a central hole. Harmonic forcing with azimuthal modulation generates standing-wave states whose existence and stability depend on the driving amplitude, the inner radius, and the imposed azimuthal charge. Bifurcation analysis shows that small inner radii produce strongly confined states with higher destabilization thresholds, whereas larger radii yield broader profiles and smoother transitions between stable and unstable branches. The cubic--quintic and saturable models exhibit similar qualitative behaviour but differ quantitatively in their critical amplitudes and parameter dependence. A variational approximation captures the dependence of the critical drive on the azimuthal charge and nonlinear parameters, and clarifies how the nonlinear response shapes the stationary states near the turning point. Time-dependent simulations show that supratransmission occurs through the emission of localized pulses, with nonzero azimuthal charge triggering symmetry breaking and producing two-dimensional localized excitations (pearls). Isosurface plots provide a complementary view of the resulting radial and angular excursions. These results establish a quantitative framework for supratransmission in two-dimensional geometries and are relevant to driven nonlinear systems in optics, Bose--Einstein condensates, and structured media.

Gradient-based inversion of reaction-diffusion systems is typically approached via surrogate models or physics-informed neural networks (PINNs), while the most direct route, backpropagation through the PDE's structure itself, has largely been avoided. We pursue this direct route as a diagnostic probe, backpropagating a steady-state loss through unrolled Gray-Scott simulation to recover its parameters, with no surrogate or neural-network augmentation. Optimization fails to converge, and plotting the landscape directly locates the failure in its geometry -- flat plateaus with no gradient signal, bounded by sharp cliffs that align with bifurcation boundaries -- a structure that recurs across loss functions and is inherited however the gradients are routed to parameters. Reading this minimal setup as an ablation of PINN, we disentangle each component's role: with the neural network fixed, the residual loss is quadratic in the PDE parameters and yields a smooth landscape, so it alone already avoids the pathology, by implicitly encoding the full PDE dynamics across all initial conditions. The neural network, for its part, cannot repair an ill-posed parameter subspace, and so serves only to complete the observed data -- a division of labor not previously made explicit. These findings carry concrete design implications for PINN-type methods and a broader heuristic on when added dimensions actually help.

This work introduces a biophysical formalism to describe the spatiotemporal evolution of the chemical profile in tissues, with the novelty of modeling tissue compartmentalization and the mechanism by which cells maintain the system far from thermodynamic equilibrium via production and/or degradation of substances. The models were derived from conservation laws, chemical kinetic theory, and geometric constraints, while considering fundamental properties of tissues to connect theoretical modeling with experimental observations. In a morphogenetic context, each morphogen is described by two coupled reaction-diffusion equations, representing intra- and extracellular dynamics, linked through membrane transport processes such as nonlinear, cross, and anomalous diffusion. We explore the models' morphogenetic potential through diffusion-driven instabilities and discuss how natural tissue heterogeneities influence Turing instabilities and self-organized phenomena. The mathematical structure reveals that two-morphogen systems can produce Turing patterns with multiple characteristic length scales, while the system's dimensionality enables chaotic behavior in well-mixed dynamics. Moreover, due to domain coupling, Turing instabilities are allowed for single-morphogen systems. We used Schnakenberg kinetics to demonstrate that Turing patterns arise even when the activator diffuses faster than the inhibitor (d$<$1), thereby expanding the parameter space for pattern formation. Our results suggest that tissue spatial structure has important consequences for Turing instability mechanisms, in some cases weakening the usual conditions for its emergence while widening the possible patterns it can produce. The proposed framework offers a minimal mathematical basis to explore emergent dynamics in biological and synthetic contexts, with potential applications in developmental biology and tissue engineering.

We study how time-periodic, spatially localized states are born from the linear spectrum of a \emph{finite} lattice as the nonlinearity is switched on. In earlier work we treated this question for a diatomic chain with on-site nonlinearity and developed a framework that continues a near-edge linear mode in amplitude and controls the resulting perturbation series uniformly in the chain length. The present paper shows that the same framework applies to the more difficult case of Fermi--Pasta--Ulam--Tsingou (FPUT) interaction nonlinearity. The key is a structural relation between the FPUT and on-site nonlinearities, which allows the estimates obtained in the on-site setting to be transferred to the FPUT setting. As before, the analysis yields a quantitative radius of convergence, $\eps=\Theta(1/\sqrt{n})$ for a chain of length $2n$, below which the near-edge mode stays extended and above which the orbit localizes and its frequency leaves the band. The diatomic chain is used only as a test case; both the formation mechanism and the method are model-independent and are expected to extend to other short-range nonlinearities and to higher dimensions.

A pure stress-based finite difference formulation is introduced for modeling elastic wave propagation in linear elastic solids with spatial heterogeneity. The approach derives from the strong form of the elastodynamic equation of motion, in which stress is the only dependent variable. A standard second-order central difference scheme is applied to discretize the equation of motion, allowing the space-time-dependent evolution of stress components to be modeled. Numerical dispersion analysis is performed for homogeneous, elastically isotropic materials. Simulations are then carried out for a spatially heterogeneous case consisting of a bimaterial with stiffness heterogeneity. This bimaterial case allows comparison with known closed-form solutions for reflection and transmission coefficients and with an analogous displacement-based finite difference model. Simulations are executed on modern graphics processing unit architectures, enabling stress-based modeling of large-scale three-dimensional problems exceeding one billion degrees of freedom. The approach shows promise for ultrasonic simulations in materials with stiffness heterogeneity and uniform mass density, conditions common in polycrystalline metals used in engineering applications. The formulation offers a potential alternative means of modeling wave propagation and scattering in heterogeneous materials, with possible applications in nondestructive evaluation, materials characterization, biomedical ultrasound, and geosciences.

Based on one-dimensional Eringen stress-gradient non-local model, by considering non-locality vector and nabla operator instead of non-locality scalar parameter and second order derivative, eight three-dimensional Eringen non-local models are formulated and classified into two groups: three scalar- and five tensor-type non-local models, according to the type of used non-locality operator which is obtained via various vector products of non-locality vector and nabla operator. The compatibility conditions ensuring symmetricity of Cauchy stress tensor in the case of the tensor-type model are derived. Furthermore, using the Fourier integral transform with respect to spatial coordinates, non-locality kernels (Green's functions), reflecting non-locality character of the material, are derived for each of the proposed models. Except for the one scalar-type model, all other models account for both local and non-local contributions to Cauchy stress tensor. Additionally, the isotropy of proposed models, as well as their non-local isotropy properties, both depending on non-locality kernel, are examined. All scalar-type models are isotropic, such that one of them is non-locally isotropic and two of them correspond to a non-locally anisotropic body, while all tensor-type models are anisotropic, such that there are two models that do not prefer direction of non-locality, thus corresponding to a non-locally isotropic body, whereas three models correspond to a body exhibiting non-locality along a specific direction(s), thus corresponding to a non-locally anisotropic body.

We present a magnetic torsional pendulum that provides a unified experimental platform for investigating forced resonance, parametric resonance, and degenerate parametric amplification in the undergraduate laboratory. The system consists of a permanent magnet suspended by thin wires and driven by externally applied magnetic fields generated by Helmholtz coils. By independently controlling a direct driving field and a periodically modulated bias field, the apparatus can realize ordinary forced oscillations, parametric excitation, and phase-sensitive parametric amplification within the same physical system. A miniature wireless gyroscope embedded in the pendulum bob enables direct measurement of the angular velocity and provides convenient real-time acquisition of quantitative dynamical data. A unified equation of motion is derived to describe all three operating regimes. Experimental studies of forced resonance, parametric resonance, and phase-sensitive parametric amplification are compared with theoretical predictions and numerical simulations. The measurements reproduce the characteristic features of all three phenomena and illustrate the influence of nonlinear effects on the system dynamics. The apparatus combines a simple mechanical design, low-cost instrumentation, and highly visible motion. By allowing direct comparison of different resonance mechanisms and their underlying energy-transfer processes,, it provides an accessible platform for studying oscillation theory, nonlinear dynamics, and parametric phenomena in advanced undergraduate laboratories.

A time-reversal characteristic-mode decomposition is developed for reciprocal lossy electromagnetic structures. The formulation is built on a transmit--receive interpretation of reciprocity: the far-field pattern radiated by a mode determines the time-reversed incident field that is optimally matched to couple energy back into that same mode. This physical picture leads to an antilinear characteristic-mode equation whose solutions remain radiation-power orthogonal even in the presence of material loss, lossy loading, or matched absorption. As a result, the modal expansion coefficients directly represent the radiated-power contributions of the corresponding modes and avoid the singular biorthogonal normalization that may arise in nonnormal classical characteristic-mode expansions. Equivalent formulations are derived in the scattering-operator, T-matrix, and method-of-moments (MoM) frameworks, thereby connecting external wave-channel descriptions with current-space and port-excitation descriptions. The proposed modes reduce to classical characteristic modes in the lossless limit. Numerical examples involving a lossy two-sphere system and a loaded folded antenna demonstrate the radiation-power orthogonality, modal-expansion stability, and power interpretability of the proposed decomposition near exceptional points, where classical characteristic-mode expansions become singular or lose their radiated-power meaning.

Thermomagnetic generators (TMGs) are devices that convert waste heat to electricity through a change in magnetization of a solid material. This causes a changing flux through a coil, which induces an electromotive force per Faraday's law. However, the influence of the coil on the performance of the TMG has not been investigated and existing TMG prototypes merely utilize some coil, not the optimal coil for a given device. In this work we present an analytical and numerical model of a TMG that calculates power by explicitly coupling the TMGs magnetic and electric circuits and use this to analyze the influence of the coil on the TMG performance. We show that analytically TMG power has a linear dependence on coil volume, independent of the specific combination of wire radius and coil turns. The model is validated with experimental data, and finally used to study prototype TMGs presented in literature, where we show that the power of these literature TMGs can be increased by a factor of 10-400 times, had larger coils been used in the prototypes.

Design fits in different fields, and it is given a plurality of titles: thinking, social, ecological, and graphic, space, etc. This discipline crosses the fields of research and engineering, which emancipate themselves from their historic fields and target other areas of public and private services. On the other hand, the sound sector, and more generally the acoustics, is more strictly categorized: musicology, psycho-acoustics or electro acoustics (see figure 1, which gives a relatively comprehensive overview) ). It is in this universe that evolves the discipline of sound design, with accents a priori industrial or environmental. But could it also allies, more unexpectedly, to health design and, if so, in what form\,? To answer this question, we try here, in a few lines, to explain the links between art (s) and health, links that aroused the interest to draw a parallel with the world of design, then to think about its integration. In the medical community. We will conclude, as an illustration, from our own research in sound design, in connection with Indian music.

The thin ice that covers the polar oceans is a complex geomaterial that is constantly stressed and fractured by winds and ocean currents. In the central Arctic, this forcing produces deformations in the form of shear bands, within which individual ice plates detach, locally generating a granular medium. Capturing this transition from a continuous to a granular sea-ice cover has implications for the adequate representation of the mechanical and dynamical behavior of sea-ice in regional and large-scale models used for operational and climate prediction purposes. Our work investigates the feasibility of a phase-field approach to capture this granularization processes and focuses on fracture propagation in the material. The model combines a double-well free-energy formulation with an overdamped displacement response. The governing equations are solved using a spectral method in Fourier space. The implementation accounts for body forces, representative of the main forcings on sea-ice, and remains computationally tractable despite the highly nonlinear character of the double-well energy formulation. We first validate the framework against a benchmark problem: the opening of an inclusion embedded into an elastic matrix under tensile loading. Then, additional simple shear configurations are investigated: an inclusion solicited under plane shear and a cylindrical Couette experiment, for which the analytical solution of the displacement field is known. The resulting fracture patterns and displacement fields demonstrate that our phase-field framework captures key features of tensile and shear fracture propagation, including the linear scaling between crack speed and applied load predicted by the Griffith's theory.

The sustainable electrogeneration of hydrogen peroxide (H2O2) via the two-electron oxygen reduction reaction (2e$^-$ ORR) represents a promising alternative to conventional production methods. In this study, CeO2 and CeO2MnOx nanoparticles were synthesized and supported on Vulcan XC-72 carbon at varying loadings (1, 3, and 5%), aiming to assess the lowest metal loading and high H2O2 electrosynthesis. Physicochemical characterizations confirmed the successful formation of CeO2 nanowires and the effectiveness of the MnOx surface modification. XRD, TEM, XPS, EPR, and contact angle analyses revealed that CeO2 loading increased surface hydrophilicity through the presence of oxygenated functional groups, thereby favoring electrochemical activity. On the other hand, all CeO2MnOx loadings were statistically equivalent to Vulcan XC-72 in terms of contact angle. Electrochemical evaluations using a rotating ring-disk electrode (RRDE) demonstrated enhanced ORR activity and high H2O2 selectivity for the 1% CeO2MnOx/C and 3% CeO2/C catalysts, achieving up to 90% selectivity and elevated ring currents. The results suggest that low metal loading and surface modification via MnOx improve the balance between active site exposure, oxygen adsorption, and intermediate stabilization, thus favoring the selective 2e$^-$ pathway. These findings support the development of cost-effective, non-noble-metal catalysts for green H2O2 production via electrosynthesis.

The widespread presence of synthetic progestins, such as levonorgestrel (LNG) and gestodene (GES), in aquatic environments poses significant ecotoxicological risks due to their endocrine-disrupting properties. In this study, nano-octahedral magnetite (Fe3O4-NO) was synthesized via a hydrothermal route and incorporated into gas diffusion electrodes (GDEs) supported on Vulcan XC72 to enhance the in-situ electrogeneration of hydrogen peroxide (H2O2). High-resolution transmission electron microscopy, X-ray diffraction, SEM, X-ray photoelectron spectroscopy, and contact angle measurements thoroughly characterized the physicochemical and morphological properties of the materials. The 3% Fe3O4-NO/C catalyst provided a two-fold increase in H2O2 selectivity compared with Vulcan XC72. Electrochemical performance was optimized using a 2^3 factorial design and principal component analysis (PCA), with current density, pH, and Na2SO4 concentration as variables. The optimized GDE (3% Fe3O4-NO/C) achieved a maximum H2O2 production of 0.44 +/- 0.02 g L-1 with a current efficiency of 43.1 +/- 0.23% and a specific energy consumption of 0.012 +/- 0.009 kWh g-1. The electrode was further applied to the degradation of LNG and GES using solar and anodic-assisted electro-Fenton processes. Under optimal conditions, over 70% removal of both progestins was achieved, with stable performance across three operational cycles. These findings demonstrate the potential of 3% Fe3O4-NO/C-GDEs as efficient, reusable cathodes for sustainable electrochemical advanced oxidation processes (EAOPs) in water treatment.

Asteroid-neutron star collision models have been proposed as possible sources of high-energy transients, such as gamma-ray bursts (GRBs) and fast radio bursts (FRBs). The sequence of events following the impact of the asteroid and finally dissolving into the neutron star can have several other observable consequences. We propose that due to the development of the off-diagonal moment of inertia (MI) components, the merger's aftermath can lead to the wobbling of the pulsar (assuming the neutron star happens to be a pulsar). Using sample values of various parameters, viz., size, shape, the locations of the deposits, and the pre-existing pulsar deformation parameter ($\eta$), we calculate the detailed pulse profile modulation of the pulsar. We observe a distinct pattern of pulse profile modulation on a characteristic timescale enhanced by a factor of $1/\eta$ compared to the pulse timing. Importantly, even small changes in the MI components, of order $\epsilon$, can produce large pulse profile modulations of order $\epsilon/\eta$ (depending on the relative location of asteroid material deposition). Thus, if an asteroid-neutron star collision is responsible for a high-energy transient, the associated pulse profile modulation may serve as a falsifiable observational signature of such an event.

Complex chemistry in nano- and microscale compartments is often governed by how quickly reagents transit a fluid-fluid interface. Mass transport across interfaces is commonly modeled by assuming local equilibrium, enforcing continuity of chemical potential across the interface. While adequate at large scales, this approximation may break down at the microscale, where interfacial processes can become rate-limiting. Here, we extend linear irreversible thermodynamics to describe nonequilibrium interfacial mass transport. We identify an interface-limited regime, in which transport is governed by interfacial resistance and exhibits exponential relaxation. Combining microfluidic and spectroscopic techniques, we introduce an experimental technique that explores this regime and provides a direct measurement of the interfacial mass transfer coefficient. For a model system consisting of acetonitrile transport across a surfactant-stabilized water-oil interface, we obtain an interfacial transport coefficient ${M \sim 7\,{\rm nm/s}}$. These results establish interfacial mass transfer resistance as a governing mechanism in microscale transport and provide a framework to predict, control and measure mass transport in multiphase systems at microscale.

We numerically investigate percolation of independent frictionless glued-sphere rod-like particles under gravity through a disordered static bed of larger spheres. We identify two distinct regimes: a \emph{trapping} regime, where rods stop after percolating a limited distance in the bed and a \emph{passing} regime, where rods percolate continuously with constant mean velocity. The transition between these regimes is governed by the length of the rod and the geometrical trapping threshold for spherical particles based on the rod diameter and the minimum pore throat diameter defined by three touching large spheres. The percolation velocity for all rod geometries, including the single sphere limit, collapses onto a single curve when scaled with the gravitational acceleration and the bed sphere diameter. The results also demonstrate that short rods percolate nearly twice as fast as long rods due to the geometric constraints associated with the disordered pore structure of the static bed. Consequently, long rods are more susceptible to trapping via specific contact configurations with the bed spheres, which differ from those for short rods. These results reveal how shape anisotropy introduces dynamical constraints and thresholds in granular percolation, with implications for predicting segregation in mixtures of non-spherical particles.

A large body of experimental studies of swift heavy ion latent tracks in dielectric materials has produced a wide range of estimates of track size. We investigate the physical meaning of these estimates by examining the different criteria of track boundary probed by various experimental techniques, including SAXS, XRD, chemical etching and conductometry. We show that different methods probe different physical aspects of ion induced modification, such as electron density redistribution, molecular ordering, chemical reactivity and charge separation, resulting in different determinations of effective track boundaries. Particular attention is paid to polymer films with electret-like properties, where post irradiation redistribution of weakly bound electrons may play an important role in the evolution of latent track structure.

Minimising bacterial surface adhesion and subsequent biofilm formation in industrial and medical settings requires understanding how bacteria are transported and adhere to complex surface geometries in the presence of non-uniform flow. In this paper, we consider the transport of a dilute suspension of motile bacteria through a corrugated two-dimensional channel with perfectly adhesive walls. We asymptotically analyse the diffusive boundary layer that forms in high velocity flows using a curvilinear coordinate system based on the fluid streamfunction, presenting a similarity solution to the diffusivity-varying diffusion-type equation that arises. From this solution, we derive an analytical expression for the bacterial adhesion rate as a function of surface arclength and the spatially varying wall shear rate. Our model predicts that bacterial adhesion becomes localised on curved surfaces, with bacteria showing preferential adhesion to wall `peaks' at lower shear rates and preferential adhesion to wall `valleys' at higher shear rates. More broadly, our results highlight how spatially varying flows generated by complex geometries can lead to localised bacterial adhesion, with potential implications for both enhancing and minimising biofilm formation.

We develop classical density functional learning to address fluids with truncated pairwise interparticle interactions in three-dimensional spherical geometry. Simulation data for systems with randomized repulsive pair potentials provide the basis for supervised training of a neural metadensity functional, thereby making efficient use of results for radial distribution functions in the bulk fluid via the test particle route. Specifically, we develop spherical local learning in order to represent the one-body direct correlation functional in terms of a neural network, which captures spatial curvature effects as well as the metadensity functional dependence on the thermally scaled pair potential. The framework yields efficient access to inhomogeneous structuring and related physical phenomena that occur in fluids and general solvents when adsorbed against curved solutes and confined inside of spherical and planar cavities. Test particle setups facilitate accurate prediction of the bulk fluid pair structure and verification of thermodynamic test particle sum rules via functional line integration. Applying the metadensity functional for Henderson inversion allows one to infer accurately the pair potential from the bulk radial distribution function. We address implications of the geometrical setup for two-body quantities and obtain the two-body direct correlation functional from automatic differentiation. For the hard sphere fluid, we confirm metadensity functional predictions against results from a standard neural density functional with fixed pair potential as well as to an analytic functional as given by fundamental measure theory. Simulation results provide further reference and corroborate reliable results of the spherical neural metadensity functional across a broad range of applications.

We investigate the linear and nonlinear rheology of dense chiral fluids composed of self-spinning particles under external shear. Using particle-based simulations of a two-dimensional Lennard-Jones model with transverse interactions, we show that chirality acts as an intrinsic source of fluctuations and shear. In the solid regime, spinning fluidizes the system, weakening hexatic order. In the liquid regime, the viscosity is quantitatively described by a Green-Kubo relation upon replacing the temperature by a chirality-dependent effective temperature. Beyond linear response, flow curves collapse when expressed in terms of the ratio between imposed shear and spinning rates, revealing a thinning-by-spinning mechanism. At large forcing, this correspondence breaks down and a pronounced handedness asymmetry emerges: when transverse interactions oppose the imposed shear, stresses relax through the formation of string-like flow channels. Our results identify chirality as a generic mechanism for fluidization and provide a unified framework for understanding the rheology of dense chiral suspensions.

How a two-dimensional solid melts remains unsettled after 60 years of study, as theory, model systems, simulations, and atomic-resolution experiments continue to suggest conflicting scenarios. The same transition can appear continuous or abrupt depending on how it is observed, where this ambiguity is especially acute in confined water. Here we study bilayer water under nanoconfinement and ask not only where its phase boundaries lie, but how the system responds to the two fields that drive them: temperature and lateral pressure. Using Lee-Yang zeros together with enhanced sampling, we find that some phase boundaries are field-selective: the two responses can differ either in continuity itself, or in how strongly they are rounded in finite systems. This distinction changes the two-step melting picture. The solid--hexatic transition is field-selective first-order, with the density channel remaining unusually rounded, whereas the hexatic--liquid transition becomes a conventional first-order transition once larger cells reveal a hidden bimodal enthalpy distribution. This framework organizes the apparent disagreement among confined-water simulations, hard-disk models and AgI experiments by identifying which thermodynamic channel each probe sees.

Mechanical computation, in which logic functions are realized through deformation rather than electronics, has been demonstrated in systems such as origami, kirigami, and mechanical metamaterials. In these systems, logic states and functions are typically determined by geometry and material properties, making it sensitive to deformation and imperfections. Here we introduce a mechanical computing architecture in which logic is defined by topology rather than geometry. The circuit is realized as a knitted textile formed from a single continuous yarn, where information is encoded in the topology of stitches and processed through controlled unraveling. By discretizing the textile into a lattice of interacting cells, we construct topological propagation rules that implement universal logic operations, including NOT, AND, and OR gates, as well as a half-adder. Experiments demonstrate that the logical output is robust against geometric deformation, while mechanical factors affect only if the computation can be executed. These results establish topology-defined computation as a model for information processing in textiles and other reconfigurable physical systems.

Topological defects govern much of the flow behavior and orientational order in active nematics, making their control relevant for active matter physics, smart materials, and microfluidics. Applied activity patterns can induce self-propulsion of active nematic defects, but general-purpose methods for exploiting this effect to control defects remain largely unexplored. Here we use deep reinforcement learning (RL) to perform minimum-time position control of +1/2 defects in hybrid lattice Boltzmann simulations of active nematodynamics. Spatiotemporally patterned activity, implemented as a control field in the active stress, steers defects through microchannel geometries and reveals finite-time reachable regions of defect position space. Reachability is shaped by director anisotropy, homeotropic wall anchoring, and the allowed activity patterns: local patterns steer defects in free domains but fail in junctions, whereas global patterns open otherwise inaccessible channels. In constrained geometries, the original defect may be unable to reach some goals intact, but controlled pair creation enlarges the effective reachable set by transferring control to a newly created +1/2 defect. The trained RL controllers outperform static and rule-based baselines, and controllers trained only on simple junctions can be combined without fine-tuning into a meta-controller that successfully steers defects through a larger test maze. Free energy visualizations show that guided defects write persistent, history-dependent distortions into the director field that can later be partially erased by -1/2 defects. Thus, RL-based control uncovers how confinement, anchoring, actuation geometry, and defect creation determine reachable motion in active nematics, providing a framework for other control tasks in soft and active matter.

We revisit the problem of scalar dissipation anomaly and scaling of scalar gradients in passive scalar turbulence using theory and data from well-resolved direct numerical simulations (DNS) on grid sizes of up to $8192^3$, spanning Taylor-scale Reynolds numbers $Re_\lambda=140-1000$ and Schmidt numbers $Sc = 1-512$. The theory is based on a joint multifractal description of longitudinal velocity increments and scalar increments, constrained by Yaglom's law and extended to gradients via a fluctuating Batchelor cutoff scale. The DNS data show that the normalized mean scalar dissipation approaches a single asymptotic value as both $Re_\lambda$ and $Sc$ increase, although larger $Sc$ requires larger $\re$ to reach this state. In the multifractal framework, this corresponds to an effective scalar Hölder exponent tending to zero, associated with sharp cliff-like scalar fronts, and saturation of inertial-range scaling scalar structure-function exponents. The joint velocity-scalar fractal dimension of the dissipative structures is inferred to approach $7/3$, indicating a non-space-filling support. The framework further predicts that for fixed $Re_\lambda$, higher-order central moments of scalar gradients are independent of $Sc$. This prediction is confirmed by DNS data and by the collapse of standardized probability distributions of scalar-gradient across Schmidt numbers. These results suggest that the $Sc$-scaling of scalar gradients is dictated solely by scalar dissipation anomaly. In contrast, their $Re_\lambda$-dependence reflects strong intermittency, which can be directly related to mixed velocity-scalar structure function exponents.

We study correlation functions in generic non-equilibrium mixtures, including multi-temperature systems and non-reciprocal field theories. The corresponding linear theory is short-ranged, and nonlinearities are irrelevant in the renormalization-group sense. Nonetheless, we find that these nonlinearities generate long-ranged three-point correlations in the isotropic disordered phase. Our analytical predictions, which are based on a phenomenological theory, are confirmed by numerical simulations of Brownian colloids in contact with thermal baths at different temperatures. Dangerously irrelevant nonlinearities in non-equilibrium mixtures thus offer a new route to long-range correlations, supporting the hypothesis that such correlations are not the exception but the rule out of equilibrium.

The theory of wave turbulence describes the properties of physical systems composed of a set of weak-amplitude random waves interacting nonlinearly. Here, we study odd wave turbulence, which arises in chiral media subjected to non-reciprocal stresses, notably odd viscosity and odd elasticity. In both cases, we consider simple models for which we can derive and solve analytically the kinetic equations describing the long-term statistical behavior of spectral quantities such as energy or wave action. For odd viscosity, we consider a three-dimensional model that exhibits wave turbulence involving three-wave interactions, which gives rise to a direct energy cascade characterized by an anisotropic Kolmogorov-Zakharov (KZ) spectrum. For odd elasticity, we consider a quasi-one-dimensional overdamped model that exhibits much slower dynamics involving six-wave interactions. In that case, the KZ spectrum corresponding to a forward cascade of a conserved quantity we call odd energy, is nonlocal and therefore does not constitute a physical solution. However, the other KZ solution, which describes an inverse cascade of wave action, is only marginally non-local and is therefore valid up to a logarithmic correction. These two analytical theories provide a rigorous interpretation of direct numerical simulations, where the KZ spectrum is observed both in the case of odd viscosity (forward cascade) and of odd elasticity (inverse cascade).

The stationary measure of equilibrium systems with detailed balance follows a Boltzmann distribution, so that for short-ranged interactions the measure is local, meaning that distant spatial domains are statistically independent. In contrast, active systems break detailed balance, and can have nonlocal stationary measure even for fully local dynamics. Here, by expanding in nonlinearity about a Gaussian-model limit, we construct the measure perturbatively deep in the disordered phase for a class of models that includes Active Model A, Active Model B+, Model AB, the Nonreciprocal Cahn--Hilliard model, and the Toner--Tu model. In this regime, nonlocality is linked to a dynamical conservation law. Our results generically preclude construction of a Landau--Ginzburg expansion of the stationary measure (as opposed to the dynamical equations) for conserved active field theories.

Physical vapor deposition (PVD) provides a route to prepare highly stable and anisotropic organic glasses that are utilized in multi-layer structures such as organic light-emitting devices. While previous work has demonstrated that anisotropic glasses with uniaxial symmetry can be prepared by PVD, here, we prepare biaxially aligned glasses in which molecular orientation has a preferred in-plane direction. With the collective effect of the surface equilibration mechanism and template growth on an aligned substrate, macroscopic biaxial alignment is achieved in depositions as much as 180 K below the clearing point $T_{LC-iso}$ (and 50 K below the glass transition temperature $T_g$ ) with single-component disk-like (phenanthroperylene ester) and rod-like (itraconazole) mesogens. The preparation of biaxially aligned organic semiconductors adds a new dimension of structural control for vapor-deposited glasses and may enable polarized emission and in-plane control of charge mobility.

Interactions between boiling bubbles are well known to influence departure dynamics and heat transfer, yet their role in governing nucleation stability, whether sites activate reproducibly, persist, and deactivate under changing thermal loads, remains poorly understood. Here we show that nucleation can be a collective process: neighboring sites at close spacings exhibit reduced variability and sustained activity, consistent with a non-local hydrodynamic shielding mechanism whereby neighboring bubbles slow the intervening flow, reducing convective heat removal and stabilizing vapor embryos. To isolate near-wall nucleation dynamics from bubble-scale vapor removal, we design surfaces comprising pairs of cavities, with intra-pair spacing tuned to the boundary layer scale and inter-pair separation to the departure diameter scale. While the former governs nucleation behavior, the latter governs collective vapor removal once sites are fully active, yielding transitions between excessive, promotive, and isolated departure regimes. Together these results establish a multiscale framework for designing robust, high-performance boiling surfaces.

High-fidelity simulations are increasingly adopted, due to advances in computational power and methods such as Direct Numerical Simulation (DNS) and hybrid Large-Eddy Simulation (LES). These approaches are particularly valuable for unsteady flows around complex geometries at high Reynolds numbers; however they still require careful experimental validation. Planar and stereo Particle Image Velocimetry (PIV) are widely used for measurements but limited by measurement-plane selection and their ability to capture vortices shapes and trajectories. This motivates the growing interest in volumetric techniques, historically difficult to implement in industrial settings. Recent advances in Particle Tracking Velocimetry (PTV) for measuring flows over large volumes make this approach suitable for validating numerical simulations of complex this http URL study compares volumetric PTV measurements against high-fidelity LES to assess the capabilities and limitations for industrial flows. The aim is to establish a benchmark PTV dataset for motorsport aerodynamics using the Shake-The-Box algorithm. The experiment was carried out in the 10x5 wind tunnel at Imperial College London equipped with a rolling road for ground effect simulation and capable of testing up to 50% scale F1 model. Volumetric PTV measurements were performed downstream of the open-source Imperial Front Wing (IFW) at Re=74896. Results are compared with planar PIV studies and implicit LES simulation using spectral h/p elements in Nektar++. This work addresses open questions in the literature concerning the wake of the IFW. Good quantitative agreement is observed in the wake topology. A previously unreported vortex is identified which has the key role of preventing the merging of other dominant structures. These results demonstrate the suitability of PTV and STB for industrial applications while providing a benchmark dataset for the IFW.

Diffuse-interface (phase-field) models are a widely used framework for interfacial dynamics in complex fluids, in which sharp interfaces are replaced by smooth transition layers and interfacial forces follow from a free-energy functional. In these models, surface tensions and diffuse thicknesses are not prescribed directly but are encoded implicitly by the bulk multiwell potential and the gradient-energy term through one-dimensional equilibrium profiles. While this link is classical in the binary Cahn--Hilliard setting, calibrating multiphase models is substantially more delicate because multiple pairwise surface tensions must be matched simultaneously and the relevant equilibrium paths are constrained by the Gibbs simplex. The practical problem is therefore: given a chosen bulk potential and a set of target pairwise surface tensions, determine gradient-energy coefficients that reproduce these targets in the full multiphase model. Here we present a thermodynamically consistent calibration procedure for N-phase diffuse-interface free energies of Cahn--Hilliard type. The method determines a symmetric capillary matrix that matches prescribed pairwise surface tensions through the model's equilibrium profiles. We further introduce a rescaling strategy that adjusts diffuse interface widths to mesh-resolvable values while preserving the calibrated surface tensions. The resulting calibrated free-energy closure can be incorporated directly into N-phase mixture simulations, and we demonstrate this by applying it to N-phase Navier--Stokes--Cahn--Hilliard flows.

Non-trivial alignments between vorticity and the strain-rate tensor play an important role in the evolution of velocity gradients and the energy cascade in isotropic turbulence. Here we explore how alignments between the fluctuating and mean density gradients impact the mechanisms governing the turbulent kinetic energy (TKE) and available potential energy (APE) across scales in stably stratified turbulence. This is motivated by analytical results that demonstrate a connection between them, and is conducted using direct numerical simulations (DNS) of statistically stationary, stably stratified turbulence for $Pr = 1, 7, 50$ in the strongly stratified regime. After demonstrating how the gradient field alignments depend on scale and $Pr$, we show that the alignments are intimately connected to the reversal of the buoyancy flux at small-scales, and that regions of strong alignment and misalignment correspond to regions where the horizontal TKE inter-scale flux becomes weak. The same is also true of the APE flux, except that at larger scales, regions of strong alignment are associated with an upscale APE flux. The TKE and APE dissipation rates, and the mixing coefficient also show a strong dependence on the alignment, especially for $Pr=1$. Finally, we explore the connection between the local alignment and stability of the flow, and we find a non-trivial relationship, with regions of strong alignment surprisingly occurring most often in stable regions. This demonstrates that the dynamical significance of the alignments on the flow energetics cannot be understood through a simple connection between the local alignments and local stability of the flow.

Large heat flux is commonly associated with vigorous convection and turbulent mixing. Here, we show that this connection is not fundamental. Using a marginal energy-stability theory, we identify near-optimal convective heat transport with the saturation of an energy-stability constraint rather than with turbulence intensity. The theory selects mean temperature profiles whose fluxes closely approach the best available optimal transport states and rigorous upper bounds, predicting the asymptotic scaling $Nu\sim0.0245Ra^{1/2}$ at large Rayleigh number. These profiles exhibit a hierarchical structure consisting of conductive inner layers, logarithmic-like intermediate layers, and a stably stratified bulk, closely mirroring optimal transport calculations and suggesting that maximal convective heat transport emerges near marginal energy stability. More strikingly, the same profiles can be converted into exact conductive states through prescribed internal thermal forcing. Direct numerical simulations show that an initially turbulent flow then relaxes to a motionless state while maintaining a large wall heat flux. Energy-stability saturation therefore provides both a physical interpretation of transport limits and a route to high-flux heat transfer without turbulence.

The gas-kinetic scheme (GKS) integrates the characteristics of flux difference scheme (FDS) and flux vector splitting (FVS) scheme, providing high accuracy in smooth regions and strong robustness near discontinuities across all Mach regimes. Leveraging these properties, an implicit discrete adjoint GKS is developed for aerodynamic shape optimization over a wide range of Mach numbers. The adjoint solver is constructed using the source-transformation-based algorithmic differentiation tool Tapenade. To enhance computational efficiency, both the flow and adjoint GKS equations are solved using an implicit time-marching strategy, also known as the Lower-Upper Symmetric Gauss-Seidel (LU-SGS) method. The effectiveness of the implicit formulation is demonstrated through comparisons with the explicit approach. To accurately impose solid wall boundary conditions, particularly in hypersonic regimes, kinetic boundary conditions and their adjoint counterparts are formulated for both adiabatic no-slip and isothermal walls. Four benchmark test cases covering subsonic, transonic, supersonic, and hypersonic flows are used to verify the effectiveness of the developed adjoint-based design optimization system.

Machine learning is beginning to influence rarefied-gas modeling at multiple levels, including equation-solving, operator learning, learned collision physics, moment closures, direct simulation Monte Carlo (DSMC) field surrogates, and gas--surface models. This Perspective argues that the central challenge is not demonstration-level success, but trustworthy use under realistic deployment conditions: multiregime Knudsen behavior, stochastic DSMC labels, sharp nonequilibrium structures, uncertain gas--surface interaction, and scarce direct experimental anchors. I classify the main method families by what is learned, distinguish soft physics penalties from structure-preserving designs, and propose evaluation standards based on extrapolation tests, noise-aware metrics, end-to-end cost accounting, and a three-level validation hierarchy. Most current evidence is solver-facing: it demonstrates surrogate fidelity to a teacher solver more often than direct physical fidelity to experiment. The aim is not to dismiss ML for rarefied and vacuum-related gas transport, but to separate what is already credible from what remains provisional, and to define a reporting standard that makes future claims auditable.

Numerical simulations are performed for an FFA-W3 wind-turbine airfoil corresponding to a section of the DTU 10-MW Reference Wind Turbine. Wall-resolved large-eddy simulations (LES) are carried out with Nek5000 and EllipSys at chord Reynolds number $Re_c=1\times10^5$ and effective angle of attack $AoA=3.1^\circ-3.3^\circ$. A spanwise domain width of 10 percent of the chord is sufficient to reproduce the time-averaged flow and the evolution of the main disturbances. EllipSys is validated against Nek5000 for LES, showing close agreement for the mean flow and most amplified perturbations. EllipSys underpredicts the amplitude of Tollmien-Schlichting waves in the attached boundary layer, owing to higher numerical dissipation, but closely predicts the evolution of the Kelvin-Helmholtz (KH) mode in the laminar separation bubble, in agreement with parabolized stability equation (PSE) results. The mode shape is extracted using spectral proper orthogonal decomposition (SPOD), revealing the KH wavepacket forming in the separation bubble. Long-time EllipSys simulations show a slow modulation of the normal-force coefficient, with amplitude 10.5 percent and period 48 flow-through times, corresponding to $f=f^*c/U_\infty=0.021$ and $St=f\sin(AoA)=0.0012$. This frequency is associated with low-frequency oscillations reported in airfoil studies, although the Strouhal number is lower than previously observed and occurs at smaller angle of attack. For the DTU 10-MW turbine, the oscillation period corresponds to 7.7 blade rotations. Periodic stalling and reattachment may trigger the oscillation, while sufficiently high reverse flow on both sides of the airfoil may permit absolute instability and periodic bubble bursting.

We develop a geometric model for the spreading of shallow, viscous puddles of arbitrary shape, building on the recent 'capillary current' model for axisymmetric droplets. In short, we assume that a spreading puddle remains close to instantaneous mechanical equilibrium as it spreads, with hydrostatic pressure balanced by surface curvature. In turn, its contact line advances so as to maximize the rate of energy loss subject to viscous dissipation. The resulting system yields a natural geometric evolution equation for both the two-dimensional footprint and the three-dimensional depth profile of a spreading puddle. In appropriate limits, it recovers the classical spreading laws for axisymmetric droplets, a local version of the Hoffman-Voinov-Tanner law for small non-axisymmetric puddles, and a nonlocal Hele-Shaw-like description for large, relatively regular puddles. We show that the model rationalizes new observations of silicone oil spreading over smooth borosilicate glass.

Xylem transport relies on a hierarchy of vessels, pits, and porous membranes that redistribute the flow across several length scales. Directly resolving this nested architecture is computationally prohibitive for network-scale studies, while existing reduced models often require prescribed inter-vessel hydraulic resistances. Here, we develop a nested homogenization framework for rigid porous membranes under single-phase viscous flow. The approach first replaces the pore-scale structure of a membrane by an effective stress-jump interface law, and then embeds this effective interface inside a second characteristic problem to obtain a conduit-scale closure for pit-mediated exchange. In this way, pore-scale geometry is systematically propagated to network-scale hydraulic response through effective tensors. The reduced model is compared against fully resolved simulations in simplified xylem-inspired vessel connections, showing that the homogenized description captures the pressure drop and flow redistribution. Finally, the resulting interface law is embedded within a xylem-like network with randomly disabled conducting elements, demonstrating that the model is suitable to describe the emergent hydraulic response from the coupling between local membrane-mediated transfer and network topology. The framework provides a tractable route for studying multiscale porous fluidic networks and forms a basis for extensions involving deformable structures and multiphase flows.

The response of particles to low-Reynolds flow can be compactly predicted with resistance or mobility tensors. However, the difficulty of obtaining accurate values for the elements of these tensors for specific geometries has held back work on particles with complex shapes. Here we show how Stokesian dynamics can be adapted to efficiently compute the resistance and mobility tensors of rigid and flexible aggregates, including confinement by walls. We introduce SHAPES, an implementation of the method, and demonstrate its capabilities for complex geometries including curved fibres, chiral dipoles, interacting aggregates, and active swimmers. Aggregates are represented by assemblies of beads designed to reproduce the geometry and motion of rigid or flexible particles. This coarse-grained description preserves the essential hydrodynamic interactions while substantially reducing computational cost. The method accurately reproduces known exact and approximate solutions, as well as experimental observations. The ability to compute the complete resistance and mobility tensors provides new insight into how aggregate shape controls translation, rotation, and coupling to fluid-velocity gradients. Previous descriptions often relied on simplified models retaining only a few symmetry-allowed couplings. While useful, such reduced descriptions are not always structurally stable under small perturbations of particle shape. Computing the full tensors makes it possible to draw robust conclusions and relate them to shape symmetry and hydrodynamic interactions. In particular, the method allows systematic analysis of non-Jeffery couplings to the strain rate that arise for helicoidal aggregates. SHAPES therefore provides a versatile framework for studying rigid and flexible aggregates in microfluidic, biological, and environmental flows.

The ability to resolve complex physical phenomena with high fidelity and at low computational cost is central to addressing key challenges in modern engineering. A prime example lies in hypersonic flows, where the precise prediction of the full flowfield topology, in particular with respect to shock wave location and intensity, is critical. Yet supersonic and hypersonic flows continue to be a stumbling block for traditional reduced-order models and neural emulators that struggle to capture steep gradients in flow states with physical consistency in applications of industrial relevance. To that end, we introduce a fully GPU based workflow that integrates accelerated data generation with the training of neural emulators augmented by uncertainty quantification and physics-aware refinement. Our workflow is enabled by a differentiable high-fidelity solver (JAX-Fluids) which we employ for rapid dataset creation and residual-based improvement of the neural emulator to enhance physical consistency. Building on this framework, we first present a suite of model architectures and analyze their scaling behavior to expose their strengths and shortcomings. We then show that residual-based refinement enables training on cases where only mesh and input parameters are available, substantially reducing residuals and improving physical consistency. Together, differentiable simulation and residual-based refinement yield physics emulators that remain reliable beyond their training distribution, a key requirement for deploying surrogates in real-world engineering design loops.

A scalar potential landscape is one of the most useful ways to understand the stability and transition of a dynamical system. For non-gradient dynamics, however, the construction of a global Lyapunov-type scalar for nonlinear flows with recurrent structures remains a major obstacle. We introduce the generalized Lyapunov function, a scalar function that is non-increasing along deterministic trajectories, as a unifying notion of nonequilibrium potential. Ordinary Lyapunov functions, Freidlin--Wentzell quasi-potentials, and Ao-type potentials are recovered as special representatives. We then propose a data-free physics-informed neural-network framework in which the Lyapunov inequality and a weak divergence-scale compatibility condition are directly embedded into the loss function. The method is tested on linear systems, the Hopf normal form, the van der Pol oscillator, and a three-dimensional Hopf-link flow with two linked limit cycles. The learned landscapes agree with available analytical benchmarks and reveal the invariant sets as low-potential or constant-potential structures, providing a practical route to potential-landscape construction for nonlinear non-gradient systems.

The Lyapunov exponent quantifies the sensitivity of a dynamical system to perturbations, and the full Lyapunov spectrum extends this to every orthogonal direction in tangent space. For cellular automata the spectrum is almost always approximated numerically, and the approximation is delicate. We show that the affine rules, those whose update is a XOR of a subset of the inputs together with a constant, admit an exact Lyapunov spectrum. An affine rule has a configuration-independent Boolean Jacobian, so the spectrum reduces to the logarithms of the singular values of a single constant matrix, with no simulation and no limit involved. Two cases carry a closed form. For an affine cellular automaton on a periodic lattice the Jacobian is a multilevel circulant matrix, and the spectrum is the discrete Fourier transform of the rule's gradient stencil, valid in any spatial dimension. For the parity rule on an arbitrary graph the Jacobian is the adjacency matrix itself, so the Lyapunov spectrum is the logarithm of the absolute adjacency spectrum, and the maximal exponent is the logarithm of the spectral radius. The long-time amplitude of a single-site perturbation then scales with the eigenvector centrality of the seeded node. Reading the periodic lattice as the Cayley graph of an abelian group unifies the two cases. Because they are exact, the affine spectra also serve as benchmarks: they reveal numerical artefacts in previously reported spectra and turn the informal correspondence between spectral radius and dynamical sensitivity into an exact identity.

Distinguishing coherent, turbulent, and chaotic operating regimes in supercontinuum generation is important for understanding nonlinear optical dynamics and optimizing broadband light sources. Experimentally identifying the onset of turbulence remains challenging because the most common metric, first-order coherence, requires access to the complex optical field and cannot be directly obtained from intensity-only measurements. In this work, we investigate whether experimentally accessible statistical observables can identify turbulence in supercontinuum generation. We compare wavelength-integrated variance and kurtosis with simulation-based first-order coherence over a chirp-controlled pulse-duration sweep implemented through additional $\beta_2$ dispersion. The study combines generalized nonlinear Schrödinger equation simulations with shot-to-shot dispersive Fourier transform measurements validated against optical spectrum analyzer spectra. Statistical intensity distributions were analyzed using histograms, complementary cumulative distribution functions, and kurtosis measurements across the generated supercontinuum bandwidth. Simulations and experiments both revealed heavy-tailed intensity statistics in the intermediate pulse-duration regime associated with reduced spectral coherence. The integrated kurtosis reached a maximum near 600 fs in simulations and near 700 fs in experiments, while the integrated variance within the first 20 dB spectral range decreased with increasing pulse duration. The agreement between simulations and experiments demonstrates that variance- and kurtosis-based observables can serve as experimentally accessible indicators of turbulence in supercontinuum generation. These results show that intensity-only statistical measurements can distinguish coherent and incoherent operating regimes without requiring direct field-resolved coherence measurements.

This work investigates how restitution modeling affects the dynamics of rocking blocks subjected to harmonic excitation. While several studies have reported discrepancies between experimentally observed impact behavior and the predictions obtained using the classical Housner restitution coefficient, the implications of adopting alternative restitution formulations on the global dynamics of rocking systems remain largely unexplored. The system is formulated as a hybrid non-smooth dynamical model and analyzed through bifurcation diagrams, Lyapunov exponents, and basins of attraction for different slenderness ratios. By comparing the classical restitution model proposed by Housner with the alternative formulation of Mao et al., we show that the choice of restitution model strongly influences the predicted system response. The alternative formulation leads to an earlier onset and greater prevalence of complex oscillations, as well as changes in the type, stability, and accessibility of attractors compared to the classical model. However, as the slenderness ratio increases, the dynamical features produced by both formulations progressively converge, indicating a reduced sensitivity to the restitution model for taller blocks. These results provide a dynamical perspective on why alternative restitution formulations, which predict impact responses closer to experimental observations, can produce markedly different behaviors from those obtained using the classical Housner model.

Stochastic dynamics with state-dependent diffusion are widely used for Brownian motion in confined, anisotropic, and hydrodynamically coupled systems. The conventional Langevin formulation includes a spurious drift associated with multiplicative noise, but its free energy generally does not transform as a scalar, meaning that the covariance is not explicit. Here, we formulate a geometrically consistent Langevin equation by introducing a scalar free energy and using the diffusion tensor as a metric on configuration space. The spurious drift is then expressed as a Christoffel contribution of the diffusion metric. While our formulation is equivalent to the conventional one through the relation between the non-scalar and scalar free energies, it makes the coordinate covariance explicit. We demonstrate its consistency in representative examples of state-dependent diffusion arising from coordinate transformations, geometrical confinement, and projection from curved to flat spaces.

Digital Alchemy (DA), introduced by Van Anders et al., is a statistical mechanics-based generalized thermodynamic ensemble method that employs computer simulations to optimize colloidal particle design. This approach applies the principles of statistical mechanics to predict and tailor particle attributes that lead to desired self-assembled structures or material properties. However, as an inverse design method, its main limitation is that the target structure must be known \textit{a priori}. Therefore, the optimal design from DA does not guarantee the targeted structure is the most or the only stable one. This highlights the importance of forward design with an exploratory scheme for optimizing novel colloid designs, which becomes more suitable in such cases. In this paper, we introduce Exploratory Digital Alchemy (EDA), an enhanced forward design scheme that begins by releasing the constraint of the target crystal from DA, followed by an exploration-oriented bias that has been extensively used in enhanced sampling methods such as metadynamics (MetaD). We demonstrate the utility of EDA through examples involving particles interacting via a two-dimensional Lennard-Jones Gauss potential (LJGP) and a three-dimensional oscillating pair potential (OPP). We applied EDA to study the free energy landscapes given different potential parameters of LJGP at different temperatures. With the exploratory scheme, we've also successfully identified a wide range of OPP potential parameters that stabilize metastable Frank-Kasper phases. Our approach fuses the standard DA framework with metadynamics, which could potentially be useful for studying alchemical reactions in a generalized ensemble.

Mechanical characterization of soft materials at high strain rates is challenging due to their high compliance, nonlinear viscoelastic behavior, and potentially history-dependent responses. Inertial microcavitation rheometry (IMR) addresses this challenge by coupling laser-induced cavitation (LIC) experiments with numerical simulations of bubble dynamics models to infer constitutive models and material parameters. Both IMR and its variants infer parameters that depend on the chosen fitting window, which suggests that a constant-parameter constitutive model is insufficient to describe the full cavitation event. We use this window dependence to identify when the constant-parameter assumption fails, rather than to report a single effective parameter set. The constitutive parameters are estimated over moving, overlapping windows using a modified iterative ensemble Kalman smoother with multiple data assimilation (MIEnKS-MDA). Within the neo-Hookean Kelvin--Voigt (NHKV) constitutive model, we obtain time-resolved estimates of the constitutive response in polyacrylamide (PAAm) hydrogels with different crosslinker concentrations. The inferred shear modulus and viscosity generally decrease and then plateau during cavitation, while exhibiting relatively weak temperature sensitivity. For gelatin gels, by contrast, the inferred property evolution shows a pronounced temperature dependence, with distinct trends at low and high temperatures. Moreover, both the apparent shear modulus and viscosity exhibit significant variations during the first two bubble collapses. These results show that time-resolved parameter estimation within the prescribed NHKV constitutive structure can diagnose where the constant-parameter model assumption falls short during cavitation, thereby guiding the development of improved physics-based models of complex bubble--material interactions.

Understanding how microscopic structural dynamics relate to macroscopic mechanical response during yielding remains a central challenge in soft matter physics. Here, we introduce rheo-echo X-ray photon correlation spectroscopy (rheo-echo-XPCS) with nonlinear acquisition synchronized to oscillatory shear, enabling direct measurement of irreversible nanoscale dynamics under strain amplitude control. Applying this to a carbon black colloidal fractal gel, we resolve time-periodic echoes in the vorticity-direction intensity autocorrelation function whose decay encodes non-affine structural rearrangements. We find: (i)~ballistic-like decorrelation with $\tau \propto q^{-1}$ at all strains, where the decorrelation velocity $v_\tau = 1/\langle q\tau \rangle$ scales linearly with the loss tangent $\tan\delta = G''/G'$, establishing $\tan\delta$ as a direct macroscopic signature of the rate of irreversible structural decorrelation; (ii)~functional form continuous evolution from compressed exponential ($\alpha \simeq 1.5$) at low strain, consistent with three-dimensional dipolar strain fields in the intact network-to stretched exponential ($\alpha \simeq 0.5$) at high strain, reflecting a dimensional reduction from $d_f = 3$ to $d_f = 1$ as stress transmission shifts from bulk to quasi-one-dimensional filamentary backbones during network fragmentation.

Directional solidification of bubbly liquids plays a critical role in shaping the microstructure and properties of many materials, yet the fluid dynamics governing bubble behavior during solidification remain poorly understood. Using cryo-confocal microscopy and particle image velocimetry, we quantify fluid flows around bubbles during solidification of water containing surfactants and tracers. Our results reveal that volumetric expansion dominates fluid motion, with velocities scaling linearly with the solidification rate (1-20$~\mu m/s$), while Marangoni flows-hypothesized to play a key role-are negligible ($< 5~\mu m/s$) under our experimental conditions. Diffusiophoresis and thermophoresis also contribute minimally. These findings challenge existing theoretical models and provide a framework for controlling bubble distribution in solidified materials

Dense granular flows made of elongated particles exhibit a strong inhibition of particle rotation compared to spherical grains, but the mechanisms responsible for this effect remain unclear. Using three-dimensional discrete element simulations, we investigate the angular dynamics of elongated particles in dense, confined shear flows. We systematically vary particle aspect ratio, interparticle friction, and boundary conditions to elucidate their respective roles. We show that the reduction of the average angular velocity cannot be attributed to particle shape, friction, or solid fraction alone. Instead, it is controlled by the degree of collective alignment developed under shear, quantified by a nematic order parameter. Based on this observation, we propose a simple scaling law linking the average angular velocity to the local shear rate through a hampering parameter that depends solely on the orientational order via the nematic order parameter. This scaling successfully collapses data obtained for different particle properties (shape, friction), different flow patterns, and, remarkably, remains valid for two additional flow configurations.

Thermal transport in long polymer molecules is commonly attributed to ballistic propagation of long-wavelength acoustic phonons, which act as Goldstone modes arising from translational symmetry, while the transport of other phonons is suppressed by Anderson localization. This mechanism leads to thermal conductivity that increases with molecular length. Consistent with this picture, strongly aligned polymers exhibit exceptionally high thermal conductivity, whereas poorly aligned polymers are orders of magnitude less conductive and function as thermal insulators. Here we show that this strong sensitivity to molecular alignment originates from phonon scattering by molecular kinks. Even in the long-wavelength limit, the kink scattering remains strong because kinks break translational symmetry both for longitudinal and transverse phonons. As a result, randomly oriented kinks cause a rapid decrease in thermal conductivity with increasing molecular length. These findings identify alignment control by means of kink engineering as a route for tuning thermal transport in polymers.

Planar turbulent mixing layers, formed by the interactions of two parallel streams with different velocities, have been studied far more than three dimensional (3D) turbulent mixing layers, in which the incoming streams are skewed, and not parallel. Yet many practical shear flows are 3D. Here, we develop and validate an experimental methodology to generate and characterize skewed turbulent mixing layers and to quantify how mean-flow skew modifies mixing layer dynamics. We introduce skew with a spanwise deflection of the mean flow using turning vanes mounted near the trailing edge of a splitter plate, and we use cross-wire anemometry to investigate the downstream evolution of the flow. Relative to the planar configuration, the skewed mixing layer exhibits systematic reductions in both mean and turbulent quantities, with deviations reaching approximately 40\%. Despite these quantitative differences, the fundamental characteristics of the mixing layer remain largely unchanged. Mean-velocity profiles collapse under similarity scaling, shear-layer thicknesses retain approximately linear downstream growth, and Reynolds-stress profiles preserve their characteristic near-Gaussian form. Townsend's structure parameter, which quantifies the efficiency of turbulent momentum transport, remains approximately invariant between the planar and skewed configurations, in contrast to skewed turbulent boundary layers, wherein comparable mean flow skewing reduces the parameter by approximately 30\%. These results indicate that mean flow skew modifies turbulent mixing layers quantitatively while exerting only a secondary influence on their underlying dynamics. This study establishes a controlled experimental framework and empirical benchmark for future investigations of three-dimensional free-shear turbulence.

DNS of Rayleigh-Darcy convection in a 3D porous domain is performed at Ra $\in [10^3, 10^6]$ to investigate heat-transfer scaling, thermal boundary-layer dynamics, and flow-structure evolution in the unexplored ultimate regime. The Nu exhibits an approximately linear dependence on Ra throughout the investigated range. However, a distinct change in slope is observed at $Ra \approx 4\times10^5$, indicating the onset of the ultimate regime. For $Ra \leq 2.5\times10^5$, our scaling is 6.25% lower than that reported by \cite{hewitt2014high}, while for $Ra \geq 4\times10^5$ our results are within 1.24% of the extrapolated ultimate-regime prediction of \cite{pirozzoli2021towards}. Analysis of thermal structure reveals formation of near-wall protoplumes that merge into large-scale columnar megaplumes. With increasing Ra, the size of the protoplumes decreases, whereas the numbers increase, thus enhancing boundary-layer convection and heat transport. The thermal boundary-layer thickness scales as ~ Ra^{-1} and ~ Nu^{-1}, corroborating the persistence of linear heat-transfer scaling in the ultimate regime. The thermal dissipation is found to be increasingly shifting from the boundary layer to the bulk with increasing $Ra$, further indicating that the finer protoplumes efficiently transport heat from walls to bulk. The flow structures are quantified using the dominant length scale using the mean wavenumber ($\overline{k}$). It exhibits linear variation with $Ra$ for near-wall structures, with a higher slope in the ultimate regime, signifying finer protoplumes. At the mid-plane, a weaker scaling suggests that the megaplumes also become finer with increasing $Ra$ in the ultimate regime, thus leading to efficient heat transport in the bulk.

Over the past decade data-driven equation discovery emerged as a powerful alternative to first principles-based methodologies traditionally used in mathematical modelling cycles. The approach provides a promising path towards deep, physical insight into systems that have previously evaded rigorous mathematical derivation procedures, often due to intractable complexity. The strengths of such techniques have been successfully established for many problem classes described by systems of ordinary differential equations and continue to be extended, with their reach into partial differential equation systems gaining momentum, though comparatively nascent. Herein we tackle such a frontier: elucidating the dynamics of liquid film flows, a problem space providing a rich backdrop in terms of asymptotic analytical building blocks. By leveraging expert knowledge and the ability to carefully curate data, we establish a best-case scenario for identifying the underlying governing equations. Even here, multi-collinearity, stemming from the choice of monomial basis functions in our multi-scale flow configuration, introduces complex identifiability issues. Early-time transients compound this further, as the most dynamically rich behaviour carries the largest residuals in training data. Pinpointing such vulnerabilities allows us to better define the boundaries of current discovery techniques and paves the way for the next generation of more resilient, numerically stable algorithms.

Direct Numerical Simulation of turbulent channel flow at friction Reynolds number around 200 is performed with spanwise wall actuation to achieve drag reduction. A quasi-square-wave waveform, featuring impulsive transitions and constant-velocity plateaus, separates the actuation cycle into distinct Reversal and Displacement Phases, thereby permitting direct observation of the underlying physics. Phase-resolved analysis reveals that the actuation modulates the self-sustaining process (SSP): during the Reversal Phase, the Stokes strain passes through zero, the SSP resumes, and streaks regenerate; during the Displacement Phase, sustained Stokes strain diverts wall-normal vorticity spanwise via vortex tilting, depleting SSP precursors and suppressing streaks. A stochastic enstrophy-budget analysis confirms this mechanism at the governing-equation level: competition between mean-shear production of wall-normal enstrophy and Stokes-driven spanwise diversion, drawing from a shared reservoir, reflects directed, phase-opposed switching. The quasi-square wave improves the gross drag-reduction margin by 2.5 percentage points over the optimal sinusoidal baseline, solely via temporal Stokes-strain redistribution, and the waveform renders duty-cycle switching directly observable, thus elucidating the causal chain of drag reduction.

Owing to inertial effects, the flow through a three-dimensional curved duct focuses finite-sized spherical particles in the two-dimensional cross-section onto either stable equilibrium points or limit cycles. This hydrodynamic inertial focusing underpins various biomedical and industrial applications for size-based particle and cell sorting. Departing from conventional particle separation in the channel cross-section, we instead focus on particle separation in the primary flow direction, i.e., longitudinal separation. We consider a duct with an elliptical centreline and a tall rectangular cross-section. For a given particle size, the nature of the cross-sectional equilibrium points depends on the local radius of curvature of the duct, and a periodical variation of the radius of curvature can result in a periodical bifurcation behaviour along its length. In particular, a duct geometry that undergoes a periodically varying saddle-node infinite-period (SNIPER) bifurcation can be used to improve longitudinal, at the expense of cross-sectional, particle clustering. For sufficiently large particles, this longitudinal clustering weakens at higher Reynolds numbers and with decreasing eccentricity, in contrast to small particles whose longitudinal clustering remains unaffected across a wide range of geometric configurations and flow conditions. Then, ducts with smaller eccentricities enable simultaneous separation along both the flow direction and the cross-section. In contrast, for larger eccentricities, the emergence of a SNIPER bifurcation promotes more pronounced longitudinal separation while compromising cross-sectional separation. These preliminary findings suggest that elliptically wound microfluidic devices might be used for longitudinal separation of particles by size, with potential biomedical and industrial applications.

While vertically-sheared stratified flows have been studied extensively, their horizontally-sheared counterparts have received considerably less attention. Yet, horizontal shear instabilities remain active even when the mean Richardson number is large or even formally infinite, and can drive turbulence in strongly stratified (low Froude number) flows at sufficiently high Reynolds number. In this work, we combine linear theory with direct numerical simulations to investigate two pathways to turbulence in low Froude / high Reynolds number horizontally-sheared flow with no initial vertical shear. In the first pathway, vertical shear emerges directly from vertically-modulated eigenmodes of the primary horizontal shear instability, and becomes unstable to secondary small-scale Kelvin-Helmholtz (KH) instabilities on the buoyancy scale at sufficiently large buoyancy Reynolds number $Re_b$. In the second pathway, a vertically-invariant eigenmode of the primary horizontal shear instability initially dominates, causing the background flow to evolve nonlinearly into a long-lived time-dependent two-dimensional (columnar) vortical flow. The vortices are subsequently unstable to secondary three-dimensional hyperbolic instabilities from which vertical shear emerges, which is finally unstable to tertiary small-scale KH instabilities on the buoyancy scale at sufficiently large $Re_b$. This shows that the emergence of vertical shear driving small-scale KH instabilities is an inevitable by-product of horizontal shear instabilities in strongly stratified flows at sufficiently large $Re_b$. However, we also find that the two pathways excite different ranges of vertical scales, which results in different peak mixing efficiencies.

Wave turbulence describes the statistical dynamics of dispersive waves with weakly nonlinear interactions. While the classical kinetic equation captures the mean evolution of the wave spectrum, the study of its fluctuations due to finite-size effects and intermittency requires a probabilistic framework for space-time trajectories of the spectrum dynamics. Following the previous large deviation theories for wave turbulence, we develop a simplification meant for qualitative and numerical predictions of measurable quantities. We derive a new large deviation principle in the case of local wave interactions. It fully characterizes typical and rare fluctuations of the spectrum. In a joint article, we obtain a theory which is a generalised form of Macroscopic Fluctuation Theory, but with 2 conserved quantities (mass and energy). In this paper, we use it to analyse the structure of the equation for Gaussian fluctuations around out-of-equilibrium spectra. In addition to the usual equilibrium contribution, we obtain long-range correlations, which can be decomposed into 3 contributions: one is driven by the flux in the bulk and another is driven by the forcing and its possible fluctuations. In addition, these contributions are computed for the first time with a method adapted to boundary conditions where only the fluxes are fixed. The results provide a general, replicable method for analyzing wave turbulence in more complex settings. Finally, the generalization of this theory to the inhomogeneous wave turbulence provides a possible explanation to the instability of the Kolmogorov-Zakharov spectra in some 1D inhomogeneous models with 4-wave interactions such as the Majda-McLaughlin-Tabak. This work opens the discussion regarding universal and non universal properties in two-point correlation functions. This opens new range of study on the phenomena of intermittency which is partially developed here.

We study the unsteady dynamics of floating planar bodies undergoing lateral oscillations along an air-water interface. Scaling arguments indicate that at high Womersley number and small oscillation amplitude the flow beneath the body can be approximated by an oscillatory Stokes boundary layer, yielding a leading-order description of the hydrodynamic resistance. Using magnetic actuation, we drive the interfacial bodies harmonically and measure the amplitude response and phase lag in steady state over a range of frequencies, masses, sizes, and shapes. This frequency-response framework enables direct extraction of effective added mass and damping coefficients, which we find to be consistent with oscillatory boundary-layer theory in the limit of small interfacial deformation. The transient behavior during startup is also shown to be accurately predicted by a history integral that captures the development of the oscillatory boundary layer beneath the body. This work also establishes a simple experimental platform for quantifying unsteady hydrodynamic forces at fluid interfaces.

The posture of the vocal folds produced by laryngeal muscle activation plays a central role in determining the dynamics of voice production. Abnormal vocal fold configurations are frequently associated with inefficient phonation and a variety of voice disorders. Although diverse glottal closure patterns have been observed clinically, the biomechanical mechanisms governing their dynamic behavior and resulting phonatory characteristics remain incompletely understood. Moreover, existing numerical models that incorporate the effects of the intrinsic musculature on posturing and glottal conformation are computationally expensive, which limits their suitability for large-scale parametric investigations. In this work, we introduce a computationally inexpensive vocal fold (VF) model wherein the body and cover VF layers are treated as a composite beam and a coupled membrane, respectively. Intrinsic laryngeal muscle activation, in addition to positioning the arytenoid cartilages and cricothyroid joint, introduces moments at the boundaries of the structure that influence glottal conformation. The model produces phonatory characteristics that are qualitatively consistent with those reported in high-fidelity finite-element models and clinical studies, thereby supporting its predictive capability while offering substantial computational advantage. The proposed framework provides biomechanical insights into the influence of incomplete glottal closure on phonation dynamics and may serve as a computationally tractable tool for investigating mechanisms underlying certain voice disorders.

We develop theoretical foundations for a practical quantum-advantage mechanism in quantum-informed machine learning for chaotic dynamical systems. A family of k-indexed higher-order quantum statistical priors (Q-Priors) hosts the k-point marginal of the invariant measure on n_q = kq qubits, extending the single-site construction of prior work. We prove a two-stage advantage. In the representation stage, superposition and entanglement compactly store non-factorisable spatial correlations of the invariant measure on n_q qubits. In the extraction stage, joint Bell measurements on two copies estimate any post hoc Pauli functional with a copy-pair count independent of n_q, whereas any adaptive single-copy protocol for the corresponding full-Pauli read-out requires Omega(2^(n_q)) copies; this is a provable quantum-classical separation in copy-measurement complexity. The two-copy read-out is realised in simulation and on IQM superconducting processors. Two case studies instantiate the mechanism in workflows of independent scientific value: a turbulent channel-flow study in which the two-copy read-out yields a named non-diagonal correlator of the invariant measure (the velocity-direction coherence), and a medium-range weather forecasting workflow on the European Centre for Medium-Range Weather Forecasts ERA5 reanalysis in which the diagonal k <= 2 Q-Prior steers a Koopman rollout, improves anomaly-correlation skill by 10-39% across 48-240 h lead times, and reduces the long-horizon collapse of rollouts onto a static mean field. The two conditions of our practical-advantage definition are met at complementary levels, identifying a candidate route to practical quantum advantage before fault-tolerant hardware.

Quantum computation of fluid dynamics has attracted growing attention as a key application of fault-tolerant quantum computers anticipated in the coming decade, with lattice Boltzmann methods emerging as a particularly promising approach. Explicit and efficient elementary-gate-level circuit simulations, however, have so far been demonstrated only in the linear case. Here we include the leading nonlinearity through second-order Carleman linearization of the one-dimensional Boltzmann equation, and demonstrate, via explicit quantum-circuit simulation, the preparation of the final-time state using a Taylor-expansion-based ODE solver based on the quantum singular value transformation. With this construction, we analyze the gate and qubit complexities, which scale logarithmically with the grid size, the nonlinearity captured by the higher-order Carleman linearization, and the practical utility of higher-order expansions in the Taylor ODE solver. The construction provides a concrete baseline for computational cost reduction and further developments such as extensions to higher dimensions, complex geometries, and the extraction of physical quantities, towards industrially useful quantum CFD.

Imploding solutions to the radially symmetric, isentropic, compressible Euler equations have been well-studied, inspired by the work of Guderley. However, these smooth imploding solutions are shown to be numerically unstable and difficult to compute in practice. On the other hand, the imploding solution of Kidder has a closed form solution and is numerically computable. But, it is unbounded in the far field. We consider Kidder's formulation in one dimension in which the unbounded far field condition is replaced with a constant density cutoff of the initial data. Strikingly, a non-centered rarefaction emerges from the cutoff and suppresses the implosion. We present an exact analytic solution to the problem with the cutoff and support our theoretical predictions with numerical simulations.

The ensemble Kalman filter (EnKF) is widely adopted for sequential data assimilation, but fails for solutions with discontinuities, such as shocks in compressible flows. Uncertainty in shock location induces multimodal ensemble statistics that violate the Gaussian assumptions underlying the EnKF, producing large-scale spurious oscillations in the analysis state. We introduce a feature-preserving latent-EnKF that performs the ensemble update in a learned low-dimensional latent space, where shock and flow features admit a smooth manifold representation, thereby preserving sharp features during EnKF analysis. The updated latent state is mapped back to physical state through a shared decoder for all ensemble members. The algorithm eliminates the member-specific ordered training and positivity flooring used in prior approaches. Numerical experiments on a Sod shock tube and Mach 2 shock interaction with a 2D cylinder, using sparse and noisy observations, show accurate feature recovery of shocks and contact discontinuities without spurious oscillations.

Residual agreement in a kinetic or moment equation does not automatically identify every higher-order closure variable entering a nonequilibrium shock. We formulate this issue as an observability problem for the fourth-order closure content of monatomic normal shocks and follow it through a hierarchy of collision models and diagnostics. The kinematic part of the result is independent of the collision operator: the one-dimensional heat-flux budget observes the projected fourth-order channel $S=R^{\cl}_{xx}+\Delta/3$, not the tensorial R26-level moment $R^{\cl}_{xx}$ separately from the scalar fourth-order excess $\Delta$. The observation map therefore has a one-dimensional null space, so a heat-flux residual can be small while the split between tensorial anisotropy and isotropic tail intensity remains wrong. A DVM-consistent scalar-excess budget supplies the missing channel and gives the two-channel reconstruction $R^{\cl}_{xx}=S-\Delta/3$ without direct $R^{\cl}_{xx}$ data. Across BGK shocks at Mach 2--5, this reduces the active-zone $R^{\cl}_{xx}$ error from about $63$--$64\%$ to $2.4$--$4.1\%$. Sparse scalar-excess interpolation is used only as an information-reduction test: a representative 24-probe operating point gives $R^{\cl}_{xx}$ errors below $4.5\%$, and below $4.7\%$ with $1\%$ probe noise. Collision-model diagnostics then separate the invariant observation channel from the model-dependent source law. Shakhov changes the heat-flux relaxation to the correct Prandtl number but is neutral in the even $|\boldsymbol c|^4$ scalar-excess source; a direct discrete Shakhov channel check recovers $S$, $\Delta$ and $R^{\cl}_{xx}$ with errors $6.4\times10^{-4}$, $2.1\times10^{-7}$ and $1.0\times10^{-3}$, respectively.

The concept of multiple, long-delayed feedback systems is introduced and discussed with reference to a paradigmatic model. We analyse how the resulting chaotic dynamics is affected by the delay distribution. Via a mean-field approach, we show that a spatio-temporal representation equivalent to the one developed for the single-delay can be extended to this wider class of dynamical systems. Numerical simulations are complemented by a theoretical study based on a multiple-scale analysis, which, in the vicinity of a Hopf bifurcation, allows mapping the initial model onto a complex Ginzburg Landau equation. As a result, we find that the only relevant feature influenced by the multiple delays is the size of the coherent spatio-temporal structures which, in turn, depends exclusively on a generalized {\it variance} of the delay distribution.

We study operator growth in quantized non-KAM systems using out-of-time-ordered correlators (OTOCs), focusing on the kicked harmonic oscillator as a representative example. Since the classical harmonic oscillator is degenerate, the dynamics fall outside the usual Kolmogorov-Arnold-Moser (KAM) framework, and resonances play a central role in shaping the phase space. We examine the system near resonances, where the ratio between the oscillator and driving frequencies takes integer values. Even though the classical Lyapunov exponent remains small at these points, and hence no conventional chaos, the phase space still undergoes strong structural changes. The OTOCs are particularly sensitive to these resonances, with a quadratic-in-time growth at resonance compared to linear growth away from it. Within a perturbative treatment, we derive closed-form expressions for the OTOCs and uncover a number-theoretic structure emerging in the behavior of OTOCs, governed by the Euler totient function of the frequency ratio. Overall, the results we present in this short note imply that resonant structures can play an important role in controlling information spreading.

In the infinite dilution limit, we show that the solvent-mediated potential of mean force (PMF) between solutes, extracted from the hypernetted-chain (HNC) closure of the Ornstein-Zernike equations, can expressed as a convolution between solute-specific generalised excluded volume functions. In the limit of a structureless solvent of point particles and hard core solutes, this recovers the exact Asakura-Oosawa depletion potential as the overlap between excluded volume spheres. The methodology can be deployed for ultrasoft particle systems such as those encountered in dissipative particle dynamics (DPD), where the solvent-mediated PMF can be recovered with considerable accuracy. These results confirm that in coarse-grained molecular DPD simulations the parametrisation of the non-bonded repulsions is sensitive to the assumed intramolecular bond lengths if they are smaller than the range of the DPD potential, due to the overlap of the soft excluded volume functions.

Origami-inspired metamaterials exploit the interplay between geometry and elasticity to achieve programmable mechanical responses. Yet the origin and tunability of snap-through instabilities in non-rigidly foldable patterns remain poorly understood. Here we show that the Mars tessellation, a degree-4 vertex origami pattern composed of alternating square and rhombic faces, is not rigidly foldable because the folding-speed ratios required for vertex compatibility cannot be propagated consistently across neighboring units. This geometric incompatibility forces the facets to bend during folding, giving rise to a reproducible snap-through discontinuity in the force-displacement curve with a mean force drop of about 92.6 +/- 5.5 %, marking a transition between metastable states. Laser scoring of additional diagonal creases, guided by strain-field simulations, enables continuous tuning of the snap magnitude. These results reveal a general mechanism by which geometric frustration can be harnessed to program multistability in thin-sheet metamaterials.

Particulate contaminants decrease the power output of solar panels, the transparency of windows, and are detrimental to microelectronics, where even a single particle can induce a short circuit. Despite significant research on particle adhesion and self-cleaning, it remains unclear when and how a drop can remove a particle from a surface, thus efficiently cleaning the surface. Here, by combining lattice Boltzmann simulations and confocal microscopy experiments, we show that at least six different scenarios arise from the complex interplay between capillary and friction forces when a drop collides with a particle. Notably, the capillary force plays a dual role in particle removal: while its tangential component always drives removal, its normal component can also hinder it. By introducing a dimensionless capillary capture parameter, we can predict particle removal across a wide range of particle and surface properties. These results provide quantitative design principles for easy-to-clean surfaces that minimize water and chemical usage.

The physics of active matter, wherein constituent particles consume energy to generate autonomous motion, has revolutionized non-equilibrium statistical mechanics. While a large body of work has successfully elucidated the behavior of dilute active systems, the dense regime -- characterized by ``active glasses and active solids'' -- presents profound challenges that defy conventional theoretical frameworks. Recent observations reveal two striking features in these dense systems: an apparent enhancement of Mermin-Wagner-Hohenberg (MWH) fluctuations leading to anomalous long-wavelength density fluctuations, and a remarkable correspondence between activity-induced annealing and annealing via oscillatory shear. In this perspective article, we propose a novel approach toward a deeper understanding of dense active matter: by developing active Hamiltonian models as equilibrium reference frameworks, we map out pathways toward non-equilibrium active systems. This strategy allows us to elucidate both the correspondence between driven and active systems and the enhanced MWH fluctuations, which likely arise from a strong coupling between spatially random active forces and long-wavelength density (phonon) modes. We outline a comprehensive roadmap employing complementary approaches, including the active Hamiltonian formalism, comparative studies of oscillatory shear in active and passive solids, and investigations of chiral active matter. Establishing this activity-oscillatory shear correspondence across diverse systems is essential to demonstrate its universality, reveal the underlying large-scale emergent physics, and place our hypothesis on a firmer theoretical ground.

The dynamics of nanoparticles within nanoscale liquid environments exhibit a range of complex phenomena driven by the interplay of processes at varying length scales. While these dynamics have profound technical implications, such as in nanoscale catalytic kinetics, ion-transport pathways in energy storage, and macromolecular crowding in biological systems, real-space imaging of dense, confined nanoparticle assemblies remains a significant challenge. Here, we present a liquid-phase transmission electron microscopy approach in which dense clouds of gold nanoparticles are formed within microfluidic channels, rendering the particle ensemble visible in bright-field electron imaging. This strategy enables direct imaging of different density-dependent particle ordering phenomena, including a local structuring of the colloidal liquid in nanoscale spaces, disordered dynamic clouds at high nanoparticle densities and the reversible formation of superlattice structures. Our results provide a unique window into the complex processes of colloidal self-organization at the nanoscale.

Cells dynamically generate, transmit, and dissipate stress. Central to these processes is the actomyosin cortex, an active contractile material that drives cellular mechanical behavior. While prior studies have focused on freely contracting actomyosin systems, the role of mechanical constraints such as adhesion to boundaries remains less explored. To address this, we employ reconstituted actomyosin gels to investigate cellular contractility. We study contraction dynamics under pinned boundary conditions, where the gel is adhered transversely to two opposing surfaces, mimicking supracellular actomyosin networks in tissues and embryos. We find that pinned contraction leads to stress buildup, delaying contraction, producing intermittent dynamics, and generating spatially nonuniform strain fields. Stress is relieved through several pathways, including active-stress-driven symmetric constriction and defect-driven processes such as boundary detachment and internal rupture. We develop a hydrodynamic model incorporating elastic, viscous, and active stress contributions that distinguishes between stress-accumulation and stress-release phases and links variations in active stress to the observed intermittent dynamics. The model predicts distinct energy relaxation rates before and after detachment events, providing insight into stress dissipation. We compare experiments with numerical simulations, which reproduce the observed behavior and reveal how internal energy is generated and dissipated during stress buildup and relaxation. Together, our results demonstrate how boundary conditions and spatial heterogeneity govern the mechanical behavior of contractile active gels. These findings provide insight into stress regulation in cellular and tissue-scale systems and may inform the design of adaptive soft materials and bioinspired robotic systems.

The temperature increase in the contact regions between solids in sliding contact can easily reach several hundred Kelvin and thereby dramatically affect friction and wear. Here I extend an earlier multiscale theory for the flash temperature (Ref. \cite{MP}) to the case of accelerated motion, and present numerical results illustrating the theory.

Meta-structures that display axial-twist coupling can be achieved through the emerging kinematics in Kresling origami patterns. A central challenge in these structures is understanding their nonlinear mechanical behaviour, specifically their equilibrium branches and bifurcation diagrams. This involves identifying relationships between desired responses and the geometric variables that define the design space, including the Kresling polygon count, initial twist angle, height, radius, and crease lengths. As the number of constituent units increases in an n-layer chain, we track complex equilibrium branches extending into the post-critical regime under successive instabilities, including branch-point bifurcations and limit-point instabilities. This work begins by establishing the relationship between the geometric design variables and the response curves of the assembled chain by modelling the crease lines as axial-load-carrying elements. Subsequently, equilibrium branches and instabilities are systematically investigated via continuation and bifurcation analysis, beginning with the single-layer system and progressively extending to two- and three-layer configurations. Finally, a generalisation strategy is proposed to extend these findings to an n-layer Kresling chain. This strategy enables the predictive construction of equilibrium paths and the inverse design of multi-layer meta-structures, using prescribed critical points to control post-critical behaviour. It provides a foundation for the inverse design and optimisation of architected mechanical metamaterials with programmable responses.

Nonreciprocal interactions in active solids violate action-reaction symmetry and produce a net response to strain. Assuming invariance under Euclidean symmetries, we derive a shape-space formulation for the elastohydrodynamics of nonreciprocal slender bodies that separates intrinsic deformation from rigid motion. The resulting nonlinear reaction-advection-diffusion system represents a geometric flow whose activity-driven instabilities generate steady, oscillatory, and chaotic patterns. These manifest as rigid, swimming, and chaotic motion, linking nonreciprocal elastohydrodynamics to geometric pattern formation and unifying recent observations in slender active structures.

Soft glassy materials display rich and complex flow behaviors across both macroscopic and molecular scales, and a fundamental understanding of these phenomena remains an outstanding challenge. Here, we propose a theoretical model for the flow of supercooled liquids -- a typical class of glassy fluids -- based on a two-state paradigm that conceptualizes the flow as a dynamic coexistence of transient solid-like and liquid-like regions. The model rests on two essential physical ingredients: a correlation length that captures medium-range structural order, and a localized elasticity-mediated interaction that restricts stress propagation within solid-like regions. Remarkably, with all parameters determined solely from equilibrium state, the model quantitatively reproduces rheological responses -- including both steady-state and start-up shear -- for a broad range of shear rates. Furthermore, it simultaneously captures the evolution of molecular dynamic heterogeneity. This dual success -- spanning macroscopic rheology and microscopic spatiotemporal fluctuations -- underscores the pivotal role of structural and dynamic heterogeneities in governing the rheological response. Moreover, it provides a direct understanding of how the flow behaviors of a supercooled liquid are embedded in its equilibrium properties.

We study the roughening of an interface with nonlinear elasticity driven by temporally correlated noise, which breaks statistical tilt symmetry. Using scaling arguments and a self-consistent Hartree approximation, we derive the crossover diagram and the steady-state structure factor. We identify three scaling regimes associated with the Larkin, anharmonic Larkin, and Edwards--Wilkinson universality classes, and obtain the crossover lengths separating them. Numerical simulations of large systems confirm the analytical predictions over the full parameter range. Our results provide a unified description of finite-size and crossover effects in a minimal nonlinear-elastic Ornstein--Uhlenbeck active interface.

Earthquakes propagating faster than the shear wave-speed are commonly thought to undergo a super-shear transition upon which they discontinuously jump from the sub-Rayleigh regime to the super-shear one. The super-Rayleigh regime, i.e., the range of propagation speeds between the Rayleigh and shear wave-speeds, is regarded as "forbidden" by the two-dimensional classical rupture theory. Here, we revisit the assumptions underlying the classical theory and develop a rupture theory that takes into account the dependence of the fault strength (frictional resistance) on the slip rate. The theory quantitatively agrees with numerical simulations nearly up to the Rayleigh wave-speed. Yet, very close to the latter, two-dimensional rupture solutions change their character due to frictional rate nonlinearity and rupture continuously propagates through the "forbidden" super-Rayleigh range into the super-shear regime, without a sharp super-shear transition. These results demonstrate that frictional rate dependence, generically observed in experiments, can have profound implications for fast earthquake propagation.

Laser-induced forward transfer (LIFT) is a nozzle-free laser-assisted printing method that provides an advanced manufacturing route for spatially selective deposition of functional inks, nanoparticle suspensions, polymers, hydrogels, biological materials, and other difficult-to-nozzle formulations. The apparent simplicity of LIFT, however, conceals a strongly coupled laser-liquid interaction. Laser energy is absorbed within a confined donor architecture, converted into thermal and plasma responses, and then transformed into bubble-mediated motion of the donor material. The cavitation bubble provides the transient mechanical bridge between optical energy deposition and the hydrodynamic ejection process. This chapter presents LIFT from a multiscale perspective centered on bubble dynamics and material ejection. It first reviews major LIFT donor architectures. Then, it examines how donor ribbon design, absorbing-layer properties, laser parameters, material rheology, control bubble inception/growth, jet formation, droplet breakup, and final deposition. Modeling approaches are discussed as tools for connecting experimental observations across time and length scales, ranging from reduced-order estimates to interface-resolving simulations and data-driven process maps. As one illustrative mechanistic example, thermal-only, plasma-mediated, and coupled plasma-thermal-thermoelastic frameworks for early-stage bubble inception are briefly compared to show how different inception assumptions can provide initial conditions for downstream bubble growth and jetting models. This chapter concludes by identifying opportunities for bubble-aware donor design, time-resolved diagnostics, benchmark datasets, and predictive LIFT process maps based on intermediate bubble and jet observables.

This study investigated how additively manufactured nozzles with body-centered cubic lattice structures reduce the flame flashback propensity in a hydrogen jet flame burner. Five different configurations of a jet flame combustor were investigated, with a focus on mixing duct walls incorporating porous media. The nozzles were manufactured by the powder bed fusion of metals using a laser beam process. The lattice parameters were varied by the volume fraction and the strut diameter. For the experiments, pure hydrogen was used as fuel under atmospheric conditions at various equivalence ratios and Reynolds numbers of 9,000 - 12,000. Flow field measurements, flame imaging, and spectral proper orthogonal decomposition of the flame dynamics were employed to identify possible transition mechanisms from a stable operation to flashback. The flow fields and the flame shapes showed only minor effects from wall modifications, preserving general flow characteristics across configurations. The flow dynamics in the combustion chamber were dominated by large-scale coherent structures in the shear layer, specifically Kelvin-Helmholtz instabilities. The results demonstrated that the nozzle with the coarsest porous wall structure significantly improved the flashback resistance compared to a nozzle with a solid wall. It is concluded that the primary mitigation mechanism was a cooling effect by unburnt mixture flowing through the porous media. The findings confirmed that the integration of lattice structures through additive manufacturing provides a viable strategy for hydrogen flashback mitigation by manipulating the coupled interaction between the flame and the thermal conditions of the wall.

Accurate modeling of tsunamis (such as those generated by landslides) requires capturing both wave dispersion in the deep ocean and wave breaking near the shore. The shallow water equations are often preferred for working with tsunamis, but neglect dispersion and may be inaccurate in scenarios where dispersive effects are significant. In this work, we develop an approach that seeks to incorporate the best aspects of both hyperbolic and dispersive models by combining either of two hyperbolic reformulations of the Serre-Green-Naghdi equations away from the shore with the non-dispersive shallow water equations near the shore. The model is discretized and implemented within the GeoClaw software, and incorporates adaptive mesh refinement as well as shared-memory parallelism. We validate it through comparison with benchmarks and real tsunami data. The results and performance compare favorably with the existing dispersive water wave solvers, including a speedup of about 2x relative to GeoClaw's existing dispersive solver for a large-scale tsunami simulation.

Thin films draining on top of curved surfaces occur in coating, manufacturing, and geophysical flows, where predicting accumulation and thinning is crucial. Unlike singularities associated with contact lines, boundaries, defects, a smooth saddle alone can produce a locally singular drainage thickness distribution. The singularity stems from competing converging and diverging flow and is regularized within a dynamically selected region where drainage, hydrostatic pressure, and capillarity balance. Saddles thus emerge as generic building blocks for thin-film drainage on complex topographies.

We propose a minimal, rotation-free model of magnetohydrodynamic (MHD) dynamo action driven by laminar thermal convection in a regular tetrahedral cavity. Unlike canonical planetary-dynamo settings, where flow helicity is supplied by global rotation, the present system generates robust flow helicity purely through the geometric constraints imposed by tetrahedral boundaries. Direct numerical simulations show exponential amplification of a weak seed magnetic field and a nonlinear saturated state in which the magnetic energy exceeds the kinetic energy. The convective flow organizes into a highly symmetric pattern with \(D_4\) dihedral symmetry. The dynamo-generated magnetic field obeys a corresponding signed \(D_4\) symmetry involving antisymmetry under \(\pi\)-rotations about the two horizontal axes of the tetrahedron. The tetrahedral dynamo provides a conceptually transparent setting for isolating geometry-induced helicity, magnetic-field amplification, and a closed induction cycle in a non-rotating laminar flow.

Mangroves are increasingly promoted as nature-based solutions for coastal protection, yet many existing models neglect the vertical variation of vegetation biomass, leading to oversimplified representations of root-flow interactions. In this study, we introduce a generalised parametrisation of the mangrove vegetation profile that is applicable across multiple mangrove species and derive a wave attenuation model that explicitly accounts for the mangrove root characteristics. Based on this parametrisation, we propose a simplified mangrove representation that reproduces a prescribed drag force profile and is suitable for both computational fluid dynamics simulations and experimental fabrication. The hydrodynamic performance of the proposed model is evaluated using OpenFOAM simulations. Our results show that the wave attenuation effectiveness of mangroves is frequency-selective and species dependent. This nonlinear behaviour contrasts with classical vegetation models and reveals a previously unrecognized mechanism by which mangrove root characteristics govern coastal protection.

The translation dynamics of two binary mixture droplets is investigated theoretically and is corroborated with experiments. The proposed model accounts for the effects of Marangoni stresses generated by evaporative cooling and concentration gradients, as well as vapour diffusion, for both components of the binary mixture. We consider thin droplets, allowing us to use the lubrication theory to derive the evolution equation for the droplet profiles. We numerically solve the evolution equations using the finite element method and examine various cases of pure and binary droplet pairs exhibiting translational behaviours like attraction, repulsion, and 'chasing'. The results show that the combined effect of solutal Marangoni, capillary effect, and thermal Marangoni determines the movement of the droplets. The non-uniform evaporation generated from 'vapour shielding' creates such effects. We observe that for droplets with the same initial composition, solutal Marangoni and capillary forces induce droplet attraction, while thermal Marangoni effects drive their repulsion. For droplets with different initial compositions, the drop with a higher concentration of the more volatile component pushes, or `chases', the drop with a lower initial concentration of this component, completely driven by the solutal Marangoni. We carried out experiments involving water-morpholine binary mixture droplets to validate the results predicted by our model.

The current study presents a three-dimensional linear stability analysis of particle-laden Couette-Poiseuille flow suspended in a Newtonian fluid between two parallel plates, with the lower plate coated by a porous medium. The influence of suspended particles is examined using a two-domain formulation in which particles are confined to the fluid layer and do not penetrate the porous substrate. The particle-laden suspension is modeled using the dusty-gas framework, while the flow within the porous layer is described by the volume-averaged Navier-Stokes (VANS) equations. In particle-laden flows over impermeable walls, particle inertia may either stabilize or destabilize the flow depending on the governing parameters. In contrast, the presence of a porous layer introduces an additional permeability-dependent destabilizing mechanism that fundamentally modifies these classical trends. Consequently, particle loading can reduce the critical Reynolds number at sufficiently high permeability, even in parameter regimes where particles stabilize the corresponding rigid-wall flow. The coupled formulation also introduces additional disturbance branches associated with fluid-particle coupling near the permeable interface. Although these modes remain stable across the parameter space investigated, they modify the eigenspectrum and influence the dominant instability by altering coupling pathways. Furthermore, unlike impermeable-wall Couette-Poiseuille flow, where increasing the Couette component generally stabilizes the flow, the porous-wall configuration exhibits a monotonic decrease in the critical Reynolds number over the range examined. These results demonstrate that porous boundaries can fundamentally alter established stability behavior in particle-laden shear flows through permeability-dependent coupling between the suspension and the porous substrate.

Droplet and particle grouping can be influenced by applying an acoustic field and have practical applications such as particle scavenging and aerosol filters of engine exhaust and air purifiers. The present work experimentally investigates the influence of a standing acoustic wave on a single stream of droplets. The experimental setup consists of an acoustic transducer and a reflector plate through which the droplet stream passes in the presence or absence of an external pressure field generated by a standing acoustic wave. A droplet stream is generated with the help of a nozzle connected to a pressurized working fluid supply and piezoelectric transducer to control the spacing between droplets. The effect of the acoustic pressure field on the droplet stream generated by the nozzle operated at different piezoelectric excitation frequencies and fluid pressures is investigated. Droplet stream characteristics at every nozzle excitation frequency are observed with a high-speed camera when the acoustic field is switched OFF and ON. The competing effect of nozzle excitation frequency and acoustic field is observed. At lower nozzle frequencies, the nozzle generates an unstable stream of droplets having different sizes and spacings between them. When the acoustic field is applied at these lower frequencies, the stream of droplets becomes organized, and in some cases, it becomes equispaced and of the same size. However, an opposite behavior is observed at higher frequencies. In these cases, as the acoustic field is applied, an equispaced mono-disperse droplet stream becomes unstable due to the coalescence of droplets within the stream.

Diffuse-interface models are a widely used framework for interfacial dynamics in complex fluids, in which interfaces are represented through smooth transition layers and capillary effects are encoded by a free-energy functional. For incompressible mixtures with more than two phases, however, robust computation is substantially more difficult because the numerical method should preserve the balance structure of the continuum model, maintain the saturation constraint, dissipate energy, and treat all phases symmetrically even when density ratios are arbitrary. Existing structure-preserving methods are largely developed for binary flows or for formulations that distinguish a reference phase, so a genuinely symmetric N-phase discretization remains lacking. The practical problem is therefore to construct a fully-discrete method for N-phase incompressible Navier--Stokes--Cahn--Hilliard mixture models that retains the key thermodynamic and conservation properties of the continuum equations for arbitrary density ratios. Here we propose a symmetric fully-discrete method for the N-phase incompressible Navier--Stokes--Cahn--Hilliard mixture model with arbitrary density ratios. The method yields a fully-discrete problem in which every solution satisfies exact phase volume conservation, phase mass conservation, total volume conservation, total mass conservation, and a discrete energy-dissipation law. In addition, if the volume-saturation constraint holds for the initial data, then it is preserved at every time step. We numerically verify these structure-preserving properties and demonstrate the robustness of the method in representative multiphase flow problems. The resulting scheme provides a computational framework for incompressible N-phase mixture flows with complex interfacial dynamics and arbitrary density contrasts.

Latent diffusion and flow matching have emerged as leading approaches for synthetic turbulence generation, yet they systematically under-represent dissipation-range amplitudes. We introduce a latent flow matching framework with a spectrally regularized compression stage that directly targets this failure mode. On a 256^2 DNS dataset at Re_f \approx 2250, replacing an MSE-trained VAE with a zone-weighted log-spectral objective raises deep-dissipation retained spectral power from 25% to 94% in reconstruction and from 20% to 79% in unconditional generation. The improved latent representation also yields a substantially better sampling cost-fidelity tradeoff: the MSE-trained latent space imposes a fundamental quality ceiling near DD bias -0.70 that no integrator or step-count can overcome, while the spectrally regularized latent space reaches DD bias -0.117 at just 20 function evaluations. Mechanistically, encoder-decoder swap experiments show that the improvement is driven primarily by encoder-induced latent reorganization rather than decoder capacity, while a support-amplitude decomposition reveals that MSE-trained models behave as conservative suppression models, minimizing pointwise error by attenuating intermittent high-wavenumber structure. Both pipelines recover the second-order structure function and the correct sign of S_3, indicating the correct cascade direction without explicit supervision. A small residual gap in the magnitude of S_3 suggests that phase-coherent triadic organization remains a complementary axis to amplitude fidelity for future generative turbulence models.

Rendezvous is a critical task for multi-agent systems, requiring agents to coordinate to meet at an unspecified location. However, achieving this in fluid environments presents a challenge, as it remains unclear how agents can exploit underlying fluid kinematics to facilitate convergence. In this study, we adopt a multi-agent reinforcement learning (MARL) approach to develop physics-informed rendezvous strategies in vortical flows. Compared to a naive strategy, where agents navigate toward their counterparts, MARL strategies significantly improve the rendezvous rate. MARL strategies also show transferability across varying vortex intensities, vortex scales, and swarm sizes. By breaking the symmetry of the state-action map, MARL strategy leverages a non-intuitive mechanism that prevents agents from becoming trapped in separate vortices, thereby enhancing rendezvous success. Additionally, a heuristic strategy is extracted from the learned strategy and also outperforms the naive strategy. Furthermore, a theoretical analysis demonstrates that fluid deformation impedes the rendezvous process. Large finite-time Lyapunov exponents identify where fluid effects separate adjacent agents, suggesting that targets should be planned in weak-deformation regions. Our findings reveal the important role that agent-fluid interactions play in multi-agent tasks and highlight the MARL capability to explore swarm intelligence in complex flow environments.

We tackle two key difficulties in the simulation of the viscous hydrodynamics of a large dense collection of rigid particles: (i) the poor convergence rate of an iterative solution of the discretized linear system as particle gaps shrink, and (ii) the large number of unknowns needed to accurately discretize the resulting lubrication-driven flows. Our focus is the 2D Stokes resistance and mobility boundary value problems for nearly-touching disks. To address both challenges, we introduce a general two-body preconditioning strategy, and implement it with the method of fundamental solutions. For each close particle pair, the hard-to-resolve interaction is represented in a basis precomputed by solving a local boundary value problem on a fine grid. In an iterative solve, the resulting flow field corrects that obtained from a coarse representation of all particles. The local fine-grid correction can even be compressed so that all particles except the pair itself are affected by an equivalent set of coarse sources. Numerical experiments demonstrate rapid GMRES convergence in challenging multi-particle settings, with iteration counts remaining low even in densely packed suspensions. For example, the mobility problem is solved for a random close packing with area fraction $\phi = 0.65$, $P = 10000$ monodisperse disks, and minimum separation $10^{-3}$, in just 47 GMRES iterations, achieving five digits of accuracy with 72 vector unknowns per body.

How can a growing biological filament remain straight despite stochastic fluctuations in growth? Motivated by filamentary structures that develop reproducibly across biological systems, we study the stability of a noisy, growing elastic filament regulated by feedback. We formulate a minimal model in which growth responds to the filament's strain, curvature, and orientation through local or nonlocal spatiotemporal feedback laws. Linear stability analysis identifies the conditions under which these feedback mechanisms stabilize a straight configuration. In the presence of noise, we show that purely local feedback requires orientation sensing to suppress long-wavelength instabilities, whereas nonlocal feedback allows stabilization through proprioceptive (curvature) sensing alone. Coupling to an elastic substrate further suppresses large-scale fluctuations. Our results establish minimal control strategies that ensure robust straight growth and suggest experimental signatures for identifying the feedback mechanisms underlying morphogenesis.

Proteins and nucleic acids form non-Newtonian liquids with complex rheological properties that contribute to their function in vivo. Here we investigate the rheology of the transcription factor NANOG, a key protein to maintain embryonic stem cell pluripotency. We find that at high concentrations, NANOG forms macroscopic aging gels that are dependent on its intrinsically disordered domain. By combining molecular dynamics simulations, mass photometry and Cryo-EM, we also discover that -- in contrast with unbounded condensates formed by other intrinsically disordered proteins -- NANOG forms self-limiting micelles with exposed DNA-binding domains. We show that these micelles can stabilize DNA entanglements and in turn modulate DNA dynamics. Based on our findings, we conjecture that NANOG may contribute to regulate gene expression by creating local gel-like environments that restrict genome dynamics and that its aging may ingrain mechanical memory in gene regulatory networks.

Evaporating sessile droplets are usually treated as capillary objects, but droplets generated by routine handling can carry tens to hundreds of picocoulombs of electric charge. Here we combine Faraday-cup charge measurements with optical imaging to determine how such charge evolves as water droplets evaporate on dry polymer substrates. A zero-time protocol shows that a reproducible initial charge is preserved on poly(methylpentene) (PMP), whereas PDMS, SOCAL-coated surfaces, and polystyrene either exchange, dissipate, or inject charge on contact. On PMP, ensemble-resolved measurements reveal two regimes: the charge remains nearly constant during early evaporation and then decreases abruptly once the droplet reaches a small-volume state. This charge collapse coincides with spontaneous lateral translation rather than jetting or breakup. A Rayleigh-normalized analysis, including a spherical-cap stress correction and measured contact-angle retention scale, shows that motion occurs only after evaporation drives the droplet into a high electro-pinning state. High-speed imaging and kinematic analysis support a picture in which the subsequent motion is governed by repeated contact-line depinning and re-pinning: the total distance traveled is strongly affected by dry-surface pinning, whereas the peak translational velocity serves as a more robust indicator of the discharge strength. These results identify a dry-substrate mode of evaporation-driven electrostatic relaxation, distinct from Coulomb fission on lubricated surfaces, in which substrate electrostatic passivity enables charge retention, droplet geometry selects the instability onset, and whole-droplet translation provides the charge-release pathway.

Across biological scales, from sperm cells to whales, locomotion commonly relies on undulatory gaits, in which traveling deformation waves interact with the surrounding fluid to generate thrust opposite to the direction of wave propagation. In viscous environments, microorganism locomotion is classically understood in terms of undulatory bending of slender filaments such as flagella, with optimal propulsion achieved when the deformation wavelength is comparable to the swimmer length. Inspired by diatom colonies, we identify a fundamentally different swimming mechanism based on sliding between neighboring elements within a chain. We show that sliding between stacked elongated cells generates internal shear that drives propulsion opposite to classical undulatory swimming, while achieving higher speeds and greater energetic efficiency. Remarkably, optimal performance occurs at wavelengths much larger than the chain length and at cell aspect ratios consistent with those observed in natural diatom colonies, suggesting that hydrodynamic efficiency may constitute an evolutionary selective pressure in diatom chains. Together, these results identify sliding as a previously overlooked mode of locomotion in multicellular assemblies and suggest new design principles for efficient bio-inspired microswimmers and swarm robotic systems.

We elucidate the stress in a system of active Brownian particles augmented with translational and rotational inertia (ABP+TRI). Stress tensors are derived for periodic systems as well as systems confined between walls by employing Lagrange's equations of motion of the first kind for the rotational motion. Using Langevin simulations of an ideal active gas in two dimensions, we confirm the existence of an equation of state for periodic systems that depends on translational and rotational inertia in general. Confinement implies a strong polarization of the propulsion direction near a wall and an enhanced density, both of which increase with increasing rotational inertia. This affects the local stress tensor normal to the confining walls, leading to a breakdown of the equation of state. Yet the local stress in the bulk part of the confined systems is identical with that of the periodic system. Importantly, for both kinds of boundary conditions, the so-called swim stress is not included in the local stress tensor; thus, in general, the swim stress is not representative of the stress in systems of ABP+TRIs.

We introduce a Langevin formulation of Vicsek-like active particles in which orientations evolve through finite-rate relaxation toward the local mean direction, with alignment strength $J$ and rotational diffusivity $D_r$, thereby combining Vicsek-type local consensus with XY-like orientational dynamics. Using large-scale numerical simulations, we determine the nonequilibrium phase diagram as a function of activity and alignment rate. Increasing the alignment rate drives a sequence of transitions from a homogeneous isotropic state to polar bands, a cross-sea phase of intersecting bands, a homogeneous polar state, and ultimately a micro-clustered regime. The isotropic-to-polar transition is strongly first order, as evidenced by Binder cumulants and bimodal distributions of local polarization and density, indicating coexistence of gas-like and liquid-like regions. Near the onset of collective motion, band size increases with activity but depends non-monotonically on alignment rate. Further increasing the alignment rate drives the system through the cross-sea and homogeneous polar phases before enhanced density fluctuations lead to micro-clustering. Our results demonstrate that finite-time orientational relaxation acts as a control parameter that qualitatively restructures collective behavior in polar active matter.

Active microcarriers capable of transporting multiple functional components and navigating complex environments are highly desirable for biomedical applications, yet their fabrication typically requires complex multistep processes. Here we show that evaporation-induced liquid-liquid phase separation in all aqueous polymer and protein mixtures provides a simple one-step route to multifunctional micromotors. During droplet evaporation, micron-sized condensates spontaneously form and encapsulate enzymes, nanoparticles, and drugs. Evaporation-induced Marangoni flows and interfacial adsorption generate asymmetric internal self-organization of nanoparticles, producing Janus-like architectures and spontaneously emergent shape anisotropy without the need for patterned fabrication. Dual functionality with internal magnetic anisotropy allowed catalytic propulsion steered by magnetic torque, enabling directional motion even in homogeneous environments. Thus, we present a versatile platform for the one-step construction of biocompatible, multifunctional micromotors with internally asymmetric architectures.

Classical nucleation theory describes the rate at which stable nuclei form within a metastable parent phase by crossing a free-energy barrier set by competing bulk and interfacial energies. In an elastic material, a pre-existing stress state modifies this barrier through an elastic contribution to the bulk driving force. This contribution is well characterized for linear elastic materials, but the corresponding finite-deformation result for soft solids remains less developed. The gap is computationally significant: in simulations that sample candidate nuclei throughout a stressed body, direct evaluation of the elastic contribution to free-energy change would require solving a new nonlinear elasticity boundary-value problem for each possible nucleus. Here, we derive an asymptotic expansion of the equilibrium elastic potential energy change for a hyperelastic body before and after formation of a small transformed region. The expansion is with respect to the amplitude of an isotropic transformation strain, while the pre-existing deformation and stress may be finite. At leading order, the elastic contribution to the formation energy is determined entirely by the known untransformed equilibrium fields, with additional terms accounting for stiffness contrast between the parent and transformed phases. Incorporating this into classical nucleation theory yields the stress-shifted transformation temperature, critical radius, and nucleation barrier. Representative results are shown for a compressible neo-Hookean solid under hydrostatic, uniaxial, and equibiaxial loading; tensile stresses promote nucleation and compressive stresses suppress it when transformation strain is expansive. Comparison with the corresponding linear-elastic result shows that finite-deformation effects can substantially change the predicted energy barrier at moderate stretches.

Confined active systems can sustain persistent vortical flows whose stability is strongly influenced by boundary conditions. At the individual level, active units generate internal stresses that drive spontaneous flows, which in turn advect and reorient the particles. This nonlinear coupling between active flow and orientational order is significantly mediated by the system's boundaries, where the specific slip condition governs how these internal stresses generate active flow then rearrange the local orientations. However, a quantitative understanding of how boundary slip dictates their dynamical stability remains lacking. Here, we study how the slip boundary condition controls the stability of a steady vortex state in a circularly confined active nematic system. Using a continuum model in a flow-dominated regime, we perform a linear stability analysis and derive an explicit criterion incorporating the slip velocity and flow-alignment coupling. We find that increasing slip velocity suppresses localized linear instabilities, thereby promoting the persistence of the steady vortex state. This reveals a relaxing the boundary friction actually stabilizes the macroscopic coherent structure by depressing flow induced reorientation that typically destroys single-vortex states. Our findings establish boundary slip as a nontrivial hydrodynamic control parameter for engineering stable active flows.

Active particles from bacteria to synthetic microswimmers often navigate viscoelastic media with complex relaxation dynamics. The classical active Brownian model that assumes instantaneous friction is clearly not applicable to describe such motility, while the non-Markovian processes combined with viscoelasticity are relatively unexplored. Here, we develop an analytical theory for an active particle in a power-law viscoelastic medium by solving coupled non-Markovian generalized Langevin equations for translational and rotational degrees of freedom. The viscoelastic memory results in novel phenomena such as fractional short-time transport, enhanced long-time persistence, and de-correlation of the instantaneous force and the swimmer orientation. We demonstrate that the memory kernel controls the anomalous scaling exponents, while the activity determines the crossover between sub-diffusive, ballistic and diffusive regimes. Our work provides a framework for theoretical description of biological and synthetic micro swimmers in complex biological and polymeric environments.

The physics of polymer chains is often probed using molecular stretching experiments and various idealized single-chain models. The majority of these models consist of a discrete sequence of links, which may be treated as rigid or extensible. Although such models are well established and many specific extensible variants have been proposed, no generally applicable theory has been presented. Moreover, most existing treatments are heuristic rather than systematically and rigorously derived. This critical gap is closed here through the development of a generally applicable asymptotic theory for including link extensibility in a broad class of discrete models for single-chain thermodynamics. The theory is verified analytically using the freely jointed chain and validated numerically using the freely rotating chain. The resulting approximation is first-order accurate in inverse link stiffness, with quadratically decreasing error, and recovers extensible behavior across all link stiffnesses from a single rigid-link reference calculation.

Force-induced dissociation of short double-stranded DNA (dsDNA) is central to single-molecule biophysics and DNA nanotechnology, yet a physically grounded kinetic description of shear-induced rupture for finite-length constructs remains lacking. Here we develop a master equation framework built on a force-dependent nucleation-zipper pathway with single-base transitions, enabling direct calculation of dissociation rates and transition state distances over a broad force range. Applied to a DNA-gold nanoparticle-DNA construct under constant shear force, the model accurately reproduces the experimental room-temperature data in the covered force regime and provides a unified interpretation of prior measurements on similarly sheared duplexes across all force regimes. A central result is that the three-dimensional helical geometry of dsDNA is essential for correctly defining the end to end distance under shear in the rod-like polymer model of short dsDNA. We further show that the extracted transition state distances are robust to variations in ssDNA polymer parameters within the experimentally relevant regime. Finally, we analyze the temperature dependence of the transition state distance and discuss how our framework captures globally-heated rupture while identifying the additional complications introduced by localized plasmonic heating in gold nanoparticle-coupled constructs. These results provide a predictive kinetic foundation for interpreting force-rupture experiments and for designing force- and temperature-actuated DNA nanostructures.

We investigate steady Stokes flow through porous media composed of two-dimensional disordered arrays of circular obstacles. We develop a theory for the statistics of flow rates based on a pore-network model that captures local flow correlations. We show that the flow rate distribution across the ensemble of pore bodies follows a Gamma distribution, and that the flow rate distribution through pore throats is fully determined in terms of it. Furthermore, this Gamma distribution can be directly linked to simple geometrical properties such as the coefficient of variation of pore throat widths, rendering the model parameterisable from minimal medium information. The resulting predictions agree closely with computational fluid dynamics simulations and show markedly better agreement than prior mean-field models that neglect local flow-rate correlations, clarifying how local splitting and merging shape flow in disordered porous networks.

We present a new framework for extending Chapman-Enskog theory beyond the hard-sphere fluid model. Rather than relying on effective hard sphere diameters, the approach makes use of on an exchange function which can be related to the thermodynamic properties of the system. We show that two existing extensions, including modified Enskog theory (MET), fit into this new framework. Based on our approach, we propose an alternative to MET that takes into account the potential interaction energy associated with the inter-particle interactions in the fluid. The proposed expression is applied to predicting the shear viscosity of several different simulated fluid models across a wide set of densities $0.05 \leq \rho^* \leq 0.8$ and temperatures $1.5 \leq T^* \leq 4.0$ in Lennard-Jones units. The fluid models considered include both the Weeks-Chandler-Anderson (WCA) fluid and the Lennard-Jones (LJ) fluid. At low and intermediate density, here taken to be $\rho^* \leq 0.3$, we report mean relative prediction errors between $2\%$ and $4\%$ for both these. Across all densities considered, the largest mean relative errors reported are $4.4\%$ and $8.1\%$ for the WCA fluid and LJ fluid respectively. We also investigate other interaction models, including a diatomic molecular model, in order to better understand the limitations of our approach.

High-entropy materials are complex, multifunctional materials that have reshaped the design of advanced functional materials. Their chemically diverse compositions enable access to a broader compositional space than conventional solid solutions, while simultaneously posing significant challenges for fundamental structure property understanding. In this study, we introduce a new highentropy spinel oxide with an exceptionally low coercivity of 1.8 Oe at room temperature, among the lowest reported for bulk spinel oxides, and a high electrical resistivity (1560 ohm-cm). Neutron powder diffraction (NPD) and magnetic measurements reveal long-range collinear ferrimagnetic ordering (k = 0,0,0) with a transition temperature at 420 K. This rare combination of ultra-soft magnetic behavior, robust ferrimagnetic ordering well above room temperature, and high resistivity highlights its strong potential as an advanced soft-magnetic oxide for low-loss, high-frequency applications. Furthermore, X-ray absorption spectroscopy (XAS), Mossbauer spectroscopy, and NPD analyses were combined to determine the cation distribution and site selectivity across the tetrahedral and octahedral sites of the complex structure.

Oscillating-foil-based energy harvesters have demonstrated strong potential for low-speed hydrokinetic energy extraction; however, the actuator-level mechanical energy balance associated with prescribed pitching motion remains poorly understood. The present work experimentally characterizes how foil mass ratio, pitching-axis location, and reduced frequency jointly govern the hydrodynamic and mechanical efficiencies of a semi-passive oscillating hydrofoil. Results show that rotational inertia redistributes actuator demand through phase-dependent torque exchange, while heave-pitch coupling can partially cancel this demand when favorably phased. Pitching-axis location modifies the phase and direction of the fluid torque through changes in the effective hydrodynamic moment arm. Reduced frequency governs the balance between enhanced unsteady loading and inertia-amplified actuator demand. Optimal performance is achieved within reduced frequency region of 0.125-0.16 using quarter-chord to one-third-chord pitching axes and relatively low foil mass ratios from about 0.5 to 2.0, yielding a peak mechanical efficiency of 33.96% -- which can diverge from the hydrodynamic efficiency by approximately 38.16% depending on configuration. Torque-loop analysis and PIV measurements show that this synchronization is a key mechanism governing the observed efficiency trends.

Data-driven modeling shows significant promise for faster-than-real-time forecasting of fluid flows. For real-world engineering applications (e.g., flow control), models must contend with limited, imperfect, and incomplete experimental measurements. In this work, we present an analysis of data-driven surrogate models trained to forecast the time-evolution of experimentally measured cylinder wakes in the subcritical vortex shedding regime. Using a dataset of two-dimensional, two-component particle image velocimetry measurements, we train fully convolutional neural networks, U-Nets, Fourier neural operators, and dynamic mode decomposition-based models to forecast the development of experimentally measured velocity fields. To characterize data-driven approaches contending with transient flow features and limited, imperfect observations, the development of predictions over extended forecast horizons is examined at a fixed Reynolds number (Re = 590). Next, models are trained at a range of Reynolds numbers (Re = 230 to Re = 2920) to investigate the impact of increasingly turbulent and three-dimensional flow phenomena, and the challenges associated with measuring them, on forecast quality. We find that experimentally trained surrogate models can provide meaningful predictions over short time horizons, propagate low-frequency dynamics over longer forecast periods, and achieve faster-than-real-time evaluation. However, the data-driven models struggle to preserve transient flow features and high-frequency energy content when faced with noisy measurements and incomplete state observations. This emphasizes the underlying challenges that remain for data-driven modeling approaches to effectively contend with fluid dynamics in real-world engineering applications, where observations are often imperfect and limited.

Hydrodynamic interactions with boundaries can significantly affect the trajectories of microscale swimmers. In simple swimmer models, a common assumption is that swimmer shape remains constant, essentially averaging over the rapid oscillations in geometry and associated fluid flows that often are the source of propulsion. Previous work in minimal force-dipole models has shown how the inclusion of time-dependent swimmer changes can lead to a fundamentally wider class of behaviours than for their classic (implicitly averaged) counterparts. However, since force dipole models correspond to the leading-order term in the far-field description of the swimmer-induced flow, they break down as the swimmer approaches a boundary and predictions can become qualitatively inaccurate. Here, we extend the minimal force-dipole model by incorporating higher order flow singularities, systematically accounting for rapid oscillations in shape and singularity strength through a multiscale analysis. We demonstrate that the inclusion of time-dependence into these higher order models significantly expands the reachable parameter space, in particular by increasing its dimensionality. In these extended dynamics, we observe three distinct behaviours: crashing, escaping and hovering. Notably, hovering states are absent from the dynamics predicted by the simplest models, but are observed in more complex models.

We report numerical simulations of a rotating rectangular annulus that isolates the Ekman-free bulk of the cylindrical baroclinic annulus, subjected to bi-directional temperature gradients imposed by a uniformly cooled inner wall and a localized forced heated plume at the outer bottom. The finite-volume OpenFOAM solver is employed across combinations of source Richardson number $Ri_0 = 99, 4, 1$ and Rossby number $Ro = 0.3, 0.1, 0.07$. A non-dimensional scaling of the governing equations identifies geostrophic-hydrostatic balance as the leading-order bulk state, a result confirmed a posteriori by the $x$ and $z-$momentum budgets. Baroclinic waves of mode $m=2$ at $Ro=0.3$ transition to $m=3$ as $Ro$ decreases, consistent with the contraction of the Eady deformation radius $L_\rho = NH/f$; Complex Empirical Orthogonal Function (CEOF) analysis characterizes the wave regime and detects a Hopf-bifurcated vacillating state at $Ri_0 = 99,~Ro = 0.1$. The plume morphology, classified through the Morton length scale and source flux-balance parameter, transitions from weak, laterally-swept structures at $Ri_0 = 99$ to sustained columnar plumes traversing the full baroclinic depth at $Ri_0 \leq 4$. The plume entrainment coefficient $\Gamma(z)$ shows opposite rotational sensitivities at low and high $Ri_0$, which we organize through a local plume Rossby number $Ro_p = w/(2\Omega b)$. A mixing-length argument predicts a bulk turbulent heat flux $\overline{u'T'} \propto Ri_0^{-1/2}$, anticipating an order-of-magnitude enhancement from $Ri_0 = 99$ to $Ri_0 = 1$, in agreement with the simulations. A regime map in the $(Ri_0, Ro)$ plane reveals that, within the explored range, the plume-regime and wave-selection problems are approximately separable: $Ri_0$ sets the plume regime while $Ro$ selects the dominant baroclinic wave mode.

Microscale locomotion in Newtonian fluids is constrained by kinematic reversibility. Here we show that viscoelasticity provides a distinct route: an achiral fore-aft asymmetric body rotating in a viscoelastic fluid generates net translation through normal-stress-driven secondary flows. Direct numerical simulations combined with scaling analysis reveal the universal scaling law, $V\sim {\rm Wi}\cdot S$, where $\rm Wi$ is the Weissenberg number and $S$ is the skewness of the axial volume distribution. This result identifies a minimal geometric principle for rotation-induced propulsion in viscoelastic fluids, and suggests a route for active microrheology via propulsion-speed measurements.

Magnetic fields have shown potential to affect flame characteristics; however, the mechanisms of interaction are not fully understood. This paper investigates the effect of magnetic fields on premixed hydrogen-air flames that are prone to intrinsic instabilities, with a focus on the role of magnetic forces on the flame behaviour. The study is conducted using direct numerical simulations. Two flame conditions, both with an equivalence ratio of 0.5, are studied, one with the reactants at atmospheric conditions and the other at high pressure and high temperature. Different configurations of the magnetic field are investigated, each characterised by a different gradient of the square of the magnitude of the magnetic field, oriented in the direction opposite to the velocity of the incoming reactants. Results show that the investigated configurations of the magnetic field can reduce the flame consumption speed, an effect that is substantial in the lower pressure case, while it becomes negligible at high pressure. The effect of the magnetic forces increases with increasing gradient of the magnetic field and is mainly due to the reduction of the flame area. Results also show that the effects of magnetic fields on the reactivity of the flame and on the small cell structures developed along the flame front are negligible. Analysis of the force contributions demonstrates that the change in the flame area is caused by the rotational component of the magnetic forces, which alter the vorticity of the flow such that the finger-like structures formed by hydrodynamic instabilities tend to close. These forces are significant at low pressure, while they become negligible compared to the pressure gradient at high pressure. Ultimately, the results of this work indicate that magnetic forces have the potential to change the flame behaviour, a mechanism that could be used for active control of flames.

Aerodynamic simulation is a key component of engineering shape design, where core quantities such as the surface pressure coefficient strongly depend on flow dynamics near solid boundaries. Neural operators provide an efficient alternative to expensive Computational Fluid Dynamics (CFD) solvers. However, conventional methods treat the boundary region isotropically, failing to account for the distinct physical behaviors along the boundaries. In reality, the aerodynamic process exhibits anisotropy: along the tangential direction, flow propagates along the wall; along the normal direction, physical quantities are constrained by the wall. To explicitly model the distinct physical behaviors, we propose GeoABC, a geometry-conditioned anisotropic boundary correction framework. GeoABC leverages the boundary geometries to introduce direction-aware boundary correction into the intermediate representations of neural operators, transforming boundary geometry from static input features into a structural prior that modulates physical prediction. On 2D airfoil and 3D car tasks, GeoABC consistently adapts to multiple neural operator backbones, reducing near-boundary relative $L_2$ error by $\sim$38\% on average, narrowing the structural near-wall gap shared by mainstream neural operators, and advancing neural operators toward high-fidelity aerodynamic simulation.

We exhibit a family of smooth incompressible velocity fields on the two-dimensional unit sphere such that the time evolution of any mean-free initial data passively advected by any of them is mixed exponentially fast. In the presence of molecular diffusivity, we show that the solution to the associated advection-diffusion equation experiences enhanced dissipation with optimal decay rates. Each member of this family is an alternating combination of two Rossby-Haurwitz flows with random amplitudes and constitutes a spherical analogue to the sine shear-alternating example of Pierrehumbert.

Continuous approximations of flow data are useful for downstream analysis, differentiation, and visualization, but purely data-driven reconstructions do not, in general, preserve the governing physics. This limitation becomes particularly important when input data are physically inconsistent, whether due to low-fidelity discretizations or unmodeled discrepancies. In such cases, reconstructed fields may exhibit inaccurate PDE residuals, violated balance laws, or unreliable derived quantities. To address this, we propose a physics-informed B-spline framework that embeds physical constraints directly into the reconstruction process. The method constructs compact, continuously differentiable representations of discrete fields using tensor-product B-splines and determines spline control points by solving an optimization problem balancing data fidelity with residuals of the governing PDEs, alongside initial and boundary conditions. Leveraging exact analytical derivatives of the B-spline basis enables efficient and accurate evaluation of physical residuals without storing full-resolution fields. We refer to this approach as physics-informed multivariate functional approximation (PI-MFA). Numerical studies on the 1D convection-diffusion, 2D coupled Burgers, and 2D incompressible Navier-Stokes equations show PI-MFA reduces PDE residuals and improves global balance-law consistency. Compared with standard and regularized MFA, PI-MFA produces more physically faithful reconstructions and, for physically inconsistent data, lower approximation errors, while offering computational advantages over tested physics-informed neural networks. Overall, PI-MFA preserves the compactness, local support, and exact differentiability of classical spline spaces while producing reliable continuous flow fields for scientific analysis and visualization.

We review random matrix approaches to chaotic wave scattering and transport in open systems. Starting from the effective non-Hermitian Hamiltonian formulation, we discuss the scattering matrix, reaction matrix, time delays, and complex resonances as complementary probes of open chaotic dynamics. We emphasize universal statistics governed by symmetry, openness, and channel coupling. Topics include the maximum-entropy description of fixed-energy scattering and its applications to quantum transport, energy correlations, resonance and eigenfunction statistics, and selected wave-chaotic phenomena induced by finite absorption. The focus throughout is on non-perturbative methods and universal structures underlying open quantum and wave chaotic systems.

Adaptive systems can exhibit similar levels of performance while relying on fundamentally different internal modes of coordination. Standard metrics such as average cooperation or payoff indicate whether a system succeeds, but do not reveal how coordination is organized across interacting components or which adaptive variables should be targeted when performance fails. Here we propose complexity synchronization (CS), the synchronization of evolving temporal complexity across coupled variables, as a diagnostic and intervention guiding principle for adaptive systems. We test this idea in an adaptive multi agent system composed of Selfish Algorithm agents interacting in a reduced Predator Prey model with a Prisoners Dilemma like payoff structure. Temporal complexity is quantified using sliding window modified diffusion entropy analysis (MDEA) and detrended fluctuation analysis (DFA). CS is defined as the correlation between the resulting time dependent scaling exponents. In the high-interaction regime, MDEA-based CS increases with cooperative performance, whereas DFA based CS captures a distinct persistence dominated coordination mode. Our results show that CS can reveal functionally relevant subsystems and provide a principled basis for targeted repair. More broadly, CS offers a general diagnostic and engineering framework for understanding and controlling coordination in biological, social, human machine, and other adaptive systems.

We study the 1D swarmalator model augmented with self-propulsion. Each swarmalator swims along the ring at a speed $v_0\sin\theta_i$ fixed by its orientation $\theta_i$. Self-propulsion unfolds the static states of the ordinary model into traveling, breathing, split-wave, and chaotic states. Several of these states admit analytic reductions: an exact drifting two-cluster branch with a closed-form stability spectrum, and a four-cluster split-wave ansatz whose active pair reduces, in a constant-orientation approximation, to an Adler equation. Our numerical evidence suggests that the transition to chaos under broad random initial conditions is not caused by local destabilization of the ordered cluster branches, but by basin reorganization among coexisting attractors. The resulting states may serve as qualitative signatures for confined active oscillator arrays.

Active rotator models provide a minimal phase description of excitable and oscillatory systems, and have long been used to study mutual entrainment, synchronization, and collective transitions. Here, we investigate fully connected active rotator networks with Kuramoto coupling, where a common intrinsic drive competes with local feedback amplitudes drawn from a zero-mean Gaussian distribution. This produces a competition between local pinning and collective phase alignment. Using mean absolute late-time drift and the fractions of positive and negative drifting oscillators, we construct numerical regime maps in the feedback-disorder-coupling plane. At weak coupling, increasing the feedback disorder strength suppresses drift, while stronger coupling can restore positive late-time drift when feedback disorder is not too strong. We interpret these regimes using analytical limits for the uncoupled and coherent strong-coupling cases. We also examine finite-size effects and zero-mean distributed intrinsic frequencies. Together, these results show that mixed-sign local feedback alone can reshape the balance between pinning and drifting in coupled active rotator networks, even when the intrinsic drive is homogeneous.

Fluid-immersed hair beds are ubiquitous in biology-from the endothelial glycocalyx and primary cilia to intestinal microvilli-where they serve as mechanosensors that transduce dynamic flow signals into biochemical regulatory responses. Despite the inherently dynamic nature of physiological flows, the dynamic mechanical properties of fluid-immersed hair beds under time-varying conditions remain poorly characterized. Here we investigate the transient rheological response of elastic hair beds to large-amplitude oscillatory shear flows at low to intermediate Reynolds number. While the hairs and fluid themselves obey linear constitutive laws, their coupled interaction produces a dynamic nonlinear response that depends sensitively on driving frequency and amplitude. We identify a crossover from a stress-lagging regime to a stress-leading regime, which is governed by an interplay between fluid viscosity, fluid inertia, and hair elasticity. A simplified rigid-beam model qualitatively captures the crossover behavior. Characterizing the dynamic flow response of soft hair beds has direct biological implications, since the lag time sensitively determines the stability of mechanosensory signaling in the feedback loops underlying essential biological processes such as vasodilation, ciliary remodeling, and tubular reabsorption. Our results establish a framework for understanding how the physical properties of biological hair beds optimize dynamic information transmission during mechanotransduction.

Here we present ARTGEL, an actively regulated-temperature gel electrophoresis platform designed for long-duration experiments under independently controlled thermal and electrical conditions. ARTGEL combines thermoelectric regulation of the gel temperature, a large heated and circulated buffer reservoir, and an automated electrode-wiping mechanism that stabilizes the voltage across the gel during runs exceeding 24 h. The platform was developed to address a limitation of conventional electrophoretic mobility shift assays, which are commonly used to analyze reversible biomolecular association but usually aim to suppress reaction during electrophoresis by dilution, competitors, or reduced temperature so that the gel reports a pre-equilibrated bulk solution. For temperature-sensitive systems, these strategies can alter the chemical state during loading and migration and obscure whether the measured band pattern reflects the original bulk sample or a re-equilibrated state inside the porous gel. Rather than attempting to quench reactions, ARTGEL enables electrophoresis to be performed at the same temperature as complementary bulk measurements, so that reversible association can be quantified directly in the gel and compared with matched measurements in solution. Using DNA origami assemblies, we show that ARTGEL preserves distinct temperature-dependent association states, resolves reaction-dependent distortions of migrating bands, and supports extraction of in-gel kinetic and thermodynamic parameters from reaction-diffusion-advection modeling.

In soft condensed matter, curvature does more than simply distort an ordered medium: it helps select defect structures, redistribute elastic stress, bias chirality, and guide self-assembly. This review examines how curved, multiply connected, and knotted boundaries in liquid-crystal colloids and confined nematics generate topological defects and localized solitonic textures, and how these structures mediate interactions between mesoscale building blocks. We introduce a unifying framework based on genus, Euler characteristic, anchoring, and chirality, and use it to discuss spherical, handlebody, and boundary-bearing colloids, together with droplets and polymer-dispersed nematics of nontrivial topology. Particular emphasis is placed on the interplay of geometry and topology in determining boojums, disclination loops, hedgehog charges, and linked and knotted defect structures. We then turn to chiral systems hosting skyrmions, torons, hopfions, and related localized textures, highlighting how chirality and confinement stabilize three-dimensional topological states. Finally, we discuss how these concepts translate into design principles for controlled self-assembly, templating, and functional composite materials. More broadly, we argue that liquid-crystal colloids and confined nematics provide experimentally accessible model systems in which curvature, topology, and chirality can be harnessed as programmable tools for designing organized soft matter.

Ferroelectric nematic liquid crystals (FNLCs) are promising soft platforms for nonlinear optics, but quantitative determination of their second-order nonlinear optical coefficients has been hindered by limited alignment control. Here, polarization-resolved second-harmonic generation (SHG) measurements on a uniformly aligned dioxane-based FNLC, combined with Jones-matrix simulations, enable determination of all principal tensor components. The resulting tensor is consistent with the expected $C_{\infty v}$ and Kleinman symmetries, while the measured coefficients cannot be explained by a simple sum of molecular first hyperpolarizabilities. These results provide a quantitative basis for understanding nonlinear optical responses and guiding the design of FNLC-based nonlinear optical materials and devices.

The hydrodynamic response of Brownian particles in liquids is fundamentally altered by inertial forces arising from unsteady momentum transport in the surrounding fluid. These forces are of two distinct types\,: the added mass and the history effect. While both are well understood in bulk and weakly-confined geometries, under deterministic driving, their respective behaviours under strong confinement and thermal fluctuations remain scarcely addressed, unclear and often entangled together. The goal of the present study is thus to fill this fundamental gap. The behaviours of the two distinct inertial contributions are quantitatively investigated in the vicinity of a flat, rigid wall, using a combination of broadrange thermal colloidal-probe atomic-force-microscopy experiments, advanced numerical simulations and theory. The separation of the added-mass and history-force contributions is achieved through their different frequency-scaling signatures within the measured high-resolution thermal spectra. Our results establish a complete picture of Brownian motion at interfaces, in the lubrication regime, with direct relevance to nanofluidics and interfacial biophysics.

Polymer chain scission is a key mechanism for fracture of soft materials. It is well known from single-molecule force spectroscopy experiments that the critical condition for chain scission depends on the loading rate and other environmental effects (e.g., temperature and solvent). Common approaches to describing the kinetics of chain scission often assume force-controlled conditions, that is, when a polymer chain is stretched by a prescribed force. As a result of this assumption, chain scission is irreversible, excluding the possibility of healing. In many soft materials, however, self-healing has been observed after fracture, suggesting possibly reversible chain scission. Here, we show that reversible chain scission is possible under displacement-controlled conditions, that is, when a polymer chain is stretched with a prescribed end-to-end distance. We present a breakable freely-jointed chain model, assuming that a polymer chain breaks when one of its links breaks while the other links remain nearly rigid. At a prescribed end-to-end distance, the free energy of the chain has two local minima and a local maximum (the transition state), giving rise to energy barriers for chain scission and healing. As the prescribed displacement increases, the energy barrier decreases for scission but increases for healing, depending on the chain length (number of links) and the potential energy of the link. With the energy barriers, we adopt a kinetic approach to predict the statistics and kinetics of a single polymer chain under tension, first by integrating the rate equation and then by kinetic Monte Carlo simulations. Notably, the present model predicts rate-dependent chain scission, with a lower bound for the rupture force that could be several orders of magnitude lower than the upper bound (which is close to the theoretical strength of the covalent bonds).

Generative models are increasingly used to capture correlations in many-body systems, but the representations they learn remain largely opaque to physical interpretation. Here, we establish an intuitive criterion that quantifies the capacity of a variational autoencoder (VAE) to faithfully reconstruct the joint probability distribution of a many body system. In a nutshell, a bound on the VAE capacity is obtained by comparing the rate of the latent channel to the bipartite mutual information of the data. Using this bound, we show that the conditionally independent decoder of any successful VAE is structurally identical to a finite-size mean-field factorization. Hence, a successful reconstruction is direct evidence for a latent mean-field theory and the microscopic parameters of that theory can be read off the trained decoder. We validate these conclusions on a hierarchy of solvable models with scalar (Curie-Weiss), vector (Hopfield) and tensor (Maier-Saupe) order parameters, recovering the full Hopfield pattern matrix from equilibrium samples alone. We find that, when applied to Salamander retinal recordings, a two-latent VAE reproduces the population statistics with only two effective collective variables allowing us to recover the `stored patterns' of the neural population and write a generalized Hopfield model which correctly models the experimental data.

We investigate the structural correlations of hard spheres confined within a narrow cylindrical pore in the quasi-one-dimensional regime, where interactions are restricted to nearest neighbors. Using a Laplace-space formulation of the radial distribution function (RDF), we determine the correlation lengths and oscillation frequencies associated with its long-distance decay. In addition to the global RDF, we analyze transverse-resolved RDFs that account for the positions of particle pairs across the pore cross section. While these observables are associated with the same underlying pole spectrum, their residues depend on the transverse configuration and can vanish due to symmetry. As a result, different particle-pair configurations may be governed by different leading poles and display different correlation lengths and oscillation frequencies. In particular, the global RDF does not always reflect the longest-ranged correlations found in transverse-resolved observables. We examine how this behavior depends on density and confinement. In the strong-confinement limit, the system approaches the Tonks-gas behavior at finite pressure, and the differences between the RDFs disappear.

Shear banding is a well-known and widespread instability in strained solids: under external strain, the deformation localizes along a line in two dimensions or a plane in three dimensions. Developing a proper theoretical description of this phenomenon is key to understanding mechanical failure in solid materials. Very recently, a nonlinear theory extending classical elasticity to include plastic deformations as topological charges was proposed, offering detailed predictions on the nature and consequences of the shear-banding instability. The theory derives a Hessian operator whose lowest eigenvalue vanishes at the onset of instability, and the corresponding critical eigenmode describes the displacement field across the shear band. The resulting soft mode possesses the selected localization scale and subsequently saturates into a finite-width shear band. The aim of this Letter is to examine this theory numerically, establishing the role of topological screening and nonlinear instability as the mechanisms governing shear banding during athermal quasistatic deformation. We show that the displacement profile around the shear band is directly determined by the screening parameter and the nonlinear coefficient, thereby quantitatively verifying the theoretical predictions. Our results demonstrate that shear banding differs fundamentally from fracture: it arises from a nonlinear instability of an elastic field screened by plastic deformations. This establishes topological screening as the essential mechanism governing shear banding in amorphous solids.

Liquid-gas equilibrium for a simple molecular fluid is considered in view of the existence of the order parameter, in terms of which the symmetry of the binodal is restored not only in the vicinity of the critical point (critical isomorphism) but also globally in the whole coexistence region. This leads to the mapping between fluid and lattice gas (Ising model). We test this approach against the data on the liquid-gas binodal of a two-dimensional Lennard-Jones fluid and monolayers of molecular fluids. The obtained results allow us to speculate about the analog of the Kramers-Wannier duality in such systems and provide the theoretical estimate for $dp/dT$ on the saturation curve at the critical point. The microscopic grounds of the proposed approach are also discussed, and the transition from the continuous fluid model Hamiltonian to the effective quasi-spin lattice model is outlined.

We investigate motility-induced phase separation in a lattice gas of self-propelled particles with hard-core exclusion, where an internal director biases particle hopping along the lattice coordination directions while undergoing rotational diffusion, together with a thermal-like translational diffusion. Rather than employing stochastic simulations, we adopt a master-equation formalism within a general mean-field approximation. By linearizing the mean-field master equation around the homogeneous stationary state and applying Bloch's theorem, the stability analysis is reduced to a $z$-dimensional tight-binding eigenvalue problem. A perturbation expansion in the wavenumber near $\vk = 0$ then yields the spinodal surface in closed analytical form for six Bravais lattices: linear, square, hexagonal, simple cubic, body-centered cubic, and face-centered cubic. The influence of lattice geometry is shown to enter exclusively through a single coefficient $\mathcal{A}$ which we evaluate exactly for each case. We further show that translational diffusion smooths the interface between the dense and dilute phases. Finally, we determine the rotational probability currents associated with the inhomogeneous stationary states, a distinctive signature of the broken detailed balance underlying active-system dynamics.

Multicomponent colloidal gels can exhibit mechanical responses that depend not only on interaction strengths but also on the temporal pathway by which their networks form. Here, we use particle-based simulations to investigate the steady-shear deformation of binary colloidal gels assembled by sequential gelation with tunable delay time and dominant interspecies attractions. Although varying the gelation delay produces markedly different quiescent morphologies, ranging from well-mixed networks to coarse shell-core structures, steady shear drives the systems toward structurally convergent, mixed states as quantified by cluster, connected-component, and coordination analyses. This structural convergence, however, does not imply rheological equivalence. The transient stress response remains strongly dependent on gelation delay and interspecies attraction strength. For moderate interspecies attractions, increasing delay enhances the stress overshoot, particularly at high shear rates. For stronger interspecies attractions, initially heterogeneous gels exhibit two-step yielding at low shear rates, indicating distinct deformation and restructuring processes. These results show that sequential gelation can imprint a persistent rheological memory in binary colloidal gels, even when shear substantially erases differences in common structural descriptors.

Most high-performance elastic textiles rely on yarns composed of chemically dissimilar polymers, rendering them difficult to recycle. Here, we demonstrate fully thermo-mechanically recyclable stretchable yarns composed of polyethylene (PE) family materials. Inspired by structure-property relationships in natural materials, we engineer a library of melt-spun PE fibers spanning mechanical properties from elastomeric to functional by tuning polymer crystallinity and chain orientation. These fibers are assembled into core-sheath yarns comprising an olefin block copolymer elastic core and a high-strength PE sheath, forming a helical architecture. The resulting yarns exceed mechanical performance of commercial PET-spandex yarns while maintaining full recyclability. We further show that PE homopolymers and copolymers can be jointly melt-processed and recycled without phase separation or loss of performance. This approach enables stretchable recyclable textiles from fibers with previously demonstrated cooling, moisture-wicking and stain-resisting performance and provides a scalable pathway toward circular garments compatible with existing polyethylene recycling streams.

A computational scheme, which utilizes neural networks, was developed to predict properties of molecular-based materials from chemical structures. The method uses a set of simple algorithms to encode the structure and composition of organic molecules directly into numerical vectors, which is used as input for neural networks. Backpropagation type neural networks are then used to correlate these numeric inputs with a set of desired properties. Calculated results for a series of hydrocarbons, hydrofluorocarbons, and crown ethers demonstrate average accuracies of 0.2-8.1% with maximum deviations of 16-20% for a broad range of thermodynamic, physical, and physical-chemical characteristics (heat capacity, enthalpy, heat of evaporation, boiling point, density, refractive index, stability constants, etc.). In addition, a number of physical and mechanical properties were estimated for polymeric materials and compared with regression analysis. Based on the neural network capabilities of formulating accurate quantitative structure property relationships, a technique called computational synthesis is suggested for performing materials design.

Multicomponent vapor-deposited organic glasses are essential in organic electronic applications, but achieving controlled component segregation at the nano- and mesoscale remains a challenge, hindering the rational development of high-performance devices. In this study, we investigate binary organic semiconductor mixtures of TPD (N,N'-Bis(3-methylphenyl)-N,N'-diphenylbenzidine) and TCTA (Tris(4-carbazoyl-9-ylphenyl)amine). Despite being miscible in the bulk liquid state, the co-deposited glassy films of these two organic semiconductors exhibit a range of segregation behaviors, from homogenous to clearly phase-separated structures. We employed differential scanning calorimetry and resonant soft X-ray scattering (RSoXS) to study the component segregation behavior and used the National Institute of Standards and Technology RSoXS Simulation Suite, paired with Atomic Force Microscopy, to interpret the energy-dependent RSoXS spectra. Our results indicate that component segregation in co-deposited TPD-TCTA films is due to a kinetically-arrested nucleation-and-growth mechanism, in contrast to the segregation mechanism of a previously reported TPD-DO37 (disperse orange 37) mixture which is strongly immiscible in bulk. This work provides a demonstration of tunable molecular aggregation in organic semiconductor glasses, enabling access to a continuum of morphologies from homogeneously mixed to segregated phases.

Successfully performing direct numerical simulations of polymeric flows remains a major challenge in computational fluid mechanics. In addition to the velocity field, such simulations must resolve polymeric degrees of freedom, often expressed via the conformation tensor, $\mathbf{c}$, which captures the local stretch of polymer molecules. A key difficulty here lies in maintaining the physical requirement $\mathrm{Tr}\, \mathbf{c}>3$, which is not explicitly enforced by the governing equations. Consequently, simulations initiated from physical conditions may silently drift into unphysical states with $\mathrm{Tr}\, \mathbf{c}<0$, indicating a loss of positive-definiteness of the conformation tensor. Existing numerical methods to prevent this are costly, making direct numerical simulations of chaotic polymer flows, such as elastic turbulence, heavily reliant on high-performance computing. Here, we ask whether simulations that violate $\mathrm{Tr}\, \mathbf{c}>3$ can still yield meaningful physical insight into the underlying dynamics. We simulate a model dilute polymer solution driven through a plane channel at low Reynolds number and observe the transition to elastic turbulence. Our simulations exhibit two threshold resolutions: below the first, they become numerically unstable and exhibit a finite-time blow-up; above the second, they maintain positive-definiteness. In between, simulations remain stable and chaotic despite local violations of $\mathrm{Tr}\, \mathbf{c}>3$. Surprisingly, these violations do not affect mid-plane statistics of velocity, its gradients, or polymer stretch, which match results from fully positive-definite simulations. This suggests that resolving flow structures or key flow statistics may not require the extreme resolutions needed to preserve positive-definiteness, potentially lowering computational barriers for studying elastic turbulence.

Fluid injection into the Earth's subsurface, performed for energy extraction, waste disposal, and resource development, is known to reactivate gouge-filled faults and induce seismicity, a key hazard in modern geotechnical operations. Nevertheless, the role of injection rate in controlling fault-gouge failure remains poorly understood. Here we present both an analytical theory and coupled fluid--granular (discrete element) numerical simulations to explain this rate dependence. Assuming a pre-stressed gouge-filled fault subject to fluid injection, we derive a pore-pressure diffusion equation with a dilative sink. Its solution predicts a rate-dependent failure criterion, arising from pressure heterogeneity within the layer: slow injection allows pressure to diffuse uniformly throughout the layer, promoting uniform weakening, whereas rapid injection produces strong gradients, leaving distal regions stronger. The numerical simulations confirm the theory and reproduce experimental observations not captured by classical, uniform-pressure effective-stress theory. The framework links grain-scale physics to fault-scale failure and provides quantitative guidance for the design of injection protocols in geotechnical operations involving granular geomaterials.

The ability to predict protein three-dimensional structures from amino acid sequences is a landmark achievement in molecular biology, where recent deep learning approaches such as AlphaFold are the culmination of decades of work. Yet, the quantitative understanding of how protein sequences give rise to dynamic conformational changes and higher-order assemblies remains unsolved. Folding and conformational states are dynamic, stochastic processes, shaped by sequence, energy, co-translational constraints, chaperone machineries, and the physicochemical conditions of the cellular environment. Recent advances now position the field to move beyond static structural endpoints toward a mechanistic understanding of folding dynamics in living systems. Single-molecule techniques enable time-resolved observation of folding trajectories and intermediate states hitherto hidden by traditional structural biology approaches, while computational innovations and data-driven approaches offer new ways to integrate heterogeneous data across scales. In this Roadmap, we review the current conceptual landscape of protein folding, examine the experimental and theoretical gaps that remain, and discuss emerging strategies that integrate high-resolution measurements with multiscale modeling. We outline a roadmap toward a quantitative and predictive science of protein folding dynamics, conformational kinetics, and macromolecular self-assembly. Realizing this vision would transform our understanding of the dynamics of molecular self-organization, from the folding of individual polypeptides to the emergence of dynamic macromolecular complexes. This will enable rational control of folding and misfolding in health and disease, extend protein engineering principles beyond static structural design, and establish a mechanistic foundation for predictive and personalized interventions in proteostasis-related disorders.

Immersed boundary methods (IBMs) are widely used to simulate flows around complex geometries and moving bodies, but they often involve a trade-off between precision and computational efficiency. Eulerian formulations require special treatments for moving walls and may generate spurious force oscillations, whereas Lagrangian formulations can suffer from slip errors at the immersed surfaces. We propose a novel sharp-interface IBM for incompressible flows involving moving, deformable, and arbitrary-thickness bodies. The method combines a fast tagging algorithm, a two-sided Eulerian forcing strategy, and a consistent mass correction that reduces the splitting error of fractional-step schemes, while preserving the structure of the discrete Laplacian operator. This formulation retains the efficiency of direct Poisson solvers, thus avoiding the overhead of cut-cell, multigrid, and projection-based approaches. The method naturally handles moving boundaries, and yields small transpiration errors with second-order accuracy in the enforcement of the no-slip condition. Numerical tests using rigid, deformable, turbulent, and biologically inspired flows demonstrate the accuracy, robustness, and efficiency of the method, without compromising computational cost.

In the presence of stratification, turbulent flows exhibit intermittency not only at small scales but also at large scales, comparable to the mean flow, as observed in the atmosphere and oceans. We study such flows through a large parametric exploration using direct numerical simulations of the Boussinesq equations with different forcing types. We examine two Prandtl numbers (1 and 6) and vary the Froude number ($Fr$) over a range of geophysical interest values, $0.01\le Fr \le 1$, corresponding to a variation in terms of the buoyancy Reynolds number ($R_{IB}$) of $0.06\le R_{IB} \le 2300$. We analyze the dependence on $R_{IB}$ of the buoyancy flux ($B_f$), the mixing efficiency, the shear parameters, and the vertical momentum flux. Strongly non-Gaussian tails in the spatio-temporal distribution of the $B_f$ are observed, with kurtosis reaching $\approx 10^2$, indicating the potential for stratified geophysical flows to be characterized by highly variable transport properties along the direction of gravity even under stable stratification. This is associated with long-time intermittent behavior of vertical velocity and temperature at large scale, which produces local turbulence and enhances dissipation and transport. We present evidence that the skewness of $B_f$ increases with $R_{IB}$ as a power-law and saturates in the passive-scalar limit. We also show that the domain-averaged $B_f$ exhibits two distinct trends: logarithmic growth with $R_{IB}$ and approach to a small offset as stratification strengthens. A simple model for the temporal evolution of energy and $B_f$ indicates that the defect between vertical and potential energy drives strong $B_f$ events. This trend directly leads to convective instabilities, the formation of two-dimensional and three-dimensional eddies, and rapid dissipation on a turnover timescale, allowing the energetic cycle to restart-also occurring in bursts.

We discuss here two major issues related to the steady functioning of the pulsating (oscillating) heat pipe (PHP): the effect of the surface properties and stopovers. They are studied with the CASCO simulation software (Code Avanc{é} de Simulation du Caloduc Oscillant: Advanced PHP Simulation Code in French) version 4. Its experimental validation against two different prototypes is presented. The first is used also to study the effect of the nucleation barrier (the wall superheating necessary for the bubble nucleation) that reflects the wall wettability and roughness. An optimal value of the nucleation barrier is found where the thermal resistance achieves a minimum for a given evaporator power. The functioning regime is continuous showing pressure waves propagating along all the PHP channel. The stopover regime is observed both for small and large barriers. The second experimental setup (PHP Smart Loop) is used to study the stopover regime. It is found that it is characterized by a chaotically repeating sequence of fast pressure growth (corresponding to oscillations) followed by a slower pressure decay during a stopover. The decrease of the thermal resistance with heating load is explained by a decrease of the stopover time caused by a faster liquid film shrinking.

Compressibility and wall heat transfer change the inner scaling of wall turbulence through the mean density and viscosity fields. Existing semi-local transformations usually act on a wall-normal profile after the profile has been chosen. Here the transformed coordinate and transformed velocity are instead defined by elliptic equations before wall-normal profiles are extracted. A semi-local wall coordinate is first formed from the local density and viscosity scaling. A Helmholtz-type elliptic equation then supplies a bounded density-induced correction to the wall-normal coordinate stretching, and projection equations give the transformed coordinate $Y^+$ and projected velocity vector $U^+$. The equations use mean velocity, density, viscosity, wall distance and wall normals. When density and viscosity are uniform, the density term vanishes, $Y^+$ reduces to the ordinary wall coordinate and each transformed velocity component reduces to the conventional mean velocity component in wall units. A single set of wall-layer constants is calibrated from two canonical cooled flat plates and then applied to attached zero-pressure-gradient boundary layers, isothermal channels and mixed thermal-wall channels. The channel cases use the same wall-coordinate equation on wall-to-centre half-domains, with density measured from the centreline. The density-induced coordinate correction improves inner and buffer-layer placement in cooled high-speed boundary layers; in mixed thermal-wall channels the isothermal side changes more than the adiabatic side.

The air--water interface governs the exchange of heat and gas between natural water bodies and their surrounding environment. Turbulence beneath the free surface imprints characteristic features: near-circular depressions (`dimples') and elongated indentations (`scars'). Recent studies have shown that these are linked to sub-surface flow features in a temporal sense. For instance, rapid increases in mean-square surface divergence due to upwelling events, precede dimple count surges. Yet the spatial structure of these connections remains unquantified. We employ spatial statistics to consider the spatial and temporal correlations between dimples and scars and two key velocity-derived fields, surface divergence $\beta=\partial_x u+\partial_y v$ and vertical vorticity $\omega=\partial_x v-\partial_y u$. The dimples and scars are modelled as inhomogeneous Poisson point-processes, with intensity fields driven by the local variance of $\beta$ and $\omega$. Parameters, including spatial support radius $r$ and time lag $\tau$, are estimated by maximum likelihood against six DNS datasets, quantifying the spatial and temporal connection between dimples, scars, surface divergence and vorticity. Our results demonstrate a clear complementarity: Dimples show strong local connection to the vertical vorticity field but has weak spatial connection with surface divergence and a spatially ``global'' model is required for dimples to work as estimators of surface divergence; scars, in a similar but opposite manner, couple locally to surface divergence but globally to the vertical vorticity. The complementarity sheds new light on the way dimples and scars may be used to infer fluxes across the surface, e.g., in remote sensing contexts.

A data-driven reduced-order modelling framework is proposed for wall-bounded turbulent flows to forecast the intermittent near-wall dynamics over extended time horizons from sparse sensor measurements. The approach combines a $\beta$-VAE-GAN, which compresses high-dimensional flow fields into a low-dimensional latent space, with a sensor-conditioned Transformer that forecasts the evolution of the latent variables. The temporal module employs Easy Attention, a static time-mixing operator that replaces the learnable query-key mechanism of standard self-attention at reduced computational cost, combined with an adapted AdaLN-Zero modulation mechanism for sensor-based conditioning. Evaluated on the Minimal Flow Unit ($Re_\tau = 200$) at $y^+ = 14$, the compression stage recovers $87\%$ of the turbulent kinetic energy within a four-dimensional latent space, exceeding the standard $\beta$-VAE baseline by more than $10\%$. The latent dimensions autonomously encode the characteristic timescales of the flow, with specific coordinates capturing the low-frequency signature of the near-wall regeneration cycle ($T^+ \approx 1724$), establishing the physical interpretability of the learnt representation. The sensor-conditioned Transformer maintains accurate forecasts over $17{,}288\,t^+$ from an initialisation window of only $128\,t^+$, whilst end-to-end inference reconstructs $82\%$ of the turbulent kinetic energy. The principal limitation is the attenuation of rare, extreme-amplitude events, a consequence of the encoder prioritising the most statistically recurrent flow states within the low-dimensional bottleneck. Nevertheless, the framework accurately reproduces the alternating active and quiescent phases of the regeneration cycle, demonstrating its suitability as a surrogate model for the intermittent dynamics of wall-bounded turbulence.