We study the equilibrium phase behavior of a fluid confined in a slit made from two patterned walls. Shearing the walls frustrates the fluid, due to a competition between capillary condensation and interface delocalization, forcing the formation of bridging phases with different pinning properties. This leads to an unusually rich phase diagram, displaying first-order and continuous phase transitions, depending sensitively on the slit width and shear. Generalized Kelvin equations determine the phase boundaries, while the bridging phases are characterized by large correlation lengths, predictions for which are tested using a microscopic density functional model.

Abrupt transitions between rest and motion can render the standard Newtonian description -- based on position, velocity, and acceleration -- incomplete, requiring higher-order derivatives such as the jerk, the third time derivative of position. Here, we show that the interplay between activity and dry friction gives rise to robust jerk-dominated dynamics in self-propelled particles: the particle speed increases quadratically with time under an active force, in contrast to the linear growth expected for conventional Newtonian dynamics. We demonstrate this behavior analytically, numerically, and experimentally using active vibrobots self-propelling on a vertically vibrating plate at low vibration amplitudes, where surface asperities generate dry friction and, thus, give rise to jerky motion when combined with activity. Our results establish dry friction as a simple mechanism for realizing higher-order dynamics in active matter and suggest that jerky dynamics may arise broadly in nonequilibrium systems with frictional contacts.

We investigate the diffusiophoretic motion of a chemically isotropic active colloid in a three-dimensional wedge formed by two distinct fluid media, in the limit of vanishing Péclet and Reynolds numbers. The concentration field is obtained using the Fourier-Kontorovich-Lebedev transform, yielding an exact representation for arbitrary wedge opening angles and interfacial contrasts. We introduce the interfacial parameter $\Gamma=(1-\lambda\ell)/(1+\lambda\ell)$, where $\lambda$ denotes the diffusivity contrast and $\ell$ the solute partition coefficient. For $\Gamma=\pm1$ and commensurate wedge angles, the solution reduces to finite image constructions, with distinct structures for even and odd commensurability. The general solution also recovers the planar-interface and semi-infinite-interface limits. The leading-order translational phoretic velocity is derived from the concentration field, revealing a strong interplay between wedge geometry and interfacial properties that governs both the magnitude and direction of particle motion. This work provides a framework for understanding and controlling phoretic transport in confined multiphase environments and offer a basis for extensions to finite-size geometries and mixed fluid--fluid and solid boundary conditions. Our results may find applications in the control of active-particle transport in confined multiphase environments, where interfacial properties and geometry can be exploited to tune phoretic motion.

Chain scission is a key molecular process underlying damage and fracture in polymer networks. In this Letter, we develop a statistical-mechanical framework for predicting chain-scission kinetics while accounting for three-dimensional (3D) conformational fluctuations. Within transition-state theory, scission is formulated as a multichannel first-rupture problem, with bond-specific rates governed primarily by self-consistent potentials of mean force. In the freely jointed limit, the additional 3D configurational freedom enhances rupture relative to the collinear 1D reference. Finite bending stiffness introduces orientational correlations that can reverse this enhancement and, at high stiffness, reduce rupture rates by orders of magnitude. These correlations also make rupture bond-position dependent, with higher rates near the chain ends and a common interior rate. For sufficiently long chains, the interior contribution dominates, yielding linear scaling of the chain-scission rate with chain length. These molecularly resolved rates provide physically grounded inputs for future network-scale models of polymer damage and fracture.

Can a boundary determine the direction of circulation in a collectively moving active fluid? We study chiral self-propelled particles with nematic bulk alignment, confined by walls whose orientational coupling varies continuously from nematic to polar. For an isolated particle at a wall, we derive the exact parameter condition under which a stable orientation is tangent to the wall. With predominantly nematic wall coupling, however, the many-body circulation changes sign at a chirality that is nearly independent of the wall symmetry. This sign change follows a pronounced decrease in nematic order and disappears when bulk alignment is removed. As the polar wall coupling becomes dominant, opposite-handed circulation is suppressed and same-handed polar locking emerges. Thus local orientation at a wall and the direction of macroscopic circulation are selected by distinct physical processes: the wall determines the possible local orientations, whereas collective order determines whether those orientations control the global flow.

According to Purcell's scallop theorem, reciprocal single-degree-of-freedom shape deformations cannot achieve net propulsion in a viscous fluid. We show that this limitation is bypassed by thermal fluctuations in a two-parameter driven potential landscape. Formulating the stochastic shape dynamics via a Smoluchowski equation with position-dependent mobility $M_\mathrm{eff}(x)$, we utilize a generalized inverse operator to evaluate the slow-driving response. Cyclic modulation of the control parameters induces a non-zero Berry-Sinitsyn-Nemenman curvature $F_{12}(\bm{\theta})$, resulting in directed geometric propulsion. Simultaneously, the non-adiabatic excess dissipation is dictated by a Riemannian thermodynamic metric $g_{ij}(\bm{\theta})$. Our results provide a unified geometric foundation that bridges hydrodynamic friction, stochastic mechanics, and thermodynamic trade-offs in micro-swimmers.

Gaucher disease (GD), the most common lysosomal storage disorder, alters red blood cell (RBC) mechanics and circulation, contributing to vascular occlusions, bone infarcts, and splenomegaly. However, the individual roles of GD-RBC biophysical properties in these processes remain unclear. Here, we present a combined computational-experimental investigation to quantitatively characterize GD-RBC biophysical properties and determine how specific mechanical parameters drive abnormal RBC behavior. Informed by experimental data, we independently quantify key RBC properties, including shear modulus (mu), surface-to-volume ratio (S/V), and bending modulus (k_c). Based on these parameters, we construct three GD-RBC subtypes (GD-RBC1-3) to systematically isolate their individual contributions. At the single-cell level, optical tweezers simulations show up to ~27% reduction in axial diameter and ~42% reduction in transverse compression. Tank-treading dynamics exhibit non-monotonic behavior, with rotation frequencies increasing by up to ~70% or decreasing under elevated bending rigidity. In confined flow, traversal times through microchannel constrictions increase by more than a factor of two, while splenic slit passage times rise from ~250 ms (control) to >1200 ms for the severe GD-RBC subtype, approaching a functional no-passage threshold. At the population level, viscosity simulations demonstrate that these alterations collectively elevate blood viscosity, with small fractions (~4.0%) of highly rigid cells disproportionately increasing flow resistance. Overall, this study provides a quantitative and mechanistic framework that disentangles the contributions of key RBC parameters to abnormal behavior in GD, linking cellular-scale biophysics to hematologic dysfunction and microvascular occlusion.

We investigate the melting dynamics of an ice disk subjected to an external oscillatory flow using two-dimensional direct numerical simulations, in the absence of buoyancy, varying the flow amplitude and its oscillation frequency. We identify two distinct regimes governed by the interplay between advection and diffusion within the boundary layer. For slow oscillations, the melting process is well described by an effective steady flow, where a description based on classical forced convection is applicable. For fast oscillations the melting time increases significantly and approaches the diffusion limit regime, as a result of the oscillatory flow being unable to renew the fluid within the oscillating boundary layer, causing cold meltwater to accumulate near the interface and reducing heat transfer.

The effects of pressure on the chemical sooting structure of equi-diffusive soot formation (SF) in a counterflow diffusion flame (CDF) are explored in a combined experimental and numerical study over pressures ranging from 1 bar to 6 bar. Experiments preserve the diffusive flame structure and carbon flux at increasing pressures and utilize measurements of soot concentrations, dispersion exponents and soot production rates. Numerical simulations are completed in OpenSMOKE++ with detailed \ce{C1}-\ce{C16} chemistry, lumped PAH consideration up to \ce{C160}, sectional soot model and tracking of the C/H ratio in particulates. Network-based tools are utilized to study the organization and evolution of carbon routing pathways. Results show that for equi-diffusive flames, soot concentration increases with residence time and pressure, whereas soot production rates are influenced only by pressure. Soot C/H ratio is observed to increase with pressure using numerical and experimental methods, but numerical solutions underestimate the increase in hydrogen abstraction reactions. The soot-forming network undergoes a percolation-like organization of its pathways before soot inception. The network then continues to grow by adding connections through its influential nodes. Acetylene is identified as a highly influential node in the carbon transfer graph, with its influence increasing with pressure.

This paper details the data-driven modelling and feedback control of vortex shedding past a circular cylinder at a Reynolds number of Re = 1000. We study the effect of varying the order of the reduced model for control design purposes and demonstrate that higher orders can lead to lower suppression of vortex shedding. We use the Bode integral theorem and a frequency-domain interpretation to show that this drop in performance is, in part, due to the classical ``waterbed effect'', which increases sensitivity in frequency bands of unmodelled dynamics. Training data from 2D unsteady simulation is used to obtain linear reduced-order state-space models of the system via dynamic mode decomposition with control. Using only lift measurement, we show that at least a 4th-order model is required for an LQG controller to suppress vortex shedding, with the best performance achieved with as few as 9 modes, whilst higher-order (>14) controllers show a significant decrease in performance. We study the influence of external disturbances, noise rejection, and parameter uncertainty on controller performance. A 28.6 dB reduction in lift coefficient variance is achieved, resulting in a 26% reduction in drag. We further show that, for control design purposes with practical actuation bandwidth, the closed-loop control delivers a significant 13.7% drag reduction within 3D DDES, despite having been trained with 2D URANS and therefore argue that 2D URANS simulation is sufficient for reduced-order model generation and control design.

The Sandia one-meter methane fire plume is an established benchmark for turbulent combustion modeling of large-scale flames. This study investigates the combustion instabilities formed close to the base of the Sandia fire plume. Finite rate chemistry and differential diffusion are considered using a flamelet/progress variable (FPV) approach. The performance of the FPV approach is assessed by comparing with the eddy dissipation model (EDM) and the experimental data for the large-scale fire plume via large eddy simulations (LES). The effects of radiation modeling and mesh resolution on the predictive capability of the model are systematically investigated by comparing the axial and radical velocities against the experimental data at various locations. Although all models successfully capture the primary flow characteristics of fire plumes, the FPV model with differential diffusion yields improved predictions in the near-flame-base region. The formation mechanism of cellular flow structures near the flame base is investigated via a budget analysis of the vorticity equation, and the type of instability governing the formation of the cellular structure is clarified. Finally, the individual effects of finite rate chemistry and differential diffusion on the prediction of the thermo-chemical quantities are quantified. Overall, this study explains the underlying physics governing combustion instabilities at the base of turbulent fire plumes, provides novel insights into the performance of flamelet models for LES of gaseous pool fires, and offers reliable guidance for the high-fidelity numerical simulation of large-scale turbulent buoyancy driven flames.

A self-contained hydrodynamic theory is proposed to reconcile the discrepancy between divergent Stokesian velocity fluctuations and finite experimental measurements in sedimenting suspensions. We show that the compensating backflow induces non-negligible inertia, giving rise to an emergent screening length $\xi \sim a\phi^{-1/3}Re_p^{-1/3}$ far exceeding the mean interparticle spacing $a\phi^{-1/3}$ even at vanishingly small particle Reynolds numbers. This backflow inertial screening, together with finite-time viscous diffusion, arrests the indefinite spatiotemporal growth of large-scale velocity fluctuations. The resulting velocity fluctuations scale as $\delta u \sim \phi^{1/3}V_sRe_p^{-1/6}$, together with the viscous correlation time $\tau_c=\xi^2/\nu$, reproducing the well-known hydrodynamic self-diffusivity scaling $D_H\sim V_s a$. The theory predicts the prefactors of these scaling laws without adjustable parameters, in good quantitative agreement with experimental measurements. It also successfully captures the experimentally observed crossover from the finite-correlation regime to the finite-system regime as the screening length becomes comparable to the system size.

We extend the generalized anomalous diffusion framework established in Part I to the short-range forcing regime ($\beta > 2/3$), where the multiscale-force dominated (MFD) subrange is intercalated after the inertial subrange, competing directly with the dissipation ranges. Focusing on electrokinetic (EK) turbulence as the prototypical example with $\beta=1$, we derive the relations for the velocity and scalar dissipation wavenumbers, $k_{MD}$ and $k_{SD}$, across all four subranges of the Quad-cascade process (inertial, constant-$\Pi_u$, constant-$\Pi_s$, and variable flux). By incorporating Golestanian's predicted anomalous diffusion regimes for electrolytes, we construct comprehensive phase diagrams showing how the relative magnitudes of $k_{MD}$ and $k_{SD}$ are governed by the scale-dependent anomalous Schmidt number $Sc_Z$. We identify two new spectral subranges that emerge exclusively in this short-range forcing regime: (i) the convective-viscous subrange ($k_{MD} \ll k \ll k_{SD}$) of velocity spectrum for $Sc_Z \gg 1$, where the scalar field drives a viscous flow yielding $E_u \sim k^{-\left(\frac{3}{2} + \frac{\xi_s}{2}\right)}$ with a stretched-exponential cutoff; and (ii) the diffusive-forcing subrange ($k_{SD} \ll k \ll k_{MD}$) of scalar spectrum for $Sc_Z \ll 1$ and $\gamma \leq \alpha$, where the scalar dissipation range determines the electric forcing, leading to $E_s \sim k^{\xi_u - 2\alpha}$. These results provide a complete analytical map of EK turbulence under anomalous diffusion, revealing how external parameters such as electric field strength and ionic diffusivity determine the cascade topology.

We present a theoretical model for momentum--scalar coupled turbulence in which both fields undergo anomalous diffusion, described by fractional biharmonic operators of orders $\gamma/4$ and $\alpha/4$, respectively. Focusing on the long-range external forcing or unforced turbulence, we derive analytical expressions for the kinetic energy spectrum $E_u(k)$, the scalar spectrum $E_s(k)$, and the characteristic wavenumbers $k_K = \left( \frac{\epsilon_u^{1/3}}{c_u} \right)^{1/(\gamma - 2/3)}$ (reciprocal of Kolmogorov scale) and $k_S = \left( \frac{\epsilon_u^{1/3}}{c_s} \right)^{1/(\alpha - 2/3)}$ (reciprocal of scalar dissipation scale) as functions of $\gamma$, $\alpha$, turbulent dissipation rate $\epsilon_u$, diffusivities of momentum ($c_u$) and scalar ($c_s$), respectively. An anomalous Schmidt number $Sc_Z = k_0^{\gamma - \alpha} \frac{c_u}{c_s}$ is defined to governs the cascade topology. It describes the ratio of diffusion times of scalar and momentum on the minimum wavenumber $k_0$. Superdiffusion ($\gamma<2$ or $\alpha<2$) is shown to counter-intuitively enlarge $k_K$ and $k_S$, broadening the inertial range. The theory unifies the classical Kolmogorov--Obukhov--Corrsin--Batchelor scalings as special cases when $\gamma=\alpha=2$, and provides a foundation for understanding non-Fickian transport in complex turbulent systems.

The linearity of the Stokes equations organises the hydrodynamic response of a rigid particle into a hierarchy of resistance operators, coupling successive truncations of the ambient-flow jet to moments of the surface traction. Since the work of Kelvin and Larmor, it has been known that this response does not resolve particle geometry faithfully: bodies with discrete rotational symmetry may be indistinguishable from bodies of revolution (Brenner's helicoidal symmetry) and a chiral body may respond isotropically, as in Kelvin's isotropic helicoid. We regard the resistance operators as elements of finite-dimensional O(3)-representation spaces and use character formulae to determine, at every level of the hierarchy, which point-group symmetries are hydrodynamically distinguishable and the dimension of each invariant space. This yields an explicit nested sequence of hydrodynamic symmetry-group sets, from the translation-force level to the quadratic-flow level. The framework reveals hydrodynamic classes that no shape can realise geometrically, gives helicoidal symmetry a level-dependent definition, and shows that polyhedral symmetry becomes visible in a strict order: tetrahedral symmetry in shear, octahedral symmetry through the stresslet, and icosahedral symmetry in quadratic flow. Projecting the resistance operators onto force- and torque-free motion provides symmetry-based parameter counts and a constructive route to the corresponding dynamical normal forms. We thereby complete the Jeffery-Bretherton-Ishimoto classification, characterise all hydrodynamic classes producing Jeffery dynamics, and identify chiral tetrahedral and octahedral normal forms that can generate irregular full-attitude dynamics.

Nonlinear terms present a fundamental challenge for quantum computational fluid dynamics, as their implementation on inherently linear quantum hardware typically requires resource-intensive workarounds that limit scalability to large-scale simulations. We present a hybrid quantum-classical tensor network algorithm that addresses this bottleneck by combining variational time-stepping with quantum tensor programming to efficiently compile operators and time-dependent fields into quantum circuits. Within a probabilistic framework, we replace prior state-based nonlinear implementations with tensor-based block encodings, stabilizing success probabilities that otherwise decay exponentially with system size. Benchmarking on turbulent flow fields demonstrates that the algorithm maintains high success probabilities and moderate measurement overhead across increasing Reynolds numbers and grid resolutions. Compared to fully classical tensor network solvers, our hybrid approach yields substantial reductions in both memory footprint and computational cost, establishing a scalable pathway toward practical quantum advantage in scale-resolving CFD simulations.

We propose a hybrid sharp-diffuse interface representation for modeling intermittent and isolated topological transitions during Cahn-Hilliard phase coarsening. Away from topological events, the evolution is approximated by the Mullins-Sekerka sharp-interface limit system and computed using a boundary integral formulation. When diffuse transition layers overlap, a novel interface surgery algorithm resolves topology changes through a localized Cahn-Hilliard pseudo-time evolution, after which the sharp-interface calculation is resumed. We develop the mathematical formulation underlying this decomposition, present a simple two-dimensional numerical implementation, and simulate a mass-exchange problem with interface coalescence. By localizing the diffuse evolution to topological events, the method achieves a speedup of two to three orders of magnitude over conventional diffuse-interface simulations.

Using monthly Niño-3.4 anomalies through July 2026, we investigate how much predictive information is contained in delayed observations of the index. Ridge regression identifies informative delays, while multilayer perceptron and sparse identification of nonlinear dynamics (SINDy) models test whether nonlinear complexity provides additional direct forecast skill; gated recurrent unit (GRU) and long short-term memory (LSTM) networks provide a complementary test in which the temporal representation is learned internally. Delayed observations substantially improve forecasts over persistence and climatology at leads of up to six months, but increasing model complexity provides no systematic improvement. Historical recursive experiments favor a simple explicit SINDy recurrence and select shallow recurrent architectures, with no appreciable gain from learning the temporal representation internally. These results support a compact predictive representation of Niño-3.4 evolution in which the representation of past information is more consequential than model complexity. As a prospective application, the selected models are used to forecast the developing 2026 event beyond the last available observation and to compare its predicted evolution with completed historical El Niño events.

In oscillator networks sustained by finite resources, synchronization can depend on both the total resource and its spatial distribution. We study a duplex system whose activity layer consists of chaotic Hindmarsh--Rose oscillators and whose transport layer redistributes a conserved resource through a degree-biased Markov process. The stationary resource field is characterized analytically, and its existence, uniqueness, and convergence are established. By embedding this field into a local adaptive feedback law, the available resource is converted into node-dependent dissipation, for which Lyapunov analysis guarantees convergence to the synchronization manifold. Numerical results show that topology bias reorganizes the transient route to synchronization. Weak bias produces an almost collective contraction, whereas intermediate bias creates a hub-initiated recruitment hierarchy that extends toward middle-degree and peripheral nodes. Under stronger bias, the degree hierarchy becomes more pronounced while peripheral recruitment slows because adaptive dissipation is concentrated on structurally privileged nodes. Across the explored parameter range, this localization--coverage tradeoff is accompanied by a non-monotonic synchronization response at fixed total resource. The largest Lyapunov exponent remains positive after synchronization and the correlation dimension changes only modestly, consistent with suppression of transverse deviations while chaotic motion is retained on the synchronization manifold.

We predict a new type of stable three-dimensional (3D) vortex quantum droplets in binary Bose-Einstein condensate arranged into ring clusters that per-sistently rotate in the external potential. In contrast to clusters composed from localized quantum droplets, the states introduced here represent interacting vortex lines with identical topological charges nested in common 3D envelope and existing in much broader parameter range in comparison with local-ized quantum droplets. The intricate interplay between mean-field nonlinearity of Bose-Einstein condensate, quantum fluctuations described by Lee-Huang-Yang correction, Coriolis force arising due to rotation, and external potential leads to substantial variations of cluster shape upon increase of its rotation frequency. Rotating vortex clusters bifurcate from single-vortex quantum droplets and exist only above critical value of the rotation frequency that decreases with increase of chemical potential and depends on the number of vortex lines in the cluster. The radius of the cluster decreases with increase of rotation frequency and weakly varies with chemical potential, which determines mostly localization of the individual vortices in cluster and overall width of its envelope. Vortex droplet clusters are very robust objects existing in stable form in wide intervals of the number of particles for any number (odd or even) of vortex lines forming them. Our results may open the route to observation of stable arrays of vortex lines of different configurations per-forming regular collective motion in condensate.

Spatial patterns, such as those in dryland vegetation models, have historically been studied in systems of reaction-diffusion systems with pattern onset via a Turing bifurcation from a spatially uniform state. More recently, spatial patterns have been considered in models that incorporate spatially extended interactions via nonlocal interaction kernels. It remains largely underexplored if and how the choice of nonlocal interaction kernel contributes to differences in pattern formation and persistence, particularly in models that contain competition and facilitation. Here, we investigate spatial patterns in a reaction-diffusion model for a single species that includes nonlocal competition and facilitation processes; Gaussian, exponential, algebraic, hat, and smooth hat kernels are considered as specific examples. Via a center manifold analysis, and using the relative spatial scale of competition to facilitation and the death rate as bifurcation parameters, we identify that the choice of kernel has impacts on the pattern forming bifurcation. Bifurcations using the Gaussian, exponential, and algebraic kernels largely follow expectations of Turing patterns, but patterns in the hat and smooth hat kernels can form even when the scale of competition is less than that of facilitation. The dynamics of patterns far from onset are investigated via numerical continuation methods. The model produces the so-called "Turing-before-Tipping" phenomenon demonstrating that the arrangement into spatial patterns is an effective resilience mechanism against harsh conditions. Again, there is a kernel-dependent dichotomy in pattern behavior. Early warning signs for population extinction are observed with the Gaussian, exponential, and algebraic kernels, but not under the hat or smooth hat cases.

Bright dissipative Kerr solitons generated in anomalous-dispersion microresonators underpin integrated optical frequency combs that have enabled applications including precision metrology, spectroscopy, coherent communications, and optical frequency synthesis. In contrast, Kerr resonators operating in the normal-dispersion regime can support dark solitons and platicons, but even the initiation of frequency comb generation typically requires auxiliary mechanisms, such as avoided mode crossings or pulsed pumping, to satisfy the phase-matching condition for four-wave mixing. Here we show that topological edge states in two-dimensional Kerr resonator lattices intrinsically satisfy this phase-matching condition, enabling the generation of optical frequency combs and novel coherent dissipative structures in the normal-dispersion regime without any auxiliary mechanisms. The resulting frequency combs self-organize into collective dark solitons that exhibit large-scale spatiotemporal synchronization across multiple resonators at the entire lattice edge. By tuning the pump detuning, we demonstrate the continuous evolution of topological dark solitons into topological platicons while preserving collective synchronization. Remarkably, we show that the topological lattice also supports collective bright-like soliton states despite all constituent resonators operating in the normal-dispersion regime. Our results establish topological Kerr resonator arrays as a versatile route for engineering a broad family of coherent dissipative structures, ranging from dark solitons to bright-like soliton states, within a single platform. They also provide a route toward integrated frequency-comb generation in material platforms and wavelength ranges where normal material dispersion has traditionally constrained comb generation in conventional single-resonator systems.

Can a source radiate when its total charge density vanishes identically? Consider a uniformly polarized sphere coated with free surface charge that cancels the bound surface charge at every point and time. Then $\rho_{\mathrm{tot}}=0$, so every electric charge multipole vanishes. Continuity determines only $\nabla\cdot\mathbf{J}$, which allows the same charge history to be supported by different conserved currents. A compensating interior current gives $\mathbf{J}_{\mathrm{tot}}=\mathbf{0}$ and produces no $\mathbf{E}$ or $\mathbf{B}$ at any frequency. The minimum-norm tangential sheet current instead leaves $\mathbf{J}_{\mathrm{tot}}$ nonzero and divergence-free. Its radiation-zone field is exact in $kR$ and proportional to $j_2(kR)$. At long wavelength the radiated power is suppressed by $(kR)^4/100$, and it vanishes exactly at the positive roots of $j_2$. The same calculation gives the interior field and a closed-form energy balance. The average work supplied by driving equals the radiated power and falls to zero at those roots even though interior fields remain. For comparison, the bare sphere has the factor $3j_1(kR)/(kR)$ and is silent at the roots of $j_1$.

Wicking in a capillary tube could happen as long as the liquid contact angle is smaller than 90 degree, making it possible for weak hydrophilic liquids to spontaneously invade the tube. For textured surfaces, energy minimization argument predicts the same. However, wicking of weak hydrophilic liquids on textured surfaces has not been possible due to energy barriers induced by the textures. We demonstrate how these barriers could be avoided by adjusting the shape and arrangement of the pillars, thus the wettability required for wicking reaches the theoretical limit. An unprecedented wicking contact angle of 82 degree is reported. More surprisingly, wicking coefficients of such surfaces can be larger than that of rectangular grooves at the same porosity. These findings may significantly advance biomedical and thermal management technologies.

AC nanocalorimetry was used to measure the reversing heat capacity Cp of low energy indomethacin glasses as they isothermally transform into the supercooled liquid. As the film thickness increases from 75 to 600 nm, the transformation time increases by more than an order of magnitude, consistent with a surface-initiated transformation mechanism. Eventually, the transformation time becomes constant for films between 1.4 and 30 microns indicating a distinct bulk transformation pathway. The observation of size-dependent transformation kinetics for glass samples approaching 1 micron is unprecedented. We interpret the crossover in thickness dependence at 1 micron to signify the average distance between transformation initiation sites in the bulk low energy glass.

In situ AC nanocalorimetry was used to measure the reversing heat capacity of vapor-deposited glasses of decahydronaphthalene (decalin). Glasses with low heat capacity and high kinetic stability, as compared to the corresponding liquid-cooled glass, were prepared from cis-decalin and from several cis/trans-decalin mixtures. This is the first report of highly stable glass formation for molecular mixtures. The 50/50 cis/trans-decalin mixture is the highest fragility material reported to produce an ultrastable glass. The 50/50 mixture exhibited high kinetic stability, with an ~500 nm film deposited at 116 K (0.86 Tg,) displaying a transformation time equivalent to 104.4 times the structural relaxation time of the supercooled liquid at the annealing temperature. Cis-decalin and the decalin mixture formed stable glasses that had heat capacities as much as 4.5% lower than the liquid-cooled glass.

We performed constant strain rate deformation and stress relaxation on a poly(methyl methacrylate) glass at Tg - 19 K, utilizing three strain rates and initiating the stress relaxation over a large range of strain values. Following previous workers, we interpret the initial rate of decay of the stress during the relaxation experiment as a purely mechanical measure of mobility for the system. In our experiments, the mechanical mobility obtained in this manner changes by less than a factor of 3 prior to yield. During these mechanical experiments, we also performed an optical measurement of segmental mobility based upon the reorientation of a molecular probe; we observe that the probe mobility increases up to a factor of 100 prior to yield. In the post-yield regime, in contrast, the mobilities determined mechanically and by probe reorientation are quite similar and show a similar dependence upon the strain rate. Dynamic heterogeneity is found to initially decrease during constant strain rate deformation and then remain constant in the post-yield regime. These combined observations of mechanical mobility, probe mobility, and dynamic heterogeneity present a challenge for theoretical modeling of polymer glass deformation.

The capillary rise of simple passive fluids in a tube is controlled by the force balance between surface tension and gravity --Jurin's law of capillary action. For fluids composed of active particles interacting via pairwise forces, mechanical surface tension is negative, but a capillary rise was nevertheless reported and remains unexplained. We establish the active form of Jurin's law from the microscopic dynamics. It includes a drag emerging from particle currents that we find responsible for capillary rise. These active currents, alongside negative surface tension, lead to complex and counterintuitive capillary action phenomena that are impossible in equilibrium. In particular the capillary rise of active fluids depends on the shape of the tube, not solely on the tube diameter.

We harness two established ingredients for collective demixing: differential speed and curvature to create a self-sorting device. In binary mixtures, motility differences drive spontaneous spatial segregation, while confinement geometry determines how rapidly and strongly this demixing develops. Using particle based simulations, we systematically identify the geometrical conditions that promote efficient segregation and use these results to guide the design of a finite sorting architecture. We then translate these physical mechanisms into a sequence of curved microfluidic units that progressively amplify the separation of the two species and direct them toward distinct collection regions. Experiments with binary Quincke-roller mixtures confirm that an initially mixed suspension progressively demixes as it propagates through the device, leading to strong enrichment downstream. Our results demonstrate how collective active demixing can be converted into a functional continuous sorting strategy, providing a route toward autonomous microfluidic separation based on particle motility and confinement geometry.

Inspired by the classical Plateau-Douglas problem for soap films bounded by two closed curves, we solve an analogous problem for fluid interfaces with fixed surface area and resistance to out-of-plane bending. The boundaries are planar but need not be symmetric or concentric. The equilibrium surfaces minimize the Willmore bending energy and generalize minimal surfaces such as the catenoid while also exhibiting characteristic features of confined elastic interfaces such as buckling. We systematically classify all possible buckling modes and solution branches by performing a weakly nonlinear analysis and developing a fully nonlinear spectral solver. Our mathematical framework provides insight into the forces and torques required to stabilize cellular membranes and other soft materials and shows that physically relevant asymmetric states can arise even in symmetric systems.

We report a study of the emergent dynamics arising in two-dimensional suspensions of semi-flexible chains whose tip is chemically active, generating a phoretic field. By varying the chain length (number of monomers per chain $N_{pc}$), the area fraction $\phi$, and the sign of the phoretic coupling $J_0$, we map out a rich non-equilibrium phase diagram in the presence of phoretic interactions. For repulsive phoretic interactions ($J_0 > 0$) between the chains, we find that short chains ($N_{pc} = 2$) develop a transient chaotic flow state that crosses over at long times to a global polar flock with super-diffusive mean-squared displacement and long-ranged velocity correlations. Surprisingly, we find this state to have suppressed density fluctuations, indicating the emergence of hyperuniformity. At intermediate chain lengths ($N_{pc} \sim 4$-$8$), the repulsive chemical field drives chaotic mesoscale flows -- a dry route to active turbulence -- without the need for hydrodynamic interactions or steric alignment interactions. For attractive phoretic interactions ($J_0 < 0$), chains self-organise into hedgehog-like micellar aggregates with heads forming the core and flexible tails radiating outward, in structural analogy with amphiphile micellisation but driven entirely by non-equilibrium self-propulsion. A coarse-grained theory of a tip-emitting active rod predicts the onset of the flocking of dimers, though overestimates the presence of polar order for longer chains. Our results establish phoretic tip activity as a minimal, experimentally realisable mechanism for a spectrum of collective states hitherto attributed to hydrodynamic interactions or steric alignment.

Ion channels and pumps drive ion-selective currents through cell membranes at localized sites, yet a cell's electrical state is routinely summarized by a single transmembrane voltage. Combining theory and numerical simulations, we resolve the spatiotemporal dynamics of charge reorganization driven by a localized current on a spherical membrane vesicle. At early times, the response is insensitive to membrane geometry: as in the case of a flat membrane ( arXiv:2407.11947 ; arXiv:2508.14001 ), the transmembrane voltage decays in a monopolar fashion, varying inversely with distance from the source, and crosses over to a dipolar tail that scales as the inverse cube of distance. Under sustained current, this monopolar response spreads outward from the source. Because the vesicle is closed, this response cannot persist indefinitely; once the monopolar front traverses the entire vesicle, the subsequent charging dynamics is dominated by a spatially uniform mode corresponding to capacitive charging of the membrane. We further decompose the bulk potentials into an electrostatic image-charge component that generates the bulk electric fields and a spatially uniform capacitive mode that can be represented as an equivalent circuit. We also derive a nonlocal cable equation governing the transmembrane voltage dynamics and show that the uniform mode is its long-time solution. This work provides a first-principles basis for the electrophysiological simplification of an electrotonically compact cell.

We present a kinetic Monte Carlo (KMC) modeling approach to describe the stochastic dynamics of a peptide molecule spanning nanosecond to second timescales. The dynamics of protein conformational changes is interpreted at a local level in terms of dihedral transitions. Taking Trp-cage miniprotein as an example, the KMC model "learns" about the transitions from multiple MD trajectories. Training is based on local divide-and-conquer strategy that identifies the discretized backbone dihedral states as building blocks for the conformational space, along with associated transition rates of dihedral flips to describe the conformational state-to-state dynamics. A key feature in our approach is the incorporation of backbone correlations, such that rates are conditioned on the local environment and steric coupling. We show that with the correlations built-in, the KMC model closely matches MD. Such an approach is shown to reach second timescales in a few CPU hours on a standard desktop computer, and can easily yield multiple stochastic realizations of the conformational dynamics. Our KMC model construction scheme should be generally applicable to a wide range of proteins, and can be used for bridging local flexibility to protein-wide dynamics.

We present a reduced-order semi-analytical model for reorientational nonlinearity in chiral nematic liquid crystals, showing that the chiral pitch acts as the dominant physical length scale governing the onset of nonlinear self-focusing and soliton formation. Starting from the full Frank-Oseen equation, we derive a closed-form expression for the optically induced molecular rotation that captures the essential saturable response of the medium while reducing computational cost by more than two orders of magnitude compared with standard relaxation-method solvers. Despite its simplicity, the model reproduces the essential features of the numerically obtained nonlinear refractive index, the onset of self-localization, and the transition from discrete to continuous solitons in one and two dimensions. It further predicts the formation of fully localized astigmatic nematicons with only minor shifts in the self-localization threshold due to the neglect of nonlocal effects. The proposed model provides direct physical insight into light-matter interactions with soft matter media and offers a computationally efficient tool for the design and optimization of nonlinear photonic devices.

We investigate the impact of charge regulation (CR) on the non-uniform swelling behavior of polyelectrolyte hydrogels. The Poisson-Boltzmann theory with electro-elastic coupling between the local polymer density and elastic deformation is considered. We investigate the spatial distributions of the elastic displacement and polymer density under different salt concentrations and compare charge-regulated gels with fixed-charge (non-CR) gels of the same net charge. Our results show that the CR induces spatially varying charge fractions, which strengthen the electro-elastic response and lead to stronger non-uniform swelling compared with non-CR gels. These findings provide a theoretical basis for understanding and controlling non-uniform swelling in responsive polyelectrolyte hydrogels.

For decades, debate has surrounded the electrostatic persistence length (EPL) controlling local polyelectrolyte stiffening, centered on two competing power laws: the linear BJ prediction, $\textbf{l}_\mathrm{e} \sim r_\mathrm{D}$, and the quadratic OSF/KK scaling, $\textbf{l}_\mathrm{e} \sim r_\mathrm{D}^{2}$, where $r_\mathrm{D}$ is the Debye screening length. Building on the asymptotic scaling theory developed in the accompanying paper, we validate a complete diagram of limiting regimes using large-scale coarse-grained Monte Carlo simulations of ideal chains with charged monomers interacting through a screened Coulomb potential. By simulating long chains of up to $N \simeq 10^{4} - 10^{5}$ Kuhn segments, we demonstrate that the electrostatic stiffening of both semiflexible and flexible polyelectrolytes obeys the same quadratic OSF/KK law. We track the exponent $\alpha$ which measures how the chain size $R$ grows with the Debye radius, $R \sim r_\mathrm{D}^{\alpha}$. For both cases, in agreement with the OSF/KK theory, $\alpha$ rises past 3/5 and slowly approaches 1 as the chain length increases, whereas within the BJ theory it can never exceed 2/5. We further find that three common size measures, the end-to-end distance $R_\mathrm{ee}$, radius of gyration $R_\mathrm{g}$, and hydrodynamic radius $R_\mathrm{h}$, reach this asymptotic behavior at progressively increasing chain lengths. Consequently, for any real polyelectrolyte, the apparent exponents obey $\alpha_\mathrm{ee} \geq \alpha_\mathrm{g} \geq \alpha_\mathrm{h}$, making $R_\mathrm{g}$ a sharper experimental probe than $R_\mathrm{h}$. Finally, we re-analyze the available experimental data and show that they rule out the linear BJ law and support the quadratic KK scaling, thereby resolving contradictions that stem from mistaking the apparent slopes measured for short chains for the true asymptotic exponent.

The problem of single-chain conformations of polyelectrolytes in salt-added dilute solutions, and the associated concept of the electrostatic persistence length $\textbf{l}_\mathrm{e}$, has remained unresolved for decades. To address this challenge, we develop a comprehensive scaling theory and corroborate it with simulations. A unified scaling diagram is constructed that encompasses both flexible and intrinsically semiflexible/stiff polyelectrolytes. Nine distinct scaling regimes are identified, each characterized by different conformational statistics. The concept of the Gaussian electrostatic blob $\xi_\mathrm{e}$ used in the description of flexible polyelectrolytes is extended to the semiflexible case, and the new characteristic length $\xi_\mathrm{e}^{|}$ referred to as the rodlike electrostatic blob is introduced. This enables delineating the important crossovers and showcasing an analogy between semiflexible and flexible chains. The concept of electrostatic excluded volume is also reconsidered and generalized. Upon increasing the salt concentration, i.e., decreasing the Debye length $r_\mathrm{D}$, chain conformations evolve from (i) rodlike stretches to (ii) Gaussian and then (iii) swollen coils with local electrostatic stiffening characterized by $\textbf{l}_\mathrm{e}$, followed by (iv) swollen coils without stiffening but with electrostatic exclude volume, and finally to (v) quasi-neutral Gaussian coils. In regimes of type (ii) and (iii), the electrostatic persistence length scales quadratically with $r_\mathrm{D}$, in agreement with the OSF and KK predictions for semiflexible and flexible chains, respectively: $\textbf{l}_\mathrm{\mathrm{OSF}} \simeq r_\mathrm{D}^{2}/\xi_\mathrm{e}^{|}$ and $\textbf{l}_\mathrm{\mathrm{KK}} \simeq r_\mathrm{D}^{2}/\xi_\mathrm{e}$. These asymptotic scalings are confirmed by coarse-grained simulations presented in the accompanying article.

Excitation-energy transfer underpins the conversion of light into usable energy in photosynthetic organisms and serves as a paradigm for evolutionary optimized transport in open quantum systems. Although this process is often described as incoherent thermally assisted hopping, such descriptions become inadequate when electronic coupling, vibronic interactions and environmental fluctuations occur on comparable energy scales. Determining how the environment controls transport therefore remains a fundamental challenge. Here, we use temperature-dependent 2DES to investigate energy transfer in the photosynthetic antenna protein allophycocyanin over the range 10 - 296 K. The dominant $\beta \rightarrow \alpha$ transfer step exhibits a pronounced non-monotonic temperature dependence: the transfer time decreases from 400 fs at 10 K to 200 fs near 30- 40 K before increasing again to 400 fs at 296 K. In contrast, the homogeneous optical dephasing time decreases monotonically across the same temperature range. To interpret these observations, we model APC as a vibronically coupled excitonic dimer interacting with a structured environment and solve the dynamics using hierarchical equations of motion. Conventional fixed-bath models, including Drude-Lorentz and explicit intermolecular-mode spectral densities, fail to reproduce the observed turnover. Quantitative agreement is obtained only when the low-frequency sector of the environmental spectral density is allowed to anharmonically evolve strongly with temperature, while the high-frequency bath remains essentially unchanged. More broadly, these findings demonstrate that transport efficiency is controlled not simply by the magnitude of environmental fluctuations, but by the distribution of environmental spectral weight across frequency space, providing new experimental constraints on theories of molecular transport in complex quantum environments.

Biomolecular condensates can undergo striking changes, such as transitioning from a liquid-like to a gel- or a solid-like aggregate due to changes in molecular interactions in response to changes in the biochemical environment. The question of how modified molecular interactions lead to such a transition in the material properties and spatial organization of condensates has not yet been elucidated. To address this question, we represent the biochemical environment as a triphasic mixture comprising a liquid-like protein-rich phase, a network-like protein-rich phase, and solvent. Owing to a change in the biochemical environment, protein molecules can reversibly switch between two conformational states. In a switched conformational state, the cross-linking domains of molecules are exposed which promote transient network formation in phase separated states. We develop a transient-network model and a continuum framework that couples phase separation, molecular switching, and dynamic cross-linking to predict condensate morphology and mechanics. The transient-network model predicts that a non-aging network behaves like a Maxwell fluid. When a network slowly ages via stabilization of cross-links, it shows Maxwell-like behavior and waiting time-dependent relaxation. However, a strongly aged network shows elastic recoil like characteristic of a Kelvin-Voigt solid. Our coupled continuum model demonstrates that the interplay of molecular switching and dynamic cross-linking in network formation shapes the spatial organization of condensate phases. In summary, this work demonstrates a mechanistic route explaining how conformational switching and molecular cross-linking regulate material properties and morphology of condensates.

Odd viscosity, the nondissipative part of the viscous response of a time-reversal-broken fluid, is notoriously difficult to measure precisely because it does no work. Here we show that parity-time ($\mathscr{PT}$) symmetry, familiar from non-Hermitian optics, converts this elusiveness into a measurement principle. The odd Navier-Stokes equations, that include the nonlinear inertial terms, are $\mathscr{PT}$-symmetric, follow from a Lagrangian, and linearize to a Schrödinger equation in which the odd viscosity plays the role of Planck's constant; potential vorticity obeys a generalized Ertel conservation law. A probe trapped in an odd liquid realizes a pair of oscillators coupled by odd friction, and supplying balanced loss and gain drives a twofold $\mathscr{PT}$ transition whose exceptional point and Rabi sidebands locate the odd viscosity with square-root-enhanced sensitivity. Upon quantization the spectrum is of Fock-Darwin form, and the dissipative pair exhibits a Liouvillian exceptional point separating linear from exponential heating. These results furnish mechanical, stochastic, and spectroscopic protocols for measuring odd transport coefficients in classical and quantum fluids.

Localized forcing in the fluid inside or outside a viscous drop can drive drop translation. Using the Lorentz reciprocal theorem, we derive an integral expression for the translational velocity of a spherical Newtonian drop subject to localized force and source distributions in either fluid and to interfacial traction. For a clean drop, we obtain explicit responses to Stokeslets, force dipoles, rotlets, general second force moments, and source dipoles as functions of position, orientation, and viscosity ratio. Interior forcing obeys a finite selection rule: only force moments through second order and the first source moment contribute directly to translation. Exterior forcing can couple to multipoles of all orders and produces distance-dependent responses. Although different enclosed singularities can produce the same drop velocity, resolving their exterior flows in drop-centered spherical Stokes modes provides additional constraints on the underlying forcing. We also distinguish regularized force distributions, governed by prescribed kernel moments, from resolved rigid particles, governed by low-order surface-traction moments and prescribed slip. The framework unifies these representations and shows how exterior-flow measurements provide information beyond drop translation, laying the foundation for constructing squirmer-like viscous drop solutions with controllable far-field behaviors.

Separation of low-abundance biological objects requires high throughput for practical use of an acoustofluidic system. Increasing the flow rate helps in achieving high-throughput if the acoustic energy density can be increased proportionally, and this may be possible with an efficient coupling of the transducer to the device. In particular, antisymmetric actuation using two electrodes with opposite phases is theoretically proven to enhance the acoustic energy density of the device. In this work, we study the symmetric and antisymmetric actuation mechanisms of an acoustofluidic system using both experiments and three-dimensional numerical simulations. The acoustic focusability experiments show that under the same electrical input power, the antisymmetric actuation mode performs better than the symmetric actuation, quantified in terms of the normalized width of the band formed by the focused particles. Numerical simulations of this particle bandwidth are performed for both actuation modes, and the results suggest that the antisymmetric actuation mode is more robust than the symmetric one, being weakly dependent of the geometric symmetry properties of the system. The simulation results corroborate the experimental findings, which indicate that the antisymmetric actuation increases the acoustophoretic efficiency and robustness for high-throughput applications.

A salient feature of fully turbulent flows far from onset is the intermittent occurrence of extreme fluctuations at small spatial and temporal scales. These have a qualitative and quantitative effect on the instantaneous curvature of a tracer particle trajectory as an intrinsically multi-scale observable. Here, we provide a complete statistical description of the curvature of tracer particle trajectories in turbulent flows that includes and quantifies intermittency effects. We derive an exact expression and a closed-form approximation for the curvature probability density function, both agree well with data obtained from laboratory experiments of different types of turbulent flows, and quantify the generic behavior of the system. The method can be extended to more complex systems such as plasma turbulence.

Simulations of surface-tension-dominated incompressible two-phase flows are computationally expensive due to the severe capillary time-step constraint. Although many studies have proposed time-implicit discretizations of surface tension to allow larger time-step sizes and accelerate simulations, these methods suffer from either artificial dissipation or complex implementation. Here, we propose a simple and novel approach: an incompressible solver with weakly compressible subcycling. The proposed approach relaxes the capillary time-step constraint, thereby accelerating simulations by more than $8.6\times$ without relying on artificially dissipative stabilization or requiring complex implementation. The key idea is to introduce lightweight substeps using a weakly compressible solver to assist the main incompressible solver. These substeps enable the main incompressible solver to use accurately computed fluxes and surface tension force, even with large time-step sizes. Numerical tests demonstrate the effectiveness of the proposed approach for practical problems, including the Rayleigh--Plateau instability and two-phase flows in porous media. This study paves the way for a new paradigm in which a weakly compressible solver serves as an assistant to an incompressible solver.

We analytically analyse the dynamics of an internally actuated particle, modelled as a compressible elastic sphere embedded with a magnetic bead at its undeformed centre, translating in a plane Poiseuille flow in the Stokes limit. The particle is constrained to translate with a prescribed velocity while remaining at an arbitrary position within the flow by applying an external point force and external point torque at its undeformed centre. The governing equations for the fluid and particle are the Stokes and Navier elasticity equations, respectively. We use the series solutions to the governing equations and the domain perturbation method to capture the deformed shape of the particle, assuming $\alpha \ll 1$. Here, $\alpha$ quantifies the elastic strain induced in the particle due to the viscous stress from the fluid. The external force and external torque are obtained until O($\alpha^2$). The particle translating along the channel length experiences an elastic-induced hydrodynamic lift as well as hydrodynamic torque both at O($\alpha$) and O($\alpha^2$). The leading-order lift depends linearly on the local shear rate and on the combined effects of slip velocity and flow curvature, where the slip velocity is defined as the particle velocity relative to the local ambient flow. The particle reaches a stable equilibrium position away from the centreline, where the net lift vanishes. We show that the direction of deformation-induced lateral migration of the internally actuated particle is qualitatively distinct from that of drops, capsules, and vesicles in the Stokes limit and from that of rigid spheres undergoing inertial migration.

We investigate the effects of horizontal oscillations on the drafting--kissing--tumbling (DKT) dynamics of two monodisperse spherical particles settling under gravity in a viscous fluid. Applying particle-resolved direct numerical simulations, we systematically vary the oscillation frequency and amplitude to assess their impact on the behavior of individual particles, their mutual interaction, and the orientation of the particle arrangement. The results demonstrate that the oscillatory effects on DKT become significant only when the particle Reynolds number $Re_p$, defined as the ratio of oscillation-induced inertial to viscous forces, exceeds unity. In this regime, oscillations alter the temporal characteristics of the DKT process, with moderate amplitudes tending to prolong and larger amplitudes to reduce the kissing phase. Moreover, oscillations affect particle reorientation. At low $Re_p$, the particles maintain their initial orientation throughout the interaction, whereas an increasing $Re_p$ promotes a preferential alignment perpendicular to the direction of oscillation. We explain these findings by analyzing the oscillation-induced pressure fields surrounding the individual particles, which develop increasingly pronounced lateral anisotropy with increasing $Re_p$. The corresponding lateral hydrodynamic forcing likewise becomes increasingly anisotropic, providing a consistent physical basis for the observed modification of particle interactions and reorientation. These findings provide a physical framework for understanding how horizontal oscillations govern binary particle--particle interactions and orientation during gravitational settling.

Travelling-wave-like wall blowing and suction is an effective approach for enhancing heat transfer with a minimal pressure drag penalty. However, achieving such a dissimilar heat transfer enhancement effect in a passive manner remains a challenge. In the present study, we propose introducing parallel perforated plates to induce travelling-wave-like disturbances passively. Pore-resolving simulations of a spatially developing laminar flow between parallel perforated plates are performed across a wide range of Reynolds numbers of $Re = 500-1500$ and pore-to-solid length ratios of $L_\mathrm{p}/L_\mathrm{s} = 0-10$. Dissimilar heat transfer enhancement is confirmed for $9 \leq L_\mathrm{p}/L_\mathrm{s} \leq 10$ at $Re = 1000$ and $4 \leq L_\mathrm{p}/L_\mathrm{s} \leq 7$ at $Re = 1500$. The highest analogy factor, i.e., the ratio of the Stanton number to the friction coefficient is obtained at $Re = 1500$ and $L_\mathrm{p}/L_\mathrm{s} = 6$, yielding an increase of more than $30$\% compared to that of an impermeable solid plate. Analysis of the fluctuating fields shows that, in the travelling-wave flow regime, a pressure-induced wall-normal velocity fluctuation transports temperature fluctuations away from the perforated plate, while breaking the correlation between the streamwise and wall-normal velocity fluctuations. This enhances the turbulent heat flux relative to the Reynolds shear stress near the perforated plate. The present results indicate that introducing a perforated plate with a suitable porosity induces travelling-wave velocity disturbances and also achieves a considerable dissimilar heat transfer effect even at low Reynolds numbers where a standard impermeable flat wall yields a steady laminar flow.

A thin volatile film carrying N particle species of different sizes evaporates on a deep immiscible liquid subphase. The spreading coefficient is positive, so nothing pins. The film ends at a receding front whose motion falls out of the film equations; no contact-line law is imposed. We solve the lubrication problem with a conservative depth-integrated treatment of species transport, and the front turns out to be a chromatograph. Every species piles into a concentration spike at the front, each held there in proportion to its Péclet number. The smaller, more diffusive species leaks continuously into the fluid that survives the front's passage; the larger species is laid down along the sweep path. The dried deposit is the time-integrated record of that sweep, and it is sorted by size: small-rich centre, large-rich mid-annulus. Pinned bidisperse droplets sort the other way. Depinned droplets on solids sort this way, but by a force balance; here, diffusivity contrast alone picks the direction. Size enters the transport problem only through the Péclet number, so diffusivity contrast is the only symmetry-breaking available to choose a direction: Marangoni stresses, colloidal interactions and wetting effects act on the magnitude and, by the symmetry of the transport operator, cannot set the direction. Adjacent-species band separations scale with the difference in inverse effective Péclet number, a law derived and measured here: the resolution of the chromatograph. That scaling points to a route to size fractionation of polydisperse nanoparticles in the few-nanometre regime, exactly where standard methods struggle.

We derive an exact and novel expression for an averaged two-point correlation function in the statistically stationary, forced-dissipative two-dimensional Navier-Stokes equations subject to the Coriolis force under the beta-plane approximation. This identity is related to the so-called geostrophic balance: it connects the effect of the Coriolis force to the pressure gradient through a two-point correlation function. Additionally, we provide sufficient conditions under which the asymptotics of the averaged third-order structure function at large spatial scales follow the universal third-order law of two-dimensional turbulence in the absence of the Coriolis force. This complements our previous results on small spatial scales. Together, our results provide a clear picture of the role of the Coriolis force in beta-plane turbulence. On the one hand, the spherically averaged rates of enstrophy and energy transfer are not affected by the Coriolis force. On the other hand, the Coriolis force contributes to anisotropic large-scale organization by altering the spatial distribution of energy and promoting the formation of zonal structures. The proof relies on a new formulation of the Karman-Howarth-Monin relation. For the geostrophic balance, we use a novel antisymmetric projection of the KHM relation under which only the pressure and Coriolis terms survive. For the cascade laws, we show that the Coriolis contribution to the averaged classical KHM relation vanishes identically at any scale.

We consider turbulent flow in a half-space along an infinite plane. We regard it as the limit to which the motion in the viscous sublayer of turbulent near-wall flows tends as Reynolds number increases indefinitely. In addition to the no-slip condition, an averaged shear stress value is specified on the streamlined surface. A numerical solution algorithm is proposed, based on the well-known spectral method, which demonstrates that the boundary conditions on the wall along with the physically justified constraint that the velocity components do not grow exponentially at infinity uniquely determine the turbulent flow under consideration. The implementation of the algorithm will allow us to draw conclusions about the validity of the idea that the flow in the viscous and logarithmic sublayers is independent of the external parameters of turbulent near-wall flows.

In an ignited design of inertial confinement fusion, the role of mid-to-high-mode hydrodynamic instabilities in degrading hot-spot performance, beyond reducing temperature, remains unclear. To address this, we propose an isobaric criterion to assess the isobaric assumption that forms the theoretical basis of the hot spot. The most dangerous mode l = 12 is determined through a balance between perturbation growth and ablation stabilization induced by thermal conduction. Thermal conduction outperforms convection when the Peclet number is much less than 1. Therefore, for mid-to-high modes, thermal conduction makes the hot spot isobaric before the outer mass inflow restores the lost heat. Consequently, neglecting thermal conduction overestimates pressure and underestimates volume. These results enhance our understanding of mid-to-high modes in degrading hot-spot performance, and suggest that thermal conduction losses may reduce performance even if perturbations are nearly stabilized by ablation.

We investigate the propagation of counter-rotating convection rolls in Rayleigh-Bénard convection initiated locally in a quiescent fluid layer under supercritical conditions. The velocity of the front separating quiescent fluid from the forming convection rolls, and the wavenumber of the convection rolls remaining behind the front, are explored. We numerically investigate fronts of forming convection rolls over five orders of magnitude of the reduced Rayleigh number, $\epsilon$, in 2D and 3D domains, for a broad range of boundary conditions, and for different front initiation approaches. In all cases, the front velocity increases as $\epsilon^{1/2}$ with increasing $\epsilon$ for $\epsilon \lesssim 1$ in agreement with predictions using the amplitude equation. The amplitude equation description of the front velocity remains accurate for $\epsilon \lesssim 10$ except when the Prandtl number is large which yields a velocity that is faster than predicted for a fluid layer far from threshold. The wavenumber of the convection rolls increases linearly with $\epsilon$ in agreement with the wavenumber that maximizes the growth rate of perturbations in the linear regime. Farther from onset, the wavenumber growth transitions to a reduced scaling of $\epsilon^{1/4}$ in agreement with predictions using the Swift-Hohenberg equation in the large $\epsilon$ limit. The scalings describing the wavenumber variation with $\epsilon$ are independent of the domain geometry, boundary conditions, and front initiation method. However, the front-selected wavenumber at criticality does not equal the critical wavenumber of the bulk instability, in general, and depends significantly upon these details. We compare our results with experimental measurements where possible.

Multilevel non-volatile memory technologies face recurring trade-offs among information density, endurance, retention, and switching energy. We investigate an alternative state variable based on the discrete vortex configuration of self-organized vortices in a boundary-driven electron fluid. A dissipative point-vortex model derived from magnetohydrodynamic dynamics yields six reproducible vortex codewords, corresponding to 2.585 bits per cell, whose write fidelity, noise sensitivity, 100-cycle endurance, and effective information capacity are quantified. The ordering of their finite-amplitude basin radii $r_{50}$ differs from that predicted by both fixed-circulation and fully coupled linear-stability spectra. A nonlinear saddle-point construction based on the reduced dynamics likewise does not recover the measured basin ordering. The discrepancy is associated with escape pathways involving coupled position--circulation dynamics that are absent from the fixed-circulation description. These results show that local stability alone does not determine the finite perturbation tolerance of the vortex states considered here. The proposed memory requires active hold power, and passive retention remains to be established experimentally.

This work presents a new two-dimensional quantifier plane that combines normalized permutation entropy and normalized permutation mutual information, both derived from Shannon's information theory and normalized consistently through the embedding dimension of the Bandt and Pompe method. Each point on the plane simultaneously characterizes the intrinsic uncertainty of a variable and the amount of information it shares with another. We further show that a third quantity, equivalent to the conditional entropy of one variable given the other, introduces a notion of informational independence and, when both projections of a variable pair are considered jointly, reveals directionality between them. \\ We analyze regular, chaotic, and stochastic dynamics to illustrate the relevance of the informational plane and show how these regimes evolve as a function of a coupling factor.

In a recent paper, a semiclassical Lyapunov exponent associated with a quantum Hamiltonian represented by a finite-dimensional Hermitian matrix was defined and placed on a mathematical foundation. The Lyapunov exponent characterizes the early stages of the evolution toward the ergodic state, while the late stages are characterized by the spectral gap of the corresponding Markov matrix. Here, we apply this formalism to five random-matrix ensembles. For each ensemble, we derive the mean Lyapunov exponent, its variance, and the spectral gap as functions of energy. We also present the corresponding thermal averages. Extensive numerical data are compared with the theoretical predictions.

The Bandt-Pompe permutation entropy framework, alongside the complexity-entropy causality plane, has become a standard tool for characterizing the dynamical properties of time series. However, observational noise distorts ordinal pattern probability distributions in ways that can systematically misplace time series within the causality plane, compromising dynamical classification. This effect is particularly relevant for geophysical signals, which are typically poorly and irregularly sampled, and have a low signal-to-noise level. In this work, we characterize the distortions on ordinal pattern statistics using the formalism of majorization. We provide theoretical results and propose corrective strategies that restore discriminability under realistic measurement conditions. To achieve this, we introduce methodology that allows the characterization of noisy dynamical series and further allows the quantification of observational noise without the need of a fitting procedure. Finally, we illustrate our methodology by analyzing paleomagnetic records to determine if the geological evolution of the Earth dipole is better described by a stochastic or chaotic system.

We consider a reduced Lorenz-like model that describes two walking droplets interacting through their mutual wave field, and investigate the emergence of strong bipartite correlations in this classical wave-particle system. The coupled nonlinear dynamics admit two invariant synchronization manifolds associated with correlated and anticorrelated states, within which the droplets display synchronized chaotic intermittency. Employing measurement protocols inspired by Bell experiments, we compute position correlations from the long-time dynamics and identify parameter regimes for which the CHSH-Bell parameter $S$ exceeds 2, corresponding to violations of Bell's Inequality. We further introduce a procedure for isolating the two subsystems, thereby ensuring the absence of wave-mediated signaling between them. Changing measurement settings following this isolation allows us to execute dynamic Bell tests in which violations persist. Our results demonstrate that nonlinear deterministic dynamics can produce Bell violations through wave-mediated synchronization mechanisms; moreover, these violations may be rationalized on the grounds that the wave form is influenced by the measurement settings. We thus provide a consistent dynamical framework for the appearance of classical entanglement in pilot-wave systems.

This work develops a discrete-time framework for identifying probability localization dynamics through finite stochastic representations adapted in space, time, memory, and state information. A compact dynamically relevant set is localized by a finite measurable partition, producing an observable probability state and a relational graph of admissible transitions. Structured stochastic liftings derived from Stochastically Structured Reservoir Computing (SSRC) give lossless polynomial representations of the observable state, while stochastic delay liftings add finite observable memory. These are distinguished from dynamically informed state-space enrichment: refinement of observational fibers containing states with the same present observation but different observable futures, yielding an exact obstruction-to-closure criterion. A route-network toy problem gives a minimal obstruction example, while four numerical laboratories (rotational phase dynamics, the chaotic logistic map, the Van der Pol oscillator, and a synthetic cyclic inventory system) show how spatial scale, temporal scale, polynomial degree, and delay depth interact. The logistic map isolates representation-induced memory in an otherwise Markovian chaotic system, using its exact invariant law as an ergodic benchmark and its zero-mass pseudospectrum to separate relaxation from transient amplification. An exact rotational cycle calibrates pseudospectra as a robustness diagnostic rather than a closure certificate. The inventory example gives a closure-driven enrichment procedure: residence-age hazards trigger age-refined states that improve predictive scores. These results motivate a minimal adequate representation: the least complex representation meeting predictive, structural, and identifiability requirements.

We analyze pattern formation from a homogeneous steady state in a one-component nonlocal adhesion model with population pressure and degenerate mobility. First, using linear stability analysis, we derive the instability threshold and a selection rule for the fastest-growing mode, and elucidate the mechanism by which the selected wavenumber shifts toward lower wavenumbers as the mean density increases. We then perform a weakly nonlinear analysis near the critical adhesion strength and derive an explicit expression for the Landau coefficient in the Stuart--Landau equation. This expression shows that the critical bifurcation is classified as supercritical or subcritical according to the mean density, the nonlinear exponent, and the second-harmonic response ratio of the kernel. Furthermore, we show that a large nonlinear exponent promotes a transition to subcriticality and confirm, through numerical bifurcation analysis and time-dependent simulations, a bifurcation structure with a fold point and the formation of mesa patterns. Finally, through the energy limit as \(m\to\infty\), we relate the observed mesa profiles to a capacity-constrained limiting structure.

We investigate the dynamics of two-component flat-top--bubble vector solitons using a variational approximation and numerical simulations. The system is described by coupled cubic-quintic nonlinear Schrödinger equations with repulsive intercomponent coupling. We introduce a self-induced mechanism in which a localized flat-top soliton (FTS) generates a density bubble in a second component: the localized density acts as a repulsive potential for the background field, creating a composite bound state. A background-subtracted formulation and normalized super-Gaussian profiles yield collective-coordinate equations for the component centers and an effective interaction potential for their relative separation. The potential forms a binding well that is nearly triangular over its global displacement range but smooth and locally parabolic near its minimum. The variational approximation consequently predicts harmonic internal oscillations whose frequency is independent of amplitude in the small-oscillation regime. Real-time simulations verify this weak-kick behavior with good agreement between the variational and numerical frequencies. For strong phase imprints, equating the exact kick energy to the variational binding depth predicts a kick scale \(K_{\mathrm{escape}}\) for the onset of partial FTS escape. Real-time simulations support this prediction: below this scale, the composite remains nearly intact, whereas above it, a substantial fraction of the localized component leaves the bubble.

The thermodynamics of cavity radiation is usually introduced through the quantum theory of a photon gas. In contrast, we investigate which features of thermal radiation follow from classical electrodynamics alone. We show, using two complementary approaches, that the proportionalities between energy density, radiation pressure, and energy flux arise without invoking photons or quantum statistics. The first approach is based on explicit solutions of Maxwell's equations and spatio-temporal averaging of electromagnetic waves. The second approach develops the classical statistical mechanics of the electromagnetic field from first principles by constructing the canonical Hamiltonian, implementing the gauge constraints, formulating the partition function as a functional integral, and evaluating the corresponding field correlation functions. By combining wave analysis, statistical mechanics, constrained Hamiltonian dynamics, and functional methods within a single classical framework, this work provides a coherent classical formulation of electromagnetic radiation thermodynamics.

The hydrogen molecular ion and the hydrogen molecule are treated in an approximate calculation based on classical electrodynamics which includes classical zero-point radiation. It is found within the classical theory that a molecular ion is less-well bound than a hydrogen atom plus a distant proton. The smaller binding energy is explained due to the repulsive nature of the force between the proton and the atom when considering the most natural resonant orbit of the electron. The approximate classical electromagnetic calculation gives a binding energy of $2.1eV$ and a proton separation of $0.916A^{o}$ for the hydrogen molecular ion. The hydrogen molecule is formed by adding a single additional electron to the ion. The electrostatic attraction of the electron to the ion gives a binding energy of $4.6eV$ and a inter-proton separation of $0.6A^{o}$ for the hydrogen molecule in this classical electromagnetic approximation.

We describe in detail and provide computer code for constructing optimal geometric braids of three strands from algebraic data encoding the braiding pattern. Our optimality criterion uses the known interpretation of braids as homotopy classes (rel endpoints) of paths in $SL_2(\mathbb{R})$ joining the identity $I$ to some $A \in SL_2(\mathbb{Z})$, i.e., elements of the fundamental group of $SL_2(\mathbb{R})/SL_2(\mathbb{Z})$, a quotient equivalent to the unit tangent bundle of the classical modular surface $\mathbb{H}/PSL_2(\mathbb{Z})$. The main technical result finds the length minimizing geodesic in a prescribed homotopy class. From another perspective, of independent interest, this amounts to shooting the shortest geodesic that connects, with a prescribed number of spins en route, two given unit tangent vectors to the Poincaré (half-)plane $\mathbb{H}$. The length is measured by a Riemannian metric from a family of deformed Sasaki metrics, sometimes called Kaluza-Klein metrics, whereby unit tangent vectors can be interpreted as infinitesimal rotors, called spinners, and the ratio of the mass to the moment of inertia is the deformation parameter. At the universal covering level $\widetilde{SL}_2(\mathbb{R})$, the geometry is one of Thurston's eight model 3D geometries. In the vanishing mass limit, it converges to the better understood Carnot-Carathéodory contact geometry, where our geodesic shooting extends known formulas. The finite mass case is more delicate, requiring numerical solution of a targeting equation. The characterization of the length minimizing geodesics (No-multiplicity Theorem) and the resulting targeting equation are the main original contribution. The exposition is complete and multi-pronged, aimed at a broad spectrum of readers. (Numerous figures are the backbone of the narrative and should be viewed in color.)

Multicomponent liquids can phase separate upon heating, exhibiting a lower critical solution temperature (LCST). Moreover, a narrow class of materials can undergo disordering transition upon further heating, yielding closed-loop phase diagrams. Previously, it was shown that LCST or closed-loop phase behavior can appear in the models of liquids in which components are asymmetric or interaction potentials have a specifically designed attraction. Here, we show theoretically that LCST and closed-loop phase behavior can occur in a significantly wider set of models. In particular, we found that these phenomena can be exhibited by the simplest and widely used coarse-grained (CG) models of any multicomponent liquid in which species are fully symmetric and where all particles interact via an arbitrary repulsive potential. In addition, we discovered that LCST and closed-loop phase behavior in these models emerges merely due to the basic property of CG liquid models, namely, the appearance of strong monomer-monomer positional correlations at low monomer number density $\rho$. We simulated the models of fully symmetric binary blends and diblock copolymer melts where nonbonded monomers interacted via a generic T-independent purely repulsive harmonic potential. As predicted, LCST and closed-loop phase behavior emerged at $\rho$ sufficiently low to cause strong monomer-monomer correlations leading to a strong T-dependence of the effective coordination number, which, in turn, induced a nonmonotonic T-dependence of the Flory-Huggins parameter. To summarize, we discovered that the simplest fully symmetric non-associating CG models of multicomponent liquids can exhibit complex temperature response due to a mechanism stemming from the basic nature of any CG liquid model. This mechanism might contribute to the emergence of LCST and closed-loop phase behavior in many existing polymer materials.

The dramatic slowing down of structural relaxation in supercooled liquids is accompanied by the emergence of dynamic heterogeneity. A monotonically increasing dynamical correlation length, measured at the $\alpha$-timescale, is one of the remarkable features of this phenomenon. Here we show that this picture is incomplete: the dynamical correlation length measured in the $\beta$-relaxation regime exhibits a striking non-monotonic temperature dependence, reaching a maximum near the mode-coupling crossover temperature $T_c$ and decreasing upon further cooling, even as local dynamical fluctuations continue to intensify. This behavior suggests a crossover from spatially extended, maximally cooperative motion near $T_c$ to increasingly compact and localized relaxation events below it. We demonstrate that this evolution is quantitatively captured by stochastic beta-relaxation theory, an extension of mode-coupling theory beyond mean-field that explicitly predicts an avoided dynamical transition in finite dimensions. Our results provide the first direct spatial evidence in favor of the avoided-transition picture of the mode-coupling crossover, and establish the peak of the $\beta$-regime correlation length as a robust indicator of the mode-coupling crossover.

We show that living microswimmers mechanically reinforce dense emulsions. Castor-oil-in-water emulsions laden with the microalga Chlamydomonas reinhardtii are compared in three states: without algae, with immobilized algae, and with motile algae, over a broad range of oil fractions spanning the jamming transition. Oscillatory rheology reveals that motile algae systematically increase the yield stress, by up to a factor of two, whereas immobilized cells at the same concentration leave it essentially unchanged. The reinforcement thus originates from activity rather than from the mere presence of inclusions. Single-cell tracking shows that the droplet network confines the swimmers in pores that shrink as the oil fraction increases, and confinement is known to amplify the propulsion force of C. reinhardtii. A simple estimate based on this confinement-enhanced force accounts for the measured excess yield stress and indicates an effective, activity-induced depletion-like attraction between the passive droplets. These results identify a feedback loop: the microstructure confines the swimmers, confinement amplifies the forces they exert, and these forces stiffen the microstructure. Active emulsions thus emerge as a model platform for programming the mechanics of disordered soft solids through activity.

Artificial intelligence (AI) is redefining the landscape of polymer science. Although numerous AI applications have been introduced in this field, the roles of polymer encoding strategies and different applications of AI models in polymer design remain insufficiently understood. Here, we build upon the foundation of polymer databases to critically examine the performance and applicability of current encoding strategies across different use cases. We then focus on two major AI application domains, property prediction and inverse design, to evaluate the strengths, weaknesses and suitable scenarios for various model architectures. Finally, we emphasize the significance of the online platforms for promoting data accessibility and accelerating the migration from experience-based discovery toward AI-driven innovation in polymer science and engineering. Through these discussions, we aim to provide practical guidance for future research and development in AI-assisted polymer design.

Thermal fluctuations can drive an interface when bulk fluctuation amplitudes differ between two phases. We study how shear flow modifies this mechanism using a stochastic non-conserved order- parameter model. For a planar interface parallel to the imposed shear, we derive its propagation velocity in the weak-noise and small-bias regime. The driving force comprises a shear-modified entropic contribution determined by bulk fluctuation spectra and a non-equilibrium contribution arising from the breaking of time-reversal symmetry. At low shear rates, the entropic term provides the dominant contribution to the velocity of an interface near the zero-velocity plane of the shear flow, and the shear-induced change in the velocity scales as the 4/3 power of the shear rate. At high shear rates, two-dimensional simulations show that the measured velocity is largely accounted for by the modified bulk entropic contribution.

Mobility links an applied force to the resulting motion and is generally positive near equilibrium. Far from equilibrium, however, internal energy input can reverse this response. Here we show that information feedback provides a distinct route to negative mobility. We consider an overdamped dimer consisting of a run-and-tumble particle coupled by a spring to a passive Brownian particle. Information enters through periodic measurements of the relative displacement, which are processed to reset the active polarity. Although the unloaded dimer has no net drift, an applied force biases its internal configuration, and an information-mechanical feedback amplifies and converts this bias into active propulsion against the force, producing negative mobility. We develop an analytical theory that captures this mechanism and yields a feedback-gain criterion for response reversal. Including the information-processing cost reveals a tradeoff: rapid feedback enhances reverse transport but incurs a growing informational cost, yielding an optimal finite feedback rate for information-inclusive efficiency. These results show that information can reshape nonequilibrium response by controlling how internally supplied energy is converted into macroscopic transport.

The mechanical properties of polymer glasses are often critical in determining the best material for a particular application. Extremely stiff materials (high modulus) may be important for some applications while avoiding catastrophic failure due to fracture (high toughness) may be more important for others. The mechanical properties of a polymer glass will depend upon both molecular structure and many experimental variables, including temperature and the mode of deformation (tension, compression, or shear). In this chapter we discuss the mechanical response of polymer glasses from a molecular perspective. In particular, we consider how deformation changes the rate at which polymer segments rearrange and how this in turn influences the mechanical response of the material. It will be shown that this focus on the changes in dynamics provides an understanding of many important features of polymer glass deformation. Of course, it is also true that the structure of a polymer glass must be altered by nonlinear deformation. Although not a major focus, we will make some comments about these structural changes at the end of this chapter.

Glasses of a model smectic liquid crystal-forming molecule, itraconazole, were prepared by vapor deposition onto substrates with temperatures ranging from Tsubstrate = 0.78 Tg to 1.02 Tg, where Tg = 330 K is the glass transition temperature. The films were characterized using x-ray scattering techniques. For Tsubstrate near and below Tg, glasses with layered smectic-like structures can be prepared and the layer spacing can be tuned by 16% through choice of Tsubstrate. Remarkably, glasses prepared with Tsubstrate above Tg exhibit much higher structural organization than a thermally annealed film. These results are explained by a mechanism based upon preferred molecular orientation and enhanced molecular motion at the free surface, indicating that molecular organization in the glass is independent of the anchoring preferred at the substrate. These results suggest new strategies of optimizing molecular packing within active layers of organic electronic and optoelectronic devices.

Optical probe reorientation measurements were performed to monitor changes in segmental dynamics resulting from the nonlinear deformation of a polymer glass. Segmental dynamics were monitored in a poly(methyl methacrylate) glass near Tg before and after a series of reversing deformations in which the sample was extended at constant strain rate and then allowed to retract back to zero stress at constant strain rate. Evidence of a rejuvenation mechanism, as quantified by a departure of the segmental dynamics from the quiescent aging dynamics after the reversing deformation, is observed for deformations which reach 60% of the yield strain or greater. By this measure, a saturation of the rejuvenation mechanism is not observed until at least five times the yield strain. For comparison, purely mechanical measurements of rejuvenation, based upon the reduction of the yield stress in a subsequent deformation, were also performed. These purely mechanical experiments show broad qualitative agreement with the probe reorientation experiments, but quantitatively differ in the pre-yield regime. The results are discussed in the context of recent theoretical approaches and simulations which provide a molecular-level description of polymer glass deformation.

A tangle of line defects coarsens as the mean spacing $L$ between neighbouring lines grows. In a viscous medium the motion is overdamped, and the velocity-dependent one-scale (VOS) model predicts a late-time attractor $L^{2}=\mathcal{A}\,\ell_d\,t$, with $\ell_d=T/\Gamma$ the ratio of line tension to drag and $\mathcal{A}$ a dimensionless amplitude. The growth law $L\propto t^{1/2}$ holds for every value of the three model parameters---the momentum parameter $k\le1$, the sink coefficient $\tilde{c}$, and the curvature ratio $\lambda\equiv R/L$---since all three enter only through $\mathcal{A}=\kappa(\kappa+\tilde{c})$, $\kappa\equiv k/\lambda$. Thus, the exponent constrains none of them, and the amplitude is the only quantity a density history can deliver. We measure it from the disclination data of Chuang, Turok and Yurke on a nematic liquid crystal, whose companion measurement of loop collapse fixes $\ell_d$ on the same samples, canceling the 5CB material constants. Treating the unmatched per-quench $\ell_d$ as a nuisance parameter with a Gaussian prior and marginalizing it analytically, we obtain $\mathcal{A}=10.0^{+1.3}_{-1.1}$ from the three quenches in the $234~\mu$m cell; the fourth, the only one in the thinner $158~\mu$m cell, gives $\mathcal{A}=3.0^{+0.8}_{-0.6}$ and is fitted separately. Converting either into $\tilde{c}$ requires $\lambda$, which these data do not determine, so the result is a curve, $\tilde{c}(\lambda)=\mathcal{A}\lambda/k-k/\lambda$, not a number. At $\lambda=1$ with $k\le1$ they give $\tilde{c}\ge9.0$ and $\tilde{c}\ge2.0$, against $\tilde{c}=0.23$--$0.57$ from relativistic $U(1)$ simulations, values reached only at $\lambda\simeq0.33$--$0.35$ and $0.62$--$0.68$. We know of no VOS calibration for a cosmological $\mathbb{Z}_2$ network, so we cannot attribute the excess to topology, and we list what a repeat experiment must measure.

Even for tension-dominated fracture propagation, porous materials may deform plastically adjacent to the propagating fracture. As is common for porous materials, existing phase-field models typically employ a non-associative flow rule for plasticity, and a Helmholtz free energy based on strain and fluid pressure. This work revisits the hydromechanically coupled formulation of the phase-field model for fracture in poro-elastoplastic media by analyzing the strength surface and fracture driving force. Our analyses show that these common choices of flow rule and free energy will lead to a discontinuous strength surface across the tension-compression transition. A non-associative flow rule introduces a jump at the strength surface, while treating fluid pressure-rather than fluid content-as the independent variable in the Helmholtz free energy omits a coupling term from the phase-field driving force, also breaking continuity. Incorporating an associative Drucker-Prager flow rule and this omitted coupling term ensures a continuous strength surface and the accurate fracture driving force. The proposed model exhibits improved accuracy in hydromechanical responses when compared against the analytical solution of the Kristianovich-Geertsma-de Klerk hydraulic fracturing benchmark. Numerical simulations of hydraulic fracturing and biaxial compression in poro-elastoplastic media show that the model can reproduce both shear-dominated fractures induced by mechanical disturbance and tension-dominated fractures driven by fluid injection in saturated porous media.

The simulation of viscous fingering in porous media is of direct relevance to displacement processes in petroleum engineering and hydrogeology. Building on recent work proposing a modelling approach for well-defined fingers at very adverse viscosity ratios, we investigate the physical mechanisms behind viscous fingering and the modelling requirements for capturing the finger scales and saturation patterns observed in experiments. We simulate and match a viscous fingering experiment at a viscosity ratio of $\mu_{o}/\mu_{w}{=}2000$, discussing the physical significance of each modelling step. Linear stability analysis is used to characterize the early-stage instability of the displacement. Subsequent numerical simulations show that, for the simulated finger scales to match the experiment, the most unstable wavelength at onset must be several times smaller than the desired finger width---so that, after accounting for shielding and merging in the nonlinear regime, the fingers remain thin. Small-scale channelling effects are also required to disrupt the trailing stable region commonly observed in simulations of viscous fingering in nearly homogeneous media. Finally, we show that including a weakly oil-wet capillary pressure function enables our model to capture the bypassed oil observed in the experiment.

We demonstrate programmable, frequency-tunable and size-selective drop motion on an elastic metastrip substrate with a centipede-like array of cantilever resonators. Under harmonic excitation, the strip experiences simultaneously an in-plane (IP) collective motion and out-of-plane (OOP) deformation, thus establishing a frequency-dependent IP-OOP phase landscape. This prescribes the direction of motion to the drops on the strip based on their position, causing the emergence of clustering and rarefaction regions. By tuning the tip masses of the resonators, we open reconfigurable OOP bandgaps that modify the IP-OOP phase makeup and locally suppress drop motion, contributing an additional layer of spatial selectivity. Using multi-frequency excitations, we selectively actuate drops based on their resonances, effectively filtering them by volume and position.

The discovery of governing partial differential equations (PDEs) directly from spatiotemporal data has emerged as a powerful tool for understanding the dynamics of complex systems. In this work, we apply PDE-SINDy to well-known phase-separating systems and examine how its performance depends on the amount of available data, the size of the function library, and the presence of noise. Our results show that the accuracy of equation discovery depends strongly on the amount of available data. Although the correct equation can be identified with limited data, several spurious terms also acquire finite selection probabilities. As the amount of data increases, these spurious terms are progressively suppressed, leading to a more robust identification of the governing equation. In contrast, increasing the size of the function library adversely affects the efficiency of equation discovery. Further, for the Glauber spin-flip Ising model, we show that the selection probabilities reveal a hierarchy of equations with varying levels of complexity. A sufficiently stringent selection threshold recovers a Model-A-like dynamical equation that accurately reproduces the dynamical and statistical features of phase separation and domain growth.

Polar liquid crystals - fluid phases in which molecular dipoles organise into ferro- or antiferroelectric states - present a highly constrained molecular design space, where small changes can entirely suppress polar organisation. Here we demonstrate, contrary to expectations, that installation of a methyl group in the 5-position of a 1,3-dioxane ring substantially increases the onset temperature of polar order. Remarkably, this effect proves transferable across several liquid-crystal families, including examples where the methylated derivative exhibits a polar phase whereas its parent compound does not. Across 8 matched pairs, we find that a 5-methyl group can enhance the onset temperature of polar order in 1,3-dioxane materials by up to 120 °C. These findings establish a simple and general molecular design strategy for enhancing and enabling spontaneous dipolar ordering in liquid crystals.

The Trachenko-Zaccone equation provides a compact nonlinear dynamical framework for describing non-Debye relaxation in disordered condensed matter. Originally developed to rationalize stretched- and compressed-exponential relaxation in liquids and glasses from the dynamics of interacting local relaxation events, the same equation has subsequently appeared in broader contexts, including polymer relaxation and nonlinear models of global population dynamics. This review retraces the conceptual development of the equation, with particular emphasis on its physical origin in Kostya Trachenko's feed-forward interaction mechanism, its mathematical structure, and its possible generalizations. We also include personal recollections of the work with Kostya Trachenko at Queen Mary University of London in August 2019, during which the equation emerged in essentially its present form. After reviewing applications to stress relaxation, glassy materials, polymer relaxation and population dynamics, we discuss future directions including time-dependent feedback parameters, coupled order parameters, heterogeneous and spatially resolved formulations, flux terms, network versions and stochastic extensions. The central theme of the review is that the Trachenko-Zaccone equation should be viewed not only as a model of glassy relaxation, but as a general nonlinear feedback equation with potential applications across complex systems.

How many memories can a local learning rule protect, and what fixes the number? Physical learning rules train resistive networks through local measurements, and the standard rules conserve a mass-like function of the conductances, a law whose general form was posed as an open problem with the expectation that no useful solution theory exists. We answer it, in the direction the expectation ran against, and the answer is a capacity theory. The Tellegen identity behind the conserved mass localizes: the feedback state is pinned to zero at the inputs, so every sector of the circuit that the input electrodes separate carries its own private conserved mass, by an argument consuming only Kirchhoff's law and that boundary condition, hence valid for arbitrary nonlinear branch laws. The number of independent sector masses is a topological property of the circuit, bounded by the number of output electrodes. An untrainable element can destroy the mass of its own sector and of no other, which says where fixed nonlinear components may be placed; per-edge learning rates select which functionals are conserved and never how many; and adjoint coupled learning, which clamps its outputs before measuring, drains every output-carrying sector at a rate set by the squared output multipliers. In linear circuits we then classify the identities: exact rational computation over all 502 circuits on up to five vertices with two inputs and one or two outputs, and hundreds of larger ones, yields a closed-form count, proved on that family and conjectured in general, with the sector statement a theorem at every circuit size. The anticipated series-parallel polynomial laws appear as exactly the series-class cubic differences, and the number the opening question asks for is a budget: one designed mass per sector, the differences the topology donates, and one broadcast scalar for each protected functional beyond.

We present a variational formulation of the incompressible vorticity equation based on Gauss's principle of least constraint using the Gauss constraint functional $\Zvec_\omega$. The central result is the Euler--Lagrange equation $\mathbf{Z}_\omega = -\nabla h$, where $h = \mathbf{u} \cdot\boldsymbol{omega}$ is the helicity density. This reveals that the helicity gradient $\nabla h$ acts as the constraint force maintaining the solenoidality of the vorticity field, exactly as the pressure gradient $\nabla p$ maintains incompressibility in Taha et al.'s pressure-gradient minimization principle. The helicity density naturally emerges as the Lagrange multiplier enforcing $\nabla \cdot \boldysmbol{omega}=0$, and at the solution the flow minimizes the norm of the helicity gradient $\|\nabla h\|^2$. This establishes the exact duality: helicity is to vorticity as pressure is to velocity. We apply the variational principle to the Burgers vortex and verify the the Euler-Lagrange equation. The variational principle connects to Moffatt's helicity conservation theorem, Arnold's geometric formulation of ideal fluid flow, and Kambe's gauge-theoretic formulation. This work provides a unified variational framework for fluid dynamics that spans classical mechanics, geometric mechanics, and topological field theory. We discuss how this work may provide a theoretical foundation for understanding the role of helicity gradients in boundary layer dynamics, with potential implications for the formation of coherent structures and the onset of transition. These applications are reserved for future work.

During drop coalescence, a connecting bridge of fluid forms and rapidly expands due to surface tension. For spherical drops, these dynamics are well understood in both the viscous and inertial regimes. However, under strong confinement, fluid motion is fundamentally altered by geometric constraints, leading to dissipation on small lengthscales. We investigate the coalescence of drops confined in a Hele-Shaw cell (two parallel plates separated by a narrow gap). In this geometry, the depth-averaged flow is governed by Darcy's law while surface tension drives the interface motion. We identify two distinct temporal regimes in the evolution of the bridge radius that evolves as a power law ($R_b$). At early times, the bridge grows as $R_b \sim t^{1/2}$, which results from a confinement-dependent meniscus instability that determines the initiation of contact between droplets prior to bridge formation. At later times, the bridge growth slows substantially and follows $R_b \sim t^{1/5}$, consistent with recent theoretical predictions for Darcy-governed coalescence. We show that the transition between these regimes is controlled by several geometric lengthscales. In particular, the onset of the Darcy regime occurs when the interface radius of curvature becomes comparable to the plate spacing, such that the flow becomes fully confined. Using a boundary integral formulation, we find that both scaling laws for $R_b$ are determined by the bridge width. Together, these results identify a new universal regime of drop coalescence in a broad class of fluids obeying Darcy's law.

The possibility of convection in a wall-heated unstirred simple fluid in zero-gravity conditions is discussed. It is shown that a low-Prandtl-number fluid possesses a stable circulating state in zero gravity, without destabilization of the diffusive state, provided geometric inhomogeneity allows the thermal cycle to perform net mechanical work. The analysis provides a quantitative explanation of why purely volumetric effects cannot induce by themselves convection in conventional fluids under zero-gravity conditions.

Interaction between energy-abundant mesoscale eddies and internal waves can lead to convection-turbulence generation and may prove important for deep-sea life and circulation. However, the size of scales of interacting flows is not well known. In this paper, a diagnostic tool of tilt is tested near the single top-buoyancy of 40 mooring lines 9.5 m apart horizontally and compared with 50-m scale relative vorticity and waterflow above a 2500-m deep flat Northwestern-Mediterranean seafloor. Whilst tilt relates to first order with flow-speed squared induced by mooring-line drag, considerable deviations from this relationship and larger tilt occur when the amplitude of relative vorticity attains values O(f), f the inertial frequency of planetary vorticity. The sign of relative vorticity is of no importance. Such larger-tilt events occur during most intense convection turbulence via warm-water slanting from above. During these events, variations in tilt-angle magnitude are as large as the average tilt O(0.1)degree, thereby reducing variational scales from 50 to 9.5 m. Thus, in a deep-sea environment where flow speeds are <0.07 m s^-1, O(0.01) m s^-1 flow-speed variations provide important turbulent mixing, without deep dense-water formation.

This study develops a low-fidelity framework for aerofoil shape optimisation under curvilinear blade kinematics, using a hovering cyclorotor as a representative case. Aerofoil optimisation can improve cyclorotor efficiency by suppressing leading-edge vortex separation during dynamic stall, but conventional approaches rely on computationally expensive CFD-based optimisation. The proposed method uses a single-streamtube model to estimate the rotor throughflow and optimises the aerofoil camberline using separate leading- and trailing-edge criteria. Assessed across configurations with varying blade counts and chord lengths, the framework consistently identifies aerofoils that improve hover efficiency, quantified by Figure of Merit. For the baseline four-bladed configuration, the low-fidelity optimum achieves 77% of the Figure of Merit improvement obtained using high-fidelity optimisation at a fraction of the computational cost. The analysis also reveals an additional torque-minimising design family at increased chord lengths, highlighting the influence of trailing-edge loading. Aerofoil optimisation is also compared to blade-pitch kinematics optimisation, which improves the efficiency through similar control of the leading-edge vortex separation. While both approaches produce comparable improvements in efficiency, the optimised kinematics substantially reduces thrust. Aerofoil optimisation may therefore be more practical, as maintaining a target thrust with optimised pitch kinematics would require higher rotational speeds, potentially introducing structural and noise issues.

Temporal fluctuations of wind farm-generated power arise from the interaction between atmospheric turbulence, turbine properties, and wind-farm layout. However, accurately characterizing these fluctuations remains an open challenge. We here present and extend an analytical framework to predict the temporal spectrum of wind farm power-fluctuations, and compare its predictions with detailed large-eddy-simulations (LES) of a wind farm operating within a conventionally neutral boundary layer. The modeling framework assembles several established concepts from turbulent boundary layer physics: a spatio-temporal turbulence spectral model accounting for mean advection and assuming random sweeping by large eddies, a top-down wind farm model of a fully developed wind turbine array boundary layer flow providing the required mean-flow and turbulence scales, and a spatial sampling kernel representing turbine positions and finite rotor size. The latter is extended to three dimensions to represent filtering of spatial fluctuations of turbulence along the vertical direction. Using only atmospheric, turbine, and layout parameters, the model predictions are evaluated against an extensive LES database of a large wind farm on flat terrain. The model accurately predicts the aggregate power frequency spectrum, including peaks associated with advection between turbine rows, the decay of inertial-range turbulence fluctuations due to rotor averaging, and spectra of aggregate power signals from various arrangements of groups of turbines within the array (e.g. staggered or random subsets). The ability to predict wind power fluctuation spectra from fundamental fluid dynamics and existing boundary layer turbulence models could help improve wind farm grid integration.

Actuator-disk models (ADM) are widely used in wind-farm simulations, but their accuracy in reproducing power and thrust temporal fluctuation statistics has not yet been compared to the more accurate and detailed predictions of actuator-line models (ALM). This work provides a detailed comparison of such model predictions under three distinct atmospheric conditions. Data is obtained from a database (JHTDB-Wind) containing actuator-line turbine-response and time-resolved flow field data from a large-eddy simulation of a small windfarm operating over a full diurnal cycle. Power and thrust time series corresponding to ADM are constructed from disk-averaged velocity signals and compared with the corresponding more detailed actuator-line signals over three temporal windows within the diurnal cycle. The analysis compares time series, power spectral densities, and both the fluctuation and increment probability density distributions. The results show that the ADM time-series capture the dominant temporal, spectral, and statistical features of the ALM values at resolved and disk-averaged flow-field time scales, i.e. slower than the rotor frequency. Effects of temporal filtering that are often applied to ADM inputs are examined. Overall, the results provide strong support for the use of ADM for predicting power and thrust fluctuation statistics in wind-farm simulations.

This work advances a fundamentally new approach to space-based construction by using liquid self organization in microgravity as a generative design and fabrication principle. Building on the LiquiFab method, we demonstrate how minimal surface architectures - traditionally dependent on complex additive manufacturing - can instead emerge directly from the physics of fluid interfaces shaped by programmable boundary conditions. We present a simulation-to-fabrication workflow, that includes a boundary-driven minimal-surface solver integrated in Grasshopper/Rhino, and an experimental system that implements in a neutral buoyancy environment simulating microgravity. This enables the generation of customizable Schwarz-P-inspired with tunable geometry and thickness, illustrating a scalable pathway for material-efficient, on-orbit fabrication. To validate performance in true microgravity, a flight experiment on the International Space Station is scheduled for the first quarter of 2027 and we here detail the additional considerations required for this experiment.

Periodic surface-wave forcing can reorganise turbulent flows through coherent spectral response, synchronization, intermittency, and changes in short-term predictability, so its dynamical effect need not vary monotonically with forcing frequency. We reanalyse laboratory acoustic Doppler velocimetry records obtained at constant discharge under four conditions (0, 0.5, 0.67, and 1~Hz) using one common KNN--GMAE forecast-error-growth protocol. A distance-weighted $k$-nearest-neighbour predictor generates out-of-sample forecasts over multiple horizons, and the slope of the early quasi-linear region of $\ln(\mathrm{GMAE})$ versus physical forecast time is reported as a finite-horizon forecast-error-growth rate, $\lFEG$. For the full 120-s records, $\lFEG$ is 5.68, 0.85, 3.39, and 4.11~s$^{-1}$ for 0, 0.5, 0.67, and 1~Hz, respectively. The ordering 0~Hz $>$ 1~Hz $>$ 0.67~Hz $>$ 0.5~Hz is preserved in all seven nearby parameter configurations, indicating that the comparative result is not an artefact of a single KNN setting. A 40-s sliding-window analysis with a 10-s step reveals substantial temporal structure. The no-wave condition remains predominantly high and the 0.5-Hz condition predominantly low, whereas the 1-Hz record has weaker local support for a single exponential-growth regime: only 3 of 9 windows satisfy the adopted early-fit criterion $\RFEG\geq0.90$, compared with 8/9, 7/9, and 7/9 for 0, 0.5, and 0.67~Hz.

Nonlinear dynamical systems manifest rich variety of dynamical states and transitions driven by fluctuations. To understand the pattern of fluctuations during dynamical transitions, we investigate the structural features of chaos to order transition in logistic map. We determine fluctuations as amplitude jumps and encode them onto a complex network where nodes represent amplitude levels and links represent transitions between distinct amplitude bins. We discover that global network measures identify points of period doubling, regimes of periodicity and chaos, including interior crises events. Using local network measures, we also unravel novel peculiar parabolic-shaped patterns in the orbit diagram that we show are reminiscent of the distribution of stable and unstable periodic points in the bifurcation diagram.

We study quantum dynamics through the lens of entanglement generation and characterize the underlying unitary evolution by the distinct signatures it imprints on the time-dependent entangling power. For a unitary operator, we characterize ergodicity by the equality between its long-time-averaged entangling power and the Haar-averaged linear entropy. We define mixing more stringently as the convergence of the time-dependent entangling power itself to the Haar value at long times. Within this framework, we establish the ergodic hierarchy of dynamical behavior, showing in particular that mixing implies ergodicity, whereas ergodicity does not necessarily imply mixing. As an application, we find that two-qubit unitary gates are neither ergodic nor mixing: their long-time-averaged entangling power can take only four discrete values, none of which coincides with the Haar average. We then investigate many-body dynamics using the kicked Ising chain and find that the long-time-averaged entangling power converges to the Haar value in both integrable and nonintegrable cases, indicating ergodicity. Remarkably, however, the nonintegrable chain exhibits mixing, whereas the integrable chain, despite being ergodic, is demonstrably nonmixing. We also introduce a Lyapunov-like exponent to characterize the rate at which the time-dependent entangling power approaches its saturation value. We find that this exponent increases systematically with the degree of integrability breaking in the many-body system. Our results establish entanglement generation as a useful framework for characterizing dynamical systems and reveal qualitatively different signatures of integrability beyond conventional diagnostics.

Strict thermodynamic scaling relations, such as the Rushbrooke inequality, are fundamentally established for equilibrium critical phenomena in the thermodynamic limit. In finite-size dynamical systems exhibiting synchronization, the direct application of such identities is hindered both by the finiteness of the network and the nonequilibrium nature of the spontaneous synchronization transition. To bypass this difficulty, we rigorously study the dynamical counterparts of the order parameter, susceptibility, and specific heat in finite systems of dynamical oscillators with nonlinear coupling. By measuring these quantities as a function of system size, we extract the associated critical exponents governing the transition. The validity of our thermodynamic mapping is tested by directly confirming the Rushbrooke inequality. Our results establish that standard equilibrium thermodynamic scaling architectures can be systematically applied to the finite-size scaling of nonequilibrium synchronization dynamics.

In this paper we investigate the behavior of localized solutions, specifically solitons, in a system of three coupled waveguides. The nonlinearity is modeled by a quasi-periodic modulation influencing the interaction between the waveguides. We analyze the evolution of the soliton profiles and their dynamics under varying modulation parameters, highlighting distinct behaviors such as attraction and repulsion among solitons. Our findings reveal that the system exhibits complex behaviors, depending on the interplay between the quasi-periodic modulation and the waveguide parameters. The study contributes to understanding the impact of quasi-periodic nonlinearity on soliton dynamics in coupled waveguide systems, laying the groundwork for potential applications in nonlinear optics and photonic devices.

In this paper we study the dynamics and stability of localized solutions in a saturable nonlinear Schrödinger equation with space- and time-dependent variable coefficients. Using a variational approach and numerical simulations, we analyze the effects of different external potential configurations. Our results reveal that the stability of the solutions is highly sensitive to the modulation parameters, leading to the emergence of alternating stable and unstable regions as a function of the modulation frequency. These findings provide valuable insights into the control of localized structures in nonlinear wave systems, with potential implications for optical waveguides, Bose-Einstein condensates, and other nonlinear media.

Recent years have seen substantial progress in elucidating the statistical physics of the vibrational properties of structural glasses. Although many real-world glasses relevant for science and technology are molecular, the majority of computational studies concerning the mechanical and vibrational properties of structural glasses employ simple atomistic glass-forming models. Thus, the effects of stiff molecular constraints on mechanical and vibrational glass physics remain largely unexplored. In this work, we directly compare the properties of a molecular computer glass with those of an atomistic model featuring the same inter-molecular interaction potential, and created using the same formation protocol. We find that the molecular glass features a higher degree of mechanical disorder, with larger mesoscopic correlation lengths, while at the same time it hosts a lower number of soft, quasilocalized vibrations per atom -- compared to the atomistic glass. We rationalize these differences by accounting for the reduction in the effective number of degrees of freedom induced by the stiff molecular constraints. We additionally find that nonlinear plastic modes --- that carry plastic deformation in driven glassy solids --- couple much more strongly to volumetric strains in the molecular glass. Future research directions are discussed.

The elastic modulus of porous materials is commonly described using power-law scaling relations with relative density, where the scaling exponent is often interpreted in terms of the underlying deformation mechanism. However, in highly disordered porous networks, changes in density are generally accompanied by changes in network topology, which can substantially modify the apparent scaling behavior. In this paper, we propose a topology-informed framework that separates the intrinsic mechanical contribution from the effects of network structure. Three representative topological descriptors are considered: the mean coordination number, the fraction of the load-bearing backbone, and the tortuosity of the load paths. For each case, the corresponding density-dependent contribution to the apparent modulus-scaling exponent is derived and analyzed. The results show that variations in connectivity, mechanical participation of the solid phase, and load-path efficiency can all lead to apparent scaling exponents exceeding the intrinsic exponent associated with the local deformation mechanism. These effects are particularly pronounced at low relative densities, where network topology evolves most strongly. The framework provides a physically interpretable basis for understanding anomalous modulus-density scaling in disordered porous materials and highlights the need to consider topology explicitly alongside relative density.

Casein micelles, one of the most studied natural association colloids, are supramolecular assemblies of caseins and colloidal calcium phosphate that constitute the fundamental building blocks of dairy matrices. Despite extensive investigation, the internal structure of casein micelles remains debated. While $\kappa$-casein is known to ensure colloidal stability of casein micelle suspension, the spatial organization of casein fractions and salts is still unresolved, and several structural models coexist. Small-angle scattering is a method of choice to probe biological colloids \emph{in situ}, yet interpretation of scattering data remains challenging due to the hierarchical nature of casein micelles. Here we address this issue by probing micelle structure during enzymatic gelation induced by chymosin, which cleaves $\kappa$-casein and triggers aggregation. Using time-resolved SAXS, we probe structural changes throughout the sol-gel transition over length scales from 3 nm to 3 $\mu$m. First, we show that enzyme-driven aggregation, counterintuitively, reveals information about the internal organization of casein micelles: the reduction of specific surface area during gelation unmasks a high-q structural peak previously observed under contrast-matching conditions. Second, we report that $\kappa$-casein cleavage leads to a gradual disappearance of the structural feature at intermediate scales. Analysis of the disappearance kinetics and comparison to structural models reveal that $\kappa$-casein cleavage induces a progressive relaxation of the colloidal porous substructure, providing direct evidence for its contribution to micellar organization. More broadly, these results demonstrate that the gelation process provides unique access to the internal structure of biological colloids and offers new perspectives for interpreting scattering data in complex soft-matter systems.

Thermoresponsive microgels undergo large reversible size changes as temperature alters solvent quality. Predicting their nonequilibrium swelling and deswelling kinetics is challenging because polymer volume fraction, mechanical response, and solvent transport evolve during large volume changes. Here we develop a solvent-flux theory for the dynamics of a spherical microgel. The radius-change rate is driven by the osmotic-pressure imbalance across the particle boundary and resisted by water transport through the polymer network, yielding a nonlinear equation for the global swelling coordinate and a state- and temperature-dependent swelling diffusion coefficient, $D_{\mathrm{SW}}(\phi,T)$. In the linear-response regime, the theory recovers Tanaka--Fillmore exponential relaxation and the scaling $\tau_\mathrm{SW}\sim R_{\mathrm{eq}}^2\gamma/K_{\mathrm{eq}}$, while providing a microscopic interpretation of the polymer--solvent friction coefficient $\gamma$. Beyond this limit, the model retains quadratic size scaling while accounting for state-dependent transport and mechanics. For pNIPAM microgels, it predicts asymmetric pathways, with deswelling faster than swelling over the same temperature interval. Finite thermalization produces a crossover from a microgel-controlled to a thermalization-controlled regime, in which the apparent relaxation time grows linearly with the external thermalization time and hysteresis-like loops emerge in the radius--temperature plane. A stochastic extension based on the Smoluchowski equation predicts transient broadening of the radius distribution during collapse, with maximal fluctuations in the volume-transition region. The theory links solvent transport, nonlinear swelling dynamics, thermalization effects, and nonequilibrium size fluctuations in responsive microgels.

The self-assembly of associative triblock copolymers composed of a central hydrophilic elastin-like polypeptide (ELP) block and short fatty acid end groups (C16) was investigated in aqueous solution. In one system, the ELP contains 80 pentapeptide units (C16-80-C16), whereas in the other two C16-ELP40 chains were oxidatively coupled through their terminal cysteine residues to form a central disulfide bond, yielding C16-(40)2-C16. Despite their nearly identical molecular weights and compositions, the two polymers exhibit markedly different self-assembly behaviors. C16-80-C16 forms large hydrophobic aggregates that remain kinetically trapped and do not develop a dynamically connected network. In contrast, C16-(40)2-C16 forms very small associative nodes with an aggregation number of only $\sim$3 chains. These nodes coexist with larger clusters and become dynamically interconnected at higher concentrations, leading to transparent hydrogels at concentrations as low as 2.5 wt %. Oscillatory rheology reveals a transient Maxwell network governed by a single relaxation process associated with the reversible association of the C16 end groups. SAXS, light scattering, cryo-TEM, and molecular modeling consistently support a model in which the central disulfide junction promotes transient network formation.

Lipid-coated microscale hydrogels provide confined, hydrated environments in which polymer phase behavior can differ markedly from that in bulk. Here, we investigate the crystallization pathway of poly(ethylene glycol) (PEG) encapsulated in lipid-coated agarose microgels. Surprisingly, polarized-light microscopy reveals birefringence in the microgels under conditions where PEG remains non-crystalline in the corresponding bulk solution. The birefringence disappears upon heating and spontaneously reappears after further cooling or upon local mechanical stimulation. Infrared microspectroscopy demonstrates that the birefringent microgels contain crystalline PEG, whereas non-birefringent microgels contain PEG in an amorphous-like state, indicating the existence of a metastable precursor prior to crystallization. Furthermore, cooling below the phase-separation temperature produces PEG-rich domains preferentially near the membrane, suggesting that membrane wetting governs the spatial distribution of PEG before crystallization. Together, these results indicate that membrane confinement and agarose gelation cooperatively alter the local hydration environment of PEG, thereby stabilizing an amorphous-like precursor and redirecting the subsequent crystallization pathway. Our findings identify the coupling of membrane wetting and gelation as a key factor governing PEG crystallization in confined soft materials.

In layered materials, spacing and stacking-order extent are usually locked. Here we show that in swollen suspensions of stiff, charged nanosheets they decouple, and that this defines a distinct regime, apart from the crystalline- and Wigner-swelling regimes such systems usually occupy. The mean spacing stays sharp and salinity-tunable while scattering-weighted stacking spans only two to three layers. We demonstrate this in a near-perfect model material, so the behaviour is intrinsic, not defect-driven. X-ray and neutron scattering, sedimentation and a Donnan analysis show the spacing is held by a parameter-free osmotic restoring slope below one pascal per nanometre. Because the slope is so weak, the spacing sits at equilibrium while faults relax slowly, a quenched metastable registry whose ageing-like relaxation of low-dimensional periodic order has not, to our knowledge, been realised before. The same decoupling is expected across stiff, swollen nanosheets, from clays to oxide nanosheets and graphene oxide.

Growth may cease at a target size or continue throughout life: the determinate and indeterminate phenotypes. We develop an active viscoelastic continuum model of a tissue growing along one axis, in which cell division and death generate active stresses. We find two asymptotic states: one in which the tissue reaches a relative size fixed by its material parameters, and one in which it elongates linearly without bound. Which state is realised is set by the ratio of active stress to elastic modulus. The transition originates in a bound on the elastic stress the tissue can support: a sufficiently large activity can never be balanced. In a tissue made of parts with different material properties, the growing phase settles into fixed length proportions, set by the mechanical impedances of the parts rather than inherited; matching impedances to initial lengths preserves the proportions the tissue began with. Determinate, indeterminate and proportionate growth thus appear as regimes of one continuum mechanical framework.

Time-varying interaction delays are ubiquitous in active matter, yet their collective effects remain largely unexplored. We show that active particles with internal dynamics and Vicsek-like delayed alignment exhibit intermittent flocking, characterized by long episodes of coherent motion interrupted by brief disordering events. This collective behavior arises from laminar chaos, a form of chaotic dynamics unique to systems with time-varying delays. Changing only the delay parameters qualitatively reshapes collective motion, producing fractal changes in global flocking order. Our results establish the temporal structure of interaction delays as a new control parameter for active matter.

Molecular docking is a vital computational task in drug discovery, wherein the objective is to efficiently identify optimal binding poses between a ligand and a target receptor protein. Due to the combinatorial explosion of possible binding configurations, docking of large and flexible molecules remains a computationally intensive problem, especially at scale. Early studies have revealed that the molecular docking can be re-cast as a maximum vertex-weighted clique problem (MVWCP) problem on a compatibility graph to be solved classically. In this work, we proposed a hybrid quantum-classical approach for molecular docking leveraging the MVWCP formalism with a variational full-basis encoding (FBE) strategy, which enables efficient encoding of classical binary variables with Bloch sphere vectors. We further prove that a global minimizer of the FBE objective can always be chosen to be a pure product state, thereby providing a rigorous justification for its optimization using a unitary variational circuit. The molecular docking problem is first mapped to a cost Hamiltonian that is minimized within a variational framework, optimized via a randomized imaginary time evolution (ITE)-inspired warm start, and gradient-based techniques. Finally, we also executed the circuit on an IBM quantum computer, underlying the feasibility and of quantum-assisted optimization for structure-based drug design and point towards the broader utility of advanced encoding techniques in quantum optimization for computational biology.

Open-porous materials exhibit pronounced compressibility, nonlinear densification, and power-law scaling of stiffness with density. In this work, we propose a thermodynamically consistent compressible neo-Hookean constitutive model for open-porous solids in which porosity serves as the primary governing variable. The strain-energy density is formulated to couple distortional elasticity of the solid skeleton with a volumetric response governed by deformation-induced porosity evolution, including a bounded representation of pore collapse. The formulation introduces a minimal set of parameters, namely the initial porosity, intrinsic skeleton moduli, and a scalar parameter controlling the onset of densification. A key feature of the model is a modified volumetric term in which the response is normalised by the current porosity, ensuring a physically consistent transition from a porous to a densified state without artificial stiffening. In the small-strain limit, the model recovers classical linear elasticity with effective moduli that may be chosen either from homogenisation bounds, such as the Hashin-Shtrikman estimates, or from Gibson-Ashby-type power-law scaling to capture topology-dependent behaviour. At finite strains, the formulation captures the characteristic nonlinear stiffening and convex stress-stretch response associated with progressive pore collapse. The proposed framework thus provides a compact, flexible, and extensible constitutive description that unifies effective-medium consistency with experimentally observed scaling behaviour, and is well suited for finite element implementation and multiscale modelling of highly compressible open-porous materials. The model is finally validated against available experimental data.

We investigate the dynamics and stability of three immiscible viscous liquid layers coating the interior of a vertical cylindrical tube, a configuration relevant to stratified core--annular transport processes. A long-wave asymptotic analysis yields a coupled system of nonlinear evolution equations governing the motion of the three interfaces. Linear stability analysis predicts a persistent long-wave instability, the capillary (Rayleigh--Plateau) instability of the air--core interface, together with secondary finite-wavenumber instability bands that emerge from interfacial coupling in certain parameter regimes. These stability characteristics depend sensitively on the layer thicknesses, viscosity ratios, and surface tension parameters, and include mode-switching associated with competing maxima in the dispersion relation. Nonlinear simulations reveal three distinct dynamical outcomes: saturation to finite-amplitude travelling waves, air-core closure through plug formation, and rupture of the intermediate liquid layer while the air core remains open. The intermediate-layer rupture mechanism is unique to the three-layer configuration which has no analogue in one- or two-interface cylindrical film flows. Numerical continuation is used to compute branches of travelling-wave solutions and their associated limit points. Comparison with time-dependent simulations shows that travelling-wave branches successfully predict the transition from saturated waves to plug formation, but do not capture the distinct rupture mechanism associated with collapse of the intermediate layer.

The influence of microscale flow structures (smaller than the pore size) on turbulent heat transfer in porous media has not been yet investigated. The goal of this study is to determine the influence of the micro-vortices on convection heat transfer in turbulent porous media flow. Turbulent flow in a homogeneous porous medium was investigated using Large Eddy Simulation (LES) at a Reynolds number of 300. We observed that the convection heat transfer characteristics are dependent on whether the micro-vortices are attached or detached from the surface of the obstacle. There is a spectral correlation between the Nusselt number and the pressure instabilities due to vortex shedding. A secondary flow instability occurs due to high pressure regions forming periodically near the converging pathway between obstacles. This causes local adverse pressure gradient, affecting the flow velocity and convection heat transfer. This study has been performed for obstacles with shapes of square and circular cylinders at porosities of 0.50 and 0.87. Understanding the dominant modes that affect convection heat transfer can aid in finding an optimum geometry for the porous medium.

We present a sharp and conservative geometrical VOF--finite-volume method for multicomponent liquid--gas mass transfer across deformable interfaces. The method solves problems in which multiple species are coupled through interfacial mass balances, latent-heat exchange, and vapor--liquid equilibrium. The key novelty is a fully sharp two-field treatment of scalar transport: the species and temperature equations are solved separately in the liquid and gas phases, while the one-sided Robin conditions for species and the two-sided flux jump for temperature are imposed directly on the reconstructed interface through an embedded-boundary discretization. This avoids both volumetric regularization of interfacial source terms and explicit coupling based on previous-time-step interfacial data. A consistent geometrical advection scheme is used for volume, momentum, energy, and species transport, and a sequential coupling strategy is developed to determine the partial interfacial mass fluxes, close the temperature equation, and update the thermodynamic-equilibrium state. The method is validated through single- and multicomponent bubble dissolution, single-component droplet evaporation, non-ideal ethanol--isooctane droplet evaporation, and sessile water--glycerol droplet evaporation. The results demonstrate second-order accuracy, accurate interfacial flux prediction, good mass and energy conservation, and the ability to capture complex multicomponent effects such as gas replacement, azeotropic volatility reversal, and composition-driven Marangoni flow.

New analytical model predicts how fluid flows around a cylinder at high speeds, capturing wake patterns, turbulence, and shock waves with less computation than full simulations.

We extend Thorpe successive approximation expansion to the forced, tide locked internal wave generation problem of Lamb and Dunphy, where a barotropic tide over a ridge radiates a discrete spectrum of Taylor Goldstein eigenmodes in a steady shear current. At second order in topographic steepness, each mode forces a bound second harmonic via diagonal mode pair kernels derived in closed form; both kernels vanish for uniform flow, recovering Thorpe limit. At third order, solvability of the resonant fundamental yields a nonlinear wavenumber correctionthe forced counterpart of Thorpe phase speed shift, with tidal frequency fixed. Computations at the parameters of Lamb and Dunphy show that the corrections are small but systematic, with the bound harmonic distorting the displacement profile modestly and concentrated in the surface shear layer for downstream modes. The corrections peak at modes 2 to 3, grow quadratically with ridge height and current strength, and amount to a nonlinear slow-down of every mode, explaining from within the theory why the linear discrete spectrum model agreed so well with fully nonlinear simulations. A pycnocline case with stratification colocated with the shear layer amplifies the nonlinear corrections substantially, showing that the uniform stratification verdict is not generic and that the corrections are controlled by where N2 sits relative to the shear.

The theory of the perturbed convective wave equation for compressible flows (cPCWE) is generalised to spatially varying mean-density fields. The resulting equation is an exact scalar reformulation of the acoustic perturbation equations and describes sound generation and propagation in moving inhomogeneous media using a single unknown. The intermediate variables of the associated workflow, in which a Helmholtz decomposition problem, a Poisson equation and the cPCWE are solved successively, are related to the vortical, entropy and acoustic modes of Kovasznay, providing a physical interpretation of each processing step. The quantitative accuracy is assessed against fully compressible direct numerical simulations (DNS) of two-dimensional isothermal mixing layer and Lighthill's analogy computed in the same framework at Mach numbers between M=0.2 and M=0.4, based on the velocity difference across the layer and the ambient speed of sound. Over this range of Mach numbers, the radiated power spans several orders of magnitude. For M>=0.25, the sound power levels obtained using the three methods agree within 0.9dB, and within 0.5dB for M>=0.3. At M=0.2, where the acoustic fluctuations are weakest relative to the hydrodynamic ones, Lighthill's analogy over-predicts the radiated power by 2.8dB. In contrast, the cPCWE deviates from the DNS reference by only -1.2dB. This closer agreement is because the cPCWE source term is confined to the vortex-pairing region, while convection and refraction are represented by its convective wave operator. Beyond reproducing the far-field sound, the cPCWE resolves the acoustic field within the shear zone itself, where the DNS' fields are masked by vortical fluctuations.

Skin friction in wall-bounded turbulence is produced by intermittent near-wall motions, yet conventional coherent-structure definitions do not identify which individual events generate wall-shear stress, and thus friction. We train neural networks to predict the future velocity field and wall-shear-stress distribution in turbulent channel flow, and use SHAP-derived importance maps to identify the the input regions most influential for each prediction. The dominant events appear as paired objects: an upstream velocity-relevant region is associated with high-momentum motion toward the wall, while a downstream friction-relevant region marks the enhanced wall-shear-stress left in its wake. Tracking these pairs reveals a recurrent cycle of growth, streamwise elongation, decay, and occasional splitting into new wall-shear-producing events. These results redefine near-wall coherent structures not by what the flow looks like, but by what they do to wall-shear stress.

In this paper, we identify a new mechanism for rogue wave formation in a shallow-water setting. We study a bidirectional shallow-water wave field in the context of the Kaup-Boussinesq equation, and introduce a weak high-wavenumber dissipative perturbation that breaks the underlying integrability of the system. In this setting, dominant solitons grow through successive interactions with weaker, co-propagating solitons, leading to the formation of a "champion soliton" in each direction of propagation. This behaviour is in contrast to the general intuition that dissipation damps coherent structures, and instead shows that weak dissipation can induce their intensification. Moreover, we find that weak dissipation alone is not sufficient for champion soliton formation; the presence of random waves plays a crucial role in the intensification process, catalysing the transfer of energy into dominant coherent structures. While champion solitons have previously been studied in non-integrable systems, these works primarily consider perturbations introduced through modifications of the nonlinear terms (e.g., higher-order Korteweg-de Vries and Schrödinger-type models). In the present work, high-wavenumber dissipation provides a more physically natural perturbation, since such small-scale damping is a common feature in many systems.

Physics-informed neural networks (PINNs) embed governing partial differential equations directly into the training loss, offering a promising alternative to costly CFD solvers for unsteady flows. Yet the growing list of techniques proposed to improve PINN training is typically validated one at a time, leaving open whether these techniques actually compose. We study this question in depth on the DFG/Schafer-Turek unsteady cylinder wake benchmark. In isolation, nearly every technique performs no better than an untreated baseline. However, combining periodic (SIREN) activations with causal weighting unlocks a previously inaccessible regime, reconstructing velocity and pressure fields to within 4.1% average relative L2 error against an OpenFOAM reference solution. Adding further techniques instead causes catastrophic performance degradation, demonstrating that individually effective PINN interventions can interact nonlinearly and that more elaborate training recipes are not necessarily better.

In the article a new approach to construction of generalized coherent states in quantum billiards is proposed. The coherent states are defined as the projections of a Gaussian wave function on the basis of the eigenstates of the quantum billiard, continued outside. The continuation is built as the solution of the equivalent Balian--Bloch equation, defined on the entire $\mathbb{R}^2$ and the projection operator is built using the resolvent of the Balian--Bloch equation. In the case of the one--dimensional potential well and billiards, belonging to the Coxeter group, the wave functions of the coherent states were expressed analytically via the Jacobi and Riemann theta functions.

The intermediate-energy double pendulum is a prototypical chaotic system. Despite its irregular motion, it exhibits recurrent flips - events in which one of the arms passes over the top. We develop a statistical prediction for the mean flip rate in terms of phase space flux. Applying this flux-based approach to the equal-mass, equal arm ("egalitarian") double pendulum, we find excellent agreement between the statistical prediction and numerical simulations: ensemble-averaged flip rates agree at about the 1% level, while even the statistics of individual chaotic trajectories agree at the few-percent level, quantifying the validity of the ergodic approximation. This agreement holds for flips of either arm and over a broad range of energies. This flux-based approach is closely related to that used for the egalitarian three-body system. A central role is played by the saddle orbits: periodic orbits that tend to the stable saddle eigenmode as the energy approaches the saddle energy from above and approximately follow the ridge of the potential at higher energies. These orbits provide a natural dividing surface for defining flips while avoiding recrossings. Indeed, the resulting distribution of crossing times exhibits a distinct gap. We also present two alternative simplified dividing surfaces, one of which is based on an accurate analytic approximation to the saddle orbits.

Weather forecasting and climate projection frequently use multi-model ensembles (MMEs) to improve short-term forecasts by averaging across models. However, this practice is often not well justified or validated. Using reservoir computing (RC) as a computationally efficient alternative to large-scale physical models, we assess the validity of the MME approach for chaotic time series. By training multiple randomly constructed RCs on the same dataset, we create a multi-model ensemble in which each model has its own unique error. These model errors lead to very different forecasting performances, with forecast error distributions that exhibit heavy tails. The arithmetic mean across forecasts from multiple models for the same target is usually closer to the ground truth than most individual forecasts, and further improvement is achieved by weighted arithmetic means where the weights are constructed based on each model's test-set performance. We show that iterated forecasts over many time steps deviate from the ground truth along the unstable manifold of the target point, in both directions, so that, if forecast errors were independent and had zero mean, the arithmetic mean forecast should approach the true target like $1/\sqrt{\nens}$ where $\nens$ is the size of the multi-model ensemble. We observe deviations from this behavior, which we attribute to the tails of the error distribution of random RCs.

Dissipative chaos often exhibits abrupt transitions to periodic windows or vanishing states, but these transitions occur far below macroscopic theoretical boundaries such as the Melnikov threshold. In this study, we re-evaluate the transversal intersections (microscopic) of invariant manifolds from a deterministic and entropic perspective for the ``Arnold tongues'' shown by synchronization to forced inputs in the parameter space. We applied an algorithm that digitally determines manifold intersections as binary values ($1.0$ or $0.0$) without numerical interpolation. As a result of scanning the $\Omega - F$ parameter plane at a resolution of $5000 \times 5000$ ($25$ million points) with the damping coefficient fixed at $k = 0.2$, it became possible to globally capture the relationship between the macroscopic phase-locked regions shown by the Arnold tongues and the microscopic manifold intersections (chaotic regions). Furthermore, from a one-dimensional cross-section whose computational accuracy was verified, we confirmed a dynamical case where the region with homoclinic intersections (topological entropy $h_T > 0$) is a necessary condition for the region where chaos manifests (Kolmogorov-Sinai entropy $h_{KS} > 0$), and simultaneously confirmed the existence of a region where the intersection of the primary saddle solution does not serve as a necessary condition.

Paleoclimate archives extend climate knowledge beyond the instrumental era, registering different seasons, variables, time averages, and memory lengths. A longstanding problem is to integrate these heterogeneous sources of information within a unified methodology. Here we present a new data-assimilation framework, Last Millennium Reanalysis 4D-Var (LMR4D-Var), which reconstructs climate trajectories from these heterogeneous datasets while balancing errors in the model, observations, and initial conditions. We compare results using LMR4D-Var to assimilate proxies from PAGES2k, Temp12k, and borehole temperature profiles without treating them as instantaneous equivalents. Instrumental verification shows that LMR4D-Var achieves the highest skill compared with previous reconstructions. Borehole assimilation preserves skill against withheld annually resolved records, increases agreement between reconstructed 300--2000-m ocean heat content and independent estimates, and yields a cooler reconstructed Little Ice Age ocean. Results for Temp12k demonstrate assimilation of decadal-to-millennial records and the potential for Holocene and deeper-time applications with suitable emulators.

It is known that the attractive singular inverse-square potential gives rise to the critical quantum collapse in the framework of the three-dimensional (3D) linear Schroedinger equation. This article summarizes theoretical results which demonstrate suppression of the collapse, caused by this singular potential, and the creation of the otherwise missing ground state (GS) in a 3D gas of bosonic particles, carrying an electric dipole moment, which are pulled to the central electric charge, with repulsive contact interactions between the particles. In the mean-field approximation, the repulsive interactions are represented by the cubic term in the respective Gross-Pitaevskii (GP) equation. In addition to the GS, excited states with angular momentum are briefly considered too. Another topic considered in the article is 1D and 2D bound states in the linear Schroedinger and GP equations with the repulsive potential, which demonstrates a singularity at r --> infinity. A very recent result is that such a potential, growing faster than the negative harmonic-oscillator potential, produces a full spectrum of counter-intuitive normalizable (localized) bound states. The article puts forward perspectives for further studies of linear and nonlinear bound states existing under the action of the potentials with the singularity at r --> 0 or r --> infinity.

We explore quantum Turing pattern zoology, where the same Lindblad equation supports a morphology atlas of stripes, spots, holes, labyrinths, and defects. The stable stripe species provides a quantitatively controlled case in which morphology and Gaussian witness loss separate parametrically. In particular, visible Turing stripes can remain after two Gaussian witness margins associated with the same $k_*$ mode cross zero in a completely positive Lindblad lattice. The witness thresholds on the exact shell fall as $\mathcal{N}^{-1}$. The stripe nematic threshold tends to a nonzero value at fixed lattice size, time window, and morphology criterion. The ratio of the morphology threshold to either witness threshold therefore grows with $\mathcal{N}$. Imaging and momentum-resolved covariance measurements probe these sectors separately.

A weakly nonlinear regime of radial tunneling is theoretically considered for a light wave in a spherical dielectric Bragg resonator containing a set of ``shell'' eigenmodes (both TE and TM) with different azimuthal numbers $l\geq 1$, which are concentrated near a defect of the Bragg structure, several layers away from the origin. A single radial mode with $l=1$ is present at the resonator center, either TM or TE. Nonlinearity of the Kerr type in the main approximation is actual for the central mode only, while all the shell modes remain in the linear regime. The tunneling occurs between the central mode and the shell $l=1$ mode of the same symmetry. Nontrivial part of the dynamics of optical field is described by a Hamiltonian system of ordinary differential equations for complex vectors ${\bf C}_{1}(t)$ and ${\bf C}_{2}(t)$, which determine the magnitude and spatial orientation of the wave structures at the center and at the shell, respectively. Depending on ``asymmetry parameter'' of tunnel coupling, the system demonstrates different variants of nonlinear behavior.

Objects rolling upward on diverging inclined rails exhibit a counterintuitive behavior that has intrigued physicists and students alike. Among the most well-known is the double-cone paradox, where a cone appears to roll uphill due to the geometry of the rails. In this paper, we extend this idea to more general rigid bodies, including spheres and ellipsoids. We examine the physical conditions under which this motion occurs, and we derive the necessary geometric and energetic constraints using analytical mechanics. We then validate our theoretical models through carefully designed experiments.

Extended electrodynamics (EED) leaves the Lorenz gauge condition unimposed and treats the scalar combination $C=\nabla\cdot\mathbf{A}+c^{-2}\partial\Phi/\partial t$ as a dynamical field. For a conserved source with no scalar initial field, $C=0$ and the theory reduces to classical electrodynamics. A source with a nonzero local continuity anomaly has no Maxwell solution, but EED remains well posed and can support a scalar-longitudinal sector. For each radiating frequency of a localized source, the far field separates into the usual transverse Maxwell channel and a scalar-longitudinal channel with a longitudinal electric field, no magnetic field of its own, and a co-propagating $C$ field. Under the field-only energy balance used here, the time-averaged fluxes add without interference. The scalar channel depends only on $\Lambda=\partial\rho/\partial t+\nabla\cdot\mathbf{J}$ and radiates when its moments at $k=\omega/c$ are nonzero. An all-orders multipole formula is derived for this flux. Bound polarization and magnetization sources conserve charge identically and cannot excite the scalar channel. A compensated polarized carrier with a globally neutral anomalous surface layer isolates the channel and gives its dipole flux in closed form. The connection between the adopted flux and a physical stress-energy tensor remains unresolved. These results are conditional predictions of EED and do not imply a failure of charge conservation in classical electrodynamics.

For two hundred years - ever since Faraday's first conception of the field lines - hearts and minds of students have been pervaded by erroneous and unsubstantiated claims about these well defined mathematical objects. The most prominent misconceptions include: (1) a notion of the field lines as of 'lines of force'; (2) a notion that the field lines coincide with particle trajectories; (3) a notion that a field line density measures a magnitude of a vector field; (4) a notion that the field lines of a divergence-free field always form closed loops. Even the modern day literature systematically perpetuates some of these claims. We compile here the trivial counterexamples to these claims, providing physics instructors with an efficient and effective way of dispelling these misconceptions.

Acoustic metamaterials can exhibit unusual effective properties through mechanisms such as energy localization and resonant behavior in their constituent building blocks. Here, we investigate the internal acoustic energy of fluid core-shell spheres and map how resonances emerge from the interplay between material contrasts and shell geometry. The resulting phase diagram reveals an organized resonant landscape across distinct impedance-contrast regimes. From this structure, we obtain two compact predictive relations: one for resonance existence and another for spectral recurrence of successive peaks. Together, they enable the rapid identification of material and geometric combinations associated with targeted resonance responses. The framework is further tested against representative systems from the literature, reproducing their observed behavior. These results provide a physics-based route for screening and tailoring resonant core-shell building blocks before full-wave numerical simulations.

Nano- or micro-particle rotation driven by light has been well known in the fields of optical manipulation and optical physics since the end of the last century. It is viewed as a sort of angular-momentum transfer from light to material, but its microscopic analysis based on the Hamiltonian or the equation of motion has been less developed. We model this rotation with a simple setup of an electrically dipolar or multipolar particle irradiated by circularly polarized laser and comprehensively analyze the Langevin-type equation of motion by using the Floquet theory for dissipative classical systems and the mode separation method. Furthermore, we numerically compute the time evolution of the particle. As a result, we accurately estimate the dependence of the laser-frequency, laser-intensity, particle mass, temperature, and friction (dissipation) on the laser-driven rotation. We determine the ``nonequilibrium phase diagram'' of the laser-driven rotation in a broad parameter regime, which consists of three regimes: the rotation frequency $\Omega\propto\omega^{-1}$, $\Omega\propto\omega^{-3}$, or $\Omega=\omega$ ($\omega$ is the laser frequency). Comparing our theoretical result with some experiments, we show that the result of the overdamped Langevin equation is qualitatively consistent with the experiments.

Our present investigation into a rather rudimentary problem is motivated by two classes of problems studied since the 70's, cosmological particle creation and its more accessible analog, the dynamical Casimir effect on the one hand, and quantum friction a neutral atom moving along a dielectric surface would experience, on the other. The backreaction effects of produced particles being able to isotropize the expansion of the universe, or to slow down the moving mirror can be understood via the concept of vacuum viscosity arising from fluctuations of the quantum field. We want to track down the origin of this effect by asking the question whether a moving massive $M$ object with a charged internal degrees of freedom $\chi$ interacting with a free unbounded classical field $\phi$ at zero temperature would experience a viscous force, similar to the said precedents. Adopting a microphysics model for optomechanics which can treat the unequal tripartite $\chi$-$\phi$-$M$ interactions, we first perform a nonrelativistic calculation, which seems perfectly legitimate considering the needs of atomic physics, and found the answer to be yes, but a relativistic covariant calculation says no. We identify where the nonrelativistic framework is defective. The resolution of this latent yet real conflict is technically nontrivial but physically quite inspirational. It results in added enriched contents to Newton's first and second laws when the principles of special relativity are enforced, and rules to follow to get the correct nonrelativistic answer

We numerically examine the impacts of particle-wall alignment interactions on active species diffusion through a structureless narrow two-dimensional channel. We consider particle-wall interaction to depend on the self-propulsion velocity direction whereby some specific particle's alignments with respect to the boundary walls are stabilized most. Further, the alignment interaction is meaningful as long as particles are close to the confining boundaries. Unbiased diffusion of active particles for various possible stable velocity alignments against the walls has been examined. We show that for the most stable configuration leading to self-propulsion velocity direction perpendicular to the wall, diffusivity becomes inversely proportional to the square of alignment interaction torque. On the other hand, when the self-propulsion velocity direction making an acute angle to the channel walls is the most stable configuration, diffusion exponentially grows with strengthening alignment interaction. Hence, particle-wall interaction plays a pivotal role in the transport control of active particles through narrow channels. Moreover, the impacts of the alignment interactions on diffusion largely depend on the particle's self-propulsion properties and its chirality. Our simulation results can potentially be used to understand unbiased diffusion of artificial or living micro/nano-objects (such as virus, bacteria, Janus particles, etc.) though narrow confined structures.

Understanding how life-like behaviors can emerge from simple molecular assemblies and primitive compartments remains a central challenge in origins-of-life research. Synthetic minimal cells provide a bottom-up platform for investigating, from scratch, the minimal physicochemical principles underlying compartment growth, reproduction, and evolution. Previously, we developed a vesicle/polymer-based compartment system in which the vesicle membranes template the formation of a catalytic polymer. This polymer promotes selective incorporation of amphiphiles into the vesicle membrane, driving vesicle growth while maintaining the compositional identity and enabling spontaneous deformation and division over several generations. Here, we report about experiments in which we advanced this system beyond reproduction by systematically constructing eight synthetic minimal cell variants from combinations of two template vesicles, two catalytic polymers, and two supplied amphiphiles. The variants exhibited distinct, composition-dependent vesicle growth responses, ranging from pronounced growth to suppressed growth or vesicle shrinkage. These growth responses were described by the Hill kinetics and characterized by three parameters, revealing a multi-dimensional fitness landscape shaped by environmental conditions, in which the relative advantage of each variant depends on both composition and amphiphile availability. This framework links molecular recognition, compositional inheritance, and differential growth, providing a physicochemical route toward evolvable synthetic minimal cells.

We experimentally and theoretically study the hydrodynamic analog of the classical brachistochrone problem: the {\it time-} and {\it energy-minimizing} paths for a spherical particle rolling down an incline within a viscous fluid. We show that in the presence of viscous dissipation, the paths of minima diverge from the classical cycloid, into curves of opposing curvature for time and energy, and are characterized by an effective dimensionless parameter, $St_p$, representing the ratio of the particle's viscous response time scale to its gravitational time scale. Using a generalized variational framework, we show that the fastest path reduces to {nearly straight ramps}, however, beginning and terminating in localized cycloids of curvature, $\kappa_c \sim St_p^{-2}$. Remarkably, the path of fastest descent on a given energy budget requires navigating a non-monotonic path ({\it``S-shaped''}) with an interior point of inflection. Our findings reveal a unification of temporal and energetic optimality for transport through dissipative media, and expand the celebrated brachistochrone solutions to the hydrodynamic regime.

Liquid bridges suspended between two parallel horizontal cylinders are studied using experiments, reduced-order mathematical modelling and numerical simulations. Both non-electrified and electrified configurations are considered, with the cylinders acting as electrodes between which a potential difference can be applied. The initial focus is on equilibrium bridge shapes, while the dynamics is examined only in the non-electrified case. In the experiments, transformer-oil bridges are investigated and modelled as perfect dielectrics. The electric field counteracts the gravitational effects and causes the bridges to rise and become flatter, with shapes that are well described by Young--Laplace-type equations containing non-local electric-field contributions evaluated using a boundary-element method. Bifurcation diagrams of these solutions are constructed by pseudo-arclength continuation to characterise the dependence of bridge shapes on liquid volume and electric-field strength. In the absence of an electric field, the transient relaxation to equilibrium is analysed using a reduced-order model developed using Onsager's variational principle, with comparison to direct numerical simulations. The steady states predicted by the reduced-order model agree closely with those of the full formulation over a wide parameter range, and the dynamics is well captured in the overdamped regime.

The near-field shock structures of underexpanded sonic jets exiting into a subsonic coflow are investigated over a range of nozzle pressure ratio (NPR) and coflow-to-nozzle-exit velocity ratio ($U_c$), representative of a propulsive nozzle in subsonic flight. Time-averaged statistics from fully-resolved axisymmetric simulations and inviscid method-of-characteristics (MOC) analysis are used to understand how coflow alters the shock-cell structures, in particular the Mach-disk formation. It is well established that increasing NPR transitions the centerline reflection from regular (characterized by oblique shocks) to Mach reflection (characterized by a near-normal Mach disk). We find that coflow has the opposite influence: a strong coflow shrinks the Mach disk until it vanishes, reverting Mach reflection to regular reflection, so the NPR for this transition increases with $U_c$. This effect has previously been attributed to a reduction in the jet-boundary inclination at the nozzle lip, which confines the lip Prandtl-Meyer fan to a smaller angle and weakens the embedded shock. We show instead that this inclination is determined by the non-uniform pressure the coflow imposes along the jet boundary, which is the primary driver of the shock-structure transitions in coflowing jets. The non-uniform pressure weakens the boundary-reflected compression waves and orients them at shallower angles, so the embedded shock reflects regularly or fails to form. A simulation-informed MOC analysis with this non-uniform pressure boundary condition reproduces the transition behavior with increasing coflow. Coflow also lengthens the first shock cell linearly, which is accurately estimated by a simple correction to Prandtl classical shock-cell length scaling.

In this work, particle-resolved direct numerical simulations are performed to investigate flow past the five Platonic solids, which represent a progression in particle sphericity with an increasing number of faces. The simulations cover particle Reynolds numbers in the range 0.1 <= Re_p <= 300 and multiple particle orientations relative to the incoming flow. Based on the numerical data, new correlations are developed for the drag, lift, and torque coefficients. The proposed drag correlation explicitly accounts for both Reynolds number and particle orientation, whereas the lift and torque coefficients are represented by orientation-dependent trigonometric and exponential basis functions whose coefficients vary with Reynolds number. The simulations are conducted using the immersed boundary method, and the resulting drag correlation accurately reproduces the numerical data. The lift and torque correlations capture the principal trends observed in the numerical simulations, including the strong dependence on particle orientation. The proposed correlations provide a computationally efficient framework for incorporating orientation-dependent hydrodynamic forces and torques into Euler--Lagrange and point-particle simulations, enabling a more realistic representation and predictions of non-spherical particle transport in multiphase flows.

Wind turbines operating downstream of others in a farm are routinely exposed to waked inflow, with reduced mean velocity and elevated turbulence driving power deficits and additional structural fatigue. The direct effect of wakes on blade-level structural loading remains under-explored experimentally, owing partly to the sparse spatial coverage of conventional point-based strain sensors. Here, we present a wind-tunnel study of wake-induced blade dynamics using two $1\,\mathrm{m}$-diameter turbine models, in which one blade of a downstream turbine ($WT_2$) is instrumented with distributed Rayleigh-backscattering fibre-optic strain sensors, providing spatially continuous strain measurement across the blade span. By changing the relative position of the upstream turbine ($WT_1$) to the downstream, waked turbine $WT_2$ across the streamwise and spanwise extent, we map power output, spanwise strain, and accumulated representative fatigue relevant loading across the wake profile. Full wake impingement suppresses blade loading through the associated velocity deficit, while partial wake overlap generates the strongest load intermittency and highest relative fatigue relevant loading, despite an intermediate power recovery. A combined performance-to-loading metric shows this partial-wake regime offers the least favourable trade-off between energy yield and structural loading. These results show that minimising partial-wake exposure, not only mean velocity deficits, should be a design consideration for wind-farm layout and turbine spacing.

Granular flows are ubiquitous in natural and industrial systems, yet their complex dynamics remain difficult to characterize. For inverse problems involving unknown inlet, outlet, and wall boundary conditions, where CFD simulations are challenging, reconstructing complete flow fields from sparse observations constitutes a challenging inverse problem. In this study, a physics-informed neural network framework driven by both physical mechanisms and measurement data is developed to reconstruct the steady-state full-field distribution of granular flows in a pipe. The proposed approach integrates sparse measurement data with governing equations and constitutive relations and is trained using high-fidelity datasets generated by CFD solutions of a continuum model. The framework incorporates a dimensionless loss formulation, physics-informed initialization, dynamic global weighting, and a locally weighted granular temperature data-loss strategy. These treatments enable accurate reconstruction of the complete flow-field evolution. This work establishes a robust methodological framework for flow-field reconstruction in complex granular flow systems.

Predicting flow-induced sound from moving and deforming bodies is computationally demanding because the near-field hydrodynamics and the far-field acoustics require substantially different spatial resolutions and domain extents. A fully parallel hybrid framework is developed to address this disparity by coupling an incompressible Navier-Stokes solver to an acoustic perturbation equation (APE) solver on independently generated, non-conforming Cartesian grids. A sharp-interface ghost-cell immersed boundary method, with radial-basis-function reconstruction, imposes the boundary conditions for complex moving geometries on both grids. The converged flow field supplies the acoustic source through a one-way, precomputed parallel interpolation operator. This arrangement confines the flow grid to the body and wake while allowing the acoustic grid to extend independently into the far field. The framework is validated for Gaussian-pulse propagation, pulse scattering by a rigid cylinder, tonal sound from flow past a cylinder, and radiation from a traveling wavy foil. The predicted waveforms, wavelengths, pressure amplitudes, and radiation patterns agree closely with analytical solutions and published reference data. Applications to eel and Jack fish locomotion, a four-eel school, a manta ray, and a harbor seal further demonstrate the treatment of realistic three-dimensional morphologies, large boundary deformation, and multiple interacting swimmers. The results resolve morphology-dependent acoustic signatures and interference-driven changes in far-field directivity without requiring the flow grid to span the acoustic far field.

This study compares three reduced-order modeling (ROM) approaches for flow simulations of generalized Newtonian fluids described by the Carreau rheological model. All three methods rely on offline snapshot generation in the rheological parameter space using the full-order model (FOM), followed by a proper orthogonal decomposition (POD) of the snapshot matrix to obtain a reduced basis, but they differ in how they reconstruct the solution for new parameter values in the online phase. The three ROM approaches examined are: (i) intrusive Galerkin projection onto the reduced basis with full operator reassembly (ROM-FULL), (ii) intrusive hyper-reduced Galerkin projection using the discrete empirical interpolation method with GappyPOD for the nonlinear term (ROM-DEIM), and (iii) a non-intrusive interpolation approach using radial basis function interpolation (ROM-RBF). We demonstrate these three ROM approaches on two benchmark flows: a lid-driven cavity and a sphere settling in a closed container, spanning boundary-driven and force-driven flows. ROM-FULL achieves the highest accuracy but requires reassembling the full-order nonlinear operator during the online phase, whereas ROM-RBF is fully non-intrusive, and its accuracy is closely tied to data availability and deteriorates outside the training data range. ROM-DEIM offers a balance between efficiency and accuracy, even when data are sparse. The results provide guidelines for selecting an appropriate ROM strategy based on solver accessibility, computational efficiency, and desired accuracy.

We study data-driven prediction of coarse-grained dynamics in multiscale PDE systems. Adopting a closure-free operator-learning viewpoint, we apply a linear coarse-graining map and learn a surrogate evolution operator for the resolved field directly from filtered high-fidelity trajectories. Motivated by the Mori-Zwanzig formalism, we propose a spatiotemporal neural operator mapping a resolved history slab on $\Omega\times[-T_{\mathrm{in}},0]$ to a resolved future slab on $\Omega\times[0,T_{\mathrm{out}}]$. Spatial mixing uses Fourier convolution, while temporal mixing uses a causal kernel operator with position-attention weights on time lags. This causal temporal operator encodes finite-memory effects in the resolved dynamics while preserving the directionality of the history-to-future map. To improve rollout robustness and suppress nonconservative artifacts, we embed a flux-form inductive bias by parameterizing the windowed update in explicit divergence form. We also provide a data-driven guideline for selecting the memory length $T_{\mathrm{in}}$ via the decorrelation time of a closure-injection diagnostic computed from filtered trajectories. We validate on the coarse-grained viscous Burgers' equation, the Kuramoto-Sivashinsky equation, and two-dimensional turbulent flows, obtaining stable autoregressive rollouts with improved long-horizon accuracy and statistical fidelity.

Noise-activated switching between coexisting stable states is a fundamental mechanism underlying stochastic dynamics in systems ranging from chemical reactions to neural networks. While this phenomenon is well understood for stationary attractors, it remains largely unexplored for limit cycles, whose periodic motion cannot be described by a static potential landscape. Here we experimentally demonstrate activated switching between two coexisting limit-cycle attractors in a driven nonlinear system of coupled resonators. Specifically, we introduce controlled fluctuations to directly observe the rare stochastic transitions between two limit cycles and measure their dependence on noise intensity and driving strength. The measured switching rates are well described by a large-deviation theory, which replaces the conventional activation barrier by the action along the most probable transition path. Our results extend the concept of activated dynamics from stationary to limit-cycle attractors and establish a framework for modeling stochastic transitions between limit cycles in driven-dissipative systems.

We study the finite-genus algebro-geometric solutions of the Wadati-Konno-Ichikawa (WKI) equation with the saturable nonlinearity and long-time asymptotic behaviors of their short-range perturbations. First, for both the focusing and defocusing reductions, we formulate the finite-genus Baker-Akhiezer functions as explicitly solvable the matrix Riemann-Hilbert (RH) problems on the complex spectral plane and obtain theta-function representations together with the reconstruction formulae for the WKI field and the reciprocal coordinate. We then consider the Cauchy problem of the defocusing WKI equation on a finite-genus algebro-geometric background. We construct the scattering data and RH problem, and perform a Deift-Zhou nonlinear steepest descent analysis. The space-time plane is divided into two transition regions, a Zakharov-Manakov (ZM) region, and a fast-decay region. The leading term is a phase-shifted finite-genus WKI solution. The transition corrections are governed by a Painlevé-XXXIV model, while the ZM radiation is described by parabolic-cylinder functions. The reciprocal-coordinate asymptotics are obtained simultaneously.

Structured environments repeatedly redirect active particles, producing transport pathways that cannot be readily inferred from individual trajectories. Here, we show that the large-scale organization of these transport pathways is governed by topological constraints. Hydrodynamic scattering generates nonequilibrium current fields whose defect structure, characterized by integer indices, constrain transport pathways and renders them robust to smooth perturbations. This principle is demonstrated with rotating colloids in obstacle arrays and extended to stokeslet and force-dipole flows, thereby linking microscale transport to the topology of hydrodynamically generated nonequilibrium currents.

We develop an analytical theory for the dense packing of hard spheres in cylinders. Physically, our theory consists of a finite cylindrical masking of a close-packed three-dimensional solid and covers the entire range of cylinder aspect ratios, thus going beyond efforts that are focused on very tall cylinders in a narrow range of widths. We explicitly derive an exact equation for resulting packing fractions, valid for any regular lattice, and it provides a basis to understand the oscillations and scaling of volume fractions that have appeared in previous works. Our analytical relation serves as a rigorous lower bound and to tighten it we derive, and implement, an efficient mathematical procedure to optimize the orientation of the cylinder. Furthermore, we suggest simple techniques to improve on the predicted packings. Overall, we provide a general theoretical foundation for the packing of balls in cylinders, valid for all container sizes.

We use the density of surface-grafted polymers as a geometry-preserving control parameter for tuning the rheology of colloidal depletion gels. Reducing brush density accelerates gelation and produces gels with higher plateau storage modulus and yield stress. This mechanical enhancement is not accompanied by increased local densification; low-brush networks exhibit lower average contact number and reduced spatial heterogeneity while displaying stronger elastic responses than their high-brush counterparts. Our findings demonstrate a reduced coordination threshold to form elastic nodes in the low-brush gel network. In addition, low-brush gels relax more slowly, accumulate less creep deformation, and exhibit lower effective noise temperatures within the Soft Glassy Rheology framework. These results establish surface-brush density as an experimentally accessible control parameter for colloidal depletion gel rheology with coupled changes in effective attraction, network architecture, and contact kinematics.

We apply a modal framework for investigating the effect of density variations on gravity-type driven flows at the nanoscale. Using eigenfunction decomposition of the density and acceleration fields, each shear-pressure mode is separated into a homogeneous contribution and an inhomogeneous contribution determined by the Fourier amplitudes of the density and applied acceleration. This decomposition provides a direct means of identifying how density variations and external forcing couple and govern the flow behavior. We first revisit the Poiseuille flow and show that for channel heights larger than the characteristic intermolecular distance the homogeneous contribution dominates the long wave length (small wave vector) response, consistent with previous simulation results. In contrast, for sinusoidally driven flow, selective excitation of acceleration modes can produce the opposite behavior, with the inhomogeneous contribution dominating the long wave length response. The results show that the effect of the density variations depends on the specific flow; specifically the detailed mode coupling between the acceleration and density fields. The framework presented here provides a direct systematic approach for understanding and predicting the flow depending on the applied acceleration.

We numerically study motility-induced phase separation of active particles in two-dimensional convection rolls. We analyse local packing-fraction distributions, density fluctuations, the corresponding phase diagrams, and diffusivity curves to characterise the interplay between self-propulsion, global packing fraction, and advection strength. In the weak-flow regime, the system exhibits phase separation characterised by bimodal density distributions, slowly decaying density fluctuations, and a sharp reduction in diffusivity. Increasing advection suppresses clustering by enhancing particle transport and reducing trapping, leading to a shift in the critical self-propulsion velocity for motility-induced phase separation and a shrinkage of the spinodal region. Beyond the intuitive suppression of clustering by weak-flow advection, our results reveal several non-trivial phenomena including a reentrant phase behaviour where extremely high self-propulsion hinders motility-induced phase separation by facilitating particle escape from dense regions. We also observe that the density distributions strongly depend on roll periodicity. These findings demonstrate that convection rolls provide an effective means to control non-equilibrium collective behaviour in active matter.

In crowded environments, active polymers can trap themselves by winding into long-lived conformations. We show that fluctuations of the surrounding confinement can resonantly accelerate escape from these self-generated traps. Brownian dynamics simulations of a driven semiflexible chain in a breathing obstacle lattice reveal intermittent switching between a compact rotating spiral and an extended translating state. Long-time diffusion increases by up to two orders of magnitude when the environmental fluctuation rate becomes comparable to the spiral's intrinsic relaxation rate. The enhancement persists under stochastic fluctuations, showing that coherent periodic forcing is not required. Activity creates a second optimum: it promotes escape once favorable conformations form, yet at strong drive stabilizes the spiral and suppresses their formation. Resonant untrapping thus provides a general mechanism by which fluctuating environments regulate transport through barriers generated by internal conformational dynamics.

The acceleration of structural relaxation or physical aging by deformation, known as overaging, has been reported in experiments and simulations of polymer and colloid glasses, and correctly accounting for overaging is important for the prediction of the long-term behavior of polymer glasses in engineering applications. Here the effects of cyclic loading/unloading on the segmental dynamics and mechanical properties of PMMA glasses are investigated using a probe reorientation technique and time-aging time superposition of the mechanical response, respectively. Sets of 5000 tensile loading/unloading cycles were performed at temperatures between Tg - 10 K and Tg - 25 K with cycle extension strains ranging from 0.003 to 0.007. After cycling, the segmental dynamics measured with the probe reorientation technique either remained unchanged or were faster relative to an undeformed sample. The relaxation times of cycled glasses recovered with a common time scale on the order of their aging time, indicating that they retain a memory of their original age, as opposed to a full erasure of their thermal and mechanical history. Surprisingly, changes as a result of cycling were more obvious in probe reorientation measurements than in the mechanical properties, suggesting that the probe reorientation technique can sensitively detect nonlinear effects of deformation. No evidence of overaging was observed in the optical or mechanical measurements as a result of these cyclic loading/unloading experiments.

The last decade has seen great progress in manipulating the structure of vapor-deposited glasses of organic semiconductors. By varying the substrate temperature during deposition, glasses with a wide range of density and molecular orientation can be prepared from a given molecule. We review recent studies that show the structure of vapor-deposited glasses can be tuned to significantly improve the external quantum efficiency and lifetime of OLEDs (organic light emitting diodes). We highlight the ability of molecular simulations to reproduce experimentally observed structures, setting the stage for in-silico design of vapor-deposited glasses in the coming decade. Finally, we identify research opportunities for improving the properties of organic semiconductors by controlling the structure of vapor-deposited glasses.

The Light-Heavy (LH) model involves two species of particles (light and heavy) coupled with a fluctuating surface (described by tilts). The dynamics include the inherent diffusion of the particles (or tilts) as well as the drive provided by the tilts (or particles). When the two are of similar magnitude, the system lies in the unscaled (uLH) regime, while a significantly weaker drive leads to the scaled (sLH) regime. In the unscaled limit, the model exhibits an order-disorder transition characterized by the fluctuation-dominated phase ordering (FDPO). In this state, interestingly the dynamics is driven by multiple modes, giving rise to dynamic clusters. Away from the critical regime the disordered phase retains vestiges of FDPO behavior on length scales smaller than the correlation length. We examine this local FDPO-like behavior by using a scaling function that links the off-critical and critical regimes. We next turn to the scaled model and show that the multi-mode dynamics present in the unscaled regime is replaced by dynamics that is effectively controlled by a single dominant mode in the scaled regime. Concurrently, the two-point correlations change from the $\mathcal{O}(1)$ FDPO form to an anomalous long-range form that decays as $1/\sqrt{L}$. Drawing on the analogy with the sABC model, where similar anomalous correlations appear at criticality, we derive an analytical expression for the two-point correlation function using the same approach used for that model.

Poroelastic materials, such as polymer tissue scaffolds, porous rocks, and hydrogels, can weaken due to interactions between the solid skeleton and chemical species in the interstitial fluid. We develop a mathematical model for a poroelastic material to provide fundamental mechanistic insight into how weakening the material can affect the time-varying mechanics of the system. Our model couples large-deformation poroelasticity with an advection-diffusion equation for the solute. Furthermore, we introduce a decay equation for the material stiffness, whose rate of decay depends on the solute concentration. In this way, we describe a three-way coupling between poroelastic deformation, weakening of the skeleton and transport of solute through the material. We exploit numerical and analytical techniques to reveal the flow-driven uniaxial compression of a weakening poroelastic material and determine parameter regimes for which weakening the material facilitates pore closure at the downstream boundary. We identify parameter regimes in which (1) a steady state is attained without pore closure, (2) pore closure occurs at a finite time or (3) the pores close instantaneously; we uncover case (2) through the introduction of weakening into the system. We provide insights into the relationship between the differing behaviours and the separation between the timescales of the system. For systems with slow weakening, we derive a leading-order approximation for the time of pore closure, treating the ratio of the timescales of poroelastic relaxation and weakening as a small parameter, and investigate the accuracy of this approximation and the new behaviours that arise when these timescales become comparable.

A body floating atop a supersaturated fluid may accumulate bubbles along its underbelly, which can render the body rotationally unstable. But rotation can strip the surface of these bubbles when they make contact with the air above. To explore this coupling we perform experiments using cylinders floating on carbonated water. The cylinders exhibit an array of distinct dynamics, including constant rolling, periodic and aperiodic oscillation, chaos, and intermittent capsizing, which can be tuned by body size, mass distribution, and gas concentration. A continuum model for the bubble density dynamics, and Galerkin projection, tie the experiment to the generalized Lorenz system and its famed chaotic attractor. Even an extremely small center-of-mass offset can have a qualitative impact on the dynamics, and an offset of as little as a few percent can fully stabilize the system. The experiment represents a highly accessible physical realization of the Lorenz system, which, owing to continuous gas loss from the fluid to the air above, sweeps slowly without intervention across a classical bifurcation diagram in time.

While the bulk structure of vapor-deposited glasses has been extensively studied, structure at buried interfaces has received little attention, despite being important for organic electronic applications. To learn about glass structure at buried interfaces, we study the structure of vapor-deposited glasses of the organic semiconductor DSA-Ph (1,4-di-[4-(N,N-diphenyl)amino]styryl-benzene) as a function of film thickness; structure is probed with grazing incidence X-ray scattering. We deposit on silicon and gold substrates and span a film thickness range of 10-600 nm. Our experiments demonstrate that interfacial molecular packing in vapor-deposited glasses of DSA-Ph is more disordered compared to the bulk. At a deposition temperature near room temperature, we estimate ~ 8 nm near the substrate can have modified molecular packing. Molecular dynamics simulations of a coarse-grained representation of DSA-Ph reveal a similar length scale. In both the simulations and the experiments, deposition temperature controls glass structure beyond this interfacial layer of a few nanometers.

This paper investigates the feasibility of using residual learning to improve unsteady aerodynamic load prediction for aeroelastic applications. The machine learning technique selected for the study is the long short-term memory (LSTM) neural network, which is used for its suitability for sequential data with aerodynamic memory effects. The approach is investigated for the NLR 7301 airfoil benchmark using high-fidelity CFD lift data for prescribed pitch and plunge motions in the transonic flow regime in the presence of shock motion. An analytical unsteady aerodynamic model based on the Wagner function is used as a physics-based baseline, and the neural network is trained to learn the difference between the CFD lift coefficient and the Wagner prediction. The residual model is compared with a direct neural-network model trained to predict the CFD lift coefficient. The comparison includes feature and normalization studies, external benchmark cases, and leave-one-out and leave-family-out generalization tests across a range of sinusoidal and non-sinusoidal motions. The residual model performs best when its inputs align with the Wagner formulation variables, generally giving lower error and more consistent performance across training runs, though the direct model remains more accurate for some high-frequency cases. The residual model also generalizes better in the leave-one-out and leave-family-out tests, with a smaller increase in error than the direct model when entire motion families are withheld from training. Overall, the results indicate that residual learning shows promise as a modular approach for augmenting classical low-order aerodynamic theories, especially when the physics baseline removes a structured part of the aerodynamic response and leaves a lower-variance correction for the neural network to learn.

Spray atomisation rapidly creates large liquid-gas interfacial areas and is central to many industrial processes. However, predicting spray behaviour and surface area remains difficult: experiments cannot access all spray regions, while CFD becomes prohibitively expensive as finer structures develop. Data driven surrogates can learn interface evolution, enabling rapid design space exploration, operating condition ranking, and ultimately spray control. We investigate how state representation, neural architecture, and physics-informed regularisation affect long horizon autoregressive forecasting of spray interfaces, particularly conservation. Our principal model is a boundary-conditioned Fourier Neural Operator (FNO) that predicts the evolution of the signed distance function (SDF) from the liquid-gas interface. It is trained on 2D sharp interface Volume-of-Fluid CFD simulations spanning several atomisation regimes. The SDF-FNO retains interface fidelity better than an FNO trained directly on volume fraction, but is outperformed by a U-Net. Objective function ablation shows that a liquid inventory penalty improves conservation at a modest cost to local interface accuracy. We also introduce a physics-informed extension combining an open-domain target-increment liquid balance penalty, a narrowband Eikonal regulariser that preserves signed distance geometry, and a phase-boundedness penalty. Although this model trains stably, it leaves forecast error, interface overlap, and inventory behaviour essentially unchanged relative to the data driven baseline. Finally, we demonstrate the surrogate by ranking injection conditions according to interfacial area generated per unit gas injection power across the operating envelope of a fixed geometry.

In coastal wave boundary layers over gravel-scale roughness, with near-bed orbital excursions ten to a hundred times the roughness height, the boundary layer is only a few roughness heights thick. A roughness-controlled layer (RCL) of the steady-flow extent two to five element heights would then leave no room for a logarithmic layer, yet experiments over densely packed marbles recover logarithmic profiles within millimetres of the crests. We resolve this contradiction by re-analysing previous Particle Image Velocimetry (PIV) records with a triple decomposition that separates the marble-locked dispersive motion from the stochastic turbulence, across eleven wave, current and wave-current conditions. The boundary layer organises into an RCL, a transition region, and a logarithmic profile layer, with the RCL only one to two tenths of a marble diameter deep. This thinness is kinematic: above a periodic bed, the dispersive field decays over a length fixed by the element spacing, so close packing caps the layer at a fraction of a diameter. The layer is destroyed and rebuilt every half-cycle, tracking the near-bed velocity quasi-steadily, while the eddies within it stay locked to the inter-crest gap. Thinness does not imply weakness: within the layer, the dispersive kinetic energy rivals the turbulent kinetic energy, and the dispersive stress matches, near the crests exceeds, the Reynolds stress, showing that separated wakes carry organised momentum. The logarithmic layer survives because the decay length imposed by the packing is far smaller than the boundary-layer thickness, a margin set by the bed geometry rather than by the forcing.

Continuous release is a fundamental source condition in transport, yet theoretical treatments have focused on downstream concentration development for passive solutes or fully developed cross-sectional distributions of active particles. We develop a spatial theory for the steady transport of active particles under continuous release in confined shear flows, resolving the concentration field from the inlet to the far field. Based on the Smoluchowski equation, we formulate a boundary-value problem with point-source inlet flux and boundary conditions. Separation of the streamwise coordinate from the cross-sectional variables yields a non-self-adjoint generalized eigenvalue problem, whose spatial modes are superposed to construct the solution. The eigenproblem is solved within a Galerkin spectral framework; downstream-admissible modes are retained and their coefficients determined from the inlet flux through a weighted biorthogonal expansion. Excellent agreement with individual-based simulations validates the theory. For plane Poiseuille flow under convection-dominated conditions, we find pronounced position--orientation coherence for spherical particles in the early developing region: swimming and shear reorientation drive the population through successive angular stages, generating alternating off-centre and centreline accumulation regions downstream, while dispersion progressively weakens this coherence. Particle elongation enhances orientational alignment, producing an early three-peaked vertical profile and stronger, more persistent lateral accumulation downstream, while reducing the coherence of centreward migration and thereby suppressing secondary centreline accumulation. The streamwise marginal concentration varies non-monotonically, reflecting changes in the mean streamwise velocity, with its far-field limit given by the reciprocal of the asymptotic drift velocity.

Purcell's swimmer is a well-known planar model of a swimming microorganism, governed by low Reynolds number hydrodynamics, which is comprised of three rigid links connected by actuated rotary joints. This model has been analyzed as a robotic locomotion system governed by first-order nonlinear dynamics with a periodic input (gait) of the two joint angles. In this work, we present a robotic macro-scale realization of this three-link swimmer moving in a highly viscous fluid. We propose a simple variant of Purcell's theoretical model with non-slender links and a central rigid sphere which represents the added drag of the robot's central flotation block, and calibrate the model's parameters to fit experimental measurements. Next, we apply optimal control formulation based on Pontryagin's Maximum Principle (PMP) in order to find optimal gaits that maximize the displacement per cycle under bounds on the joint angles. Employing a differential geometric method that transforms the problem to area integral enclosed by the gait trajectory in the plane of joint angles, enables visual interpretation which explains topological changes in displacement-optimal gaits upon varying the bound on the joint angles. We then apply PMP formulation to the problem of maximizing Lighthill's energy efficiency in order to obtain a boundary value problem (BVP) whose solution gives efficiency-optimal gaits for Purcell's swimmer model, as well as its variant with a central sphere. Finally, we utilize numerical methods such as parameterizing the input gait as a truncated Fourier series, as well as GPOPS-II solver, to produce sufficient initial guess values for solving the BVPs and obtaining efficiency-optimal gaits.

Time-resolved direct simulation Monte Carlo (DSMC) fields are used to test whether a detached rarefied hypersonic bow shock contains a slow collective displacement that can be separated from correlated particle-sampling fluctuations. Mach-10 rotationally relaxing nitrogen flow over a circular cylinder is analysed for diameter-based Knudsen number $0.01\leq \KnD\leq1$, where $\KnD=\lambda_\infty/D$, $\lambda_\infty$ is the freestream mean free path and $D$ is the cylinder diameter. A density half-jump front is extracted on body-normal rays, unsupported solid-side points are excluded, and temporal coarse graining is performed before feature extraction. Persistent and sampling covariance components are compared using a penalized composite-fit score, design-scale cross-validation, block resampling, synthetic controls and complementary full-field matched filters. Corrected field proper orthogonal decomposition (POD) is high rank at every Knudsen number, yet a weak, same-signed angular displacement is resolved at $\KnD=0.01$ and $0.025$. Independent random-seed and simulator-particle-loading repeats recover the angular shape and relaxation time while the raw sampling variance changes with loading. Across the two resolved states the mean density layer broadens by $82\%$, while the angular shapes remain strongly aligned. Density and pressure recover the marker motion most strongly; the reduced Mach-number and translational-temperature participation at $\KnD=0.025$ is evidence consistent with moment-selective weakening, although observable-dependent signal-to-noise remains a possible contributor. The signal is interpreted as a low-pass bow-layer response embedded in broadband kinetic fluctuations, not as a newly discovered discrete oscillation or a demonstrated linear instability. The higher-Knudsen records are not sufficiently sensitive to establish physical disappearance.

Turbulence modeling in porous media can be greatly improved by combining high-resolution numerical methods with modern data-driven techniques. The development of accurate macroscale models (length scale greater than the pore size) will enable real-time systemic simulations of porous media flow. We consider the case of turbulent flow in homogeneous porous media, typically encountered in engineered porous media (heat exchangers, metamaterials, combustors, etc.). The underlying microscale flow field is inhomogeneous and determined by the geometry of the porous medium. Neural Networks are able to resolve the geometry-dependence and the non-linearity of porous media turbulent flow. We are proposing to separate the macroscale model into individual blocks that predict a unique aspect of the microscale flow, such as microscale spatial flow distribution and vortex dynamics. In the present work, we determine the feasibility of the prediction of the Reynolds-averaged microscale flow patterns by using Convolutional Neural Networks (CNN). The porous medium is represented by using a square lattice arrangement of circular cylinder solid obstacles. The pore-scale Reynolds number of the flow is 300. The porosity of the porous medium is varied from 0.45 to 0.92 with 60 steps. The microscale flow field is simulated by using Large Eddy Simulation (LES) with a compact sixth-order finite difference method. We demonstrate satisfactory prediction of the microscale flow field using the CNN with a global error less than 10%. We vary the number of training samples to study the deterioration of the model accuracy. The CNN model offers a O(106) speedup over LES with only 10% loss in accuracy.

Snow is a complex geomaterial whose macroscopic response is governed by density, temperature, and the topology of its evolving microstructure. Its mechanical behavior spans elastic, plastic, viscous, and failure dominated regimes, imposing significant challenges for numerical methods, which intends to simulate large deformations, evolving free surfaces, and complex boundary interactions. This work presents the first integration of a Modified Cam-Clay constitutive formulation for snow into a purely meshfree strong-form collocation framework based on the Generalized Finite Difference Method. The main methodological contribution is a numerical coupling that combines a global implicit mixed formulation for pressure and velocity with a constitutive return-mapping algorithm. The hydrostatic pressure contribution is obtained from a Poisson equation and subsequently corrected through the Modified Cam-Clay return-mapping procedure, while the deviatoric response is treated semi-implicitly using a numerical viscosity formulation. This partitioned treatment of the volumetric and deviatoric stress contributions enables stable simulations with comparatively large time steps while producing smooth spatial pressure fields. As a result, forces on complex boundary geometries can be evaluated accurately. Numerical results of this coupling illustrate the algorithmic stability of the framework, the effective imposition of boundary conditions, and the suitability of local spatial refinement. The feasibility of applying the framework to vehicle-snow interaction through rigid-body coupling is also illustrated. The presented formulation provides a robust basis for future simulations of dynamic snow loading on vehicle structures.

We describe two open-source, 3D-printable, flexure-based tools for the quantitative measurement of extensional properties of viscoelastic fluids. These low-cost, portable, and scalable devices (which we have termed ``PocketCaBER'' and ``PocketDoS'') are particularly applicable for use in the field and in graduate-level teaching environments due to their low cost, printability on hobby 3D printers, compatibility with cell phone cameras, portability and user-friendly operation. We characterize and benchmark each device's performance against its lab-equivalent counterpart and provide downloadable STL files for rapid fabrication. We discuss experimental limitations of these devices compared with their bench-top counterparts. Finally, we illustrate the use of such tools in facilitating student engagement in polymer science and complex fluids classes---specifically, how progress in learning goals can be uniquely and effectively accelerated by providing the necessary rheological instruments directly to each individual student (especially for advanced modules such as nonlinear extensional rheology). By giving students personal, indefinite access to laboratory-level instrumentation through these open-source frugal science tools, we discuss our efforts to expand participation and engagement within the field of nonlinear rheology.

Chaotic itinerancy (CI), brought to attention, among others, by K. Ikeda, I. Tsuda and K. Kaneko in the early 1990s, is a phenomenon in which trajectories in a dynamical system experience periods of ordered motion near quasi-attractors interspersed with chaotic transitions between them. Possible maps in which CI was found include coupled map lattices (CML) and globally coupled one-dimensional chaotic maps (GCM). We study such maps using numerical methods and graph algorithms. Specifically, we partition the state space into a finite grid of compact subsets, and we represent the map using a multivalued mapping of grid elements. This mapping can be perceived as a directed graph, with grid elements as vertices and individual mappings between them as weighted edges. This setup provides a coarse view of global dynamics and opens the opportunity for using Markov chains and efficient graph algorithms to study dynamical features. In particular, invariant sets can be found by computing strongly connected components in the graph. Analysis of the transition matrix of the graph makes it possible to find its stationary distribution and to compute local entropy as a measure of expansion or instability in the system. Using these tools, we propose an algorithm for assessing whether a certain map possesses the CI property and show its application to dynamical systems: a globally coupled system of logistic maps and a variant of a CML system for which we conduct computations for a large range of parameters.

Synchronizing nonlinear dynamical networks typically requires solving matrix inequalities or detailed system models, which fail for large networks. This paper offers a simple fix : a purely graph-theoretic framework using only a single Lipschitz-like bound on the dynamics. Coupling strengths are computed directly from the digraph, bypassing inequality solvers entirely. The method succeeds where existing approaches encounter infeasibility due to connectivity patterns. It examines only $n-1$ directed paths per strongly connected component versus $\frac{n(n-1)}{2}$ undirected paths before, achieving $O(n^3)$ complexity. Results show network connectivity can be exploited to synchronize a large class of nonlinear dynamical networks.

The solar wind is a turbulent, weakly collisional plasma characterized by non-Gaussian fluctuations, long-range correlations, and multifractal dynamics. We investigate the long-term evolution of these properties using hourly proton density measurements obtained directly by the Wind spacecraft over 1995--2025. The use of a single-spacecraft dataset provides an independent test of previous results derived from the multi-spacecraft OMNI database. The three components of the nonextensive $q$-triplet are estimated within one-year sliding windows shifted monthly: $q_{stat}$ from the distribution of density increments, $q_{rel}$ from the decay of the autocorrelation function, and $q_{sens}$ from the multifractal spectrum. Their mean values, $q_{stat}=1.71\pm0.07$, $q_{rel}=4.62\pm0.52$, and $q_{sens}=-0.45\pm0.27$, confirm the persistent presence of heavy-tailed statistics, slow relaxation, and weakly chaotic multifractal dynamics. The parameters nevertheless exhibit distinct temporal variability and relationships with solar activity. The Fourier spectrum of $q_{stat}$ contains a dominant period of approximately $10.1$ years, while its correlation with the sunspot number is positive and moderate ($r=0.611$). Correlation and mutual-information analyses show that $q_{stat}$ is primarily associated with solar proxies, whereas $q_{sens}$ displays stronger relationships with geomagnetic indices and $q_{rel}$ exhibits weaker dependencies. An anomalous enhancement of $q_{stat}$ around 2004 coincides with a sequence of intense interplanetary disturbances, although possible effects related to Wind's orbital transition must also be considered. These findings demonstrate the robustness of the nonextensive description and show that the statistical and dynamical properties of solar wind proton density show evidence of modulation by solar activity.

We present a systematic comparison between arbitrary precise arithmetic and integration, IEEE-754 compliant floating point arithmetic (fp16, bfp16, fp32, double precision fp64, and quadruple precision fp128), and two implementations of Posits (type III unum) for solving Newton's chaotic N-body problem. Each implementation is benchmarked with arbitrary precise calculations to objectively evaluate their performance in precision as well as speed. We rely on hardware and compiler implementations for fp64, and software implementations for arbitrary-precision arithmetic and Posits. Half precision arithmetic (fp16, bfp16, and Posits$<16,1>$) are insufficiently precise for solving Newton's equations of motion. Single precision (fp32, and Posits$<32,2>$) could be used for statistical ensemble calculations, but lead to relatively large errors in any individual strong encounter. All 64-bit implementations fp64 as well as Posits (Posits$<64,3>$) experience difficulty in our tests. One of the implementations of Posits (Universal) gives precision comparable to fp64 but is slow (by at least an orders of magnitude compared to fp64 after correcting for the more efficient hardware support for the latter). The other (CPPPosits) has a speed comparable to fp64 but has systematically larger errors (by about an order of magnitude compared to fp64 with excesses exceeding two orders of magnitude). As a consequence, this implementation leads to a systematic drift in the result space and has difficulty resolving close encounters. Posits and fp64 have difficulty when integrating a dynamical system in a moving reference frame; testing Galileo invariancy. In their current implementation, Posits do not seem to be the ideal alternative for fp64 when integrating chaotic or stiff ordinary differential equations, such as Newton's equations of motion.

We investigate vector Akhmediev breathers (ABs) in the degenerate and nondegenerate regimes for the coupled Sasa-Satsuma system describing two coupled ultrashort optical pulse envelopes. Based on the carrier-wavenumber relations of the two-component background, we examine three configurations: a single vanishing wavenumber, a pair of opposite wavenumbers, and two nonzero wavenumbers of unequal magnitudes. These configurations admit distinct maximal degrees of nondegeneracy. For each configuration, we derive the reduced spectral equations, construct the existence diagrams, and compare the resulting branches with the modulation-instability gain spectra. Owing to the distinct carrier-wavenumber symmetries, nondegenerate-type modes can occur in spectrally degenerate regions, whereas degenerate-type ones may also appear in spectrally nondegenerate regions. Moreover, all admissible branches in the degenerate regimes satisfy the state-transition condition and correspond to periodic-wave states, while such branches are also present in nondegenerate regimes. Direct numerical simulations of representative solutions further confirm the analytical predictions.

We study integrable variable-mass sine-Gordon model (vmSG) with point defects. Using the Lax and Bäcklund-gauge formulations, we construct type-I and type-II defect matrices, derive the corresponding sewing conditions, and generate the bulk and defect contributions to an infinite hierarchy of conserved charges. The lowest members reduce to the standard sine-Gordon energy and momentum in the homogeneous limit, while for inhomogeneous backgrounds they define integrability-generated energy- and momentum-type quantities. Defect compatibility imposes matching conditions on the variable-mass functions across the defect. An analytical transmission factor $z$ characterizes soliton transmission, topological conversion, and absorption/emission processes. We then deform the type-I sewing conditions by parameters $\alpha$ and $\beta$ and derive the associated defect anomalies. Consistent one-soliton transmission is recovered for $\alpha \beta =1$, whereas for $\alpha \beta \neq 1$ parity-centered kink-kink and kink-antikink transmissions display vanishing lowest order integrated anomalies but no generic vanishing at higher order. Numerical simulations reproduce the integrable transmission/conversion regimes and show that non-integrable defects generate weak radiative tails and lowest order quasi-conserved charges, while quasi-conservation of the higher order charges remains unestablished. These results elucidate how exact defect integrability deforms into charge-dependent quasi-conservation and establish a framework for defect-controlled soliton transport in inhomogeneous media, with potential applications to nonuniform Josephson junctions, magnetic and nonlinear-optical systems, and effective molecular and DNA models.

Colloidal gels are frequently modeled as monodisperse particle networks, although practical formulations commonly contain particles with multiple characteristic sizes. Here, we use large-scale, hydrodynamically resolved simulations of colloidal depletion gels to isolate the effects of particle size and local packing in bimodal systems with a small-to-large size ratio of 1:2. Increasing the large-particle fraction introduces new heterotypic angular motifs and substantially increases the fraction of bonds participating in tetrahedral structures, with a maximum at intermediate composition. However, these additional rigid motifs do not reorganize into larger or more highly connected tetrahedral aggregates. The mean coordination and characteristic aggregate size remain nearly composition independent. By contrast, the void and cluster-size distributions coarsen systematically as the large-particle fraction increases. These mesoscale distributions largely collapse when normalized by a composition-dependent particle length scale, indicating that changes in composition primarily rescale gel architecture rather than producing distinct rigid-network topologies. An elastic modulus estimated using Cauchy-Born theory similarly follows this effective length scale more closely than the abundance of local tetrahedral motifs. These results show that, for moderate size disparity, particle size controls the structural scale and predicted mechanical response of bimodal colloidal gels more strongly than enhanced local packing.

We formulate a physics-informed data-driven method for modeling anisotropic pairwise interactions in the presence of long-ranged electrostatics. The method separates the total interaction into a long-ranged electrostatic interaction that is approximated using a multipole expansion truncated at the dipole level and a short-ranged residual interaction that is approximated using multivariate Chebyshev polynomials fit to measurements from a limited number of configurations. We assess the approach on a sequence of aromatic molecules (benzene, benzonitrile, and phenoxide), finding that it produces satisfactory results using a modest cutoff distance for the short-ranged interaction. This method has applications for modeling complex interactions for, and conducting dynamic simulations of, synthetic and biological materials with charge.

We report structural and physical investigations on the biaxial smectic-A phase exhibited by a compound consisting of asymmetric bent-core molecules. Upon cooling from the isotropic phase, the compound exhibits the following phase sequence: Isotropic (403.9 K) $\rightarrow$ biaxial Smectic-A (359.8 K) $\rightarrow$ Crystal. The polarized optical microscopy, X-ray diffraction, and polarization reversal current measurements clearly establish the biaxial nature of the smectic-A phase without any layer polarization. The measured layer spacing in the entire temperature range of the smectic-A phase is close to the molecular length. The schlieren texture in a homeotropically aligned sample shows both $\pm \frac{1}{2}$ and $\pm 1$ defects which indicate the biaxial nature of this smectic-A phase. The dielectric spectroscopy studies on the samples revealed Debye-type relaxation processes with the relaxation time following the Arrhenius equation with temperature. Interestingly, the observed biaxial smectic-A phase exhibits a remarkable electro-optic response for a planar-aligned sample without any reorganization of the smectic layer structure.

Soft materials remember their deformation history, and identifying that memory from experiments is essential for predicting how these materials behave under real-world loading conditions. Chirp rheometry has recently emerged as a way to accelerate this characterization, compressing hours of conventional measurement into seconds and yielding thousands of stress-strain pairs per experiment. That density is then largely discarded: the standard pipeline reduces the record to a handful of frequency-domain estimates before any constitutive model is fitted. We introduce a physics-informed Gaussian process framework that infers the material's constitutive law directly from the raw time-domain record of a single chirp, selecting among candidate memory kernels and parametrizing the selected one without any intermediate signal processing step. Because the framework infers the memory kernel rather than the specific waveform used during training, it predicts the response to deformation histories it never saw, without retraining. The method also resolves material evolution within a single chirp directly in the time domain.

In this work, we adopt a finite strain computational homogenization approach to characterize the response of semi-flexible biopolymer networks modeled as idealized 8- and 14-chain periodic networks. We use the geometrically exact special Cosserat rod theory to model the microscale fibers forming these 8- and 14-chain networks. This allows us to capture arbitrarily large microscale deformations. Both macroscopic strain- and stress-driven homogenization are performed to study the macroscopic uniaxial tension, compression and simple shear responses. Several phenomena unique to biopolymer networks are recovered such as strain-stiffening and volume shrinkage under uniaxial tension, softening under compression and reverse Poynting effect under simple shear. We find that nonlinearity and non-affine deformation at microscale, especially bending and buckling of microscale fibers, plays an important role in these phenomena. We obtain the postbuckled solutions of the homogenization problem using a nonlinear, imperfection-free path following approach and also check for their stability. We further compare our homogenization results with experimental data for uniaxial tension and compression of biofilament networks and find good agreement. When the fibers are replaced by helical rods in the 8-chain unit cell, we are also able to capture the enlarged stretching behaviour as shown in recently fabricated compliant metastructures.

We investigate the nonlinear shape dynamics and autonomous propulsion of actively driven quasi-spherical vesicles with locally inextensible membranes at low Reynolds number. Starting from Stokes hydrodynamics, linearized membrane elasticity, and harmonic active forcing, we derive a reduced description in terms of spherical harmonic deformation modes. The global area constraint enforced by local inextensibility is the sole source of dynamic nonlinearity. It confines the dynamics to compact manifolds in the space of possible shapes. Autonomous propulsion arises through nonlinear mode coupling and is determined geometrically by the oriented area swept by the trajectories in shape space. For two active modes, the dynamics reduces to a periodically driven phase equation exhibiting synchronization, phase slips, and mode locking. Introducing a third active mode fundamentally changes the dynamics, giving rise to quasiperiodic invariant tori and resonant periodic cycles. A recurrence diagnostic reveals the resulting resonance structure, while fluctuations of the cycle-averaged propulsion provide an experimentally accessible signature of the underlying shape dynamics. Our results demonstrate that, for actively driven vesicles, a geometric constraint is sufficient to transform an otherwise linear dynamical system into one exhibiting rich nonlinear dynamics.

GEMSS (GEnerator of Multi-Sphere Shapes) converts 3D surface meshes or voxel grids into multi-sphere representations of granular particles using the recently published MSS algorithm. It computes key physical properties required for discrete element method (DEM) and general multibody dynamics simulations, including particle volume, center of mass, and principal moments and axes of inertia. Implemented as a header-only C++ library, GEMSS is easily integrated into DEM and molecular dynamics frameworks. The library has been integrated into MercuryDPM, which enables on-the-fly generation of multi-sphere particles directly within the simulation loop.

The Multi-Sphere Shape Generator (MSS) [1] places spheres according to a feature-enhanced residual field, but the geometric basis of this strategy has remained unknown. We prove that every local maximum of the residual field lies on the medial axis of the target shape, implying that MSS places spheres at the centers of maximal inscribed spheres without explicit skeleton extraction. Numerical tests show that deviations from the exact medial axis are limited to the voxel resolution. This result provides a mathematical explanation for the placement strategy that underlies the accuracy of MSS.

Motile Escherichia coli bacteria can alter salt crystallization patterns during the evaporation of sessile droplets. In dilute bacterial suspensions in deionized water, dried bacteria cells predominantly accumulate at the droplet periphery, consistent with the classic "coffee-ring" effect. At higher cell densities, however, the bacterial distribution becomes more uniform. In the absence of bacteria, pure Phosphate Buffered Saline also forms salt crystals in a coffee-ring pattern. When bacteria are present alongside the salt solute, additional isolated crystals appear near the droplet center, with their abundance increasing with bacterial concentration, while crystals at the periphery adopt dendritic morphologies that extend radially. To investigate these phenomena, we used a Stokes-based analytical model to estimate the evolution of internal flow fields and compare them with bacterial motility. Then a finite volume model is implemented for bacteria and salt transport and adsorption, and a stochastic model for salt nucleation was developed, which successfully explains the crystallization pattern seen in the experiments. Our results show that bacterial motility can overcome evaporation induced flow during early stage, enabling bacteria cells to serve as nucleation sites and thereby altering the final crystalline morphology. This work highlights the potential of motile microorganisms to actively control evaporative crystallization, with implications for porous media flow and microfluidic deposition processes.

Growth is a fundamental process in living systems. Although the stress-deformation response of growing materials is often described as either purely elastic or purely viscous, many biological tissues, from biofilms to tumors, exhibit both elastic and viscous behavior. Here, we show that this viscoelastic response can crucially control the mechanics of proliferating matter when the growth rate becomes comparable to the rate of stress relaxation. Focusing first on the prototypical case of a growing elastic beam, we find that the dynamics are governed by a single dimensionless parameter, $g \tau$, where $g$ is the growth rate and $\tau$ is the viscoelastic relaxation time. While the limits $g \tau \to 0$ and $g \tau \to \infty$ recover purely viscous and purely elastic behavior, respectively, the intermediate regime is not merely a smooth crossover between them. Instead, qualitatively new dynamics emerge at $g \tau \sim 1$, including rapid transitions between metastable states that occur in neither limiting regime. We then develop a general, growth-compatible theoretical framework in which unconstrained growth is intrinsically stress-free, extending the analysis to other prototypical geometries and enabling simulations of more realistic growing biological materials. Within this framework, sharp mechanical transitions arise when stress generated by exponential growth accumulates faster than it can be dissipated by viscoelastic relaxation.

A flexible body placed in a steady flow bends to reduce drag. This self-streamlining is a hallmark of fluid-structure interaction (FSI). Granular-structure interaction is equally ubiquitous in nature. However, it remains poorly understood. Thus, we investigate inertial granular-structure interaction (IGSI). Specifically, ejection induced by a flexible plate sweeping a granular bed is experimentally examined. We find that a faster sweep results in less ejection, particularly for a flexible plate. To understand the underlying physics of this behavior, a dimensionless number Sk is introduced as the ratio of the plate elastic timescale to the sweep timescale. At $\mathrm{Sk} \lesssim 1$, the plate deflection follows the self-streamlining law of FSI and induces substantial ejection. At $\mathrm{Sk} \gtrsim 1$, on the other hand, the plate skims the bed and the mass of ejected grains decreases sharply. Sk organizes IGSI as the granular counterpart of FSI.

We demonstrate optical coherence tomography (OCT) as a measurement technique for dense, optically opaque suspensions. Conventional optical methods cannot access the interior of such suspensions. OCT resolves individual potato-starch particles (${\sim}20~\mathrm{\mu m}$) as distinct scatterers, even though the suspension appears opaque to the eye. By tracking the vertical centroid position of the particle-laden layer $\langle Z \rangle(t)$ and the supernatant boundary $Z_\mathrm{sup}(t)$ in the same OCT image sequence, we obtain the instantaneous settling velocity $V(t)$ and the time-evolving effective volume fraction $\phi_\mathrm{eff}(t)$ simultaneously and continuously in time. To our knowledge, this is the first measurement to combine settling velocity and particle concentration into a single continuous trajectory within one sedimentation run. Conventional batch measurements yield only one velocity value per run. We applied this method to dense potato-starch suspensions, varying the initial volume fraction $\phi_0$ from 0.30 to 0.50 and the solvent density $\rho_\mathrm{L}$ from 1.0 to $1.3{\times}10^3~\mathrm{kg~m^{-3}}$ using aqueous sodium polytungstate solutions. The normalized velocity $V/V_\mathrm{Stokes}$ plotted against $\phi_\mathrm{eff}$ collapses onto a common trend consistent with both the Krieger--Dougherty model and the Richardson--Zaki law over $\phi_\mathrm{eff} \simeq 0.30$--$0.52$, confirming that the method captures physically reasonable hindered-settling behavior. These results establish OCT as a viable tool for probing internal dynamics in dense suspensions that were previously inaccessible to optical measurement.

Mechanical properties of biological tissues, driven by passive and active forces, play a vital role in several processes ranging from development to cancer metastasis. However, the dynamical responses of cells in tissues, subject to mechanical deformations such as shear and the associated rheological properties, are not well characterized. Here, we use three-dimensional agent-based models for normal and cancer tissues to investigate their responses to simple shear as a function of cell stiffness and stochastic active forces. In the normal epithelium, with uniform strength of active force, the yield stress as a function of shear rate follows the Herschel-Bulkley form over a range of cell volume fraction. Strikingly, the shear rate dependence and the elasticity-dependent changes in the yield stress fall on master curves upon suitable scaling. To model cancer-like behavior, a certain fraction ($N_p$) of cells was chosen to have enhanced activity and decreased stiffness. As $N_p$ increases, the extent of collective cell movement decreases, transitioning from affine (collective) to non-affine (individualistic) movement, a finding that is in accord with imaging experiments. Simulations of a model of a stiff solid tumor, with radius $R_s$ embedded in normal tissue, show that as $R_s$ increases, the yield stress increases. Interestingly, the cells migrate collectively as $R_s$ increases. A Gaussian Mixture Model (GMM) and a mean field theory quantitatively account for the simulation as well as experimental results on cancerous, non-cancerous, and a mixture of these two types. The combined theoretical and experimental study establishes that heterogeneity in stiffness and activity determines non-affine movements in normal and cancer tissues.

ESPResSo++ is an open-source software package for molecular dynamics (MD) simulations with a particular emphasis on coarse-grained (CG) models of soft matter systems. Written in C++ with a flexible Python interface, it is designed for high-performance computing (HPC) environments and supports massively parallel simulations through MPI. The package enables simulations of polymers, membranes, colloids and complex fluids with a wide range of interaction models and advanced algorithms.

The glass transition temperature ($T_{g}$) of alkali borate glasses is strongly composition-dependent and difficult to predict from first principles due to the structural complexity of the boron network. Here, we apply physics-informed symbolic regression (combining evolutive search with physically meaningful descriptors) to derive an interpretable closed-form expression for $T_{g}$ in the $x\mathrm{M}_2\mathrm{O}\cdot(100-x)\mathrm{B}_2\mathrm{O}_3$ glass family, with M = Li, Na, and K and $x$ expressed in mol%, and subsequently extrapolate it to M = Rb and Cs. The resulting model achieves a root-mean-square error of 14-16 K while maintaining clear physical interpretability, explicitly capturing the interplay among $T_{g}$, structural dissociation energy, and network packing. Critically, models built on the Rigid Unit Packing Fraction (RUPF) yield substantially more realistic $T_{g}$ predictions than those using the conventional Atomic Packing Fraction (APF), as APF overestimates structural rigidity at intermediate compositions. The fitted dissociation energies are further validated against the revised Makishima-Mackenzie model, confirming that the inferred parameters are physically consistent, not merely statistically effective, within the alkali borate family. Finally, Monte Carlo uncertainty quantification reveals that prediction uncertainty is highest in the compositional regions associated with the boron anomaly, directly linking model limitations to a known structural transition in these glasses. This result highlights the potential of physics-informed symbolic regression as a transparent and interpretable alternative to black-box models for property prediction in glass systems.

A major challenge in the field of heterogeneous catalysis is selecting an optimal catalyst support structure. Commercially available structures can be easily manufactured at scale, but their stochastic nature makes their chemical and transport properties suboptimal. This is particularly relevant for gas-generation reactions, where non-uniformity of a porous structure leads to bubble trapping. Such trapping impedes the flow of reactants to catalyst sites, leading to conversion inefficiencies. Previous experimental work demonstrated that spinodally-derived architectures, in particular bicontinuous interfacially jammed emulsion gels (bijels), can alleviate these issues and deliver superior performance. However, to the best of our knowledge, numerical studies to optimize the operating conditions for such a morphology have not been performed yet. In this work, we aim to close this gap using color-gradient lattice Boltzmann simulations of reactive flows with a novel central moments collision operator. We develop an analytical model to predict catalyst performance based on our simulation data. Our findings show that this type of morphology can achieve very high conversion efficiencies. Moreover, we demonstrate that its catalyst performance can be optimized using superhydrophilic surface coatings.

Mechanical separation of enantiomers is an attractive alternative to synthetic methods for producing enantiopure samples. Shear flow that produces solution vorticity has been shown to be a viable means for separating chiral objects on the micro- to nano-scale due to the tensorial nature of the interactions between chiral objects and the surrounding fluid. A recently-developed theory of molecular pitch characterizes these interactions using the resistance tensor and predicts the shear-induced separation of drug-like molecules from their optimized molecular geometries. We present a molecular dynamics study on the effects of incorporating molecular flexibility into the molecular pitch framework. We also evaluate the potential for enantiomeric separation of two drug molecules: bicalutamide (Casodex) and montelukast sodium (Singulair). Simulations reveal the emergence of flexibility-induced pitch distributions that result from conformational changes occurring in a realistic solvent environment. However, these distributions are weakly influenced by the solvent identity and the shearing process, producing mean scalar pitch values that are close to those from optimized gas phase structures. Despite the opposing effect of translational diffusion at the molecular scale, racemic mixtures of flexible enantiomers show linear rates of separation at the 10 ns timescale, and we predict that cm-scale separation can be achieved within hours. Additionally, we provide estimates for parameters of a Taylor-Couette device for generating laminar shear flow, as well as considerations for future experiments.

The generalised Lagrangian mean (GLM) theory of Andrews & McIntyre provides a powerful framework to study the interactions between waves and flows. A drawback of this theory is that the Lagrangian mean velocity is divergent even for incompressible fluids because the mean flow map, which sends the Lagrangian labels of fluid parcels to their mean positions, does not preserve volume. This results, for instance, in vortices shrinking under Lagrangian averaging. We overcome this drawback by revising the definition of the mean flow map, choosing it as the volume-preserving map closest to the "bare" GLM mean map. A standard result of optimal-transport theory then shows that the new mean map is the volume-preserving factor in the polar factorization of the GLM mean map. We develop and implement a numerical method for the computation of the corresponding Lagrangian mean fields from simulation data. The implementation builds on recently developed algorithms for the on-the-fly computation of Lagrangian means using the exponential and Butterworth filters. We demonstrate the value of volume-preserving Lagrangian averaging in simulations of the two-dimensional incompressible and shallow-water models. We compare the Lagrangian-mean fields obtained with and without the volume-preservation constraint.

In this work, a novel phase-field method is proposed for the six- and seven-equation non-equilibrium models for simulating compressible two-phase flows. Such formulations allow for monotonic mixture speed of sound, minimizing artificial wave delay during transmission across an interface. The proposed phase field formulation is constructed from the baseline seven-equation model, and interface-regularization terms are added in divergence form, while maintaining consistency between the partial differential equations without introducing spurious source terms. It admits conservative phasic and mixture entropy transport equations, thus facilitating the construction of discrete conservative schemes. The six-equation formulation is obtained under instantaneous velocity equilibrium. To avoid eigenvector degeneracy of the system of PDEs, the volumetric interface regularization flux is modified to account for a finite amount of conjugate phase, which improves on how phasic density is captured implicitly. Stability of compressible two-phase flow rely on the preservation of the interface-equilibrium conditions, and the preservation of discrete kinetic energy and entropy. A detailed analysis of IEC demonstrates additional requirements on the consistency of flux splittings between the convective and interface-regularization terms for all quantities, as well as the effects on the phasic internal energy flux splittings. A KEEP discretization is proposed and evaluated over a suite of high-density ratio test cases, including interface advection, acoustic wave-induced bubble oscillation, oblique acoustic wave reflection and transmission, and two-phase Taylor-Green vortex flow. Results demonstrate accuracy, stability and robustness for very long time integrations, a desired feature for simulation of turbulent flows and acoustics, since the framework does not rely on the addition of numerical dissipation.

Wall-pressure fluctuations beneath a turbulent boundary layer drive the flow-induced noise and structural loading of rough surfaces. On a smooth wall their variance grows with the logarithm of the Reynolds number, a growth carried, in a source-term reading, by the nonlinear turbulence--turbulence part of the pressure source acting across the logarithmic layer. We ask what sets the same growth once the wall is fully rough. Standard rough-wall phenomenology answers it: above the roughness the mean flow keeps its smooth-wall logarithmic form, so the active source range is cut off at the roughness height rather than the viscous length, and the variance grows on the logarithmic span between the roughness height and the layer thickness in place of the Reynolds number. Splitting the pressure source into its two physical parts then distinguishes separate contributions to the energy: a roughness-local one from the mean-shear source, fixed at high frequency on the roughness scale, and an energetic one from the nonlinear source at the outer scale, which alone carries the growth. Calibrated against rough-wall cases, the model collapses the spectral shape onto this energetic peak and holds it Reynolds-independent at fixed geometry. The canopy contribution decays with distance from the wall and contributes a finite offset. The growth coefficient is predicted to be the smooth-wall one. The present range is too narrow to discriminate that rate from twice or half it, so the contribution is a parameter-free prediction and the identification of a suitable roughness-size sweep that would test it.

Inclined gravity currents on shallow slopes can exhibit pronounced turbulence intermittency. Using direct numerical simulations, we investigate this behaviour for a temporal gravity current over a range of initial Reynolds numbers $Re_0$. For $Re_0=2500$ and a slope angle of $0.5^\circ$, the outer layer of the current exhibits large excursions in turbulence intensity and repeated transitions between turbulent and weakly turbulent states. Analysis of the flow energetics reveals that the intermittency is associated with a finite delay between shear production and dissipation of turbulent kinetic energy. During transitional phases, this delay permits a transient amplification of turbulence, which significantly weakens the mean shear by extracting kinetic energy from the mean flow and promoting entrainment-driven layer growth, ultimately leading to relaminarisation. Increasing $Re_0$ reduces the delay and progressively suppresses intermittency, steering the flow towards a more sustained turbulent state. Motivated by these observations, we develop an autonomous delay-differential model based on the coupled evolution of the mean and turbulent kinetic energies. The model reproduces the observed transition from intermittent to sustained turbulence as the delay is reduced and predicts an increased tendency towards intermittency at larger flux Richardson numbers. The results support an interpretation of intermittent turbulence in inclined gravity currents as a delay-induced oscillation arising from the finite adjustment time of turbulence to changes in the mean flow.

We investigate the collision dynamics of hydrodynamically interacting inertialess spherical particle pairs sedimenting in a homogeneous isotropic turbulent flow. The analysis focuses on the rapid-settling limit, in which the particle settling time across a Kolmogorov eddy is much shorter than the Kolmogorov time scale. We also consider continuum breakdown during lubrication interactions, which is important when the separation the particles is comparable to the $O(100)$ nm mean-free path of a gaseous media. Owing to the sub-Kolmogorov particle sizes considered here, we approximate the local flow field in the vicinity of a particle pair as a stochastic linear flow induced by the background turbulence. In the rapid-settling regime, the cumulative effect of turbulent strain fluctuations is weak, and the relative particle motion may therefore be described as a diffusive process. In addition, hydrodynamic interactions generate a net relative drift between the particle pairs. We obtain the hydrodynamic diffusivity and relative drift velocity from the Lagrangian autocorrelation function of the fluid velocity gradient evaluated along the settling trajectory. The rapid-settling assumption further enables us to relate the autocorrelation function to the turbulence energy spectrum. Using these results, we solve the advection-diffusion equation for the pair probability density function to determine the collision rate. We show that the ideal collision rate increases monotonically with increasing relative strength of gravity to turbulence, whereas the collision efficiency decreases monotonically over the same range.

This paper is associated with a video winner of a 2025 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, this https URL . We investigate bioconvection in a colony of Thiovulum sp. ST bacteria, a recently isolated enrichment culture, confined within a Hele-Shaw chamber. Driven by chemotactic and gravitactic responses, the cells collectively develop striking emergent patterns and convection-like dynamics. Starting from a dense, homogeneous suspension, the swimming bacteria generate large-scale bioconvective flows within minutes. Although these flows resemble thermal convection, they arise in the absence of an imposed temperature gradient. Instead, they arise from the collective swimming of bacteria responding to oxygen gradients and gravity.

This study investigates the spatial development and recovery of near-wall flow steering induced by yawed widely-spaced riblets. To accurately measure the mean spanwise velocity in the near-wall region, we developed a unique, customised rotating probe equipped with a single hot-wire. This novel technique demonstrates high sensitivity, reliably detecting small spanwise velocity components. We applied this probe to map the flow over straight-to-yawed and yawed-to-straight riblet configurations. For the straight-to-yawed transition, the downstream distribution of the mean spanwise velocity closely aligns with the step-forced spatial Stokes layer (SSL) solution, achieving an equivalent active wall motion of $V^+_\mathrm{equ} \approx 2.0$. This offers a simplified analytical pathway for future passive flow manipulation studies. Conversely, flow recovery over the yawed-to-straight configuration diverges from the SSL step-down phase prediction. Instead, a spatial lag was observed where crest-adjacent flow recovered quickly, but significant residual spanwise flow ($V^+ > 0.5$) persisted far downstream ($\widehat{x}{}^{+} > 1000$).

Here, an improved phase-field method for simulating the impact dynamics of solidifying molten metal droplets is developed using targeted free-energy modifications. Conventional Cahn-Hilliard-Navier-Stokes (CHNS) formulations generally do not capture melt retraction over a solidified portion of the droplet, because the newly formed solid region is not treated as an actual internal boundary in a single-order-parameter diffuse-interface model. As a result, the formulation lacks an internal wetting condition or localized wall-energy mechanism capable of driving melt retraction over a solidified splat. To address this limitation, a diffuse-domain wall-energy term is added to the free energy, with a chemical-potential contribution that is active near the diffuse liquid-solidified-material-gas triple-line region, enabling the remaining melt to retract over a solidified splat. In addition, a solidification penalty term is introduced to immobilize the solidified splat formed during impact and suppress unphysical interface motion caused by residual Cahn-Hilliard diffusion inside the frozen region. The proposed formulation is validated against benchmark experiments on impacts of solidifying tin droplets. The results reveal that the localized wall-energy term captures post-maximum-spread melt retraction, while the penalty term effectively arrests motion of the solidified splat. Qualitative and quantitative comparisons with experiments, volume-of-fluid simulations, and standard phase-field predictions demonstrate that the proposed formulation captures post-maximum-spread melt retraction and provides an accurate estimate of the stabilized final splat diameter.

We investigate the start-up flows through ordered porous media (hexagonal close-packed, face-centred cubic and body-centred sphere packs) by means of direct numerical simulations. The flows are initiated from rest and driven by a constant pressure gradient, allowing us to examine the transient development across a wide range of Hagen numbers. Dimensional analysis identifies two relevant time scales: the viscous diffusion time $\tau_\mathrm{visc}$ and the inviscid time $\tau_\mathrm{inv}$. While the small-time behaviour follows the viscous asymptotics of Johnson et al. [J. Fluid. Mech. 176, 379 (1987)], the subsequent emergence of nonlinear effects is universally governed by the inviscid time $\tau_\mathrm{inv}$, rather than by any critical Reynolds number. At the pore scale, the transient evolution is characterised by the growth of thin vorticity layers on the sphere surfaces, their detachment into the pore space around $t \sim \tau_\mathrm{inv}$, and the formation of inertial cores. Despite geometric differences, these processes occur in a remarkably similar sequence across all three packings. Vorticity magnitude exhibits laminar boundary-layer scaling with Hagen number, while in the body-centred cubic sphere pack case a transition towards turbulent-type scaling is observed. These results establish $\tau_\mathrm{inv}$ as a unifying measure for the onset of nonlinearity in strongly accelerated porous media flows, with direct implications for the modelling of unsteady transport in natural and engineered systems.

Aft sections of military cargo aircraft employ flat surfaces at high upsweep angles to accommodate ramp doors, producing flow features that affect cargo-drop accuracy, paratrooper safety, and aerodynamic performance. Fundamental studies have primarily examined near incompressible flow over a canonical surrogate consisting of a freestream aligned cylinder with a planar, sharp edged upswept base. The flow exhibits peripheral separation, a horseshoe vortex, and a counter-rotating streamwise vortex pair that persists downstream. The present investigation delineates the effects of compressibility on the wake and examines how these effects depend on basal upsweep angle. Wall-resolved large-eddy simulations are performed at Mach numbers of $0.1$, $0.3$, and $0.5$ for upsweep angles of $32^\circ$ and $45^\circ$ at a nominal Reynolds number of $25{,}000$. For the $32^\circ$ afterbody, increasing Mach number enlarges the upstream recirculation region and delays vortex-pair formation, while these effects diminish downstream. For the $45^\circ$ afterbody, similar recirculation-region growth triggers a bifurcation at Mach~0.5 from the vortex-pair state to a broad separated turbulent wake. A descending-Mach sequence to 0.3 and 0.1 reveals hysteresis, with the separated-wake state persisting at lower Mach numbers and remaining robust to Reynolds-number variation. Thus, both states can occur at identical Mach and Reynolds numbers, with topology and pressure loading governed by Mach number history.

Geological fractures exhibit heterogeneous aperture fields that localize flow along preferential pathways and produce nonuniform fluid-matrix contact times. Heat transport results from channelized advection coupled to conductive exchange with the rock matrix. For non-Newtonian fluids, this coupling is constitutively dependent: shear thinning biases the aperture-to-flux mapping toward larger apertures, while yield stress suppresses flow below the mobilization threshold. This study examines rheology-controlled hydraulic selection in fracture-matrix heat transport using thermal-front advance, longitudinal spreading, and outlet breakthrough as diagnostics. A stochastic semi-analytical channel model represents aperture classes as parallel pathways with constitutively determined fluxes, and the thermal response is obtained by flux-weighted superposition of channel-scale advection-conduction solutions for a semi-infinite matrix. This separation allows late-time scalings and response amplitudes to be analysed independently. Rheology affects observable spreading not only through mean velocity, but also through high-order flux-weighted aperture moments that set the amplitude of persistent inter-channel variance. Matrix diffusion sets the late-time scalings of breakthrough curves and front moments, while aperture variability and rheology control amplitudes, crossover behavior, and inter-channel spreading. Global sensitivity analysis shows that shear thinning controls flux reweighting, while yield stress controls hydraulic accessibility and retained flow. After normalization to a fixed flux-weighted mean velocity, aperture variability and the flow index jointly redistribute heat-carrying flux and shift the residence-time spectrum. The model defines an interpretable reference limit separating rheology-controlled hydraulic selection from matrix-controlled thermal transport.

Weak shock reflection at nearly glancing incidence is governed, after the transonic weak-shock scaling, by a self-similar unsteady transonic small-disturbance (UTSD) free-boundary problem. We derive and differentiate the first finite-strength perturbation of the corresponding isentropic potential-flow problem along paths of fixed canonical incidence $a=\alpha/\delta$, where $\mu=\delta^2=2(M^2-1)$. A second-order refluxed adaptive finite-volume method, exact discrete tangents and adjoints, and a Rankine--Hugoniot-constrained fitted principal front give the fixed-$a$ canonical sensitivity $H_{2,a}^{\PF}(0.5;1.4)=-0.217\pm0.012$; a fully differentiated physical back-map gives the diagnostic fixed-$a$ coefficient $K_{2,a}^{\PF}\simeq-0.266$. We derive the exact chain rule that converts these quantities to the distinguished fixed-$\lambda$ path $\lambda=(M-1)/\alpha^2$, showing explicitly that the conversion requires the independent incidence derivative of the leading UTSD branch and therefore cannot be inferred from the fixed-$a$ calculation alone. A matched-boundary self-similar Euler study with strength-dependent refinement contains 21 qualified nonlinear states and 252 evaluations of a common front-functional family. Coupled extrapolation gives $g_0^{\Eul}=0.510\pm0.006$ and the physical leading-angle coefficient $G_0^{\Eul}=0.256\pm0.004$, consistent with the shock-fitted UTSD limits. A separate same-strength phase-bracket audit using 18 Euler states shows that the captured-shock subcell phase is comparable to the desired cubic signal. The resulting finite-resolution Euler secants are compatible with the potential-flow correction, but their $\rho=h_\eta/\sqrt\mu\to0$ extrapolation is not model-stable. Thus leading-order Euler--UTSD correspondence is numerically verified, whereas cubic-order Euler correspondence remains unresolved.

One of the most critical challenges in turbulent combustion modeling is the chemical source closure. In the recently developed filtered turbulent flame model (FTFM), a oneto-one correspondence between filtered scalar quantities and filtered chemical sources can be constructed by inversely solving the filtered flame equations, without the use of conventional presumed probability density functions (PDFs). However, the turbulence induced flame wrinkling, and thus the enhancement of the chemical source, has not been explicitly considered at the resolved scale. In the present study, the wrinkling effect is analytically quantified in a counterfow flame setup, from which FTFM is then further updated by incorporating such a physics grounded stretching correction on the chemical source. The satisfactory accuracy and robustness of the present model are justified from case tests of the non-premixed Sydney swirl flame and the Delft III flame.

Stochastic geometric mechanics (SGM) is known for its potential utility in quantifying uncertainty in global climate modelling of the Earth's ocean and atmosphere while also preserving the fundamental advective transport properties of ideal fluid flow. This paper is a pedagogical review of the recent developments of the mathematical framework of stochastic geometric mechanics obtained from Lie group-invariant stochastic variational principles in the context of model building for upper ocean dynamics, The paper is divided into the following five parts. Part I discusses the origins of geometric mechanics applications in deterministic fluid dynamics. Part II focuses on the example of the deterministic 3D Euler Boussinesq (EB) equations. Part III adds stochastic transport to the 3D Euler Boussinesq (EB) and derives its SALT equations. (SALT is the abbreviation of Stochastic Advection by Lie Transport.) Part IV focuses on Lagrangian Averaged Stochastic Lie Transport, abbreviated as LA-SALT. LA-SALT treats atmospheric `climate' as the ensemble expectation, while the atmospheric `weather' is treated as a field of pathwise fluctuations, as discussed in Ed Lorenz's famous 1995 lecture. Part V applies SALT and LA-SALT to create stochastic Ocean--Atmosphere Models, abbreviated as SOAM.. The SOAM approach brings us back to Hasselmann's 1976 paradigm, which decomposes a general climate model into its deterministic and stochastic parts.

Rayleigh-Bénard convection of large horizontal extent sometimes self-organizes into domain-filling structures. In two dimensions, domain-filling rolls persist - from some but not all initial conditions - when velocity boundary conditions are stress-free. When velocity boundary conditions are no-slip, domain-filling rolls are not found with fixed-temperature thermal boundary conditions, but they have not been sought with fixed-flux thermal boundary conditions. Here we explore the latter missing case, which is hard to predict because no-slip boundaries do not encourage domain-filling rolls, but fixed-flux boundaries give domain-filling structures in three dimensions for either boundary condition on velocity. We simulate convection with fixed-flux, no-slip boundaries in two-dimensional domains with horizontal period 20 times their height and at various combinations of the fixed-flux Rayleigh number R and Prandtl number Pr. Domain-filling rolls, which are easily found when they are weakly nonlinear at small R, are continued to other (R,Pr) by changing these parameters slowly in time. The (R,Pr) regime where we find domain-filling rolls is substantial but has a boundary. When R is too large or Pr too small, relative to each other, a domain-filling roll pair breaks up into two pairs. These findings contrast with other combinations of dimension and boundary conditions, where scale selection has not been seen to depend strongly on parameter values. The present case helps disentangle competing effects of dimension and boundary conditions, and it offers a more stringent test for explanations of scale selection that have been proposed.

This study presents a hybrid computational framework for simulating non-reacting inviscid high-speed flows of nitrogen gas (N$_2$) around a circular cylinder. Owing to the strongly convection-dominated nature of the compressible Euler equations, the compressible-flow streamline-upwind/Petrov--Galerkin (SUPG) formulation is combined with the YZ$\beta$ shock-capturing technique to stabilize the finite element discretization in the presence of strong discontinuities. Building upon the stabilized solution, a physics-informed neural network (PINN) is employed as a post-processing correction stage (\underline{P}INN-\underline{A}ugmented \underline{S}UPG with \underline{S}hock-\underline{C}apturing---PASSC). The network is anchored to the finite element solution through a shock-weighted data-consistency loss, while the governing equations are enforced in a conservative space--time control-volume form supplemented by macroscopic conservation windows, an entropy-admissibility penalty, and the boundary conditions of the underlying problem. Two-dimensional simulations are performed for free-stream Mach numbers ranging from $2.0$ to $12.0$, and the results are assessed against analytical normal-shock and stagnation relations, the semi-empirical Billig correlation, and reference solutions from the literature. The correction is designed to improve the numerical representation of shocks by reducing localized discretization-induced oscillations and mesh-scale serrations while preserving the agreement of the stabilized solution with the analytical and semi-empirical reference quantities.

We present a Maxwell-Demon nonequilibrium molecular dynamics method for measuring the shear viscosity of a Lennard-Jones fluid. The simulation cell is divided into two regions of width $w$ in the $x$-direction, with particles free to move between the two sides. The Demon maintains equal and opposite regional average particle velocities in the $y$-direction ($\pm u_p$), by applying an acceleration $g_{total}$ that includes both total force balance and a correction for diffusion of particles across boundaries. The momentum relaxation rate needed to sustain the nonequilibrium steady state (NESS) is $\gamma=g_{total}/u_p$. We show that the driven velocity profile is not imposed point-wise in $x$ by the constraint, but is selected by the regional hydrodynamic response of the fluid. For this shear geometry, the measured NESS profile in Eulerian slabs is well represented by a piecewise parabolic form, reminiscent of planar Poiseuille flow. The parabolic profile estimates the kinematic viscosity from work done on the shearing fluid, $\nu_{para}=\gamma_{total}w^2/12$, as well as an entropy production estimate, derived from heat removal by the Nosé--Hoover thermostat that keeps each regional average temperature constant. For a representative run, the work and entropy routes agree to within $0.6\%$, confirming consistency between the mechanical work supplied by the Demon and the heat removed by the thermostat. Once NESS driving is removed, the parabolic velocity profile relaxes exponentially rapidly to sinusoidal, the natural transverse momentum-diffusion eigenmode. These results establish the Maxwell-Demon shear method as a direct NEMD route for obtaining shear viscosity from momentum diffusion, work, and entropy balances. Our results in 3D for increasing system size $N$ (the number of particles) demonstrate that shear viscosity approaches an asymptote (the hydrodynamic limit) as $1/\sqrt{N}$.

Recovering high-resolution states from sparse, low-resolution observations is a central challenge in scientific machine learning and data assimilation. Classical data assimilation exploits temporal information through forecast-analysis cycles, but often requires repeated access to expensive high-resolution forecast models. Generative super-resolution can recover unresolved structure from coarse observations, but is commonly used as a one-shot mapping that does not fully exploit constraints from past states. We introduce Iterative Refinement (IR), a learned data assimilation framework that combines these perspectives. Instead of performing a single coarse-to-fine reconstruction, IR decomposes the task into resolution-wise forecast-analysis operations across a multiresolution hierarchy. At each stage, a shared neural operator with resolution-dependent spectral mode slicing provides a dynamical prior, while a shared conditional diffusion corrector uses the current coarser-resolution state to produce a refined posterior at the next finer resolution. We evaluate IR on one-dimensional stochastically forced Burgers dynamics and two-dimensional Kraichnan turbulence. On the challenging 256x256 Kraichnan benchmark, IR achieves an RMSE of 0.184 and an SSIM of 0.836, outperforming spectral upsampling, one-shot diffusion super-resolution, enhanced deep super-resolution, and an autoregressive forecaster. On the more constrained Burgers testbed, IR remains competitive with one-shot diffusion, which achieves the lowest RMSE. These results show that one-shot generative reconstruction can be effective for simpler settings, while hierarchical forecast-analysis refinement becomes advantageous in strongly multiscale and underdetermined regimes. Overall, IR combines temporal priors, generative correction, and multiresolution reconstruction for learned data assimilation in complex physical systems.

Largest Lyapunov exponents (LLEs) quantify exponential sensitivity, but data-driven estimates are often obtained from finite-precision trajectories. We show that increasing the length of a single reduced-precision chaotic record can eventually degrade a forecast-error LLE estimate. Using the logistic map at r=4, an ESP32 single-precision trajectory is reproduced bit-for-bit by NumPy float32. Across 10,000 random float32 initial conditions, every trajectory reaches an exact recurrence before iteration 7612. For one long float32 record, the estimated LLE changes from 0.6853 at N=15,000 to 0.1827 at N=20,000 and approximately zero at N=30,000 as exact train-test histories saturate. At N=100,000, the long float32 record gives 0.0016, whereas independently restarted length-100 trajectories give 0.6917; matched float64 controls remain near ln(2)=0.6931. The collapse is reproduced for 28 representative initial conditions, and its onset is strongly correlated with the recurrence scale set by transient length and digital period (Pearson r=0.982). Thus, finite-state recurrence can turn additional samples into duplicate futures rather than new dynamical information, while independent restarts substantially delay this saturation.

A scuba diver holding constant depth balances on an unstable equilibrium: the gas carried in the suit and buoyancy compensator compresses with depth, so the buoyant force falls as the diver sinks and rises as the diver ascends. We represent the diver as a proportional-derivative controller that regulates this compressible-buoyancy saddle after a finite reaction delay, and we derive the governing delay differential equation from the vertical force balance and the isothermal gas law, reducing it to a damping ratio, two control gains, and a dimensionless delay. The characteristic spectrum, obtained by pseudospectral collocation of the semigroup generator and checked against a direct Newton solution of the characteristic equation, locates the Hopf boundary that separates stable hovering from sustained porpoising; for the baseline diver the critical reaction delay is 3.36 s and the onset period is 28.8 s. The bifurcation is supercritical, and because the saturating force is the quadratic hydrodynamic drag, the limit-cycle amplitude grows in proportion to the delay excess rather than as its square root. The safe-operating envelope shows that runaway ascent is triggered by saturation of the compensator, not by loss of linear stability, so a stable and an unstable diver can share the same escape threshold. As onset is approached, the lag-one autocorrelation and variance rise while the fitted recovery rate falls and matches the spectral abscissa, giving an eigenvalue-exact early warning of the transition.

Abrupt transitions in complex systems are often preceded by early warning signals. However, most indicators rely on the notion of critical slowing down and do not generally extend to rate-induced tipping where transitions can occur without local loss of stability. This is problematic in stochastic, nonautonomous systems where internal variability and time-varying variables interact to shape tipping onset. We use Koopman operator theory to develop a unified early warning framework for both bifurcation and rate-induced tipping in stochastic systems. Our approach builds on residual Koopman mode decomposition that measures discrepancies between dynamics and their finite-dimensional approximation, and extends it to the control setting by augmenting the observable space with time-varying control variables. In idealized examples, the resulting indicators recover expected signatures near bifurcation points and improve detection in rate-induced regimes where classical indicators fail. We further show that learned embeddings through deep learning outperform prescribed dictionaries, especially in a high-dimensional setting. Applied to simulations of the Atlantic Meridional Overturning Circulation, our Koopman-based indicators distinguish tipping from non-tipping trajectories and reveal interpretable spectral signatures prior to critical transition.

Neural autoregressive models have rapidly emerged as powerful emulators of high-dimensional chaotic systems, yet their long-term instability and error growth remain poorly understood, leading to ad-hoc solutions. Here, we develop an eigenanalysis framework that reveals the dynamical origin of this error growth. By analyzing the Jacobian of the learned one-step update map with respect to the state, we show how inference-time error growth, and thus model stability, is governed by its spectral radius. Direct-step architectures (models that predict the next state from the previous one) generically admit unstable eigenvalues with magnitudes exceeding one, explaining the rapid divergence of these widely used models. In contrast, integration-constrained models (where the time derivative is estimated and integrated with a higher-order integrator) collapse their eigenspectrum onto the unit circle, yielding neutral stability and a universal linear error-scaling law. The largest eigenvalue of this Jacobian provides an architecture-agnostic, a priori diagnostic of short-term skill, long-term stability, and spectral bias, without requiring an expensive rollout. Leveraging this theory, we introduce a stability-promoting loss that explicitly regularizes Jacobian-driven error amplification, improving both forecast accuracy and dynamical robustness. Demonstrated across $29$ models spanning two architectures, several explicit and implicit integrators, and multiple loss functions on the Kuramoto-Sivashinsky system, our results establish a theoretical foundation for the design and evaluation of neural emulators of chaotic multi-scale dynamics. More broadly, our framework is a step toward the kind of a priori stability analysis that numerical analysis provides for discretizations of differential equations and that scientific machine learning currently lacks.

Adjoint methods provide a powerful route for gradient-based optimization, but their physical implementation is obstructed in generic nonlinear systems because the adjoint dynamics requires backward-time evolution, Jacobian transposition, and terminal-value constraints. Here we show that nonlinear parity-time ($\mathcal{PT}$)-symmetric systems overcome this obstruction. Using a class of nonlinear non-Hermitian resonator networks, we establish symmetry relations that map the formal adjoint dynamics onto experimentally accessible forward-time evolutions supplemented by controlled injections. This construction enables exact in-situ evaluation of adjoint gradients without requiring explicit backward propagation or matrix transposition. We demonstrate the approach in nonlinear $\mathcal{PT}$-symmetric resonator chains, where the resulting optimization protocol autonomously discovers parameter configurations that realize prescribed spatio-temporal functionalities, including uniform energy redistribution and targeted wave transport at predefined time windows. Our results identify $\mathcal{PT}$ symmetry as a resource for implementing computational sensitivities within physical systems and establish a route toward self-optimizing nonlinear machines.

We compute the dynamic critical exponent $z$ of the Yang--Lee edge singularity in relaxational dynamics using perturbative renormalization-group methods to the three-loop order. The calculation combines diagram reduction, analytic two-loop evaluation via parametric integration with hyperlogarithms, and numerical evaluation of three-loop integrals using the Sector Decomposition method. The perturbative series obtained is resummed using Padé and Padé-Borel-Leroy methods to produce estimates of $z$ in various spatial dimensions. The resulting values are consistent with previous perturbative and functional renormalization-group calculations.

In the late 1980s, Baulieu and Grossman demonstrated that the supersymmetric formulation of Langevin stochastic differential equations (SDEs), proposed earlier by Parisi and Sourlas, belongs to the family of Witten-type topological field theories (TFTs). From a certain angle, this finding may appear puzzling: TFTs have no local degrees of freedom, whereas SDEs do exhibit local fluctuations. In this paper, we address this apparent contradiction in the context of the supersymmetric theory of stochastic dynamics (STS), a generalization of the Parisi-Sourlas-Baulieu-Grossman approach to SDEs of arbitrary form. We further discuss how, within STS, dynamical chaos can be identified with the spontaneous breakdown of the corresponding topological supersymmetry, while 1/f noise can be understood as a consequence of the Goldstone theorem. The butterfly effect, in turn, calls for an effective field-theoretic description that may itself possess a hidden topological structure, as we speculate on the basis of the Ginzburg-Landau approach and insights from AdS/CFT duality.

In this paper, we study the emergence and dynamics of pure-quartic optical dispersive shock waves governed by the nonlinear Schrödinger (NLS) equation with self-defocusing Kerr nonlinearity and fourth-order dispersion. The corresponding dispersionless hydrodynamic system reveals a distinct mechanism for wave breaking, driven by the nonlinear self-steepening of the hydrodynamic velocity. We illustrate this mechanism through optical dam-break configurations described by Riemann problems and show that, in contrast to the classical quadratic NLS equation, wave breaking occurs prior to wave splitting even in the small amplitude regime. Numerical simulations of the pure-quartic NLS (PQNLS) equation and its hydrodynamic approximation confirm these qualitatively distinct dynamical regimes.

New types of soliton and periodic waves are identified for a nonlinear dissipative medium where the pulse propagation is governed by the cubic complex Ginzburg-Landau equation. We find that the dynamical equation for the pulse amplitude supports two distinct types of kink and antikink solitons with different functional forms. It is found that the obtained kink and antikink soliton waveforms occur under the same fixed inverse velocity. The results also indicate that the periodic waves can propagate with variety of wave forms such as sn, cn, dn and their rational forms as well. It is also shown that in the long-wave limit, the derived periodic waves degenerate into different bright and dark soliton pulses. The stability analysis based on the theory of dispersive waves in nonlinear optics is developed. It is shown that some elliptic and soliton solutions are quasi-stable in the context of passive mode locking lasers described by complex Ginzburg-Landau equation.

We construct novel higher-order lump solutions of the modified Kadomtsev-Petviashvili-I (mKP-I) equation by applying the generalized long-wave limit method with spectral perturbations. By tuning the phase parameters in the soliton solution, we obtain second- and third-order lump solutions, which, to the best of our knowledge, are reported here for the first time for the mKP-I equation. A detailed asymptotic analysis reveals that these degenerate lumps exhibit anomalous scattering analogous to that in the KP-I equation. However, in contrast to the KP-I case, no complete energy equipartition occurs after the collision, and the two lumps remain distinguishable in the subleading terms of their asymptotic amplitudes. This distinction highlights a difference in the interaction dynamics between the modified and standard KP-I equations.

Since the first gravitational-wave (GW) detection of September 14th 2015 and with hundreds of gravitational-wave sources identified by the LIGO-Virgo-KAGRA network, GW have produced many important results in astrophysics and fundamental physics. Along with planned new data takings, current detectors will be upgraded and new project, such as Einstein Telescope and Cosmic Explorer, are under study. Among noises limiting low frequency sensitivity, vibro-acoustic noises are particularly important. In this work, we focus on the gravity gradient noise (also called Newtonian noise) of acoustic origin, which refers to the small fluctuations in the gravity field resulting from the acoustic pressure field present in the experimental areas of the detector. The induced noise is quantified in an original way, using a detailed nu- merical acoustic model of the experimental room, when the pressure field is excited by the air conditioning system. The method is used for Virgo, but it can be easily extended for future detectors and used to guide the design of caverns and experimental areas.

In thermodynamics, reversible adiabatic expansion can be understood as a limit of stepwise irreversible processes. We make this idea concrete by studying an ideal gas in an insulating cylinder with a frictionless piston supporting a load divided into $N$ blocks. If blocks are removed one at a time, the resulting expansion is a stepwise, irreversible process, but we prove that for a fixed total load, the work done by the gas approaches the reversible limit as the largest block mass tends to zero. On the way to this limit, an interesting work optimization question arises at finite $N$: how does the work done by the gas depend on the order and sizes of the removed blocks? Guided by numerical experiments accessible to advanced undergraduates, we motivate and then prove general answers to these questions. Our main finite-$N$ result proves that for fixed $N$, the optimal stepwise expansion corresponds to a geometric progression of equilibrium pressures, settling a conjecture previously made by Andresen, Berry, Nitzan, and Salamon.

Radio detection of ultra-high energy particles ($\gtrsim10^{18}$ eV) depends on how broadband radio pulses reflect from natural media boundaries. We extend the spherical-wave (Sommerfeld--Weyl) treatment of a single homogeneous interface to stratified media by replacing the Fresnel coefficient of each plane-wave component with the characteristic-matrix reflection coefficient of a layered medium, evaluated in the local tangent plane on the spherical surface. The calculation reduces to the single-boundary result at machine precision when the layer contrast is removed and agrees with the published spherical-surface calculation to better than $1.1\%$ at ten HiCal-2 elevation angles, with a mean deviation of $0.6\%$. We apply the formalism to shallow firn stacks proposed as explanations for anomalous-polarity ANITA events. For realistic firn contrasts, layering changes the reflected amplitude but does not reverse the pulse polarity over $150$--$850$ MHz for the elevations studied. In a reference $s$-polarized two-layer model, a coefficient sign change requires buried refractive index $n_2\simeq2.56$, $2.04$, and $1.79$ at local elevations of $8^\circ$, $15^\circ$, and $25^\circ$, respectively. We also test the specular factorization used in fast propagation models, finding $0.2\%$ agreement with the full angular integral for high-altitude balloon geometries, while near-boundary sources require the full integral. The calculated reflected pulses reproduce the expected polarity inversion in $101$ of $106$ HiCal-1 direct/reflected pulse pairs. Because the medium enters through its complex refractive index, the framework applies to ice, lunar regolith, and conducting media.

Thermal monitoring in practical applications is often constrained by sparse sensing, measurement noise, and limited spatial resolution, which hinder the identification of heat transfer dynamics. In such settings, calibrating high-fidelity physical models is computationally demanding, motivating data-driven approaches. Dynamic Mode Decomposition (DMD) provides a framework for extracting spatiotemporal structures from measurement data, but its standard formulation is sensitive to noise and degraded observations. This chapter examines the use of DMD under these constraints, focusing on preprocessing and truncation strategies that affect stability and interpretability. Two cases are considered: forced convection with thermocouple data and transient heat conduction from degraded thermal images. The number of retained modes is treated as a modeling parameter that governs the trade-off between reconstruction fidelity and noise sensitivity. The results indicate that DMD recovers dominant thermal behavior from both sparse and degraded datasets when the truncation level is appropriately selected. Low-rank models provide stable but simplified descriptions, while higher-rank models improve spatial detail at the cost of increased noise sensitivity.

Altermagnets have emerged as a new class of magnetic materials that combine spin-split electronic bands with zero net magnetization. Extending this paradigm to classical-wave systems has, however, been fundamentally challenging because conventional realizations require broken time-reversal symmetry (TRS). Here, we overcome this limitation by introducing two pseudospin degrees of freedom and constructing a pseudo-time-reversal operator that faithfully reproduces the action of its physical counterpart while preserving actual TRS. Building on this framework, we theoretically propose and experimentally realize the first time-reversal-invariant altermagnetic acoustic crystal. Acoustic measurements directly reveal pseudospin-dependent band splitting--a defining hallmark of altermagnetism--under strictly TRS-preserving conditions. Moreover, the altermagnetic acoustic crystal exhibits sublattice-pseudospin locking, enabling flexible control over acoustic pseudospin splitting and filtering. Our work establishes acoustic crystals as a versatile platform for exploring altermagnetic physics and opens new avenues for spin-inspired wave manipulation in nonmagnetic devices.

Magneto-active elastomers (MAEs) -- composites of magnetic nano-/micro-particles embedded in a soft polymer matrix -- are promising for soft robotics, as their shape and mechanical properties can be controlled by an applied magnetic field. Most MAEs are filled with magnetically soft (MS) micro-particles, such as carbonyl iron powder (CIP). We employ molecular dynamics to study the differences between thin MAE layers with MS and magnetically hard (MH) filler particles having the same saturation magnetization. We find that both MH and MS elastomers converge to the same high-field state -- a labyrinth of bundled, field-aligned chains -- but do so through distinct pathways: MH MAEs break their zero-field chains, which lie parallel to the MAE layer plane (in-plane), and rotate them into alignment with an external magnetic field, whereas MS MAEs gradually build up field-aligned chains from neighboring particles. We show that the MS model reproduces the magnetization curves and surface roughness of CIP-based MAEs for magnetic fields close to saturation, while maintaining the observed qualitative features at lower field strengths. The mismatch between simulation and experimental results at low fields suggests the need for a MS model that accounts for the multi-domain nature of carbonyl iron microparticles.

Fourier quasicrystals are aperiodic structures whose diffraction spectrum consists not of a dense set of Bragg peaks, as in ordinary quasicrystals, but of isolated ones scattered across a discrete, nonperiodic set. This sparse reciprocal-space structure should leave wave transport largely undisturbed except at a few selected wavevectors. We put this prediction to the test using surface water waves scattering off a two-dimensional Fourier quasicrystal. Full-field measurements reveal three distinct transport regimes as the incident wavevector increases: transparency, selective scattering, and strong scattering. By reconstructing the structure factor from the measured wavefields, we directly relate these regimes to the underlying reciprocal-space structure. Our results establish Fourier quasicrystals as a physical platform in which wave transport can be controlled through the organization of diffraction peaks in reciprocal space.

Adhesive contact measurements on soft polymers are commonly interpreted using Johnson-Kendall-Roberts (JKR) theory, which is formulated for circular contacts. Here, we examine contact formation and detachment in non-circular soft adhesive contacts using PDMS crossed-cylinder experiments. The crossing angle was varied from 30 to 90 degrees, producing contacts from highly elongated ellipses to nearly circular geometries while keeping the material pair fixed. During loading, the contact aspect ratio b/a rapidly approached an angle-dependent plateau, indicating approximately self-similar growth. This motivates use of the area-equivalent radius c=sqrt(a*b) and geometric-mean curvature radius Reff=sqrt(R1*R2). The loading branches follow a JKR-type linearization and yield a nearly angle- and preload-independent work of adhesion, W_load=24 mJ/m^2. Johnson-Greenwood elliptical-contact fits give comparable values. In contrast, unloading and pull-off are strongly history dependent. The unloading branches require a substantially larger effective separation energy, W_unload,eff, which increases with preload and decreasing crossing angle. A reduced viscoelastic model based on the same area-equivalent description captures the principal unloading response over 50-80 degrees using a single shared parameter set across angles and preloads. These results show that contact formation is governed primarily by area-equivalent scaling, whereas detachment is governed by geometry- and history-dependent dissipative separation.

The reptation model postulates that entangled polymers slide within a fractal tube. Here we employ a model-independent relation between the zero-displacement probability and the mean-square displacement that applies to time-dependent fractal structures, enabling direct measurement of the fractal dimension $d_\mathrm{f}$ of the geometry experienced by monomer motion. For two-dimensional obstacle arrays and in the slip-link model, $d_\mathrm{f}$ agrees with the reptation prediction $d_\mathrm{f}=1/\nu$ (where $\nu$ is the Flory exponent). In polymer melts, however, we find $d_\mathrm{f} \approx 2.6$ --- a value close to the fractal dimension of percolation clusters, not the reptation value $d_\mathrm{f}=2$. This contrasts sharply with the reptation picture, in which a Rouse chain slides in a fractal structure with $d_\mathrm{f}=2$, spectral dimension $d_\mathrm{s}=1$, and walk dimension $d_\mathrm{w}=4$; our results point instead to a percolation-like scenario, characterized by $d_\mathrm{f}\approx 2.6$, $d_\mathrm{s}\approx 1.3$, and $d_\mathrm{w}\approx 4$ --- revealing a dynamically emergent, finite-size fractal geometry distinct from the static tube.

Drying particle suspensions is widely used to assemble particles and to fabricate porous functional layers for various applications, in which microstructural properties critically influence the overall device performance. Understanding the mechanisms governing drying-induced microstructure formation is therefore essential for predictive control of the resulting structures. In this work, we numerically investigate the evolution of microstructures during the drying of particle suspension films, with a particular focus on the role of particle-particle interactions. For weakly interacting particles, the particles assemble into hexagonal structures at the interface, and upon drying, trigger subsequent layer-by-layer assembly. We present a simple theoretical model to predict the time evolution of the layer thickness, validated against our simulation results. With strong particle interactions, the particles aggregate and form a network-like structure during drying, leading to a porous deposit. The porosity of the structure follows a power-law relationship with a dimensionless adhesion parameter that characterizes the particle-particle interaction force relative to the capillary force. By systematically varying the adhesion parameter, three packing regimes of the final structure are identified: hexagonal close packing, random close packing, and adhesive packing. Overall, our results demonstrate that particle-particle interactions play a decisive role in determining the final porous structure, providing practical guidance for tailoring functional layers through controlled manipulation of particle interactions.

The dependence of ion pairing on osmotic stress may strongly affect the performance of ionic materials and membranes whose interior is often osmotically stresses, yet quantitative understanding of this dependence and, specifically, the effects of water and ion activities is limited. Motivated by this gap, we analyze the enhancement of ion pairing with osmotic pressure for concentrated aqueous KCl, NaCl, and LiCl solutions using molecular dynamics simulations. Based on rigorous thermodynamic relations, we separate the contributions of ion non-ideality to the pairing constant, varying with osmotic pressure, from other effects including water release and type of ion-pair. Our analysis reveals that ion non-ideality indirectly generates a stronger effect on pairing than the direct one of water release. However, its effect is moderated and may even be reversed for more hydrated pairs by a similarly large and opposite effect of ion-pair non-ideality assigned to varying dielectric properties of the solution and water restructuring upon pairing. The interplay between these contributions, including large and pair type-specific hydration effects on the cost of pairing, explains the observed opposing trends: pairing decreases with osmotic pressure for more hydrated solvent-separated pair types while increasing for contact pairs. The trend becomes more pronounced for more hydrated smaller cations, but was fairly independent of the water model used. The results further suggest that dielectric effects enhanced in ionic materials-and, as a result, larger variations of ion-pair non-ideality, compared with aqueous solutions, should have a more significant impact on pairing than water release.

Collective cell migration emerges from the interplay between motility, deformability and mechanical interactions, yet incorporating these ingredients into computationally efficient tissue models remains challenging. Here, we benchmark self-aligning deformable active membranes in a confined-flow geometry that mimics epithelial monolayer migration around a circular obstacle. In this model, cells are represented as deformable, adhesive membranes whose self-propulsion direction relaxes towards their velocity. By systematically varying the self-alignment timescale, cell-cell adhesion and inlet forcing, we characterize the resulting flows through collective alignment, relative density, neighbor rearrangements and spatial velocity fields. The model captures a broad spectrum of tissue behaviors, ranging from disordered, liquid-like flows to highly aligned, solid-like states. Compared with a related multiparticle model, self-aligning active membranes achieve stronger collective alignment, exhibit a more systematic density response and access states closer to both limits of the solid-liquid spectrum. We further show that increasing the target shape index promotes cell elongation and accelerates tissue flow, directly linking cell-scale deformability to tissue-scale transport. Finally, we compare simulated velocity profiles with experimental measurements from in vitro migrating MDCK epithelial cell monolayers and find qualitative agreement across multiple horizontal and vertical transects around the obstacle. These results establish self-aligning deformable active membranes as a versatile framework for connecting cell mechanics, shape adaptation and self-alignment to collective tissue migration in confined geometries.

Fluid-structure interaction (FSI) in viscoelastic flows past deformable structures at low Reynolds numbers remains poorly understood, despite its relevance to biological systems such as cilia and flagella, and to engineered microsystems. We investigate viscoelastic FSI in side-by-side flexible cantilever arrays using a bottom-up approach that systematically varies the number of cantilevers and the rheology of the test fluid, comparing weakly shear-thinning (WS) and highly shear-thinning (HS) polyethylene oxide solutions. For both fluids, with increasing Weissenberg number (Wi), an elongated elastic wake develops behind a single isolated cantilever. For multiple cantilevers, the WS fluid undergoes a transition at a critical Weissenberg number (Wi*) from separated to merged elastic wakes, accompanied by the emergence of a divergent flow field and coordinated inward spanwise cantilever deflection. The critical Wi* increases as the number of cantilevers in the array is increased from two to three, demonstrating a strong dependence of the onset on the array configuration. For the HS fluid, wake merger, flow divergence, and inward cantilever deflection are suppressed across the full range of Wi investigated, despite comparable elasticity and the formation of elastic wakes. This contrast shows that elasticity alone promotes wake formation but is insufficient to produce the collective instability, which instead requires both shear-thinning and interactions between neighboring cantilevers. These findings demonstrate that viscoelastic FSI in flexible arrays is governed by the combined effects of fluid elasticity, shear-thinning, and geometric configuration, with elastic wake interactions mediating the collective instability and linking local elastic wakes to array-scale structural response.

Self-organized spatial patterns are central to nonequilibrium physics and cell biology, yet locating instabilities in multi-component, reaction-diffusion networks remains challenging because standard eigenvalue analyses scale with the number of biochemical states and rely on reaction kinetics often poorly constrained by experiments. Exploiting the common mass-conserving structure of protein reaction kinetics and the fact that nonlinear feedback is typically confined to membrane reactions while lateral membrane diffusion is negligible, we develop a geometric classification that predicts stationary, and approximately also oscillatory, pattern-forming instabilities from reactive equilibria. The developed criteria reduce the stability analysis from the full component space to the space of conserved species. On this reduced space, slope matrices---describing the change of equilibrium cytosolic densities with respect to total species densities---govern onset. Based on densities in chemical equilibrium, this approach eliminates the requirement of comprehensive kinetic knowledge frequently lacking in experimental systems. Thus, a broad range of instabilities can be understood as mass-redistribution instabilities---self-amplifying mass redistribution caused by shifting local equilibria. We apply these criteria to models for the Escherichia coli Min system and the Caenorhabditis elegans polarity system and show that the reduction extends to the mixed-dimensional dynamics in systems coupling bulk cytosolic dynamics with membrane dynamics on the boundary. Together, these results provide an interpretable, broadly applicable, and experimentally accessible framework for diagnosing and designing pattern formation in multicomponent nonequilibrium systems on the basis of conservation laws.

Hypersonic flows involve extreme thermochemical non-equilibrium, where strong energy dissipation leads to tightly coupled chemical reactions, radiation, and energy exchange. In this regime, surface chemistry, particularly catalytic wall reactions, can significantly affect boundary-layer composition and surface heat transfer. Accurate simulations of such flows may require repeated evaluations of detailed thermochemical libraries, which represent a major computational bottleneck in high-fidelity reactive-flow simulations. To mitigate this cost, we employ the data-driven reduced-order framework introduced by Scherding et al. (2023), which combines nonlinear dimensionality reduction, community clustering, and local surrogate models to efficiently approximate high-dimensional thermochemical mappings. In this work, this framework is extended for the first time to hypersonic reactive flows with localized catalytic surface discontinuities, introducing sharp variations in wall chemistry and heat transfer. To address the increased complexity of the thermochemical state space, the dimensionality reduction method is enhanced with a Sammon-type stress penalty that mitigates topological folding of the latent manifold and improves the robustness of the clustering and surrogate stages. The resulting model accurately captures the effects of discontinuous catalytic properties, including sharp gradients in wall species mass fractions, diffusion fluxes, and surface heat transfer, while reducing the overall simulation cost by 50% without compromising accuracy.

We investigate the long-time behavior of optimal mixing in an advection-diffusion equation using a shell model framework. Our focus is on quantifying the decay of the scalar variance, measured by the negative Sobolev norm $H^{-1}$, under enstrophy-constrained stirring. We perform long-time computations using both local-in-time (maximizing the instantaneous mixing rate) and global-in-time (maximizing mixedness at a prescribed final time) optimization strategies. For mixing with diffusion ($\kappa>0$), the numerical results show that the scalar length scale eventually becomes limited by a generalized Batchelor scale, in close agreement with theoretical predictions. In this regime, the $H^{-1}$ mix-norm decays exponentially in time with a decay rate that is independent of the diffusivity $\kappa$. Compared with the purely advective case ($\kappa = 0$), diffusion significantly enhances the long-time mixing rate; moreover, increasing diffusivity further improves mixing efficiency by reducing the prefactor of the exponential decay. Guided by these numerical observations, we derive new conditional lower bounds on the $H^{-1}$ norm whose exponential decay rates are strictly independent of the diffusivity parameter $\kappa$, for all $\kappa > 0$. We further establish conditional upper bounds on the maximal rate of enhanced dissipation of the scalar variance, showing that the effective diffusion time scale is at least of the order $|\log\kappa|$.

A large-eddy simulation (LES) of a laminar separation bubble (LSB) induced by an adverse pressure gradient over a flat plate is performed at an inflow displacement-thickness-based Reynolds number of 410 and a free-stream Mach number of 0.25. With a mean peak reverse flow of 21.4%, the bubble sustains self-excited vortex shedding through a local region of absolute instability, in the absence of any external forcing. Spectral proper orthogonal decomposition (SPOD) applied to the LES data identifies three dominant coherent structures within the LSB: two-dimensional and oblique Kelvin--Helmholtz (KH) waves in the separated shear layer at the vortex-shedding frequency, and stationary spanwise-periodic streaks near reattachment at near-zero frequency. Classical resolvent analysis of the mean flow identifies strong convective amplification of the KH waves over a range of spanwise wavenumbers, but predicts only weak amplification in the low-frequency, streak-forming region, where the leading gain is orders of magnitude smaller and no dominant rank-one mechanism is present. This discrepancy with the SPOD energy indicates that the streaks are not sustained by same-frequency linear amplification, but are instead energized by the intrinsic forcing, which the classical framework treats as an unexplained input. Harmonic resolvent analysis of the time-periodic base flow reveals the underlying mechanism: the base-flow unsteadiness couples the oblique KH wave at the shedding frequency to the stationary streak through cross-frequency amplification, yielding a gain far larger than that of the direct same-frequency amplification. This cross-frequency route provides a likely explanation for how the stationary streaks observed near reattachment are energized.

The presence of sidewalls in turbulent duct flows leads to the emergence of secondary flow structures in the form of counter-rotating streamwise vortices near the corners (Prandtl's secondary flow of the second kind). This work develops reduced-order Galerkin projection models that can predict the emergence and structure of these turbulent mean secondary flows in a square duct geometry, without requiring any prior knowledge of the turbulent statistics. The models are obtained by projecting the Navier--Stokes equations onto eigenmodes of the linearised system, with the resulting systems of ordinary differential equations simulated with the addition of zero-mean forcing. We show that most models obtained using leading streamwise-constant eigenmodes predict the correct shape and direction of the secondary mean, with the minimal such model requiring only two modes. In these models, the secondary mean contribution arises due to the nonzero average coefficient of an eigenmode that possesses all of the symmetry properties expected of a secondary mean. The models are sufficiently simple such that the relationship between this mean coefficient and the joint second moment of other mode coefficients can be computed analytically. We confirm that running streamwise-constant direct numerical simulations (DNS) with the same forcing structure as used in the reduced-order models produces similar secondary-flow structures. We additionally demonstrate that our models produce qualitatively similar Reynolds stress distributions to fully resolved direct numerical simulations, with improved agreement as model dimension increases.

We study optimal control problems for incompressible fluids in two-dimensional domains with a cold boundary and internal heat sources and sinks. Given a kinetic energy budget, measured by the square of a nondimensional Péclet number $\mathrm{Pe}$, the goal is to maximize a cooling efficiency inversely proportional to the mean square gradient of the fluid's temperature. Using Lagrange duality, we formulate a well-posed dual problem whose solution yields an upper bound on the maximum cooling efficiency $\mathcal{E}(\mathrm{Pe})$. We then numerically approximate the dual problem using a convergent hierarchy of semidefinite programs obtained via discretization. We illustrate this computational approach on optimal cooling problems in a square and in an annulus, explaining also how problem symmetries can be exploited to reduce computational complexity. Finally, we construct admissible points for the dual problem to obtain new analytical upper bounds on the optimal cooling efficiency $\mathcal{E}(\mathrm{Pe})$. Specifically, we prove that $\mathcal{E}(\mathrm{Pe}) \lesssim \mathrm{Pe}^{2}$ for arbitrary domains and heat distributions, and that $\mathcal{E}(\mathrm{Pe})\lesssim \mathrm{Pe}^{2}/ \ln^2\mathrm{Pe}$ for cooling flows in disks and annuli with heat source/sink distributions with a positive azimuthal average. These results generalize and improve known efficiency bounds for energy-constrained cooling flows in a disk.

The immersed boundary (IB) method models fluid--structure interaction using the natural Lagrangian and Eulerian formulations of structural mechanics and fluid dynamics, respectively, but explicit time discretization of the IB force imposes a stiffness-dependent upper bound on the time-step size. Treating these forces implicitly removes this restriction, but the resulting coupled linear systems become increasingly difficult to solve as the structural stiffness increases. Algebraically eliminating the Lagrangian degrees of freedom yields a reduced Eulerian velocity--pressure IB system. Here we introduce a coupling-aware Vanka (CAV) smoothing strategy to enable effective multigrid preconditioning of this system. CAV patches are built as unions of standard pressure-centered Vanka patches, with the graph of the Eulerian elasticity matrix determining which patches are combined. Under grid refinement, CAV patch sizes remain bounded, and the computational cost of each multigrid cycle thereby grows linearly with the number of Eulerian degrees of freedom. Tests using target-point, membrane, and beam force laws show that CAV-preconditioned FGMRES reduces the relative residual by ten orders of magnitude in $9--15$ iterations, with little growth under grid refinement. In a nonlinear benchmark modeling flow past a flexible fiber, the average number of FGMRES iterations per Newton solve increases only from $8.6$ to $9.5$ as the Eulerian grid is refined from $32\times32$ to $256\times256$ cells. To our knowledge, CAV provides the first robust multigrid strategy for time-dependent implicit IB formulations.

Clinically actionable, patient-specific hemodynamic assessment, specifically wall shear stress, vortex structure and pressure distributions, is critical for determining risky or unfavorable evolution in Abdominal Aortic Aneurysms (AAA). While Physics-Informed Deep Operator Networks (PI-DeepONets) show promising results in complementing established 5 tools such as Computational Fluid Dynamics (CFD), a persistent architectural challenge remains for complex 3D flows. In this direction, we propose a Modified Multi-Input Multi-Output PI-DeepONets (M3PI-DeepONet) designed for predicting unsteady flows in an idealized AAA geometry. Central to our model is the Aggregated Injection strategy, where latent representations from multiple input branches are fused prior to trunk injection, allowing the coordinate basis to adapt to multiple physical constraints. To the best of our knowledge, this is the first architecture to combine the layer-wise gating mechanism with a multi-branch operator-network topology, yielding an input-adaptive trunk basis. Additionally, we integrate the 3D Navier-Stokes equations as governing physical laws, so the model is trained based on physics-informed residuals, initial and boundary conditions, and only 0.3% of the labeled internal data together with the selected branch-conditioning signals. The M3PI-DeepONet simultaneously predicts unsteady 3D flow velocity and pressure fields with an average relative L2 velocity error below 4% and pressure error around 5% while achieving a conservative retained-cycle inference speedup of approximately 36x compared to reference CFD simulations once the branch inputs used for conditioning are available. This work advances the application of deep learning in cardiovascular disease modeling, marking step toward real-time, non-invasive clinical diagnostics.

We derive a one-dimensional reduction for nonlinear dynamics on simplicial complexes containing both pairwise and triangular (higher-order) interactions. The effective state is defined using a mixed weight determined by the pairwise and triangular degrees of each node. The resulting reduced equation retains two structural coefficients, associated separately with the pairwise and higher-order coupling channels. A fluctuation expansion identifies the closure assumptions underlying the reduction and shows how deviations of individual node states from the effective state contribute to the approximation error. We numerically validate the proposed framework on Gene-regulatory dynamics, the double-well system, and SIS spreading. The states of the reduced model are compared with full-network simulations through coupling-parameter sweeps, steady-state branch calculations, and progressive node-removal experiments on synthetic and real-world networks. The reduced model successfully reproduces the principal transitions and steady-state branches in all three dynamical systems considered. Agreement is strongest for relatively homogeneous networks and deteriorates when structural heterogeneity produces a broader distribution of node states. The closure diagnostics account for this loss of accuracy and indicate when a single effective state is no longer sufficient. The reduction therefore provides a tractable description of resilience in systems with coexisting pairwise and higher-order interactions.

The standard master stability function (MSF) formulation has traditionally relied on a diagonalizable network Laplacian, since diagonalizability allows the variational equations to be decomposed into independent equations. Directed Laplacians, however, need not be diagonalizable. We show that every weakly connected digraph admits a strictly positive arc weighting for which its weighted in-degree Laplacian is diagonalizable. Our construction first extracts a weakly connected spanning directed acyclic graph having exactly one source vertex in each root strongly connected component and assigns positive weights so that the weighted indegrees of all remaining vertices are pairwise distinct. The remaining arcs of the original digraph are then assigned a common sufficiently small positive weight. The nonzero eigenvalues remain pairwise distinct under this perturbation, while the zero eigenvalue is semisimple, with multiplicity equal to the number of root strongly connected components. Consequently, the resulting Laplacian admits a complete set of eigenvectors and restores the fully decoupled form of the MSF variational equations. We further give a discriminant-based criterion for computing an admissible interval of the common arc weight.

A one-dimensional SQUID (superconducting quantum interference device) array/metamaterial is investigated numerically with respect to its localization properties due to nonlinearity in the absence of dissipation and periodic driving. The system possesses a conserved Hamiltonian function representing its energy, and supports localized modes of the discrete breather type even in the presence of a moderately high dc flux bias. The appearance of discrete breathers in that system has been largely overlooked in literature. We find a new type of discrete breather that is asynchronous, meaning that the frequency of oscillation of the SQUID at the central breather site is different than that of the SQUIDs at the other sites of the metamaterial. Nonlinear localization is investigated by initializing the system with a single-site excitation of given amplitude (initial amplitude) for a fixed value of the coupling coefficient, while parameters such as the dc flux bias, the single-site initial excitation amplitude, and/or the SQUID can vary independently. Using the energetic participation ratio as a measure of the degree of localization, the existence of asynchronous highly localized modes and transitions between delocalized (extended) and localized modes re identified.

We investigate the dynamics and spectral stability of traveling kink and antikink solutions in a dissipative sine--Gordon equation with two distinct fourth--order regularization mechanisms: a mixed space--time (inertial) term and a purely spatial (elliptic) term. The model includes damping, bias forcing, and higher--order dissipative effects, and is motivated by refined descriptions of fluxon dynamics in long Josephson junctions. Using a collective--coordinate reduction, we derive a Melnikov--type condition for speed selection, yielding explicit predictions for asymptotic propagation speeds, which are validated by direct numerical simulations of the full partial differential equation. Spectral stability is analyzed using Evans function techniques adapted to the singular slow--fast structure induced by the regularization. By formulating the linearized problem on a consistent--splitting domain, we show that no additional point spectrum bifurcates from the origin. Near the edges of the essential spectrum, a square--root transformation is used to resolve branch singularities and establish analyticity in a lifted spectral variable. Numerical Evans function computations near $\lambda=0$ and near the essential spectrum edges confirm the analytical results, indicating absence of unstable eigenvalues for both kink and antikink solutions.

We introduce a procedure to obtain lump solutions via the formation of a kink-antikink pair, consisting of the superposition of kinks whose distance from the origin is controlled by a single parameter $a$. For large values of $a$, a wide plateau appears in the solution, which we call a large lump. The procedure involves the use of a first-order equation that allows the construction of the potential associated with the lump solution. We then investigate several known scalar field models where the parent kinks are capable of giving rise to novel lumps. The lump inherits the tails of the parent kink, allowing for either short-range exponential profiles or long-range profiles characterized by distinct power-law decays. We also show how to verify if an arbitrary lump solution can be obtained via our method and illustrate this possibility with a novel vacuumless lump.

We study a two--dimensional discrete nonlinear Schrödinger equation with saturable nonlinearity on the lattice $\mathbb Z^2$. Using a variational approach based on the Nehari manifold, we establish the existence of nontrivial periodic ground states on finite lattices and establish the existence of exponentially localized ground states in $\ell^2(\mathbb Z^2)$. A principal result is the rigorous passage from periodic to localized states: we show that, up to lattice translations, periodic ground states converge strongly in $\ell^2(\mathbb Z^2)$ to a localized ground state as the lattice periods tend to infinity. The analysis combines variational methods, spectral properties of the discrete Laplacian, and concentration--compactness techniques adapted to the two--dimensional discrete setting. We further derive qualitative properties of the resulting solutions, including positivity and exponential localization, and establish a conditional orbital stability result within the Grillakis--Shatah--Strauss framework. Numerical computations illustrate the theoretical results and confirm the predicted convergence and localization behavior.

We develop a systematic adiabatic perturbation theory for the integrable $F=1$ spinor nonlinear Schrödinger equation under nonvanishing boundary conditions, formulated entirely within the framework of the associated Riemann--Hilbert problem. In this setting, localized nonlinear excitations are characterized by discrete spectral data consisting of a complex eigenvalue and an associated polarization vector. For a general class of small perturbations preserving the background, we derive the perturbation-induced evolution of the scattering data directly at the level of the Riemann--Hilbert problem. In the one-soliton sector, this yields a closed finite-dimensional dynamical system governing the slow evolution of the effective soliton parameters, including the spectral variables, the soliton center and phase, the residue amplitude, and the internal polarization state. The latter evolves according to a constrained dynamical equation with no scalar analogue. For localized perturbations, the modulation equations are expressed in explicit integral form in terms of the one-soliton eigenfunctions, providing a fully computable description of the dynamics. In the limit of vanishing boundary conditions, the resulting system reduces to the perturbation theory obtained by E. V. Doktorov, et al, Phys. Rev. A 77 (2008), no. 4, 043617.

Maxwell's wave equation in the presence of a cubic nonlinearity and a periodically time-varying refractive index (a photonic time crystal) is reduced, for spatially monochromatic waves, to a nonlinear Mathieu equation. Near the principal momentum gap this equation admits an autonomous two-dimensional reduction whose complete Hamiltonian phase portrait can be obtained analytically. We derive the two homoclinic separatrices corresponding to temporally localised momentum gap solitons, identify the nonlinear centres and the critical Hamiltonian value $H_c$, and calculate the point of maximum linear parametric gain. We then consider spatially localised pulses and show how the nucleation of multiple spatiotemporal gap solitons can produce a broad supercontinuum in momentum space; for stronger seeds, transient extreme nonlinear localisation can accompany an abrupt additional broadening of this momentum spectrum. These results establish a direct connection between Floquet amplification, nonlinear saturation, homoclinic dynamics, and momentum space spectral broadening in nonlinear photonic time crystals.

Frequency-domain Huygens' principle and equivalence relations for an infinitely long cylindrical surface enclosing the field sources or scatterers are addressed. Assuming the harmonic dependence of the fields along the cylinder axis, we derive three equivalent versions of line-integral representations for the fields in free space at any point outside the enclosing cylinder. In one of the forms, similarly to the Helmholtz-Kirchhoff scalar diffraction theory, the integrals contain a longitudinal field component and its normal derivative. Another presented form contains longitudinal and normal field components, similarly to the three-dimensional boundary integral representations by Stratton and Chu. This form eliminates the need to calculate the field derivatives. Furthermore, we present a two-dimensional version of the three-dimensional Schelkunoff-Franz representation, which contains only tangential components of the fields, complies with the field equivalence theorem and can be regarded as a rigorous formulation of Huygens' principle for a cylindrical enclosing surface. All three forms of the line-equivalence relation are exact and describe the fields through equivalent field distributions on a line enclosing the cross section of the source region. A physical interpretation of Huygens' principle in terms of conical waves emanated by virtual linear sources on the cylindrical surface enclosing the true sources is given. Specialization of the relations to the intermediate and far-field zones are presented. The derived expressions are applicable for studies of scattering and radiation in a very general class of structures that are infinite and periodic along one direction.

Mesoscale self-assembly provides a route toward the design of programmable microsystems. Here, we construct flexible chains of floating monomers whose curved branches impose upward or downward deformations of the liquid interface, corresponding to effective positive or negative capillary charges. These geometrically encoded deformations generate local attractive or repulsive interactions along the chain. By tuning the capillary sequence, we obtain distinct folded configurations, including straight lines, zigzag patterns, and loops. For short chains, folding is largely governed by nearest-neighbor interactions and leads to well-defined structures. As the chain length increases and non-neighboring segments come into proximity and interact, however, the folding landscape becomes increasingly complex, with multiple metastable states whose number grows exponentially with chain length. We map these landscapes numerically and demonstrate experimentally that mechanical agitation allows the chains to transition between metastable configurations. Beyond encoding a target geometry, the capillary sequence therefore controls the complexity of the folding landscape as well as the degeneracy and mutational robustness of folded structures. These results establish capillary chains as a controllable mesoscale platform for investigating how local interaction rules give rise to collective folding and complex sequence-to-structure relationships reminiscent of those encountered in biomolecular systems.

Bicontinuous interfacially jammed emulsion gels (bijels) facilitate efficient mass transport across multiple length scales due to their interwoven structure of particle-stabilised liquid channels. This unique morphology imparts considerable potential for applications in separation and catalysis, particularly when fabricated \textit{via} solvent-transfer-induced phase separation (STrIPS). STrIPS enables the continuous, large-scale production of nanostructured bijel films on solid substrates, yet the influence of the substrate properties on the formation dynamics and final morphology remains insufficiently understood. In this study, this relationship is elucidated by preparing STrIPS bijel films on silane-functionalised glass substrates with selectively controlled wettability and analysing the resulting structure with confocal microscopy. The results showed the presence of notable wetting layers at the bijel-substrate interface, whose thicknesses could be tuned through the nanoparticle weight fraction. In line with numerical simulations, increasing the substrate hydrophobicity drove a transition from a laminar, water-rich surface layer to a patch-like, progressively oil-rich structure. These findings provide crucial insight into the structure-directing role of substrates in supported bijel films, which aids their application as functional materials.

Nonequilibrium membrane pattern formation is studied using meshless membrane simulation. Bound proteins are considered to have two states that generate different membrane spontaneous curvatures. Protein binding and unbinding occur cyclically owing to chemical potential differences, as an off-lattice active Potts model. It is found that this cyclic binding/unbinding can induce blinking domains, with oscillating size: convex domains of the proteins with a higher spontaneous curvature grow, and subsequently, the proteins change to the other state with a lower spontaneous curvature, resulting in domain shrinkage. These processes repeat. In thermal equilibrium, hexagonal convex domains are formed by the competition between bending and surface tension energies, so that they are stably formed only under positive surface tension. However, blinking domains can form even in tensionless membranes.

Time-resolved infrared spectroscopy probes protein dynamics over timescales spanning more than ten orders of magnitude, yet the molecular motions underlying the observed kinetic signatures have remained elusive. Here we combine transient infrared spectroscopy with nonequilibrium molecular dynamics simulations to establish a direct connection between experimental relaxation times and local structural motions. Studying single-domain allosteric proteins, we find that inter-residue contact distances provide the structural representation that most faithfully reproduces the experimental dynamics. Correlation analysis identifies localized networks of coordinated contacts that mediate communication between secondary-structure elements. The characteristic timescales of these contact networks quantitatively match the experimentally observed relaxation processes, enabling each kinetic step to be assigned to a specific molecular motion. Applied to allosteric signal propagation in PDZ3 and photoinduced ligand unbinding in PDZ2, this framework provides an atomistic picture of hierarchical protein relaxation and establishes a general framework for connecting transient infrared spectroscopy with the molecular mechanisms of protein dynamics.

Liquids exhibit collective behavior that depends sensitively on thermodynamic conditions, interfaces and confinement, yet predicting each new state commonly requires a separate atomistic simulation. Classical density functional theory offers a reusable variational description, but its central excess free-energy functional is generally unknown, and learned approximations have largely remained restricted to planar or lower-dimensional settings. Here we show that this functional can be learned directly from fully three-dimensional equilibrium density fields while preserving spatial symmetry and variational consistency, without free-energy or chemical-potential labels. A single learned functional transfers across temperatures, system sizes and statistical ensembles, and recovers structure factors, the equation of state, liquid--vapor coexistence and interfacial broadening, none of which are used as training targets. Applied to complex three-dimensional geometries, it predicts the non-monotonic force associated with formation and rupture of a solvent-depleted bridge between colloids and adsorption in an interconnected gyroid pore. These results demonstrate that equilibrium density data can be converted into a transferable thermodynamic generator connecting microscopic liquid structure to response, phase behavior and collective phenomena.

We solve the Fokker-Planck equation for a Brownian particle in a tilted cosine potential and derive the intermediate scattering function (ISF), which captures the full spatio-temporal dynamics of the system. The model consists of a single overdamped Brownian particle in one dimension. We derive a generalized ISF comprising two wave vectors to describe correlations in the periodic potential. Exploiting the periodicity via Bloch's theorem, we formulate the problem within a spectral-theoretical framework and numerically compute the corresponding eigenfunctions and eigenvalues, from which we obtain the ISF and the probability density. Using time-dependent perturbation theory, we expand the ISF and derive low-order moments, including the mean-square displacement, time-dependent diffusivity, skewness, and the non-Gaussian parameter. Our analytical results are validated by Brownian-dynamics simulations and analyzed focussing on different regimes of the tilting force. The results are compared to a harmonic approximation and the deterministic limit.

Deep learning surrogates for RANS flow prediction around airfoils face two persistent bottlenecks. A single neural architecture cannot simultaneously resolve sharp near-wall boundary layers and smooth far-field potential flow. Additionally, force prediction is undermined by the numerical instability of computing wall-normal velocity gradients from continuous-field approximations. Both of these points are addressed with a DD-RNO (domain-decomposed routed neural operator), combining a spectral geometry encoder with two physics-guided innovations: (a) a differentiable domain routing mechanism that partitions the flow field into inviscid, boundary-layer, and wake regimes---dispatching query points to specialized regional decoders, and (b) learned canonical quadrature (LCQ), which replaces unstable pressure integration with flow-conditioned, learned integration weights that predict lift and drag directly from surface pressure. On the AirfRANS benchmark, DD-RNO cuts velocity field mean-square error (MSE) by 17$x$ ($u_x$) and 12$x$ ($u_y$) over the strongest baseline, widening to 23$x$ under out-of-distribution Reynolds extrapolation---evidence that the routing mechanism generalizes with the physics it encodes rather than merely fitting the training distribution. LCQ reduces drag MSE by 7.5$x$ relative to conventional pressure integration and raises drag rank correlation from $\rho = 0.250$ to $\rho = 0.997$. Ablations confirm that both components are indispensable to performance: removing domain routing increases velocity error by 8.2$x$, and removing LCQ increases relative drag error more than 40-fold. At ~144 ms per sample---a 10,000$x$ speedup over conventional RANS solvers---DD-RNO offers a surrogate accurate and fast enough for real-time aerodynamic design and optimization loops.

We report the formation of an original dome-shaped air-water cavity at the impact site of closely-packed plunging water jets. The injector assembly consists of concentric rings of circular jets, similar to a shower-head configuration. We infer from high-speed imaging, LASER-induced fluorescence, and optical phase detection probes that the cavity consists of multiple stems and sheets of air that stretch, retract and pinch off to produce bubbles. We also illustrate various bubble production mechanisms in the cavity, along with coalescence and bubble breakup scenarios in the subsequent bubble cloud. Thereby, we describe the wide range of bubble sizes generated by such jets, from a few micrometers up to about $5$~mm. Measurements of the cavity size are carried out for varying impact velocity, number of jets, and jet spacing. We propose that this distinctive air-water cavity is generated by liquid entrainment when successive rings of plunging jets progressively mix with the pool water.

A lattice Boltzmann scheme for the three-dimensional compressible Navier--Stokes--Fourier equations, derived automatically from the declared system by a symbolic compiler, is validated against exact solutions and published reference data. The declared system carries the viscous stress and the heat flux as transported state, and is discretized on a D3Q7 lattice in single precision. Against the exact Sod and Becker solutions the captured shock thickness converges at first order. On the supersonic Taylor-Green vortex at $M_0 = 1.25$ the scheme at $512^3$ matches the reference dilatational dissipation more closely than seven compared solvers, by thirty percent over the next best. Every operator in this solver, the generated collision and constitutive closure and the added shock sensor alike, reads only the cell it acts on, and data reaches a neighbor only by streaming along the lattice characteristics.

Aerodynamic unsteadiness is inherent to the operation of many engineering applications, especially those that involve large-scale rotating blades, such as modern wind turbines. Over the past few decades, wind turbine rotors have grown rapidly and are now exceeding 200 meters in diameter, causing them to operate in conditions where limited empirical data are available, and where models have not been validated. Here, we use a highly pressurized wind tunnel to probe these conditions and evaluate the quasi-steady approximation, often used to simplify the modeling of the unsteady aerodynamic response of an airfoil to slow changes in inflow conditions. We find that the quasi-steady approximation is not valid for a large range of frequencies where it is normally applied. This finding suggests that the loading on wind turbine blades will be significantly underestimated when using conventional models, especially near stalling conditions, which modern wind turbines typically encounter.

Intermittent departures from nominal Kelvin--Helmholtz shedding can produce rare and pronounced drag excursions in transitional airfoil flow. We examine these events using two-dimensional direct numerical simulations of flow over a NACA0012 airfoil at an angle of attack of $5^\circ$, a freestream Mach number of $0.4$, and chord-based Reynolds numbers of $5\times10^4$ and $5\times10^5$. At the lower Reynolds number, event-resolved analysis shows that individual primary vortices are released from the separated shear layer through the eruption of wall-generated, opposite-signed secondary vorticity. Each eruption interrupts the connection between a developing primary vortex and its feeding shear layer, releasing the vortex downstream. During nominal shedding, the vortex reaching the trailing-edge region is associated with a single such release and remains sufficiently isolated to pass the trailing edge without strong collective interaction. Extreme events instead arise through clustered vortex release, in which several secondary-vorticity eruptions occur within a short interval and produce a compact group of primary vortices with small initial streamwise spacing. Differential convection further reduces their spacing and promotes strong near-trailing-edge interactions, where the combined pressure footprint of these vortices produces a localized suction peak and a sharp increase in drag. These interactions range from prolonged deformation and filamentation to rapid core coalescence. Similar compact vortex organization and near-trailing-edge interactions are recovered at $Re=5\times10^5$, indicating that the downstream event pathway persists despite the smaller vortical this http URL findings suggest that controlling vortex-release timing through secondary-vorticity dynamics may provide a route to disrupt clustered release and mitigate extreme aerodynamic loading.

Particle resuspension models are commonly evaluated using the macroscopic resuspended fraction, although this integrated observable may conceal the temporal dynamics leading to detachment. Here, a second-order Markovian Lagrangian stochastic model is developed by augmenting the angular-velocity state with a finite-correlated tangential acceleration. The model is examined over turbulent channel flows with ($Re_\tau \in [60, 430]$) and compared with an established first-order formulation. The two models produce nearly overlapping resuspended fractions, revealing a macroscopic degeneracy between distinct stochastic descriptions. Multiscale trajectory statistics break this degeneracy. The acceleration-augmented formulation changes the short-time regularity from $S_2(\tau) \propto \tau$ to $S_2(\tau) \propto \tau^2$, sustains angular-velocity correlation, and produces stronger directional asymmetry and heavier increment tails. The survivor-conditioned mean square displacement exposes a Reynolds-number-dependent anomalous-transport window, in which the attached-particle ensemble grows more rapidly than the diffusive reference and locally approaches ballistic and super-ballistic scaling before crossing toward diffusion-like transport. This finite-time pathway records how particles approach detachment and is compressed out of the macroscopic resuspended fraction. At $Re_\tau \approx 60$, the trajectories enter a distinct low-Reynolds-number statistical state characterized by converging velocity and acceleration decorrelation and near-Gaussian increments. These results establish multiscale trajectory statistics as essential discriminants between stochastic resuspension models and identify finite acceleration correlation as a source of dynamical information beyond macroscopic detachment kinetics.

As a non-contact control approach, electric field (EF) can be utilised to drive droplet dynamics on a lubricant-infused surface (LIS), with numerous potential applications ranging from drug manufacturing to 3D printing. However, the resulting droplet dynamics remain poorly understood, especially as there are several possible droplet lubrication states on LIS. Here, we develop a lattice Boltzmann scheme that fully captures the interplay between the interfacial flows and electrohydrodynamics and harness it to investigate EF driven droplets on micropillar LIS. Combining simulations and analytical calculations, we establish quantitative expressions for the drag force and the electric force acting on a moving droplet. We demonstrate that the models can accurately capture droplet dynamics during programmable manipulation, including periodic motion and long-distance transport. Such reliable theoretical models can potentially transform precision control of droplet dynamics by removing the reliance on trial and error tests.

Dimples offer a promising route to reducing drag on aerodynamic surfaces. However, whether such shallow concavities yield a net benefit depends sensitively on their topography, which demands systematic mapping and exploration of their comprehensive design space. In this study, dimple design is examined as a mixed-variable optimization over four design variables: dimple type, depth, in-plane scale, and streamwise stretch. The design space is explored using MixMOBO, a Bayesian optimizer, coupled with immersed-boundary large eddy simulations of channel flows at a constant flow rate corresponding to a flat channel at a friction Reynolds number of 180. The optimal solution, a relatively deep, fully packed, streamwise-elongated diamond dimple, attains a 13.2% drag reduction, notably above previously reported values. A Gaussian process metamodel sensitivity analysis identifies dimple topology as the dominant factor, with coverage and elongation acting mainly through interactions, and depth itself carrying no universal sign. A near-wall flow analysis links the leading designs to fully attached, groove-like flow, whereas poorer designs tend to produce local flow separation that incurs adverse form drag. From these findings, key design insights for drag-reducing dimples are provided.

This paper is associated with a poster winner of a 2025 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, at this https URL

Motivated by the application of spray combustion in aviation industry, this work investigates the dispersion of non-spherical droplets in turbulence. The most common strategy for modeling sprays relies on LPT method, which represents the spray as a discrete collection of spherical particles. One limitation of LPT is that it neglects the influence of droplet deformation on spray dynamics. Prior studies have highlighted the importance of non-sphericity in droplet vaporization, combustion and drag coefficient. However, these works are restricted to idealized configurations such as an isolated droplet in a uniform flow. To study droplet deformation in a more realistic configuration, we adopt homogeneous isotropic turbulence (HIT) as the framework to investigate its effect on droplet dispersion. Droplets of various Stokes number are studied to investigate the interplay between deformation and inertia. Analysis of droplet statistics reveals that the impact of droplet deformation on both dispersion and clustering is dependent on the inertia regime. For weakly-inertial droplets, deformation weakens both dispersion and preferential concentration, whereas for strongly-inertial droplets, deformation tends to enhance preferential concentration while weakening dispersion. The results also suggest that to achieve the same level of clustering, deformed droplets require a higher Stokes number. Interestingly, for non-inertial droplets, the deformation seems to induce an effective inertia. This is verified by a comparison between the full unsteady TAB model and its steady-state limit, which suggests that unsteady shape dynamics affect temporal correlation statistics, but leave the mean clustering pattern unchanged. These findings demonstrate that accounting for droplet deformation and its unsteady shape oscillation is essential for accurately predicting droplet dispersion and clustering in turbulence.

Wave-assisted propulsion (WAP) systems harvest ocean wave energy to generate propulsive thrust, offering a promising approach for improving endurance and energy efficiency of marine vehicles. Previous studies have focused primarily on monochromatic or unimodal wave conditions, leaving WAP performance in realistic ocean environments largely unexplored. This study investigates the hydrodynamic and hydroelastic response of a submerged flapping hydrofoil operating in bimodal sea states generated by the coexistence of swell and wind-sea wave systems. High-fidelity fluid--structure interaction simulations are performed for representative calm, transitional, and storm conditions, with passive pitching provided through a torsional spring. Simulations show that, despite increased complexity of bimodal wave forcing, propulsion performance follows the same effective peak frequency scaling previously established for monochromatic and unimodal waves, demonstrating the robustness of this scaling framework across a broad range of sea states. The findings further reveal that while the optimal normalized tuning ratio remains within a narrow range, dimensional torsional spring stiffness varies with sea state characteristics, highlighting the need for adaptive hydroelastic tuning to maximize thrust. Overall, the results demonstrate that WAP systems provide a robust means of generating wave-powered thrust under realistic ocean conditions while providing practical guidance for improved design of wave-powered marine propulsion systems.

The Dynamic Mode Decomposition (DMD) has been consolidated as a basic tool for data-driven analysis of dynamical systems, allowing simultaneous identification of coherent structures and their dynamics from time-resolved measurements. However, with a linear regression at its core, DMD is unable to produce accurate models from recordings of dynamics that are inherently nonlinear, such as the response to large perturbations and the evolution on chaotic attractors. Recent approaches attempt to simultaneously fit the linear and nonlinear contributions to the dynamics by performing a regression onto a physically motivated model structure. However, although the resulting nonlinear models can produce accurate short-term predictions, their linearization does not necessarily agree with that of the original system. In this work, we introduce a novel data-driven method --- nonlinearity-subtracted DMD (NSDMD) --- that focuses on producing an accurate linearization of a system when the nonlinear contribution to its dynamics are available while the linear part is not. This scenario is encountered, for example, when the nonlinear terms in the governing equations are known, while the linear operator contains uncertain material properties or it accounts for the closure of unresolved dynamics. This also arises when the data is generated by a black-box simulation code that is able to output the nonlinearity, but not the action of the linear operator on the snapshots. NSDMD leverages data snapshots of the nonlinearity to explicitly account for the purely nonlinear contributions to the dynamics and formulate a regression problem that finds a low-rank approximation of the underlying linear operator. We demonstrate the approach on several numerical examples, showcasing its improved capabilities for data-driven linear analysis of chaotic, partially observed, advection-dominated, and high-dimensional dynamics.

Thermal transport in dielectric, non-magnetic crystals is mediated by quantized lattice vibrations, which drift and interact when driven out of equilibrium by a temperature gradient. This phenomenon can be described at multiple theoretical levels, ranging from fully quantum descriptions to semiclassical and mesoscopic continuum approaches. This review rigorously discusses the theoretical steps and approximations connecting these levels, bridging quantum phonon Dyson and Kadanoff-Baym equations and semiclassical Boltzmann transport formalism, and discussing the coarse-graining procedures that yield mesoscopic viscous heat equations for non-diffusive, hydrodynamic heat transport in devices. We show how the Guyer-Krumhansl and dual-phase-lag equations emerge as special linear-isotropic-band and inviscid limits of the viscous heat equations, respectively; most importantly, we demonstrate that these equations predict not only Poiseuille flow and second sound, but also more exotic effects such as negative thermal resistance, steady-state thermal backflow and vortices. We highlight how combining these frameworks with first-principles simulations connects microscopic phonon physics to observable non-diffusive heat-transport phenomena and guides their detection, amplification, and control. We recast the viscous heat equations in terms of Helmholtz and biharmonic equations solved analytically, and use this to discuss similarities and differences between the macroscopic behavior of the phonon fluid and other hydrodynamic systems, such as classical and electron fluids, focusing on compressibility, vorticity, and their influence on phonon hydrodynamics. We conclude with a roadmap to generalize the tools used to describe phonon hydrodynamics to other quasiparticles, motivating future advances in collective quantum transport phenomena in solids.

For the 2-D incompressible Euler equation, we prove the existence of $m$-fold symmetric uniformly rotating vortex patches with 90-degree corners for all $m\geq 12$. Properties of these patches and the induced stationary flows in the co-rotating frame are characterized. Our construction is based on a novel fixed-point method.

At every scale they occupy, magnetic fields affect various phenomena, including star formation, cosmic ray transport, charged particle acceleration, space weather, transport in planetary atmospheres, and laboratory plasmas. These fields are often generated and sustained by turbulent flows in a process called the dynamo. In 1955, E. N. Parker parameterized the effects of small-scale turbulence to propose a mean-field dynamo theory. The widely used theory reproduces observed large-scale fields but suffers from difficulty in tuning parameters as they are not justified from first principles: Studies of turbulent flows show tangled magnetic fields, which are folded and fragmented into small-scale structures due to shear-flow straining. Here, considering a shear flow that is unstable and driven, we develop analytic theory and perform three-dimensional (3D), advanced computer simulations of turbulence with up to 4096 x 4096 x 8192 grid points, showing ab initio generation of quasi-periodic, large-scale magnetic fields. The generation occurs via the mean-vorticity effect---an additional mean-field dynamo process postulated in 1990. Crucial to this dynamo is the prior generation of large-scale 3D jets, robustly produced as topologically protected and exact nonlinear solutions of the magnetohydrodynamic equations. The jet-driven dynamo applies to shear-driven laboratory and astrophysical systems. These include binary neutron star mergers, where the reported dynamo likely operates on microsecond timescales to produce in milliseconds some of the strongest magnetic fields in the Universe, providing signals for multimessenger astronomy.

Accurate numerical simulation of rarefied hypersonic plasmas is increasingly important for optimization of re-entry spacecraft design and the development of advanced aerospace technologies. For kinetic simulation methods, it is convention to enforce ions and electrons to diffuse at the same rate, known as the ambipolar diffusion approximation. This approach circumvents costly resolution of fast electron motion, but neglects the complex plasma dynamics of ions and electrons. Almost all studies that investigated the efficacy of the ambipolar diffusion approximation in hypersonics report noticeable differences in flowfield properties when electrostatic modeling is used, including increases in vehicle surface heat flux and decreases in electron temperature. However, it is unknown whether these reported differences originate directly from acceleration and deceleration of charged species through the electric fields and momentum-exchange collisions between charged and neutral species, defined as first-order effects, or from subsequent interactions with particles experiencing first-order effects, defined as second-order effects. Kinetic hypersonic flow simulations with electrostatic modeling are performed with argon to quantify the validity of the ambipolar diffusion approximation in terms of capturing first-order plasma effects along a one-dimensional stagnation streamline. Three different plasma diffusion regimes are studied under two sets of rarefied freestream flow conditions. The approximation is evaluated in terms of predicting plasma density distributions, electron temperature, and stagnation point heat flux. New criteria are proposed for identification of plasma diffusion regimes in hypersonic flows and use of the ambipolar diffusion approximation.

We describe turbulent hydrodynamics of superfluids in two spatial dimensions via the dynamics of point-like vortices coupled to an emergent 2+1 dimensional $U(1)$ gauge field. The cascade of superfluid kinetic energy is equivalently described by a cascade of dual electric field energies. We study superfluid turbulence using the equations of motion of the dual gauge theory in the presence of a drive and dissipation. In the limit that the vortices are point-like, the dual equations of motion directly yield the hydrodynamical equations of the superfluid. We obtain a turbulent cascade consistent with Kolmogorov's scaling law for two dimensional fluid turbulence. We observe clustering of like-signed vortices and compute the kinetic energy flux to show that the turbulent regime exhibits an inverse energy cascade.

We present a stability analysis of a dark-fluid model described as a non-relativistic, rotating, non-viscous, self-gravitating fluid. We assume spherical symmetry and model the matter by a polytropic equation of state. The resulting coupled nonlinear partial differential equation system is solved using a self-similar ansatz known from the Guderley-Landau-Stanyukovich problem. We find that three of the four Lyapunov exponents are negative, while only one is positive. This indicates one unstable direction and three contracting directions in phase space. The single positive exponent is relatively small, suggesting that the self-similar solution is only weakly unstable and remains dynamically robust over the investigated interval.

Low-dimensional reductions provide a useful framework for studying high-dimensional dynamics on complex networks, but most existing approaches are restricted to pairwise interactions. Here, we develop a one-dimensional reduction for dynamical systems on networks with purely higher-order interactions. The reduction is formulated through an effective higher-order interaction strength ($\beta_{\Delta}$), associated with the triangular interactions of the underlying network and the dynamical system's effective state. We present a theoretical framework for the dimension-reduction approach and validate it across three dynamical models with exclusively higher-order interactions. We find that the reduction accuracy is mainly determined by the homogeneity of node states, i.e., the deviations in state values become very small. Numerical results on synthetic and real networks show that the reduced model captures the effective steady states and transitions of the full system with good accuracy.

We identify a general mechanism for the finite-time thermalization of macroscopic observables, such as coarse-grained charge densities, in terms of elementary forms of the quantum dynamics of initial states: (1) aperiodicity, which provides a computable measure of (2) a dynamical partially ergodic exploration of the Hilbert space. Specifically, this mechanism predicts the equilibration of all (concentrated) macroscopic observables, in almost all states in an initial ensemble and almost all times within finite and longer intervals, given only the observable-independent information that the return probability of the ensemble of initial states is small over a finite time range. As a special case, it also accesses standard results on equilibration over infinitely long times in terms of (stronger versions of) the effective dimension of initial state delocalization in the energy eigenbasis. Our results incorporate macroscopic thermalization into the domain of operational quantum statistical mechanics, recently developed to provide finitely computable criteria for microscopic thermalization. We discuss an overall characterization of this approach as establishing connections between (1) the decay of a (theoretically or experimentally) computable probe indicating memorylessness, (2) a fundamental invariant mechanism in terms of the alignment of observables or states in the Hilbert space, and (3) predicting different natural forms of (classical and) quantum thermalization, most of which rigorously recover conventional eigenstate-based descriptions of infinite-time thermalization as a special case but provide stronger accessible predictions over finite observation times in the thermodynamic limit.

The study of magnetic chaos has traditionally focused on macroscopic variables under external driving. Here we demonstrate a new type of magnetic chaos, termed moiré magnetic chaos, associated with mesoscopic magnetic domain variables in twisted bilayer CrI3 without external driving. The domains are stabilized by a characteristic interlayer exchange frustration, which supplies the multiple dynamical degrees of freedom required for autonomous chaos. Through micromagnetic simulations, we show that relaxation toward moiré magnetic textures is extremely sensitive to minute local perturbations of the initial state, characterized by substantial finite-time Lyapunov exponents and a final-state sensitivity that persists over five decades of perturbation amplitude. Statistical analysis further reveals that the resulting domain configurations are stochastic and pairwise uncorrelated. Our results identify a form of microscopic, undriven chaos in twisted magnets that extends nonlinear magnetism beyond the conventional driven regime.

In this article, the nonlinear Helmholtz equation with non-Kerr nonlinearity, such as self steepening and self frequency shift, is considered. A travelling wave transformation is applied, and the extended nonlinear Helmholtz equation is reduced to a Hamiltonian dynamical system. Then, the reduced Hamiltonian system is analyzed by classification of equilibrium points, phase space analysis, and the construction of exact wave solutions. The relationship between the reduced dynamical coefficients and the original physical parameters is further established through a parameter space analysis. It is shown that self steepening directly modifies the reduced dynamics, whereas self frequency shift acts through the compatibility condition for the real travelling wave reduction. Together, these non-Kerr effects reshape the phase space geometry and travelling wave structure. Localized and periodic travelling waves are obtained, with their existence determined by the balance among dispersion, nonparaxiality, Kerr nonlinearity, and non-Kerr effects. Furthermore, a periodically forced version of the reduced system is examined to study the transition from regular to irregular dynamics. It has been observed that external forcing can induce complex oscillatory behavior. Bifurcation analysis, time series evolution, phase space analysis, largest Lyapunov exponent, and Poincaré section demonstrate the emergence of quasiperiodic and chaotic responses under sufficiently strong forcing. All analytical branches are verified through full-equation residual evaluation, while a few selected branches are additionally examined through direct numerical propagation and robustness tests under complex Gaussian perturbations. The results show that self steepening directly renormalizes the effective nonlinear dynamics, whereas self frequency shift restricts the admissible real-envelope travelling wave manifold.

In this paper, we travel through an unknown territory of dromions, to unearth and show the new properties/attributes of dromions which have never been brought to the fore since they were first discovered by Boiti etal [1]. These new attributes are brought out by investigating a generalized (2+1) dimensional Nonlinear Schrodinger (NLS) equation by exploiting Truncated Painleve approach. The signatures that can be attributed to dromions include existence of firewall and reflection at the boundary, uneven distribution of energy among different bound states, amplitude dependence on adjacent dromions, etc. We have corroborated the main analytical results with numerical simulations also. We categorically state that these properties are universal and can be extracted in any (2+1) dimensional nonlinear partial differential equation. We do believe that these properties which shed more light on the behaviour of dromions may have wider repercussions in nonlinear optics, Bose-Einstein condensates and plasma physics.

I present an overview of different phases used in the literature to describe the phase of travelling waves in reaction-diffusion equations. The discussion is tailored to understand the effectiveness of these different phase descriptions in a stochastic setting in 1D. The explicit computation of the autonomous isochronal phase for the Nagumo equation is a new result.

It has been known for a long time that the equation of motion for dissipative linear dynamical systems with constant coefficients cannot be derived from the classical principle of stationary action because the term proportional to velocity in the equation of motion leads to the time derivative of order one half in the Lagrangian. Thus, approaches utilising fractional calculus have been used; however, they suffer from deficiencies both from mathematical and physical points of view. We here present our version of such fractional calculus based approach that provides correct Euler-Lagrange and, ultimately, the Hamilton equations, energy change of the moving body, and an attempt for a geometric interpretation of how energy dissipates.

The most well-known beyond-Fourier heat conduction model, the Maxwell--Cattaneo--Vernotte equation is solved analytically in the presence of heat transfer boundary condition. In contrast to the corresponding Fourier problem, this boundary condition renders the underlying differential operator non-selfadjoint. With a suitable scalar product, the adjoint eigenvalue problem is established. The resulting left and right eigenfunctions constitute a biorthogonal system, allowing the expansion coefficients to be determined from arbitrary square-integrable initial conditions. This enables a convenient infinite-sum analytical solution, which is presented and thoroughly investigated for various values of the model parameters (including near-Fourier and highly hyperbolic regimes) and for two practically important initial conditions (equilibrium and flash pulse initiated). The spectral structure is analyzed in detail, including the occurrence of real, imaginary, and complex-conjugate eigenvalue roots, their asymptotic distribution, and their dependence on the dimensionless relaxation time and Biot number. We find good agreement with corresponding finite-difference numerical solutions. The comparison also illustrates the effects of spectral truncation (i.e., the Gibbs phenomenon) and numerical dissipation near propagating thermal-wave fronts. Completeness of the eigenfunction set is numerically demonstrated. The initial condition induced by the flash pulse is derived analytically. The results provide an analytical benchmark for non-selfadjoint hyperbolic heat conduction, unveil how boundary heat transfer and relaxation time influence the transition between Fourier-like diffusion and thermal-wave propagation, and open the possibility to find and investigate beyond-Fourier heat conduction via heat transfer in experiments and practical applications.

Accelerated aging is widely used to study the long-term behavior of materials within laboratory time scales, particularly for materials exposed to solvent environments over extended periods. This is especially important for additively manufactured (AM) polymers, whose increasing use in naval and commercial undersea applications requires reliable methodologies for assessing durability under in-service conditions. A common approach relies on elevating the temperature below the glass transition or melting temperature to accelerate degradation. However, the temperature limits for accelerated aging of AM polymers remain poorly understood, particularly because temperatures beyond a threshold may activate deformation and degradation mechanisms that are absent under service conditions. To address this gap, this paper investigates fused deposition modeling (FDM) Acrylonitrile Butadiene Styrene (ABS) exposed to saltwater and deionized (DI) water to establish a temperature threshold for accelerated aging in aqueous environments and propose a methodology for determining such thresholds. Controlled geometries and varying print directions were employed to explicitly probe the underlying mechanisms. We show that samples exposed to temperatures above the threshold exhibit pronounced shrinkage and warping along the printing direction due to the relaxation of process-induced internal stresses. These observations establish an accelerated-aging temperature threshold of 50$^\circ$C for ABS, beyond which additional mechanisms absent under service conditions become active. Additionally, the resulting geometric distortions are masked in thick geometries but become highly pronounced in thin structures. Moreover, solvent ionic content strongly influences water uptake, with saltwater reaching saturation in 1 day, whereas DI water did not reach saturation even after 30 days and exhibited greater mass uptake.

We present \texttt{rcpgenerator}, an openly available code for generating $d$-dimensional dense, disordered, non-overlapping close packings from an arbitrary prescribed list of particle diameters. The method adapts the Clarke--Wiley inflation protocol, but instead uses the Adam optimizer to relax the particle configuration. Typically, particle coordinates are advanced with a single, global step size, which must shrink as the size ratio $S\equiv D_{\max}/D_{\min}$ grows, generally stalling the optimization. Adam instead gives each coordinate its own adaptive step size, stabilizing the optimization time across a broader range of $S$. We demonstrate this in three-dimensional periodic tests that reach $S\sim5\times10^{5}$ for a continuous lognormal distribution ($N\sim10^{6}$ diameters) and particle numbers up to $N\approx5.6\times10^{6}$ for power-law distributions, with the densest packings reaching $\phi\simeq0.87$, each completed in minutes to hours on a multicore machine. Across truncated-lognormal, truncated-power-law, and Weibull distributions, the resulting $\phi$ reproduces trends such as the locations of peaks and knees with distribution shape and $S$ found in prior numerical results and in the parameter-free Farr--Groot prediction, with a remaining offset typically $0.005$--$0.01$. Additionally, results are commensurate with multimodal packing densities measured in vibrated-bed experiments. The code and the complete per-case census behind every figure are released with the paper.

Aqueous foams possess multiple structural motifs across different length scales: macroscopic foam, bubbles, foam films and the air/water interface. In this study, macroscopic foams are generated by sparging gas through an aqueous dispersion of PNIPAM microgels which act as foam stabilisers due to their surface activity. The stiffness of the microgels and thus their interfacial activity are tuned by variation of the cross-linker density. The effect of the cross-linker density and the microgel concentration on the resulting foam formation properties (foamability) and the foam stability are investigated. A lower cross-linker density and a higher microgel concentration enhance the foamability, generate foams with smaller bubbles and higher liquid fractions, and increase the foam stability. These observations are correlated with the microgel behavior at the single air/water interface examined by pendant drop tensiometry and Langmuir compression experiments as well as the mobility in single free-standing foam films determined using a Thin Film Pressure Balance. Our findings highlight good agreement across all length scales: increased foamability correlates with a faster decrease in surface tension, and higher foam stability with a higher surface elastic modulus of a microgel-covered single air/water interface and decreasing mobility in foam films.

Dilute solutions of linear polymer chains with tangentially active monomeric beads are simulated using a Brownian dynamics (BD) algorithm over a range of solvent quality in the crossover regime between $\theta$ and athermal solvents. The conformational changes with increasing P{é}clet number ($Pe$) (which is proportional to the strength of activity) suggest deswelling of the chains resulting in a collapse of the radius of gyration data to a random walk (RW) statistics at a unique value of $Pe$, independent of the solvent quality. The swelling behaviour of active polymers in the crossover regime relative to their size at the $\theta$ state is found to follow the same universal characteristics as that of passive polymer chains. Furthermore, based on polymer blob theory we present a novel scaling of the thermal blob size with tangential activity of the monomeric beads. Altogether, this work establishes a connection between the configurational properties of active polymers and scaling laws in polymer physics, which provides a useful framework to study the dynamics of activity induced motion of polymeric molecules for various biophysical applications.

The melting of stripe-forming systems involves changes in connectivity that are not fully captured by conventional structural and orientational descriptors. We investigate a two-dimensional model with competing interactions whose low-temperature phase consists of one-particle-thick stripes. Molecular dynamics simulations along seven heating isochores are analyzed using thermodynamic, orientational, dynamical, and graph-based observables. Heating produces a multistage reconstruction in which the loss of stripe alignment and the reorganization of filament connectivity occur over distinct temperature ranges. Density controls whether the disordered filaments fragment into finite polymer-like clusters or remain joined in a dynamically fluid, system-spanning network. The topological observables distinguish these outcomes, which are not resolved by the thermodynamic and orientational responses alone. Thus, the same ordered stripe microphase can melt into topologically distinct fluids selected by density.

Magnetic interactions provide a versatile and powerful tool for controlling and organizing active matter, where individual units continuously consume energy to drive autonomous motion. These interactions arise naturally in biological systems, such as magnetotactic bacteria, and can be engineered into synthetic platforms, including colloidal microswimmers, magnetic nanoparticles, and macroscopic granular robots. This review focuses on active, self-propelled particles that carry an intrinsic magnetic dipole moment, powered by their own energy consumption rather than driven by external fields; here, the dipole moment mediates interactions and self-organization, not propulsion. We survey experimental and theoretical studies across all length scales, showing how dipolar interactions shape single-particle dynamics, collective behavior, and self-organization. We discuss models incorporating pairwise dipolar forces and confinement, and examine emergent phenomena such as chaining, swarming, and tunable pattern formation. We close by outlining challenges and opportunities in the design, control, and application of magnetic active systems, from programmable materials and biomedical actuation to nonequilibrium physics.

Biological systems such as bacteria and cells undergo growth or degradation, resulting in weak violations of mass conservation. We investigate how such weak non-conservative dynamics affect phase separation in scalar active matter by incorporating a reaction term into a minimal continuum model. Through numerical simulations and linear stability analysis, we show that even weak non-conservative reactions arrest coarsening and stabilize nonequilibrium microphase-separated states. With increasing activity, the system undergoes a morphological transition from interconnected labyrinthine patterns to worm-like structures and eventually to isolated droplets. Quantitative analysis of the correlation function and static structure factor reveals a well-defined steady-state characteristic length. Qualitative analysis of the resulting phases shows that the non-conservative reaction primarily promotes microphase separation and enhances local hexagonal ordering, while activity predominantly controls the domain morphology. Our results demonstrate that weak violations of mass conservation fundamentally alter the nonlinear coarsening dynamics of active phase separation and provide a minimal framework for understanding pattern formation in related systems.

An essential component of food items like mayonnaise and salad dressing is hen egg yolk. Phosvitin (PVT) is a phosphoprotein, which exists in the granules of this hen egg yolk which stabilizes the food emulsion by preventing phase separation. To understand, how this protein is adsorbed at the interface of water and edible oil in the presence and absence of lipids is essential for improved control in food production. To monitor the kinetics of this adsorption, the dynamic interfacial tension has been determined in the current investigation. The drop in interfacial tension over time indicates the adsorption of protein at interface which is enhanced on increasing the concentration of protein in water phase. However, at higher concentration, the positive activation energy hinders the adsorption process resulting a saturated interfacial tension. The dilation rheology of the macromolecular film at this oil-water interface shows the elastic nature of the film to be greater than the viscous nature, indicating the formation of a soft gel film. At low concentration, the zwitterionic lipid, 1-palmitoyl-2-oleoyl-sn-glycero 3-phosphocholine (POPC), promotes this protein adsorption at the interface. Interestingly, at high concentration, the lipid overtakes the interface removing the protein from there. The lipid-protein composite film again shows the nature of a soft gel. The non-monotonic effects of lipids on assembly of protein at the water-edible oil interface is an important observation to optimize the composition of relevant food products.

We report a combined rheology and x-ray photon correlation spectroscopy (XPCS) study of the structural and mechanical relaxation of a ductile, nanocolloidal glass following the cessation of shear flow. After the glass is sheared to 300% strain at various shear rates and then held at fixed strain, the stress undergoes a protracted, quasi-logarithmic decay with hold time that depends weakly on the initial strain rate. Recovery rheology measurements reveal that this stress relaxation is accompanied by a logarithmic decrease in the elastic component of the recoverable strain; hence, the rates of decrease of the stress and recoverable strain are proportional. XPCS measurements during the stress relaxation reveal dynamics dominated by a convection-like backflow that is divided into two dynamically distinct regions indicative of banded motion. In one region, the flow can be modeled by an affine strain, while in the other region the glass moves as a plug while undergoing slow, glassy relaxation. The rates of these dynamics approximately track the rate of loss of recoverable strain, indicating this motion is the predominant microscopic mechanism driving the conversion of recoverable to unrecoverable strain during stress relaxation. In contrast, XPCS measurements during strain recovery reveal purely affine flow with no evidence of heterogeneity and with strain rates that agree quantitatively with the rheometry measurements. Together, these results provide a unified microscopic picture connecting the evolving internal dynamics of a ductile glass to its macroscopic mechanical relaxation following flow cessation.

Room-temperature strong coupling in organic microcavities is usually achieved by combining high-quality optical resonators with highly ordered excitonic media, a requirement that limits scalability and processing flexibility. Here we show that this constraint can be relaxed by using molecular aggregation as a design parameter rather than treating it as a parasitic effect. We realize solution-processed Rhodamine 6G-poly(vinyl alcohol) films embedded in low-quality-factor silver Fabry-Perot microcavities and demonstrate clear angle-resolved anticrossing with coupling energies up to 324 meV despite the large optical losses of the metallic mirrors. A two-exciton coupled-oscillator model shows that the relative weight of these species controls the collective coupling strength and can be tuned through dye loading and spin-coating conditions. In contrast, angle-resolved photoluminescence is dominated by a broad, red-shifted lower-polariton emission, consistent with relaxation through excimer-like states formed in densely packed molecular domains. These results identify molecular aggregation as a practical design lever for loss-tolerant strong coupling in wet-processed metallic cavities and suggest that ground-state aggregates and excited-state excimer-like species play distinct roles in polariton formation and emission.

Ultra-lean hydrogen flames under terrestrial gravity are governed by a coupled interaction among preferential diffusion, thermal diffusion, heat loss, and self-induced convection. This study numerically examines combustion in a quiescent 6~vol.\% H$_2$--air mixture using detailed chemistry and a low-Mach-number formulation. A complete calculations set was considered, with Soret diffusion and optically thin radiative heat loss independently enabled and disabled. One-dimensional spherical calculations were used to isolate the initial post-ignition flame kernel growth, while two-dimensional planar and axisymmetric simulations described its subsequent buoyant rise, deformation, and breakup. Over the analyzed interval, the spherical flame-front radius followed $R_f^2\approx Kt$ rather than constant-speed expansion. Soret diffusion increased the effective growth coefficient $K$, whereas radiation reduced it. The axisymmetric calculations reproduced the experimentally measured leading-point trajectory substantially better than the planar formulation. Soret diffusion produced larger, faster-rising kernels and maintained a more nearly circular upper cap, whereas radiation had a weaker effect on trajectory but increased relative lateral flattening. In all cases, a toroidal vortex stretched the flame segment and caused local extinction and fragmentation. Soret diffusion delayed breakup, while radiation advanced it; their combined effect on breakup time was nearly compensating. The results show that Soret transport and radiation primarily alter kernel growth and resistance to vortex-induced extinction, while the qualitative breakup pathway remains hydrodynamically controlled.

The distortion of turbulence by mean strain - through component amplification, pressure-mediated redistribution and spectral rescaling - is central to flows ranging from wind-tunnel contractions to stagnation regions near lifting surfaces. Capturing this process economically remains difficult: scale-resolving simulation is expensive, linear rapid-distortion theory omits nonlinear relaxation over finite strain, and second-moment closures discard spectral information. We present a strain-coupled formulation of one-dimensional turbulence (ODT) that evolves strained turbulence with one-dimensional scale resolution at low computational cost. Mean-strain production is imposed as a continuous forcing of the line velocity, the rapid pressure-strain contribution is introduced as an energy-conserving redistribution operator consistent with homogeneous rapid-distortion theory, and scale compression is represented by dilatation of the ODT domain. The model predicts a broadband distorted spectrum that departs from the rigid spectral translation of linear theory at a strain-to-turbulence ratio of approximately 0.8, where rapid distortion and nonlinear eddy dynamics are both active. Under axisymmetry of the undistorted turbulence about the ODT line, the nonlocal three-dimensional rapid pressure-strain integral reduces to a closed single-line functional. The formulation reproduces rapid-distortion theory at onset and quantitatively captures the Reynolds-stress anisotropy trends of Lee and Reynolds (1985).

The source term of an acoustic analogy is not unique: different rearrangements of the Navier-Stokes equations attribute the same radiated sound to different apparent sources. Although this non-uniqueness has long been recognised, it has never been given a quantitative structure. We provide one by organising acoustic analogies into a fibre-like family over the space of effective media and defining transport between analogies through unique frequency-preserving, rotation-free linear space-time maps. Three exact results follow. First, the classical family of convected analogies is not closed under transport: successive uniform-flow regaugings generate effective media with anisotropic sound-speed tensors, recovering the generalised media introduced by Goldstein. Second, the discrete holonomy of analogy transport is obtained in closed form. It consists of an exact spectral dilation and a rotation that vanishes to fourth order in Mach number; transport becomes singular on a sonic horizon in analogy space. Third, in the continuum limit the boost sector is flat, while curvature is confined to anisotropy directions and is given by the commutator of sound-speed-tensor increments. The geometry does not imply any change in the physical sound field: all exact analogies yield the same far field. Its significance is operational. When an approximate source model is transported between analogies, as commonly occurs in hybrid prediction methods, the resulting far-field predictions acquire an exact, parameter-free bias consisting of a rigid spectral dilation and directivity rotation. An exact far-field law for anisotropic media extends these results to open transport paths. All identities are verified symbolically and numerically.

This investigation employs direct numerical simulations (DNS) of high-Mach-number turbulent boundary layers under three flow conditions: a low-enthalpy calorically perfect gas, and two high-temperature gas mixtures, one in chemical non-equilibrium state and the other in full thermochemical non-equilibrium state. The influences of the two-temperature model on turbulent statistics and the coupling among turbulence, chemistry, and vibrational energy are examined. It is found that while high-enthalpy effects leave the velocity statistics virtually unchanged, they dramatically modify the near-wall temperature field. A pronounced disparity between the translational-rotational temperature and the vibrational temperature arises in the near-wall region, rendering the conventional generalized Reynolds analogy (GRA) inaccurate for vibrational temperature. To remedy this, a novel composite GRA is proposed that blends a vibrational-temperature-based relation with the standard formulation, and it demonstrates excellent agreement with the DNS data. Thermal non-equilibrium effects also substantially alter near-wall chemical reactions: it suppresses O2 dissociation while promoting NO formation, leading to a corresponding decrease and increase in the mean concentrations of O and NO, respectively. Spectral analyses of the turbulence-chemistry and turbulence-vibrational relaxation interaction terms reveal that temperature fluctuations dominate these flow quantities at energy-containing scales. Integrating the resulting spectral functions, we evaluate subgrid-scale closure terms for large-eddy simulation. At small filtering scales, the magnitude of the cross-correlation term rivals or exceeds that of the temperature fluctuation term, whereas the temperature fluctuation term becomes dominant at larger filter scales.

Plasma reactors present themselves as a unique means of electrified chemical production, particularly in the conversion of greenhouse gases (e.g., CO2) back into chemical feedstocks. Warm plasmas, such as gliding arc discharges, represent a growing class of catalyst-free plasma reactors that demonstrate high energy efficiency and scalability. Here, we introduce mean discharge time as a characteristic descriptor of gliding arc dynamics, extracted directly from voltage and current waveforms. Electrical signatures for distinct plasma behaviors (modes) were established using high-speed photography, and discharge time distributions were evaluated as a function of Reynolds number. Mean discharge time is shown to decrease non-linearly with Reynolds number, providing a link between arc behavior and underlying fluid dynamics, which is otherwise neglected in traditional reactor characterization. Mean discharge time thereby provides a quantitative, operando descriptor of transient gliding arc dynamics and stability, offering insight into discharge behavior that traditional characterization approaches do not capture.

We present a deterministic discontinuous Galerkin (DG) finite-element solution of the Boltzmann equation, without moment-closure approximations, under a class of far-from-equilibrium deformations. Specifically, we consider affine flows which reduce the Boltzmann equation to a purely velocity-space problem for the reduced distribution function in a reduced velocity field. We solve the reduced equation using a tensor-product Lagrange DG discretization for four representative flows: simple shear, pressure shear, bi-directional shear, and a vortex flow. Our principal finding is that the velocity distribution is well-approximated by an anisotropic Gaussian throughout the evolution, despite the non-equilibrium conditions. Further, we show the evolution of the covariance tensor of the Gaussian distribution is equal to the inverse of the right Cauchy-Green tensor in the free-streaming limit without collisions. This prediction compares very well with the numerical solution at short times; at longer times, they grow apart, reflecting the influence of particle collisions.

We establish a self-consistent 2D hydrothermodynamic analytical model for the localized thermal ablation of dense human tumors using high-intensity focused ultrasound. By expanding compressible Navier-Stokes equations up to second order, we demonstrate that within a structurally stationary cellular tumor matrix, acoustic streaming (acoustic wind) velocity is suppressed. This constraint forces the absorbed wave momentum flux to transfer entirely into localized, time-averaged, static, second order, pressure gradients, converting the bulk acoustic energy directly into localized heat. Using a short, 1 s, duration, high-amplitude top-hat pulse, we solve the simplified Pennes bioheat transfer equation within non-diffusive timescales. Adapting the hydrodynamic optimization framework established by Tsiklauri~(2026), we derive a natural physical criterion where the acoustic absorption coefficient matches half the inverse target depth, $\alpha = 1/(2x_0)$, proving that the optimal operational frequency scales inversely with transmission distance. We show that while incident plane waves overheat upstream tissues due to exponential decay, a spherically focusing wave geometry effectively bypasses healthy tissue boundaries via geometric convergence ($\propto 1/r^2$). Analytically solving the non-isothermal Arrhenius injury integral yields a sharp lesion boundary radius at $r_b = 0.75\,w_0$. Volumetric averaging bounded strictly within this necrosis perimeter demonstrates that the average tumor temperature reaches $72.1^\circ\text{C}$ while central point values peak at $90^\circ{\rm C}$. Finally, convolving the post-pulse thermal profile with a 2D free-space Green's function verifies immediate, monotonic temperature decay below $60^\circ{\rm C}$ at the boundary, demonstrating complete structural containment and explaining the $>90\%$ localization rates observed in clinical applications.

Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration. However, a systematic end-to-end differentiable formulation for coupling deep-learning-based reduced-order surrogates with variational parameter estimation remains underdeveloped. In this work, we introduce a physics-aware neural-network-based latent-space framework for reduced-order forward modeling and variational parameter estimation. The proposed autoencoder-based approach yields a differentiable surrogate that maps physical parameters to predicted flow fields through a latent representation. The observable supervision is used during offline training to encourage the latent variables to retain information correlated with system parameters, while the online inverse problem is solved in the parameter space through the surrogate-induced observation operator. The method is evaluated on two computational-fluid-dynamics benchmarks. The results show that reconstruction accuracy alone is insufficient for inverse modeling, owing to the lack of end-to-end differentiability or physics awareness for variational parameter calibration. Quantitative latent-space analysis further shows that observable supervision improves case-level separability and temporal organization of latent representations. Experiments with realistic measurement settings, including noisy, low-resolution, randomly masked, and block-wise partial observations, demonstrate the robustness of the proposed framework and show that it generally reduces calibration error and variability compared with the standard surrogate models.

Memory is a key determinant when cultural items compete for attention and, consequently, for success, as in the case of songs on a music chart. For modeling, one adds memory to Lotka-Volterra models, the reference for Markovian competitive processes. Here we treat memory in terms of an exponential moving average, finding that it leads to an extended region of winnerless chaos characterized by log-normal popularity statistics in trailing top-k charts. Importantly, the observed log-normal behavior collapses to a power-law distribution when the feedback dynamics is fast on the scale of the charting period. This result is in agreement with the observed statistics of real-world music charts (e.g., Billboard and Spotify). In a chaotic state, the size of the largest Lyapunov exponent is a measure of how unpredictable the system is. We find that the largest Lyapunov exponent varies strongly as a function of parameters in the phase where winnerless chaos is stable. Interestingly, the sets of parameters obtained by comparing simulations with real-world cultural-item dynamics extracted from Google Books and Google Trends, movies, Reddit, Wikipedia, Twitter, and scientific publications, are located close to the points in parameter space where the largest Lyapunov exponent reaches its local maximum, namely, close to the point of maximal unpredictability. This result suggests that cultural competitive processes are maximally chaotic when memory is a key determinant.

We present quasistationary ring-shaped soliton necklaces in a two-component envelope propagating in a medium with competing cubic-quintic nonlinearity. Metastable propagation of soliton necklaces results from a balance of repulsion between adjacent out-of-phase solitons in one component and confinement by the boundary of a flattop region in the other. Numerical simulations demonstrate metastable propagation over about a hundred diffraction lengths, even with random noise added to the input envelopes. The maximum number of solitons in metastable necklaces can be controlled either by changing the size of individual solitons or by adjusting the width of the flattop region hosting the necklace.

We investigate the collision dynamics of two bright sphalerons in a (1+1)-dimensional deformed $\phi^6$ scalar field theory with a symmetric potential possessing false vacua. Two one-parameter realizations of the model, referred to as the barrier and well models, are considered and their static and linear instability properties are first reviewed. We then study head-on collisions of boosted sphalerons over a broad range of initial velocities and deformation parameters. The scattering dynamics exhibit a rich variety of final states, including the production of kink-antikink pairs, long-lived oscillons in true and false vacuum, multiple oscillons propagating in false-vacuum regions, and radiative decay. A particularly remarkable outcome is the emergence of a long-lived bubble of the false broken vacuum bounded by a kink-antikink pair, which repeatedly collapses and re-expands before eventually decaying into an oscillon. These results demonstrate that deformed $\phi^6$ theories with false vacua exhibit considerably richer sphaleron dynamics than previously known and provide new insight into the role of unstable localized configurations in nonlinear field theories.

In this paper we present Open Multi-Processing (OpenMP) Fortran 90/95 programs to solve the Gross-Pitaevskii equation for a rotating dipolar Bose-Einstein condensate (BEC) in two and three dimensions, which is a new version of our previous published programs for a dipolar Bose-Einstein condensate without rotation. After the recent experimental study of a rotating dipolar BEC [L. Klaus et al., Nature Phys. 18, 1453 (2022)], the present programs will be useful tools for related theoretical investigation. The algorithm used is the split-step semi-implicit Crank-Nicolson scheme for imaginary- and real-time propagation to obtain stationary states and BEC dynamics, respectively, as in the previous version [L. E. Young-S. et al., Comput. Phys. Commun. 286 (2023) 108669].

Third-order elastic constants (TOEC) play an important role in nonlinear material characterization, but measurements of TOEC are laborious with large error margins. This Letter presents the equations of wave velocity changes caused by homogeneous temperature variation and uniaxial stress in isotropic media and the expression of TOEC in terms of thermally induced velocity change and thermal strain. TOEC of an aluminum sample were experimentally determined by measuring ultrasonic wave velocity changes in the uniaxial loading test and the thermal modulation test. Experimental results showed good agreement between the two test methods. Owing to the simple test setup and high measurement sensitivity, the thermal modulation test is a potential experimental method to determine TOEC and absolute acoustic nonlinearity parameters.

To understand the phenomena displayed in active phase separation, general top-down theories like Active Model B+ (AMB+) add fluxes that break time reversal symmetry. Starting from an Enskog-like kinetic theory of hard-core active Brownian particles in the high persistence regime, we derive AMB+ from first principles. For the effective free energy to have two minima, we propose an effective parametrization of the pair correlation function. Explicit expressions for all coefficients in the model are given as a function of the microscopic parameters to leading order in the Péclet number.

We investigate vapor-deposited glasses of a phenanthroperylene-ester, known to form an equilibrium hexagonal columnar phase, and show that liquid crystal-like order can be manipulated by the choice of deposition rate and substrate temperature during deposition. We find that rate-temperature superposition (RTS), the equivalence of lowering deposition rate and raising substrate temperature, can be used to predict and control the molecular orientation in vapor-deposited glasses over a wide range of substrate temperatures (0.75Tg to 1.0Tg). This work extends RTS to a new structural motif, hexagonal columnar liquid crystal order, which is being explored for organic electronics applications. By several metrics, including the apparent average face-to-face nearest-neighbor distance, PVD glasses of the phenanthroperylene-ester are as ordered as the glass prepared by cooling the equilibrium liquid crystal. By other measures, the PVD glasses are less ordered than the cooled liquid crystal. We explain the difference in the maximum attainable order with the existence of a gradient in molecular mobility at the free surface of a liquid crystal, and its impact upon different mechanisms of structural rearrangement. This free surface equilibration mechanism explains the success of the RTS principle and provides guidance regarding the types of order most readily enhanced by vapor deposition. This work extends the applicability of RTS to include molecular systems with a diverse range of higher-order liquid crystalline morphologies that could be useful for new organic electronic applications.

Amorphous solids subjected to athermal quasistatic oscillatory shear undergo a transition from periodic reversible dynamics to irreversible diffusive dynamics at yielding. How irreversibility arises in such deterministic, dissipative dynamics remains unclear. Here we show that trajectories remain locally stable, with perturbations decaying rather than growing even in the irreversible regime, ruling out the sustained exponential sensitivity to initial conditions associated with chaotic dynamics. Rather than diverging continuously, nearby trajectories initially remain close before eventually separating through rare branching events, after which their separation grows diffusively. A mean-field soft-spot model reproduces the same branching statistics and reveals their microscopic origin. We find that branching originates from competition between nearly-degenerate plastic instabilities, in which a small perturbation changes which instability activates first and thereby alters the subsequent sequence of plastic events. These results identify instability-selection-induced branching as a dynamical mechanism for irreversibility in cyclically driven amorphous solids.

Traditional models for stress-strain behavior of glassy polymers are based on the assumption that the critical features of the stress-strain response can be explained by changes in the molecular mobility. The four-step deformation experiments consisting of (i) an initial constant strain rate loading, (ii) unloading to specified stress, (iii) creep under that stress and (iv) second constant strain rate loading, challenges that assumption. Specifically, existing models fail to predict the experimentally observed large second stress overshoot in case of a slight unloading. Until now there has remained a possibility that the mobility was actually lower in case of a partial rather than complete unloading, which would preserve the main assumption, if not particular details, of these specific constitutive models. By performing direct optical experiments using the photobleaching technique simultaneously with the mechanical four-step experiments it is shown that a lower molecular mobility upon partial unloading does not take place. As traditional models cannot account for these experimental results, a new model has been developed where the changes of molecular structure manifest not in the relaxation time, but in the shear modulus, which is function of an internal variable that is the fraction of the efficiently packed material. This fraction obeys a population balance equation, where the steady-state fraction is controlled by the applied stress. In the absence of deformation, the efficiently packed fraction increases, which explains the increase in the modulus in the course of physical aging below Tg. The model qualitatively describes the four-step experiment as well as single step loading experiments.

This study deals with both spontaneously-formed and electrically-induced structures observed in the nematic phase of two dielectrically negative twist-bend nematogens. In planar cells, the nematic layers are inhomogeneous, existing in a quasiperiodic ground state that involves essentially azimuthal director deviations. This phenomenon is understood using a simple model based on the relative flexoelectric and elastic contributions to free-energy. In an external electric field, a variety of instabilities are obtained. In an increasing static field, for example, the initial periodic surface electroconvective instability is followed by the volume periodic flexoelectric instability. Uncommonly, the growth of the latter takes place via nucleation and front propagation. Due to the low bend elastic deformation cost, flexoelectric bands progressively distort as they narrow (mediated by edge dislocations) under an increasing field to eventually form fanlike objects. In the megahertz region, in each half cycle following 0 V, the electroconvective and flexoelectric instabilities appear transiently with the latter setting in at a higher voltage. Above a few hertz, flexoelectric instability ceases; the sequence of patterned states then is oblique roll to bimodal-grid to normal-roll to chevron. Above 100 kHz, periodic wide bands oriented normal to the rubbing axis are obtained at a threshold voltage that decreases with increasing frequency. Our measurement of threshold voltage corresponding to different frequencies (or electrical conductivity and permittivity values) in this regime agrees well with the earlier theoretical predictions relating to the inertial conduction instability.

When a liquid thread pinches off, its neck thins as it separates into two unconnected regions. Using continuum mechanics, we can predict that the neck reaches zero radius in finite time while its curvature grows without bound. Together, the vanishing neck and diverging curvature form a finite-time singularity. However, a real fluid does not realise these mathematical limits as molecular or material physics takes over once the neck becomes sufficiently small. Similar singularities arise throughout soft matter whenever a smooth continuum description is used at vanishing length scales. This review asks what the shrinking region forgets, what it retains, and which material length, time, or stress cuts off the apparent divergence. The dynamics near a singularity often become self-similar, with profiles at different times collapsing onto one shape when rescaled by the shrinking local length. Sometimes that collapse is universal enough that the surrounding geometry and forcing no longer determine the local dynamics. Nonetheless, the measured output could still depend on how the shrinking region is fed by the surrounding flow and on the small-scale physics that finally replaces the ideal divergence. Complex fluids and active matter change the same local balance by bringing their own timescales into the shrinking region. Beyond interfaces, the same logic applies when the localised object is a stress concentration or a defect in geometry or order rather than a moving surface. Singularities matter because they show where continuum theory stops being the relevant description and how the small-scale cutoff sets the outputs that count in printing, coating, aerosols, and stretchable solids.

We study the axisymmetric partial engulfment of a small rigid sphere by a fluid Helfrich membrane. When the size ratio $\eps$ between the particle and the membrane is small, the neck that joins the wrapped cap to the surrounding membrane is an elastic boundary layer, and we analyse it by matched asymptotic expansions. The leading inner surface is a catenoid, a minimal surface that stores no Helfrich energy, so that the energy of partial engulfment is carried by the first correction and appears only at order $\eps^{2}\ln(1/\eps)$. We obtain it by solving the inhomogeneous Jacobi equation of the catenoid, forced by the spontaneous curvature and by the ambient mean curvature that the neck must match, and we give its coefficient in closed form. The boundary layer can then be integrated out, and the neck replaced by a scalar self-energy carried at the pole, so that the outer field can be closed independently of the inner one. For a membrane coupled to a tension reservoir we derive the binding threshold, which turns out to be independent of both the tension and the spontaneous curvature, the complete-wrapping threshold, and the hysteresis of the envelopment transition. The neck self-energy law is confirmed against the full nonlinear shape equations.

Transient spatially localized activity underlies a broad range of biological processes, yet the statistical property of fluctuations that controls its nucleation remains unclear. We systematically investigate noise-induced dynamics in a spatially extended FitzHugh-Nagumo excitable system and identify three regimes: a quiescent phase, a spatially extended alternating phase, and a pattern-forming phase characterized by transient localized excitation patches. Surprisingly, we find that temporal noise correlations are not required for patch formation: Gaussian white noise produces localized patches when its amplitude is sufficiently large, whereas weaker fluctuations can achieve the same effect when temporal correlations allow them to persist. Our results identify the instantaneous amplitude and the persistence as joint stochastic control parameters for transient pattern formation in excitable media. These distinct quantities are linked through the integrated noise strength, which quantifies the accumulated stochastic forcing available to nucleate an excitation. In addition, the inhibitor response time subsequently determines whether the excitation remains localized or spreads throughout the system.

Excluded-volume interactions, arising solely from steric constraints, play a crucial role in determining the structure, dynamics, and phase behaviour of colloidal suspensions. This is particularly important for non-spherical particles, where orientation-dependent effects also become significant. In this study, we employ depletion-driven phase separation to develop a scalable, size-selective method for purifying spherical and non-spherical colloidal clusters that exhibit an interplay of concave and convex surface areas. Phase diagrams of charge-stabilised polystyrene spheres ranging in size from 267 to 1008 nm demonstrate that the mixing-demixing transition occurs across a range of surfactant concentrations rather than at a single threshold. Taking advantage of this transition width enables the purification of a single component from binary mixtures at size ratios as low as 1.6 in a single step. When the same approach is applied to tetrameric colloidal clusters, these are enriched fifteenfold relative to uncoordinated spheres. Importantly, the efficiency of sorting depends not only on the effective size but also on the geometry of the aggregate. For instance, anisotropic, weakly fused clusters separate more efficiently than spherical aggregates because their concave surface curvature is reduced compared to unfused clusters. These findings establish excluded-volume-driven sorting as a practical and scalable route for purifying colloidal building blocks for hierarchical assembly.

Auxetic behavior, characterized by a negative Poisson's ratio, is a counterintuitive mechanical response exhibited, among other systems, by certain polymer networks. Here, through in silico simulations we investigate the mechanical response of thermoresponsive microgels across the volume phase transition upon varying crosslinker concentration down to ultralow conditions, a regime so far unexplored. After refining the method to estimate the elastic moduli based on equilibrium shape fluctuations for the challenging case of ULCs, which are very sparse networks with rather anisotropic shape, we are able to show the onset of auxetic behavior near the volume phase transition for microgels with crosslinker concentration of ~ 1%. In addition, we find that ULC microgels exhibit a slightly negative Poisson's ratio across the whole swollen regime. Further examining the auxetic response within the inner region of the network, we also demonstrate that, for ULC microgels, this extends at all length scales, suggesting that it is an intrinsic property of the weakly connected polymer network. The present findings should likely stimulate novel experimental investigations, aiming to measure the Poisson's ratio of individual low and ultralow crosslinked microgels, to verify these intriguing numerical predictions.

The instability of glassy solids poses a key limitation to their use in several technological applications. Well-packed organic glasses, prepared by physical vapor deposition (PVD), have drawn attention recently because they can exhibit significantly higher thermal and chemical stability than glasses prepared from more traditional routes. We show here that PVD glasses can also show enhanced resistance to crystallization. By controlling the deposition temperature, resistance towards crystallization can be enhanced by at least a factor of ten in PVD glasses of the model organic semiconductor Alq3 (Tris(8-hydroxyquinolinato) aluminum). PVD glasses of Alq3 first transform into a supercooled liquid before crystallizing. By controlling the deposition temperature, we increase the glass to liquid transformation time thereby also increasing the overall time for crystallization. We thus demonstrate a new strategy to stabilize glasses of organic semiconductors against crystallization, which is a common failure mechanism in OLED (organic light emitting diode) devices.

When a liquid drop impacts a solid surface, rebound and splashing are known to be suppressed by additives that induce elastic effects; however, the influence of elasticity on the maximum spreading radius remains debated. The difficulty lies in isolating elastic resistance from the enhanced spreading caused by viscous shear thinning. Here, we experimentally decouple these effects by investigating Boger fluid drops (constant-viscosity solutions with high elasticity) of polyethylene oxide (PEO) and polyacrylamide (PAAM). We demonstrate that elastic properties do not alter the maximum spreading ratio, even at high concentrations up to 1000 ppm. We formulate an energy balance that accounts for the inertial, capillary, viscous, and elastic contributions, and yields a dimensionless criterion ($\Gamma$) that estimates the degree of elastic effects. We show that $\Gamma \ll 1$ for all impact conditions tested, demonstrating that elastic effects are energetically negligible during droplet spreading, opposite to what Weissenberg and Deborah numbers would predict.

Finite-memory optical tracers encode upstream transport histories rather than instantaneous local flow velocities. We introduce optical-memory transport (OMT) imaging, a framework in which finite memory couples internal-state relaxation to transport through memory kernels. Under structured illumination, these histories are converted into measurable complex spatial-frequency response, whose local transfer-function limit yields constant-velocity inversion. Fisher-information analysis establishes kernel-dependent information limits and design principles for finite-memory transport imaging.

This work investigates Deep Reinforcement Learning (DRL) as a tool for model-free closed-loop active separation control in a fully turbulent wind tunnel flow over a one-sided diffuser. The agent controls an array of magnetic valves (on/off) that eject compressed air into the boundary layer, while the environmental state is reduced to the signal from a single wall-shear-stress sensor placed near the natural transitory detachment point. The control law is learned in real time using Proximal Policy Optimization. Compared to the standard learning design based on the weighted sum of all rewards following an action, we demonstrate that a horizon aligned with the convective time of the flow leads to faster convergence and a more robust control strategy. The resulting control law corresponds to a low-duty-cycle actuation pattern that yields a forward-flow fraction of approximately $53\%$. This compares favorably with conventional and optimized periodic open-loop control ($\sim 40\%$ and $\sim 51\%$, respectively). The findings of this article indicate that, when embedded into an online experiment, DRL represents an efficient tool to identify robust and interpretable active separation control strategies.

Representing flow states over a wide range of flow parameters and control inputs in a low-dimensional state space is a central challenge in fluid mechanics. Rather than representing the instantaneous flow field in a fixed subspace spanned by the leading proper orthogonal decomposition (POD) modes, this study regards the POD subspace itself as the flow state at each flow condition. The set of POD subspaces associated with flow conditions defines a state space on the Grassmann manifold. Diffusion maps identify the intrinsic low-dimensional structure of the family of POD subspaces, while Grassmannian rank-one update subspace estimation tracks the temporal evolution of a POD subspace online. The framework is experimentally demonstrated for flow around an airfoil. POD subspaces are extracted from wall-pressure fluctuations measured by a microphone array over a range of angles of attack and under different control inputs. The subspaces are found to lie on a one-dimensional submanifold of the Grassmann manifold. Moreover, the transition from separated to attached flow, induced by a plasma actuator, follows a reproducible trajectory along the same submanifold identified from statistically stationary flow data. The temporal evolution of the subspace is consistent with the transient evolution of the flow field observed using particle image velocimetry. These results show that POD subspaces can serve as representative flow states, enabling their temporal evolution across a wide range of flow conditions to be tracked online in a low-dimensional space based on wall-pressure fluctuations. This low-dimensional representation provides a basis for real-time flow-state estimation and feedback control.

Advanced air mobility operations hold the potential to enhance and expand regional transportation of both people and goods in populated areas. However, hazardous flight conditions arising from interactions between wind and the built environment remain a significant challenge for aerial vehicles in urban settings. This work proposes a novel framework towards safe flight planning of aerial vehicles in windy urban environments. A learning-based surrogate model is trained to rapidly predict flow fields from readily available information such as building geometry and incident wind. This surrogate prediction is used to calculate a volumetric flight challenge scalar field based on critical flow parameters and proximity to structures. A safe, flow-informed flight trajectory is then identified through a cost-minimizing pathfinder. The complete system is demonstrated experimentally through flight tests of a micro aerial vehicle through a model urban geometry placed in a large fan-array wind tunnel. Comparing this approach to trajectories generated without knowledge of the wind field, we find the flow-informed approach reduces undesired vehicle displacement and improves flight stability. This work is among the first practical demonstrations of safe, wind-aware methodologies for advanced air mobility in urban environments.

Natural transition from laminar to turbulent flow can be modeled by using only the Spalart-Allmaras (SA) working variable. The variable serves as its own transition indicator, in a one-equation Reynolds-averaged Navier-Stokes (RANS) closure. Its sub-O(1) range is dynamically inert in the baseline model. That range becomes a Tollmien-Schlichting amplification factor. A blended production term then drives the SA transport equation through laminar instability growth and turbulent eddy-viscosity production. Computations with this formulation on a zero-pressure-gradient flat plate, the NLF(1)-0416 and Eppler 387 airfoils, a two-element section, a circular cylinder through the drag crisis, the Daedalus human-powered-aircraft wing, and a 6:1 prolate spheroid are compared with experimental data and with other transition models.

In this paper, we study the Couette-Taylor instability of a viscous fluid between two rotating cylinders in the small-gap, slow rescaled rotation rate, high Reynolds number regime, focusing on the very counter-rotating case $\mu < \mu_c \approx -0.8$ where the primary instability is non-axisymmetric. Starting from the Navier-Stokes equations, we derive a limit system that captures the leading-order dynamics and compute the critical Taylor number $T_c(\mu)$ together with the critical axial and azimuthal wavenumbers. Near criticality, the weakly nonlinear behaviour is governed by a system of two coupled complex Ginzburg-Landau equations. All coefficients of this amplitude system including the cubic nonlinear terms are evaluated numerically from the linearised eigenfunctions and the associated adjoint problem. The reduced equations admit helicoidal waves (travelling in both the axial and azimuthal directions) and ribbon waves (standing axially, travelling azimuthally), and their existence and stability criteria are discussed. We also examine more exotic spatially modulated solutions that satisfy a third-order dynamical system, whose complete classification remains an open challenge.

Uncertainty in wind farm layout optimization regarding model choice and the impact of global blockage always exists. This paper evaluates these interactions by extending a multi-objective approach that maximizes mean Annual Energy Production (AEP) from a model ensemble while minimizing their variance. By incorporating the Self Similar blockage model into an ensemble of five wake models, we assess the impact of blockage physics on layout robustness. Results from a linear mixed-effects model indicate that including blockage leads to a non-significant average AEP reduction of 0.0624 GWh ($p$-value = 0.323). Conversely, it caused a highly statistically significant increase in uncertainty, with model disagreement rising by 0.177 GWh ($p$-value < 0.001). Additionally, computational runtime increased nearly nine times. These findings highlight an accuracy vs. certainty paradox, where theoretically necessary physics can compromise model consensus if implemented without re-calibration. Ultimately, this work suggests that simple blockage couplings act as a diagnostic for model incompatibility, emphasizing the necessity of careful model tuning for wind farm design.

Gravity driven sediment flows are responsible for a major portion of sediment redistribution within oceans, reservoirs, and lakes, with important implications in coastal erosion, siltation, carbon burial, and contaminant migration in aquatic systems. Despite the ubiquity of this phenomenon, current mechanistic understanding of sediment gravity flows (SGFs) remains limited. This knowledge gap is particularly acute in the case of cohesive, fine-grained sediments (i.e., muds) due to the complex properties of the clay matrix, including low permeability, viscoplastic rheology, and flocculation. In this work, we develop a computational fluid dynamics model that accurately predicts key features of cohesive, clay-rich SGFs based on independent measurements of the relation between sediment solid fraction and rheological yield stress. In particular, the model captures the four primary flow regimes (low density turbidity currents, high density turbidity currents, mudflows, and mudslides) observed in lock-exchange experiments with slurries containing smectite or kaolinite clay. The model is validated through comparison with previous experimental observations of sediment flow morphology, speed, and runout distance. Overall, we demonstrate the ability to predict the influence of intrinsic (particle size, grain density, and rheology) and extrinsic sediment properties (sediment topography and solid fraction) in the development of self-sustaining cohesive SGFs.

Ocean waves erode the waterline of Antarctic ice-shelf fronts and carve a thermo-erosional notch. The notch is hidden from satellites, yet it preconditions front collapse and footloose calving, so the link between notch growth and observable front retreat matters for how wave-exposed ice shelves lose mass. We study this link at the Fimbul Ice Shelf, East Antarctica, in January-February 2024. The widely used White (1980) erosion formulation is extended in two directions: a component-wise spectral treatment of irregular seas, and a breaking-aware wave profile that accounts for shoaling over the submerged ice foot revealed by remotely operated vehicle (ROV) profiling. Forced with hourly ERA5 waves, the extended model predicts about 110 m of cumulative waterline erosion over the matched 7 January-27 February window. Satellite observations show considerably more retreat: about 264 m from an S1-guided Sentinel-2 plateau-break method, and 266 m from manually digitised Sentinel-1 fronts over a slightly longer window. Under the baseline assumptions (alpha = 1, Delta T_wi = 1 degree C), the model therefore falls short of the observed retreat by a factor of about 2.4. Part of this residual may be hydrodynamic, since post-breaking turbulence is not represented; part may be mechanical, because collapse and footloose calving can convert notch erosion into larger observable retreat. Unmeasured near-ice thermal driving remains a first-order uncertainty, and front-position observations alone cannot separate these contributions.

Obtaining equilibrium distributions of nonlinear systems is essential for accurately computing macroscopic observables. Conventional theoretical corrections are typically limited to weak nonlinearities, where interaction terms can be treated as effectively uncorrelated perturbations and the random phase approximation applies. In this Letter, we develop a framework to determine equilibrium distributions based on the generalized energy equipartition principle. Our approach recovers existing corrections in the weakly nonlinear regime and, crucially, remains valid for strong nonlinearities, where perturbative contributions become correlated and conventional approaches break down. Numerical simulations of the nonlinear Schrödinger equation, the Majda-McLaughlin-Tabak model, and the Fermi-Pasta-Ulam-Tsingou model demonstrate accurate corrections for nonlinearities more than an order of magnitude stronger than those accessible to conventional theories.

Friction does work when two objects in contact slide past one another. This process is studied using a simple numerical model consisting of two flexible asperites, one for each object. The force of friction is modeled as a conservative electric force that can be either attractive or repulsive. The concept of pseudowork plays an important role throughout the analysis. The difference between work and pseudowork is equal to the change in internal energy. Because the asperites are not rigid, the work done in a typical interaction is greater than the psuedowork, leading to an increase in internal energy. For a real physical system, this is the source of thermal energy. The processes discussed here fall into two categories: forced sliding and free sliding. With forced sliding, applied forces keep the objects moving with constant velocities. With free sliding, the only force on one of the objects (in the direction of motion) is friction. For free sliding, friction not only increases the internal energy but also decreases or increases the object's translational kinetic energy. The change in translational kinetic energy is determined by the pseudowork done by friction.

Spectroscopic techniques measure the dynamical response of physical systems subjected to oscillatory perturbations. For small perturbations around the equilibrium state, these spectroscopic methods are unified by the common mathematical framework of linear response theory. This work presents a unified perspective on rheological or mechanical spectroscopy, electrochemical impedance spectroscopy, and broadband dielectric spectroscopy through the lens of linear response theory. Subtle conceptual similarities and differences among these techniques are highlighted by analyzing their mapping to the linear response theory, basic building blocks, elementary models, and time and frequency domain response functions. Data validation and analysis approaches, including Kramers-Kronig relations, equivalent circuits, and multimode models are discussed. The shared fundamentals of different spectroscopies enable seamless exchange of ideas across domains.

In this study we investigate the behavior of additive binary square-well mixtures within the framework of classical density functional theory. By leveraging on the geometrical structure of the square-well interaction, we propose a novel form of the perturbation theory contribution to the density functional in terms of weighted densities, inspired by fundamental measure theory. We apply this functional in order to study the effective one-body interaction due to the liquid-vapor interface of the solvent acting on a dilute component of dissolved nano particles. The effective one-body interaction attracts the nano particles strongly to the interface. We show that this effective interaction potential can be calculated either from the density profiles of the full mixture, at low but non-vanishing concentrations of the nano particles, or by employing the Widom insertion theorem in the dilute limit of vanishing density of nano particles. Both routes display excellent agreement.

We report on a Marangoni flow-driven pathway for non-equilibrium transport of metal ions across an oil-water interface. Under specific conditions, we show that the adsorption of a metallic species onto the extractant-decorated oil-water interface creates interfacial tension gradients that give rise to Marangoni flows. Strikingly, we observe that these flows are accompanied by removal of metal from the aqueous phase and that the extraction kinetics follow a non-diffusive behavior. The extraction rates are significantly higher - at least a threefold increase - when Marangoni flows are present. We show that the strength of the interfacial instability is coupled to the lowering of the interfacial tension- which is metal-dependent and therefore can lead to rate-mediated selective extractions. Overall, our study shows a fundamentally different paradigm for liquid-liquid extractions opening up a range of new directions of inquiry and future technologies.

We report on the phase behavior of solutions of a chromonic liquid crystal, disodium cromoglycate (DSCG) resulting from the presence of DNA that acts as a depletant. We show that DNA (both single and double stranded) can induce phase condensation of DSCG at volume fractions a thousand-fold lower than a commonly studied depletant of similar size, namely polyethylene glycol. Twist angle characterization via polarized optical microscopy reveals DNA introduces macroscopic chirality within the condensed phase, despite being present only in the continuous phase- as confirmed by imaging of fluorescently tagged DNA. UV-vis absorption spectroscopy reveals that the introduction of chirality reduces the absorption coefficient strongly, indicating that induced chirality leads to considerable increase in the average lengths of DSCG aggregates. We also show that DNA at concentrations (~nmol/L) typical for a post amplification event (such as PCR) can induce an isotropic-biphasic phase transition of DSCG enabling a fast optical method to report the presence of DNA. Overall, these findings establish DNA as exceptionally efficient depletants that regulate both phase condensation and chirality transfer in lyotropic liquid crystals and thereby providing a simple optical platform for detection of amplified DNA.

We rely on a hydrodynamic description of living tissues to describe the interface separating two of them with distinct constitutive properties. Using the difference in their homeostatic pressures as a control parameter, we show that the interface generates an emergent capillary surface tension that depends on the hydrodynamic scale, and that makes it very stable to large wavelengths perturbations. Using the difference of active forces the two tissues experience as a control parameter, we not only find that the front propagation mechanism shifts from the pushed wave to the Burgers wave, but we also find that the emergent surface tension is not sufficient to stabilize the interface at large enough drive and low enough viscosity.

Fluids with nonvanishing antisymmetric components of the transport coefficient tensor are named odd fluids. In our previous works, we proposed a mesoscale simulation model for isotropic two-dimensional odd fluids and then extended it to the three-dimensional case to model an anisotropic odd fluid with cylindrical symmetry. The Navier-Stokes equation and the viscosity tensor of this three-dimensional mesoscale odd fluid were derived previously via a kinetic theory. Herein, we derive the heat conduction and self-diffusion equations, along with the corresponding thermal conductivity and self-diffusivity tensors. These theoretical results are validated by simulations. We further investigate heat and mass transport behaviors of three-dimensional odd fluids in a confined geometry through our mesoscale model. In striking contrast to normal isotropic fluids, the steady-state temperature and density distributions of confined odd fluids are significantly deformed by the odd transport coefficients.

We study transient fluid removal in cylinder-on-flat contacts between stiff PMMA cylinders and a soft PDMS substrate. The cylinder geometry eliminates the edge-scraping mechanism that can occur for deformable rubber blocks, allowing the influence of sliding on fluid squeeze-out to be examined more directly. Experiments were performed mainly in glycerol at the low sliding speed $v=3 \ {\rm \mu m/s}$ using cylinders with different surface roughness. After the initial elastic-loading stage, we find that the friction during sliding depends primarily on the total time elapsed since application of the normal load rather than on the preceding sliding distance. The subsequent friction evolution follows approximately the same dependence on total contact time. Stationary squeeze-out calculations predict the evolution of the mean surface separation and real contact area, in reasonable agreement with that inferred from the measured friction. These results show that essentially the same squeeze-out process governs fluid removal during stationary contact and low-speed sliding, and that sliding-induced elastohydrodynamic effects have only a minor influence under these conditions.

Ferroelectric polymers combine switchable polarization with the processability of soft materials, but their development has been dominated by poly(vinylidene fluoride) and related fluoropolymers, whose crystalline polar phases restrict mechanical compliance and domain design with spatial precision. Here we establish a generic design principle for creating intrinsically flexible ferroelectric liquid-crystal polymers through reactive polar mesogenic self-assembly. The approach creates polyfluoroalkyl-free polymer films in which robust ferroelectric order arises from liquid-crystalline molecular organization rather than crystalline phase formation. By transferring ferroelectric order from fluid mesogenic states into polymer networks, the resulting materials combine mechanical adaptability with programmable polar architectures. Especially, the photoalignment technology enables these polar states to be organized into pixelated domain architectures. This work establishes a design space towards soft ferroelectric polymers that integrate molecularly programmed polar order, mechanical tunability and environmentally conscious chemistry, expanding the design space of adaptive materials for flexible electronics, wearable systems and soft robotics.

Smallenburg reports near-melting point simulations and observes a well-predicted spontaneous nucleation with mixed, finite-time morphology, in a Comment on our recent Perspective. The Comment's incorrect broader takeaway --- that equilibrium coexistence is "readily achievable" --- rests on an untested generalization from a single state point near the phase envelope, and misses entirely the intriguing role played by Frenkel's underlying mechanism. We reiterate the salient point missed by the Comment: the nucleation time grows astronomically with just tenths of a percent of volume fraction away from 53%. This phenomenology emerges from the entropy exchange mechanism Frenkel described, which predicts that spontaneous phase separation is dynamically accessible only down to about 53% volume fraction from the melting point, and astronomically long waiting times through most of the remaining phase envelope. We provide here calculations to address the potential misconception created by the Comment.

Polyelectrolyte (PE) hydrogels exhibit complex behavior characterized by large mechanical deformations, nonlinear stress response, solvent transport, and ion diffusion. The interplay between these mechanisms can lead to unexpected swelling dynamics, deformation patterns, and stress response. As such, advanced computational tools are needed for the efficient design of PE hydrogel-based devices, such as actuators and sensors for soft robotics, microfluidic valves, and drug delivery systems. In this work, we develop a numerical framework to simulate the coupled electro-chemo-mechanical behavior of PE hydrogels using finite element analysis. Applying this framework, an electro-chemo-mechanical model for PE hydrogels in a dilute ionic solution is implemented as a user element (UEL) subroutine in Abaqus/Standard. The model and UEL implementation are validated by comparing to experiments in the literature for transient free-swelling of a DMAEA gel in a solution of varying ionic strengths, then applied to study the consolidation behavior under confined compression and the transient bending behavior of a hydrogel bilayer. The simulations show that the ionic strength of the external solution, fixed charge density, and Flory-Huggins parameter play significant roles in the magnitude of the transient swelling and consolidation behavior.

Charged colloids coated with a polymer brush can be designed to preferentially self-assemble into different crystal structures by varying easy-to-tune experimental conditions. For a given set of conditions, we have observed in experiments and simulations a distribution of thermodynamically (meta)stable self-assembled crystal structures. Properly quantifying the free energy landscape of these colloidal systems is essential for rationally choosing conditions to preferentially target particular crystal structures. For some of the structures we have formed, standard crystalline order parameters are not able to differentiate between crystals or between crystals and amorphous aggregates. We show that local environment similarity descriptors are able to distinguish the relevant metastable states, but are too expensive for use in biased MD simulations. Here, we adopt an approach from machine-learned interaction potentials showing that SE(3)-equivariant transformer networks can serve as an efficient-to-evaluate machine-learned proxy. As a result, we can compute the relative free energies of accessible colloidal structures as a function of different experimentally-relevant physical knobs that can steer our system between two observed crystal types. As an example application, we then show how changing surface potentials of positive and negative colloids while maintaining the same attractive energy can shift which crystal structure is favored.

We provide an exact and complete solution for the dynamics of a rigid particle of uniform density with $C_{2v}$ and $S_4$ symmetry, settling under gravity in a viscous fluid at a Reynolds number much smaller than unity. The $S_4$ symmetry renders the problem exactly integrable, with all orbits labelled by a single conserved quantity $0\le C\le 1$. We show that, for $0

This study investigates ion beam sputtering (IBS)-induced surface wrinkling phenomena in three polymers with varying hydrophilicity: poly-hydroxy-ethyl-methacrylate (pHEMA), poly-4-vinyl pyridine (p4VP), and poly-2,4,6,8-tetramethyl-2,4,6,8-tetravinylcyclotetrasiloxane (pV4D4). It is observed that pHEMA and p4VP films wrinkle only when exposed to ion bombardment and subsequent water vapor exposure. No wrinkling is observed in pV4D4 under these same conditions. X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared spectroscopy (FTIR) are performed before IBS, after IBS, and after exposure to humidity. XPS shows that IBS drives chemical changes within the surface layer, creating a graphitized film at the surface. For the polymer films that exhibit wrinkling (pHEMA and p4VP), XPS and FTIR indicate water absorption in both the surface and the bulk of the films, resulting in swelling. We conjecture that the formation of wrinkles arises from this swelling being mechanically constrained by the rigid underlying silicon substrate and the stiff graphitized surface layer. In contrast, the absence of wrinkle formation in pV4D4 under the same experimental conditions can be attributed to its comparatively low water absorption and the correspondingly limited swelling response.

The chemical potentials of multi-component mixtures underlie many physical and chemical phenomena, but remain challenging to compute. The S0 method enables the computation of chemical potentials from equilibrium molecular dynamics simulations, by leveraging the thermodynamic relationship between particle number fluctuations and derivatives of chemical potentials, followed by numerical integration along different compositions. Here we generalize the S0 method from two-component mixtures to neutral multi-component mixtures. We first extend the statistical mechanical formalism to high-dimensional compositional space, and then introduce a Gaussian process integration scheme combined with active learning to efficiently integrate chemical potentials and sample diverse compositions. We use this method to compute the mixing free energies of a molten metal alloy, and the solubilities of two paracetamol polymorphs in water-ethanol solvents. The extended S0 method provides a practical and scalable route for computing chemical potentials in neutral bulk multi-component mixtures from atomistic simulations.

Memory is traditionally incorporated into transport theory as a constitutive correction acting on an already prescribed kinematic structure. Here we develop a different framework in which finite memory itself generates the geometry of transport. By reconstructing deformation from causal transport histories, the instantaneous velocity gradient is replaced by a memory-dependent transport connection whose ordered evolution gives rise to noncommutativity, curvature, and holonomy in transport-history space. We show that finite memory generates a nonvanishing geometric contribution to transport even in time-periodic, irrotational flows, providing a purely kinematic mechanism for irreversible Lagrangian transport without invoking vorticity, constitutive nonlinearities, stochastic forcing, or explicit symmetry breaking. We introduce an intrinsic curvature invariant, independent of the transport representation that measures the accumulated geometric structure generated by transport history. The framework predicts universal scaling governed by the dimensionless parameter (\omega\tau_m), identifies a characteristic memory scale (tau_c) separating rapid geometric accumulation from asymptotic saturation, and reveals a monotonically decreasing memory susceptibility with globally concave accumulation dynamics. Numerical simulations confirm these predictions and show that geometric irreversibility emerges through progressive curvature accumulation rather than resonance-driven amplification. These results establish finite memory as a generator of an intrinsic geometric structure rather than merely a modifier of dynamical evolution, revealing causal history as the microscopic origin of curvature, holonomy, and irreversible transport across a broad class of non-Markovian systems.

High-fidelity numerical simulations of bubble-laden, vertical channel flow in the upward configuration, where the bubbles undergo topological changes (breakup and coalescence), were performed with the purpose of exploring the effect of the surface tension on the turbulence anisotropy in the carrier phase. A qualitative analysis shows that velocity fluctuations are enhanced in the wake of large bubbles. Moreover, as shown by the velocity spectra, these structures seem to scale with bubble size and interact with those closer to the wall. Finally, a barycentric map and other indicators of turbulence anisotropy clarify that, except at the core of the channel where the largest bubbles reside, the multiphase flow cases are actually more isotropic than the single-phase flow at a matching friction Reynolds number. This unexpected behavior is attributed to a better redistribution of energy due to an enhancement of sweep events (high-speed fluid towards the wall) in the presence of large bubbles.

The deformation of viscoelastic drops in alternating electric fields is relevant to electrohydrodynamic applications such as microfluidics, inkjet printing, and drop manipulation. We investigate the dynamics of a neutrally buoyant Oldroyd-B drop subjected to a uniform alternating electric field using asymptotic analysis and direct numerical simulations with the open-source solver Basilisk. An analytical solution is derived for small deformation and weak elasticity for an Oldroyd-B drop suspended in an Oldroyd-B medium, with both fluids modeled as leaky dielectrics under axisymmetric Stokes flow. Depending on the conductivity and permittivity ratios, six electrohydrodynamic regions are identified, characterized by distinct deformation modes, flow directions, and nonlinear responses; while some exhibit stable spheroidal deformation, others undergo pointed-tip, multi-lobed, or oblate breakup beyond a critical electric capillary number. Across high-, intermediate-, and low-frequency regimes, the deformation oscillates at twice the applied field frequency, with its mean and amplitude governed by the field frequency and viscoelasticity. For cases that produce prolate deformation under a steady field, the drop remains prolate at high frequency, exhibits brief oblate excursions at intermediate frequency, and undergoes large-amplitude oscillations between near-spherical and highly deformed states at low frequency. The mean deformation varies monotonically or non-monotonically with $De$, depending on frequency and electrical property ratios. For cases producing oblate deformation under a steady field, the drop remains oblate at high frequency, develops dimples at intermediate frequency, and breaks up at low frequency for sufficiently large $De$ and $Ca_E$; the mean deformation increases monotonically with $De$.

Micromixing of non-Newtonian fluids remains challenging because laminar flow at microscales restricts transverse transport primarily to molecular diffusion. In this study, we investigate the transport mechanisms governing passive micromixing of a Carreau--Yasuda fluid in two-dimensional sinusoidal converging--diverging microchannels and develop a surrogate-assisted framework for their multi-objective design. We perform high-fidelity finite-volume simulations by systematically varying the wall-amplitude ratio, phase offset, and wave count under creeping-flow conditions. The results show that successive contraction--expansion units enhance mixing through the combined effects of interface stretching, elevated shear rates, and shear-thinning-induced viscosity reduction. These mechanisms improve scalar transport but simultaneously increase pressure drop, creating an inherent trade-off between mixing performance and hydraulic resistance. To efficiently explore the multidimensional design space, we construct surrogate models from high-fidelity numerical simulations and identify Gaussian Process Regression (GPR) as the most accurate predictor of both the mixing index and pressure drop. Coupling the validated GPR surrogate with Non-dominated Sorting Genetic Algorithm II (NSGA-II) accurately reproduces the Pareto front obtained from the high-fidelity simulations and identifies optimal microchannel geometries that balance mixing enhancement against pressure loss. The proposed machine learning framework provides a fast, accurate, and physically consistent strategy for the multi-objective design of passive micromixers for non-Newtonian fluids.

We use high-resolution, interface-resolved direct numerical simulations (DNS) to investigate the origin of Kolmogorov (K41) scaling in bubble-induced turbulence (BIT). Region-wise velocity structure functions show that the 2/3 scaling appears only within bubble wake regions. Comparison with matched single-bubble DNS further indicates that the K41 scaling observed in the full BIT field arises from the superposition of individual bubble wakes. On this basis, we derive a scaling for the dissipation rate in dilute BIT that is consistent with experimental results from the literature.

This is the first in a series of papers aimed at understanding the statistics of coalescing particles in turbulent flow and their relation to collisionless ghost particles. We perform three families of Direct Numerical Simulations (DNS) under identical flow conditions: ghost particles without mutual interactions; particles that coalesce upon collision with lost monomers replenished at random positions (CR); and particles with the same collision-coalescence kinetics without replenishment (CN). All analyses are monodisperse and concern only monomers. Across $St=0.01\text{-}3.0$, the ghost-particle system has higher collision kernels ($K$) and radial distribution functions (RDFs, $g(r)$) near contact than the coalescing systems. A velocity-filtered RDF, $g_{\mathrm{G}}^{(-)}(r)$, provides a reasonable estimate of the CR contact RDF, $g_{\mathrm{CR}}(d)$. We show that the residual discrepancy between $g_{\mathrm{G}}^{(-)}(d)$ and $g_{\mathrm{CR}}(d)$, and between the corresponding kernels, arises from correlations among successive collisions in the ghost-particle system. A history-filtered ghost-particle kernel, excluding such correlations, reproduces the coalescing-system kernel. We introduce a collision-correlation time $\tau_{\mathrm{cc}}$ that quantifies how long current collisions influence future events and find that it has a finite, narrow range across the studied $St$. Filtering particles with collisions within a period comparable to $\tau_{\mathrm{cc}}$ yields a history-filtered RDF that reproduces those of both coalescing systems. Finally, the fraction of repeated collisions involving identical particles decays exponentially with $St$. These results unify the coalescing and ghost-particle systems as a history-filtered framework.

Physics-informed neural networks applied to the level-set formulation of interface advection commonly augment the residual and initial-condition losses with an eikonal regulariser, penalising the deviation of $\|\nabla\phi\|$ from unity. A previous two-dimensional study identified this weight as the dominant hyperparameter and found its optimum shifts by four orders of magnitude between rigid-body and deforming flows, but left open whether these principles transfer to three dimensions and whether single-seed results survive run-to-run variability. We answer both by repeating the weight selection across four 3D benchmarks (translating sphere, rotating sphere, slotted sphere, reversed vortex), sweeping six weights with three seeds at full training budget under a pre-registered selection rule. The ordering transfers: the selected weight tracks how far the exact solution departs from the signed-distance property, spanning four decades from $10^{-1}$ where it holds exactly to $10^{-5}$ where the interface is stretched. Values transfer only benchmark by benchmark; two of four carry over unchanged and two do not, so inheritance must be verified. The multi-seed protocol reveals that at small weights the seed-to-seed standard deviation equals the error itself, and the regulariser reduces it by more than an order of magnitude, buying reproducibility as well as accuracy. We benchmark against a fifth-order WENO solver on identical grids and error measures; the classical scheme is more accurate on all four problems, by two orders of magnitude on smooth rigid advection, with a margin that narrows with geometric difficulty and is smaller in volume conservation than in the field norm. Finally, we show that the relative $L_2$ error cannot certify the preservation of thin features, and report a feature-restricted measure that can.

In this work, viscous fluid flow governed by the Stokes equations in highly perforated domains is studied using physics-informed neural networks (PINNs). Perforated microstructures induce complex boundary conditions and fine-scale flow features that are difficult for standard neural networks to resolve. Conventional PINNs, even when combined with advanced training techniques, can suffer from a loss of accuracy and efficiency as the number of perforations increases. One important source of this difficulty is the soft enforcement of boundary conditions through penalty terms, which can lead to stiffness, gradient conflicts, and poor resolution of near-boundary flow structures. Hard constraints provide an alternative by encoding boundary conditions exactly into the network ansatz, but may introduce undesirable non-local effects due to the global nature of the approximation. To address these challenges, finite basis PINNs (FBPINNs), which are based on domain decomposition and localisation principles, are used together with hard boundary constraints that efficiently encode perforation-related boundary conditions. This approach helps mitigate spectral bias, improves overall accuracy, and exhibits convergence that is only weakly affected by the number of perforations, thereby providing an efficient and highly parallelisable neural network framework. The proposed approach is further supported with theoretical arguments, specifically focusing on the localisation and approximation properties of FBPINNs.

Squeezing of a liquid film between two approaching solid surfaces can generate a high-speed peripheral splash. Despite extensive studies on squeeze-film hydrodynamics, quantitative prediction of the splash velocity remains unresolved, with existing theory significantly overestimating experiments. Here, we present a theoretical framework to predict the ejection velocity of viscous liquid squeezed between two parallel circular disks. We show that discrepancy of theory from experiments arise due to incomplete treatment of liquid inertia and from using peak ejection velocity to represent splash velocity. By accounting for both local and convective inertia, and introducing a momentum-averaged ejection velocity, we obtain good agreement with experiments over a wide range of parameters.

The Atmospheric Boundary Layer (ABL) plays a critical role in influencing objects exposed to atmospheric conditions, making its study crucial. Due to the high cost of real-world testing, this thesis focuses on replicating marine ABLs in a wind tunnel environment. Two profiles were developed: one that served as a framework for establishing commonality among the various international wind engineering standards ('Profile 1'), and a second profile, which is more suitable for modelling the inflow to wind farms in the English Channel and the North Sea ('Profile 2'). The ABLs were generated using Irwin spires without floor roughness elements, and the flow characteristics were measured using Laser Doppler Anemometry (LDA) and a multi-hole probe (MHP). MHP showed a reasonably high accuracy when compared to LDA, with less than 1% deviation in the streamwise velocity and under 5% standard deviation in the streamwise, spanwise, and wall-normal velocity components. The profiles achieved good agreement with target metrics such as normalised velocity and turbulence intensity. Spanwise uniformity and spectral analysis confirmed the robustness of the simulation across varying inflow velocities. Overall, Irwin spires proved to be a cost-effective and reliable method for simulating marine ABLs, offering valuable insights for optimising offshore wind energy systems.

This study presents a comprehensive numerical investigation of the dynamic behavior and fluid-structure interactions (FSI) of metallic cylinders undergoing hydrostatic collapse in semi-confined fluid environments using a structured Arbitrary Eulerian-Lagrangian (ALE) formulation in LS-DYNA. The numerical model reproduces the experimentally measured collapse pressure of 3.69 MPa and predicts the first water hammer peak with a 1.01% error, demonstrating high predictive fidelity. Following validation, the effects of material type (aluminum and titanium), cylinder slenderness ratio (L/D), and confinement diameter on collapse behavior, pressure evolution, and fluid motion are examined. Titanium cylinders exhibited sharper collapses, higher water hammer pressures exceeding 70 MPa, and greater kinetic and strain energy accumulation than aluminum due to their higher stiffness and yield strength. Lower L/D ratios produced more abrupt collapses, whereas higher L/D ratios promoted more gradual, axisymmetric deformation. Larger confinement diameters intensified jet formation and increased fluid velocities. The simulations provide mechanistic insight into the coupling between structural deformation and surrounding fluid, showing that geometry, material stiffness, and confinement govern collapse-induced energy transfer. Full-field FSI analysis captures key phenomena, including radial jetting, peak fluid velocities, and internal cavitation, that are not evident from pressure-time histories alone. These findings provide quantitative guidance for the design and safety assessment of subsea pressure housings, marine pipelines, and other underwater structures subjected to extreme hydrostatic loading.

The discretization of second-order (viscous) terms in Discontinuous Spectral Element Methods (DSEMs) typically relies on an auxiliary gradient variable, whose treatment at element interfaces affects the accuracy and stability of the scheme. The Bassi-Rebay (BR1) formulation is attractive for its simplicity and parameter-free character, but suffers from sub-optimal convergence at even polynomial orders and requires an extended five-element stencil. Inspired by Huynh's Flux Reconstruction formulation, we develop a compact, fully-centered scheme for second-order fluxes within the Spectral Difference (SD) method. The proposed approach modifies the reconstruction of the auxiliary gradient using interface-dependent, one-sided continuous fluxes, reducing the stencil from five to three elements while preserving the centered and parameter-free nature of BR1. The formulation is developed in one dimension and extended to multiple dimensions. Temporal eigenanalysis is used to characterize its dissipation and dispersion properties, including the effects of interior penalty terms. Numerical tests consider the linear diffusion equation, an under-resolved localized Dirac's delta, the nonlinear porous medium equation, and implicit large-eddy simulations of the three-dimensional Taylor-Green vortex at $\mathrm{Re}=1600$ and $5000$. The compact scheme restores the expected convergence order for all polynomial degrees, including even orders, and reduces spurious oscillations in under-resolved and nonlinear regimes. It also remains stable in turbulent cases where the standard formulation fails, owing to improved damping of high-wavenumber numerical modes. The proposed approach provides an attractive compact alternative to BR1 for second-order fluxes in the SD method.

A discrete entropy inequality is the principal nonlinear stability estimate available for systems of conservation laws, and evaluating it presupposes a physically admissible state. So far, however, the two have been secured separately. Entropy-stable schemes are almost always semi-discrete, are built around one selected entropy pair, and take for granted the positivity of density and pressure that makes the entropy well defined in the first place, whereas bound-preserving limiters keep the solution admissible but deliver no entropy estimate. For the special relativistic Euler equations, the two cannot be separated at all, since the conservative-to-primitive map is implicit, and an inadmissible state therefore has no entropy to correct. Here we construct high-order discontinuous Galerkin and finite volume schemes that, to our knowledge, for the first time, are entropy stable in the fully discrete sense for an arbitrary prescribed finite family of convex entropy pairs, a property we call multi-entropy stability, and are provably admissible wherever an entropy is evaluated. All of this is achieved by a single cellwise projection, and neither conservation nor the design order is lost. The construction rests on relativistic causality, which bounds every characteristic speed by the speed of light. Consequently, the numerical viscosity can be fixed once for all states and all equations of state, and one two-point building block then serves the whole entropy family. Since only the convexity of the admissible set and this speed bound are used, the same route remains open for related systems. Finally, in computations with four equations of state, the schemes retain high-order accuracy close to vacuum, produce no inadmissible state in strong shocks, near-vacuum shock--vortex interaction or jets with Lorentz factor above $70$, and confirm the monotone decay of every enforced discrete entropy.

We study radial nonlinear instability of compactly supported nonrotating equilibria of the three-dimensional Euler--Poisson system with a physical-vacuum boundary. Let $n^u(\mu)$ denote the radial instability index furnished by the turning-point theory of Lin and Zeng. Under general structural assumptions on the pressure law, suppose that $n^u(\mu)>0$ and that the equilibrium is not a mass extremum, $M'(\mu)\neq0$. Conditional on the existence of a sufficiently regular radial solution on the relevant time interval, we establish two nonlinear escape criteria. First, every perturbation with Hamiltonian strictly below that of the equilibrium exits a fixed neighborhood on a logarithmic time scale controlled by the least unstable linear growth rate. For the subclass of data for which the associated Lyapunov functional is initially nonnegative, we also obtain an explicit exponential lower bound in the weighted displacement norm. Second, sufficiently small perturbations whose Riesz projection onto the finite-dimensional unstable subspace is not too small escape on a logarithmic time scale. The second argument uses the exponential trichotomy of the linearized Hamiltonian flow and an invariant-cone estimate. In the polytropic class, the conditional estimates combine with the radial physical-vacuum local theory to yield unconditional nonlinear instability in the corresponding classical-solution topology. The results complement Jang's nonlinear instability theorem for Lane--Emden stars by treating mechanisms that do not require initial alignment with a leading growing eigenmode and by applying, conditionally, to unstable branches for general equations of state.

High-fidelity immersed-boundary simulation resolves the coupled motion of a deforming swimmer and its surrounding flow, but the resulting cost limits repeated evaluations for engineering design, parameter studies, and control. We develop neural-operator surrogates for temporal prediction of the hydrodynamic fields generated by planar and volumetric eel swimmers. The surrogates are trained on regular-grid fields exported from adaptive fluid--structure simulations and are conditioned on swimmer geometry and Reynolds number. The planar model jointly predicts two velocity components, scalar vorticity, and pressure. On five held-out high-Reynolds-number trajectories, its full-domain global relative L^2 error is 3.51 %. The volumetric formulation uses three target-specific models with a common multichannel input: one model predicts three-dimensional velocity, one predicts vorticity, and one predicts pressure. Their full-domain global relative L^2 errors on five held-out within-range trajectories are 3.44 %, 5.58 %, and 19.2 %. Together, the results demonstrate the feasibility of field-resolved neural surrogates for moving-boundary swimmer flows while identifying pressure accuracy and physical consistency as priorities for further development.

The present paper is devoted to the study of integral properties of alpha unpredictable functions. The problem of invariance of recurrence under integration is one of the most challenging and interesting in the theory of functions. Let us start with periodicity. Next, the problem was solved for quasiperiodic, almost periodic, and Poisson stable functions. All of the problems were subjected to the condition of bounded integrals. The alpha-unpredictable functions are the endpoint in the row of recurrent functions. The class is the cross-border point from regularity to chaos in the dynamics presented through the elements of the row. In the present research, we finalized the proof that any theoretical functional recurrence is invariant with respect to integration, provided the result is bounded.

Building upon our previous studies on nonlinear variable-length pendulum systems, we investigate the Swinging Atwood Machine with a massive string. In contrast to the classical model, string inertia introduces a configuration-dependent moment of inertia, leading to a modified Hamiltonian structure and substantially richer dynamics. To uncover the global organization of the phase space, we combine Poincaré sections, bifurcation diagrams, and Lyapunov exponent maps with our recently developed numerical framework, ,,Lyapunov Refined Maps". This approach provides a unified visualization of periodic, quasi-periodic, chaotic, and terminating motions, revealing intricate resonance networks and high-order periodic structures. We investigate the influence of the string mass, system parameters, and energy by constructing Lyapunov maps in parameter and initial-condition spaces and on fixed-energy surfaces. Liouville integrability is studied within the Morales--Ramis theory. By analyzing the normal variational equations along explicit non-stationary radial solutions and applying the Kovacic algorithm, we prove that the differential Galois group is generically SL(2,C), providing a rigorous obstruction to meromorphic Liouville integrability for every nonzero string mass. Thus, the exceptional integrable case of the classical Swinging Atwood Machine is destroyed by the inclusion of string inertia.

We study the emergence of complexity in finite-size quantum systems as their dynamics transition from closed and coherent evolution to interacting and effectively open behavior. Using a state-based geometric framework, we represent mixed quantum states as probability measures on complex projective Hilbert space. This representation allows us to track how interactions reshape the underlying pure-state geometry. We introduce two complementary diagnostics: a distinguishability measure, based on the Wasserstein distance between probability-measure representations of mixed states, that quantifies sensitivity to initial states, and a state-space coverage index that measures long-time exploration of the subsystem state space. These diagnostics provide a geometric perspective on the emergence and evolution of quantum dynamical complexity. When applied to the quantum kicked top, both diagnostics generally increase with interaction strength. Their dependence on environment size is structured by parity symmetry, with integer-spin systems often exhibiting greater sensitivity and state-space coverage than half-integer-spin systems. These results highlight finite-size quantum effects and provide a geometric approach to quantifying dynamical complexity deep in the quantum regime

We investigate the dynamics of entanglement in a generalized version of the kicked Ising chain, extending the model from the standard qubit case (local dimension $q=2$) to higher local dimensions ($q > 2$). We identify the existence of ''dual-unitary'' points where the model's space-time duality allows for exact analytical solutions. Our analysis reveals that while a few unique dual-unitary points exist analytically for systems with local dimensions $q=3$ and $q=4$, such points do not exist for $q \ge 5$ due to the lack of a unique kicking strength that satisfies the required matrix element conditions. Utilizing the transfer matrix method and a replica trick specifically adapted for higher dimensions, we derive exact expressions for the growth of entanglement entropy in the $q=3$ (kicked Potts-type) model starting from a class of solvable initial states. Our results demonstrate that at the dual-unitary point, both Rényi and von Neumann entanglement entropies grow linearly with time until reaching a maximum value determined by the subsystem size.

While conventional rogue wave statistical models rely on linear or weakly nonlinear descriptions of random seas, we demonstrate experimentally that moderately or strongly nonlinear wave fields can be represented by sparse ensembles of coherent soliton-like packets. These packets exhibit log-normal amplitude distributions together with uniformly distributed phases and peak emergence times. This sparse coherent structure framework naturally leads to an extreme value description in which the probability of exceedance is governed by the tail of the coherent-structure amplitude distribution. The prediction is validated against laboratory hydrodynamic experiments across a variety of unidirectional sea states, showing good agreement with the experimental observations and comparing favourably with conventional statistical prediction models while retaining analytical simplicity. Our results provide a direct physics-based link between sparse coherent structures and rogue wave probabilities, with broader implications for nonlinear wave physics in optics, cold gases, and plasmas.

We investigate two parity-time-symmetric ring resonators coupled over a finite angular region described by a super-Gaussian profile. In the linear regime, analytical spectra are obtained in the homogeneous-coupling and fixed-amplitude narrow-contact limits, while the finite-width problem is treated numerically. Local coupling introduces nonzero spatial Fourier components that mix angular harmonics and lift the degeneracy of counterpropagating modes, resolving each excited doublet into parity-dependent branches. Collisions among these branches generate multiple exceptional-point boundaries and disconnected broken-PT domains. The resulting phase diagrams exhibit re-entrant unbroken-broken-unbroken transitions when the gain-loss strength, coupling width, or peak coupling amplitude is varied. The numerical spectra continuously recover both analytical limits. In the nonlinear regime, selected ground and excited linear modes are used as seeds for adiabatic propagation into finite-amplitude Kerr waveforms that remain dynamically persistent over the simulated observation interval for finite ranges of nonlinear strength. These results show that the spatial profile of inter-resonator coupling provides a geometric means of controlling multimode PT transitions and selecting dynamically accessible nonlinear waveforms in coupled-ring systems.

Four-wave mixing provides a simple setting in which dispersion, nonlinearity, and non-Hermiticity compete to select resonant energy-transfer channels. We study degenerate four-wave mixing in a Kerr dual-core coupler with balanced gain and loss and frequency-dependent intercore coupling. The dispersive coupling changes the symmetry from conventional $\mathcal{PT}$ symmetry to a combined $\mathcal{CPT}$ symmetry and reshapes the two-branch linear spectrum. We determine the unbroken-$\mathcal{CPT}$ domain and classify the branch configurations that can satisfy the degenerate phase-matching condition. In the parameter ranges examined, three resonant channels persist over broad regions, whereas a same-branch channel appears only close to the symmetry-breaking threshold. In this near-threshold regime, a single pump can simultaneously satisfy two distinct nonzero sideband resonances. Direct pulse simulations confirm the predicted resonances and reveal secondary-wave generation and multifrequency cascades near eigenmode coalescence. A reduced three-wave model captures the initial dynamics away from the exceptional point but loses accuracy as the modal basis becomes ill-conditioned. These results show how dispersive coupling reorganizes resonances, group-velocity mismatch, and nonlinear energy exchange in a non-Hermitian wave system, and they identify the exceptional-point region as a regime where a few-mode description can break down.

Two identical scalar dynamical systems coupled through a scalar diffusion equation are studied herein, with respect to bifurcations from a symmetric steady-state to symmetric and asymmetric steady-states and to in-phase and anti-phase oscillations. Numerical continuations based on the developed theory show the shape of the bifurcation branches and the attracting nonlinear states far from bifurcation onset and confirm their, for the most part, derived stability. This study extends the work on the dynamical properties of a single scalar dynamical system coupled to its own delay through an adjacent diffusion field and quantifies further the delay of diffusive information transmission between two such Wentzell boundaries. The mathematical system is motivated by modeling biological membranes with yet unknown effective local fluxes that are coupled to bulk diffusion.

In this Brief Communication, we establish the notion of critical damping for generic two-degree-of-freedom system. For given set of masses and stiffnesses, the critical damping corresponds to the real eigenvalue with maximal multiplicity, equal to minus geometrical mean of the eigenfrequencies. This case corresponds to the fastest possible asymptotic decay rate for generic initial conditions. The damping matrix for the critical case is unique up to reflection of one modal coordinate and, generically, non-diagonal. Quite surprisingly, for large difference of the eigenfrequencies, it is also not positive definite. Therefore, physical realization of the critical case will require active elements that provide negative effective damping.

The motion of a projectile released from a simple pendulum is analyzed, with particular emphasis on investigating the optimal release angle that maximizes the horizontal range and the corresponding maximum range. This system serves as a simplified model of the Tarzan jump problem. Using simple analytical methods, the optimal release angle is shown to be characterized by a cubic equation and to increase with the initial velocity. In addition, asymptotic expressions for both the optimal angle and maximum range are derived in the limits of low and high initial velocity.

Cells often estimate chemical concentrations from only a few diffusing molecules, whose stochastic motion limits sensing precision. We consider a perfect monitoring instrument that records the instantaneous molecular density throughout a finite region without perturbing the concentration field or distinguishing molecular identities. The standard Berg-Purcell estimator weights all positions uniformly. Here we derive the optimal spatial weighting within a large class of unbiased estimators for both concentration and gradient sensing. Variance minimization maps to an electrostatic problem. Surprisingly, although the instrument monitors the entire volume, the optimal estimator assigns all weight to its boundary, reducing the uncertainty in both concentration and gradient sensing. We extend the results to arbitrary geometries and spatial dimensions.

Classical fractons are Hamiltonian systems that can develop attractors after projection onto configuration or shape variables, although the full phase space admits none. We study a scale-invariant, dipole-conserving two-parameter family of fracton Hamiltonians $H_{\alpha,\beta}$. By separating coordinates into scale and shape, we obtain autonomous shape dynamics that admit fixed points which leave a purely scale evolution of the form $R(t)\propto |t|^{\alpha/(\alpha-\beta)}$. The shape fixed points, which determine the distribution of the expanding particles, are central configurations of power-law Riesz potentials. The distinguished model $(\alpha,\beta)=(-2,1)$ is unique: its scale evolution takes the Einstein-de Sitter form $R(t)\propto |t|^{2/3}$, its fixed-point equation is the equal-mass Newtonian central-configuration, its large-$N$ distribution is a homogeneous ball, and its homothetic trajectories admit a zero-energy Newtonian gravitational dual. The fixed points are locally stable, and simulations at moderate $N$ approach them from random initial data. Large $N$ simulations reveal a richer class of fixed-points: bound clusters of approximately fixed physical size retain internal motion, while their centers approach unequal-mass Newtonian central configurations and preserve large-scale homogeneity. A scale-separation conjecture yields an effective unequal-mass fracton dynamics for the centers and a corresponding zero-energy Newtonian gravitational dual. Trajectories generically exhibit a bidirectional arrow of time: scale and shape complexity grow away from a Janus point, while Boltzmann entropy grows logarithmically. Together, these features reproduce the salient structure of a flat matter-dominated cosmology. In the distinguished fracton model, all these cosmological analogues emerge as attractor properties, making it a toy model for cosmological dynamics without fine-tuning.

Strain-hardening is a feature of polymer glasses during large deformation, which helps to stabilize the glasses against breakage. Experimentally, little is known about the segmental dynamics during strain-hardening, and such data is important for building a molecular-level theory of polymer glasses deformed in this regime. Here, using a photobleaching technique, we measured the segmental dynamics of lightly-crosslinked poly(methyl methacrylate) (PMMA) glasses with and without melt-stretching, which were deformed into the strain-hardening regime with local engineering strain rates from 10^-4.6 s^-1 to 10^-4 s^-1 at Tg-23K and Tg-33K. We find that melt-stretched PMMA glasses show a more prominent strain-hardening feature and faster segmental dynamics by a factor of about 15% compared to PMMA without melt-stretching. At a given true strain rate, the segmental dynamics of PMMA without melt-stretching are accelerated in the deep strain-hardening regime from the value just beyond yield, by up to 40% at 0.8 true strain. Our observations are in agreement with previously published simulation results.

It is well known that physical aging of polymer glasses increases their yield stress and affects their failure behavior. Studies indicate that application of moderate levels of stress during aging results in higher yield stress compared to aging in the absence of stress (quiescent aging). This has been interpreted to indicate that stress accelerates physical aging, and has been described as overaging. In this study, we age PMMA glasses under stress, and carry out direct measurement of segmental dynamics during and after aging by using a probe reorientation technique. We observe that samples aged under stress, despite having higher yield stress, have faster segmental dynamics after stress release than quiescently aged samples. This contradicts the overaging interpretation, for the range of conditions explored here. Our results indicate that yield stress is not a simple function of structural relaxation time and theoretical models based on this understanding need to be revised.

Active Brownian particles (ABPs) in viscoelastic (VE) media exhibit fascinating dynamical phenomena set by self-propulsion, thermal fluctuations, and fluid viscoelasticity. We extend our model, in which the Brownian dynamics within a slowly diffusing harmonic well emulates that in a single-relaxation VE fluid, to study active Brownian motion in such media. Consequently, the resultant dynamics is governed by the interplay of the characteristic timescales of the systems: the crossover and equilibration times of the VE fluid, $\tau_k$ and $\lambda$, respectively, and the persistence time of the ABP, $\tau_{\mathrm{R}}$. Following analytical predictions and simulations, we study two practically relevant regimes where the dynamics is dominated by the persistence of active motion and the elastic confinement of the VE fluid, with a phoretically active Pt-coated Janus colloid in a dynamic optical trap, and show quantitative agreement with the simulations. This approach provides a VE environment with tunable VE properties that remain unaffected by the strength of self-propulsion, allowing us to systematically investigate active Brownian motion in VE media in ways that are not otherwise possible with physical VE fluids.

Dense-liquid relaxation evolves from local particle collisions to cooperative structural rearrangements. While hard-sphere kinetics determines an early $t^{3/2}$ fractional decay in density correlation functions, collective theories describe the subsequent structural relaxation. A central open question has been how short-time contact physics supplies an exact starting point for the memory kernel governing later times without being modified by subsequent many-body rearrangements. Here we resolve this problem for a broad class of reversible Brownian systems. We prove that hard particle contacts act as reflecting boundaries in configuration space, uniquely dictating the amplitude of the leading $t^{3/2}$ density relaxation. Mechanistically, diffusion samples a contact boundary layer of thickness $O(\sqrt{t})$, which combines with the local density response to produce the fractional signal. We derive an explicit surface formula expressing this amplitude in terms of equilibrium contact probability, normal mobility, and density sensitivity. For monodisperse hard spheres, this yields an exact, fit-free prediction determined entirely by static structure $S(k)$, radial contact value $g(\sigma^+)$, and short-time diffusion $D_0$. Extending the construction, we determine the corresponding normalization for soft interfaces and prove via a Gram--Schur projection hierarchy that regular collective variables leave the leading contact amplitude strictly invariant. The resulting formulation connects microscopic collision kinetics directly to caging and glass-like structural relaxation, providing an exact microscopic boundary condition for scattering experiments, molecular simulations, and memory-kernel reconstructions.

We investigate the different coefficients of restitution $e$ of a dissipative, frictional disc as a function of the impact angle $\theta$ and the friction coefficient $\mu$. We observe a non-monotonic, non-linear behaviour of $e_{\mathrm{T}}$ and $e_{\mathrm{kin}}$ with a clear minimum at $\mu$-dependent values of $\theta$ and a convergence for all $\mu$ at large $\theta$, bounded by the cases of pure rolling and pure sliding. Changing the dissipative normal interaction affects the $\mu$ convergence at large $\theta$ and leads to a convergence at low $\theta$. The presence of initial angular velocity $\omega$ can significantly alter the functional behaviour of $e_{\mathrm{T}}$ at steep impacts and slightly change the magnitude of $e_{\mathrm{kin}}$, with friction playing only a minor role. Overall, our results indicate, that any value of $e_{\mathrm{T},\mathrm{kin}}$ is highly situational and can describe entirely different configurations.

In order to determine the structural relaxation time of a polymer glass during deformation, a strain rate switching experiment is performed in the steady-state plastic flow regime. A lightly cross-linked poly (methyl methacrylate) (PMMA) glass was utilized, and simultaneously the segmental motion in the glass was quantified using an optical probe reorientation method. After the strain rate switch, a non-monotonic stress response is observed, consistent with previous work. The correlation time for segmental motion, in contrast, monotonically evolves towards a new steady-state, providing an unambiguous measurement of the structural relaxation time during deformation, which is found to be approximately equal to the segmental correlation time. The Chen-Schweizer model qualitatively predicts the changes in the segmental correlation time and the observed non-monotonic stress response. In addition, our experiments are reasonably consistent with the material time assumption used in polymer deformation modeling; in this approach, the response of a polymer glass to a large deformation is described by combining a linear-response model with a time-dependent segmental correlation time.

While previous work has identified the conditions for preparing ultrastable single-component organic glasses by physical vapor deposition (PVD), little is known about the stability of co-deposited mixtures. Here, we prepared binary PVD glasses of organic semiconductors, TPD (N,N-Bis(3-methylphenyl)-N,N-diphenylbenzidine) and m-MTDATA (4,4,4-Tris[phenyl(m-tolyl)amino]triphenylamine), with 50:50 mass concentration over a wide range of substrate temperatures (Tsub). The enthalpy and kinetic stability are evaluated with differential scanning calorimetry and spectroscopic ellipsometry. Binary organic semiconductor glasses with exceptional thermodynamic and kinetic stability comparable to the most stable single-component organic glasses are obtained when deposited at Tsub=0.78-0.90Tg (where Tg is the conventional glass transition temperature). When deposited at 0.94Tg, the enthalpy of m-MTDATA/TPD glass equals that expected for the equilibrium liquid at that temperature. Thus, the surface equilibration mechanism previously advanced for single-component PVD glasses is also applicable for these co-deposited glasses. These results provide an avenue for designing high-performance organic electronic devices.

It has been more than twenty years since conductive polymers began to receive attention as an emerging thermoelectric material. However, the trade-off between electrical conductivity ({\sigma}) and thermopower (S) has proven to be a major challenge that has obstructed their use in actual devices. Here we report the discovery that the thermopower of the p- and n-type legs of organic thermogenerators can be substantially enhanced, without significant deterioration of {\sigma}, by constructing an in-plane segmented structure consisting of a homojunction with different doping levels on either side. In such segmented layers, the S is abnormally higher than the average value of the constituent parts when applying a forward temperature gradient (heating the heavily doped counterpart), while it is lower upon a reverse temperature gradient. Typically, for a two-stage segmented film of p-type PDPP-Se, an abnormally large S of 210 uV K-1 and {\sigma} of 2.5*10^4 S m-1 are obtained, resulting in a large power factor (PF) of 1100 uW m-1 K-2 and a record ZT of 1.36 at room temperature. The enhanced thermopower is attributed to an additional voltage developed at the homojunction under heating as explained by kinetic Monte Carlo simulations. This finding provides a breakthrough approach to the modulation of thermoelectric transport properties of conductive polymers.

We aim at calculating an explicit expression for the finite-size probability distribution of the radius of gyration $R$ of an Interacting Self-Avoiding Walk (ISAW), as a function of chain length $N$ and monomer-monomer interaction energy $\varepsilon$. We first derive the explicit free energy expression for a non-interacting Self-Avoiding Walk, introducing a new natural scale variable $t = \rho^g$ expressed as a power of the density $\rho$. Then, thanks to a cumulant expansion approach introduced by Lhuillier, Victor and coworkers, we extend it to the interacting case, capturing both the coil-globule transition and finite-size corrections to scaling, including entropic and surface-energy contributions. The radius of gyration distribution determined by the new free energy expression is then compared, using Bayesian inference to estimate the model parameters, to results from extensive Monte Carlo simulations of three-dimensional ISAWs, showing excellent agreement except very close to the $\Theta$-point, where finite chain lengths limit the accessible scaling regime. This validates our resulting free energy expression and allows us, as an application, to construct a phase diagram of the coil-globule transition.

Dynamic electrowetting of conducting droplets under mechanical deformation is conventionally modeled as a quasi-static variable-capacitance system, in which the electrical response is assumed to be governed solely by the evolution of the droplet--electrode contact area. Under the assumption of instantaneous charge equilibration, this framework successfully describes the cyclic steady-state electromechanical response of the system. However, its validity for transient interfacial electrical dynamics remains largely unexplored. Here, the transient electrowetting response of mercury droplets confined between a polymeric dielectric-coated electrode (PTFE or PVDF) and an opposing copper electrode is investigated under periodic mechanical excitation with multiple waveforms at 2 Hz. The measured contact area and corresponding capacitance evolve closely as predicted from instantaneous surface-energy minimization, confirming that the liquid-interface mechanics remain quasi-static. In contrast, the measured transient current and instantaneous electrical power exhibit pronounced asymmetric excitation and relaxation phases that are independent of the excitation waveform, demonstrating that transient charge evolution cannot be inferred from the instantaneous geometric capacitance alone. This transient behavior is phenomenologically interpreted using constituent first-order interfacial dielectric charge-relaxation kinetics, indicating that the measured current arises from slow dielectric charging followed by dielectric relaxation over the timescale of the imposed periodic mechanical oscillations during discharging. These findings establish that transient electrowetting is governed by the coupled interplay of droplet electrohydrodynamics and dielectric interfacial polarization, requiring a constitutive description beyond quasi-static variable-capacitance models based solely on contact-line dynamics.

We perform three-dimensional variational data assimilation (3DVar) using a discrete adjoint approach to optimise the time-averaged momentum equations. The experimental data consist of sparse stereoscopic particle image velocimetry (PIV) measurements collected along $12$ cross-stream planes in the wake of a vehicle-like bluff body at a Reynolds number $Re_L = 5.64 \times 10^5$ based on the streamwise body length. Adjoint localisation is proposed and implemented to reduce the memory footprint of the discrete adjoint method for spatially-varying control variables in 3DVar by confining the control variable space to a user-defined subdomain. Restricting the control variable to $12$ % of the full control space yields a maximum reduction in peak memory of $64$ %, while producing assimilated fields of comparable fidelity with respect to mean velocity and the optimised momentum forcing field. The localised adjoint case improves upon the baseline Spalart--Allmaras turbulence model and recovers the correct asymmetric topology of the complex three-dimensional (3D) recirculation bubble. The assimilated Reynolds shear stress agrees well with the experiment, and the assimilated mean pressure is shown to be physically consistent when correlated with the in-plane vorticity fields. A data efficiency study is also performed, in which the number of planes provided for assimilation is progressively reduced, demonstrating that the data coverage must extend at least to the end of the primary recirculation bubble to adequately constrain the near-wake dynamics. The efficiency that adjoint localisation affords is crucial for assimilating sparse, experimental data for 3D separated flows on fine meshes that can tackle industrial problems of interest.

Autoregressive reduced order models suffer from compounding long horizon rollout errors, typically treated as unstructured noise. We demonstrate that for bluff body wakes across Re=100 to 800, this rollout error is highly structured and reveals what these models actually learn. For a convolutional autoencoder LSTM model, 95 % to 98% of the error is pure phase error, peaking sharply at the vortex shedding frequency. The network reproduces the attractor geometry almost exactly, matching limit cycle amplitudes within 0.15%, but traverses the cycle at slightly the wrong rate. This timing error, accumulating to just a few thousandths of a cycle over the entire rollout, drives the long horizon error even while one step validation errors appear virtually perfect. Because phase error drifts linearly, it can be corrected offline without retraining using just one parameter per latent coordinate, fitted on a short calibration window. The signal to noise ratio of this phase fit serves as a diagnostic that reliably predicts correction success (r=0.85 across 50 networks). While simple periodic baselines match this performance on stationary limit cycles, they fail by over an order of magnitude when applied to wakes driven by slowly varying inflows. Conversely, our phase correction requires only phase coherence, successfully removing roughly half of the rollout error during non stationary flow.

Subgrid-scale parameterization of 2D turbulence must preserve the geometry enabling the dual cascade. Classical and data-driven closures often lack the symmetries required for online stability. We introduce the Symplectic Geometric Closure (SGC), derived from a geometric reduction of Multilayer Stochastic Models. Its core is a hidden reservoir of unresolved symplectic degrees of freedom feeding back on the resolved flow through a constrained Hamiltonian exchange. Stability is enforced geometrically. The interaction is generated by a symplectic functional $\mathcal{G}$ that preserves augmented enstrophy, yielding pullback boundedness for the Navier--Stokes--$\beta$ core and a compact random pullback attractor in the hyperviscous realization. The same generator produces an emergent Hamiltonian subgrid velocity whose forcing is exactly the Lie transport of resolved vorticity. Unresolved stochastic activity thus renormalizes the advecting geometry while maintaining the Hamiltonian structure of incompressible 2D motion. Eliminating the reservoir yields a finite-memory Eulerian theory. At one-loop line-renormalized order, reservoir contractions reproduce the operator architecture of Kraichnan-type Direct-Interaction Approximation theory. Crucially, the nested Jacobian vertex is compatible with Random Galilean transformations and imposes an intrinsic fourth-order infrared suppression, $\mathcal{O}(p^4)$, of uniform sweeping modes within the Eulerian interaction. With decorrelation controlled by strain-induced deformation rather than sweeping, the dressed Eulerian transfer theory self-consistently admits the classical $k^{-5/3}$ inverse-energy and $k^{-3}$ forward-enstrophy cascades. SGC thus provides an Eulerian geometric realization of Kraichnan's program and a principled foundation for geometrically constrained, stability-preserving data-driven closures.

This study investigates the influence of the spatial distribution of flexibility along a propulsor on thrust generation and propulsive efficiency in wave-assisted flapping foils. While flexibility is known to enhance propulsive performance, the role of its chordwise placement remains poorly understood. Here, the effective flexible length is systematically varied by shifting the flexure location along the tail while maintaining constant flexural rigidity and total chord length. Experiments are conducted in quiescent flow at heave frequencies of 0.8 Hz and 1.25 Hz, and non-dimensional heave amplitudes of h* = 0.13 and 0.22. Simultaneous measurements of hydrodynamic forces, flow fields, and tail kinematics are used to quantify performance and elucidate the underlying fluid-structure and fluid-particle interactions. The fully flexible configuration consistently achieves higher propulsive efficiency (up to approximately 164%) across all conditions, which is attributed to enhanced jet persistence and increased streamwise vortex spacing, indicative of a more coherent and sustained momentum jet. In contrast, the mid-flexible configuration yields substantially higher thrust (up to approximately 66%) at the largest heave frequency and amplitude, driven by a pronounced increase in near-wake jet velocity and momentum flux. These results demonstrate that the chordwise distribution of flexibility governs the trade-off between thrust and propulsive efficiency by modulating wake coherence and momentum transfer. The findings establish flexibility placement as a key design parameter in flapping propulsion and provide physics-based guidelines for enhancing the performance and endurance of wave-driven unmanned surface vehicles.

We investigate whether the two flow-index thresholds previously found for isothermal shock profiles persist when the full nonisothermal dynamics is taken into account in a hyperbolic power-law relaxation model of Rational Extended Thermodynamics. The nonisothermal profile problem is structurally different from its isothermal counterpart: restoring the energy balance determines the temperature along the traveling wave and feeds it back into the pressure, the relaxation production, the temperature-dependent consistency coefficient, and the characteristic structure. Under thermodynamic stability, $p_\theta\ge0$, and strict convexity of the reduced Hugoniot pressure, no nontrivial constant-temperature compressive profile can satisfy the full equations. We derive an exact global characteristic-ordering identity and prove that the positive nonequilibrium characteristic speed has its strict global minimum at the unperturbed upstream state. Consequently, a monotone continuous profile exists for $1\Mst$ the Boillat--Ruggeri theorem excludes a $C^1$ profile and any admissible piecewise-smooth connection must contain a subshock. Despite the thermomechanical coupling, the shock-thickness classification remains unchanged: $m=2$ is the weak-shock threshold and $m=1$ the near-critical threshold as $M_0\nearrow\Mst$. The corresponding exponents are constitutive-independent within the present class, while finite limiting values and prefactors depend on the equation of state, internal energy, and temperature-dependent consistency coefficient. For the Tait--Murnaghan example, increasing the reference temperature lowers the critical Mach number when the dimensional viscous--relaxation scale is fixed and, for the thermally thinning law considered, reduces the resolved shock thickness.

From a dynamical systems perspective of subcritical transition in shear flows, the basin boundary separating the laminar and turbulent attractors, along with the edge state that governs the long-term dynamics on that boundary, are of fundamental interest. As the Reynolds number is increased from small values, a multiplicity of simple exact coherent structures (ECS) appear in phase space, of which one often undertakes the role of the edge state. At higher values of the Reynolds number, however, the dynamics on the basin boundary and the edge state are sensitive to initial conditions, as shown by a wealth of numerical and experimental studies. The mechanism behind this transition remains unclear. To address this, we examine the subcritical regime of Taylor-Couette flow using a minimal computational box and reveal a generic mechanism whereby the edge state becomes chaotic. The first step in this process involves the formation of a heteroclinic tangle between a travelling-wave-type ECS and an independently engendered chaotic saddle. The interaction causes the basin boundary to incorporate the saddle, thus inheriting its fractal structure, while the edge state itself remains the simple ECS. The transition of the edge state to chaos requires a second step: the formation of a heteroclinic cycle involving the ECS and the chaotic saddle. In consequence, the observation of a simple non-chaotic edge state at given values of the parameters is no guarantee that the same situation will hold at nearby values.

A fast-converging and asymptotic-preserving adjoint shape optimization method is proposed for drag reduction of multiscale gas flows in vibrating micro-electro-mechanical systems. The convergence of the Boltzmann kinetic equation is accelerated by macroscopic synthetic equations, whose constitutive relations integrate continuum-limit terms and high-order kinetic corrections to faithfully characterize spatiotemporal rarefaction effects. As such, this method maintains near-continuum limit consistency while retaining high kinetic accuracy in rarefied flow regimes. Fourier stability analysis performed in an infinite domain demonstrates that the present method yields a spectral radius below 0.5, indicating that the numerical deviation from the converged solution is halved per iteration. Numerical simulations are conducted on an oscillating cylinder and a comb-shaped resonator. The results verify the high accuracy of the derived adjoint sensitivities and the excellent drag reduction performance of the proposed method across various Knudsen and Strouhal numbers. Compared with conventional kinetic iteration methods, the present method produces convergent primal and adjoint solutions within dozens of iterations and features asymptotic preserving behavior, permitting spatial cell sizes far larger than the molecular mean free path. This facilitates efficient design of vibrating micro-electro-mechanical systems.

Distinguishing chaos from noise using time-series data is fundamentally challenging because both exhibit irregular fluctuations and share many statistical and dynamical characteristics. Existing methods face two key limitations: temporally correlated noise can yield spurious signatures of chaos, and analyses of scalar time series often require explicit choices of embedding parameters. Here, we propose a purely data-driven method for distinguishing chaos and noise based on a reservoir-computing framework with a cross-prediction scheme. In the proposed approach, the model is trained to predict the future change of a variable from its current value, thereby combining a short-term predictability test with a test of the smoothness of deterministic flows. The recurrent structure of reservoir computing enables effective prediction of high-dimensional chaotic dynamics even from scalar time series without explicit delay-coordinate reconstruction, while the cross-prediction framework strongly suppresses spurious predictive correlations arising from noise. We apply the proposed method to diverse synthetic and empirical time series. Chaotic systems consistently yield strong correlations between the true and predicted future changes, whereas noise processes remain clearly separated in a low-correlation regime. The method also exhibits substantial robustness to practical limitations in empirical data, including measurement noise, limited data length, and increasing prediction lag. These results demonstrate that the squared Pearson correlation coefficient provides a simple quantitative criterion for distinguishing chaos from noise directly from observed time-series data.

The period of biological and chemical oscillators scales with temperature in a characteristic way. Some oscillators are very well described by an Arrhenius law, while others show systematic deviations. Several frameworks have been proposed to explain such deviations, but they are either phenomenological, focus on activation energy imbalances in specific circuits, or restrict themselves to sequential processes. Here we develop a mechanistic account of the temperature scaling of relaxation oscillators, using the Belousov-Zhabotinsky (BZ) reaction as a model system. We distinguish two typical scenarios by their temperature-scaling signatures. In the first, an Arrhenius-dependent timescale separation parameter produces a biphasic Arrhenius scaling of the period as the oscillator approaches a Hopf bifurcation. In the second, Arrhenius-dependent nullclines hide the same bifurcation behind a canard explosion, yielding apparent single-line Arrhenius scaling. Measuring the electrode potential of a classical and an uncatalyzed BZ reaction, over a very wide temperature range ({\approx} 100 °C), and comparing to dynamical models, we find that the two reactions represent these two distinct scenarios. Furthermore, we show that a single parameter characterizing the waveform asymmetry between fast and slow phases quantitatively predicts the temperature scaling of three other observables close to the Hopf bifurcation: the period, amplitude, and phase noise. This analysis also recovers elementary activation energies of the BZ mechanism, including a new estimate for the autocatalytic step. We discuss how this framework and its waveform-based diagnostics apply to the analysis of general biochemical relaxation oscillators

Living matter undergoes continuous turnover. The hydrodynamic theory of Malthusian flocks describes polar active matter with turnover, but its phase diagram and nonlinear scaling behavior is not well understood. Using a nonperturbative renormalization group approach, rotationally invariant to second order in derivatives, and without defects, we explicitly obtain the strong-coupling fixed point governing true long-range order, uncover a quasi long-range ordered phase, and identify a critical point similar to, but distinct from the Berezinskii-Kosterlitz-Thouless universality class at the transition.

Novel phases, beyond long-range order in two dimensions, have continued to be discovered within flocking models, establishing flocking as one of the pivotal paradigms in active matter. However, much of the discussion around ``Malthusian'' (constant density) flocks, an analytically more tractable alternative to the Vicsek model, has centred around the scaling exponents governing the intermediate regime prior to the proliferation of asters, leaving open the question of what other phases the model might display. Here, we study the two-dimensional dynamics of Malthusian flocks and identify a previously unnoticed phase, where the dynamics is that of the equilibrium XY Model. By identifying the symmetries of the model, we derive the effective equations of motion for the Goldstone modes and analyse the spin-wave fluctuations. We identify a novel critical point separating two distinct phases and, using a perturbative RG procedure, determine the RG flows in its vicinity. This allows us to calculate the universal scaling behaviour at the critical point, along with its logarithmic corrections. The novel phase transition here is due to the interaction of activity and spin-waves, unlike the equilibrium counterpart, which undergoes a phase transition in effective degrees of freedom, namely vortices. Nevertheless, the RG flows are similar to those of the Berezinskii-Kosterlitz-Thouless transition, and we show that for sufficiently strong noise, the activity becomes irrelevant and the system crosses over to the equilibrium XY universality class.

Spatial confinement profoundly impacts the transport and self-organization of active matter across diverse biological systems. While the collective orders in confined active matter have been extensively characterized, how geometric constraints reshape near-field flows and the resulting inter-particle correlations remains largely unexplored. In this study, we combine experiments and hydrodynamic simulations to investigate inter-particle correlations within quasi-two-dimensional Chlamydomonas reinhardtii suspensions. We reveal two disentangled modes characterizing cell pairs: a dipolar mode and an entrainment mode, which exhibit a density- and distance-dependent competition. Combining single-cell flow field analysis, hydrodynamic simulations, and active-passive mixtures, we link these two modes to singular hydrodynamics and lubrication-induced entrainment. Our results demonstrate that spatiotemporal correlations in confined active matter are fundamentally rooted in the interplay of these two hydrodynamic mechanisms.

Reported maxima of the advancing contact angle scatter from $87^\circ$ to $147^\circ$ in a single systematic study, and liquids on surfaces with static angles as low as $5^\circ$ reach dynamic maxima near $90^\circ$. We show that both observations follow from the hinged motion of the free surface near a moving contact line. The local Stokes solution for a wedge rotating about its contact line has two singular angles of opposite character: at $90^\circ$ the hinged motion generates no wall shear and the rotation is free, and at $\theta_h = 128.73^\circ$, where $\tan 2\alpha = 2\alpha$, a resonance with the $r^2$ eigensolution arrests the rotation through an $r^2 \ln r$ term. Between the two angles lies a band that a transient advancing angle cannot leave while the interface near the contact line remains a quasi-steady wedge. A compilation of 68 liquid-solid systems from nine sources and five configurations confirms the band and its two exits: systems not limited by the apparatus, with $\theta_s \le 40^\circ$, reach $87^\circ$ to $119^\circ$ regardless of chemistry, and every exceedance of $\theta_h$ occurs either where chemistry places the static angle above the band or where the flow leaves the quasi-steady regime. The record of a waterline on a vertical wall exhibits the band within a single unsteady experiment, together with a distinct quieting of the local contact angle at the crossing of $90^\circ$.

The object of investigation in this paper are the nonlinear equations of motion for two-dimensional inviscid water flows with piecewise constant density stratification in a three-layer fluid with a flat bottom, a free surface and two interfaces. We establish a Hamiltonian formulation for the nonlinear governing equations in this setup. The Hamiltonian of the system and the equations of motion of the surface and of the interfaces are expressed with the help of the Dirichlet-Neumann (DN) operators, which are introduced for each of the layers. Then, the linear equations for small amplitudes of the elevation of the surface and of the interfaces in the leading order are derived from which a bi-cubic equation for the dispersion relation is obtained, whose solutions are analysed. The six real solutions for the possible propagation speeds (three positive, related to right-moving waves and three negative, related to left-moving waves) have magnitudes of different order. Upper and lower bounds for the previously mentioned roots are also given in terms of the coefficients of the equation. Subsequently, approximate formulae for the propagation speeds are derived. The importance of the DN operators is further illustrated in a separate analysis of the three-layer model with flat surface (rigid lid). The full nonlinear evolution equations are expressed again in terms of the DN operators, and the equations in the linear regime and the weakly nonlinear propagation regime (the Boussinesq approximation) are derived by a proper expansion of the DN operators. Limits to the two-layer free surface model are obtained as well. The obtained results are applicable to internal waves in lakes and in the ocean as well as to laboratory experiments with three superimposed fluid layers.

The development of a solid rind or carapace at the surface of lava flows and domes results in a transition in deformation mechanism from dominantly viscous to elastic or plastic. This transition has a significant impact on the rate and style of emplacement, including on the construction of channelized flows, over-steepened margins, and flow advance due to lava breakouts. These processes are particularly important in subaqueous, subglacial, and extraterrestrial environments in which cooling is accelerated, requiring models specifically calibrated for these environments. We present a new numerical model, Viscous-Elastic Numerically Unified Solver for Solidifying flows (VENUSS), for cooling and solidifying free surface flows. The model couples a viscous fluid interior with an elastic shell whose thickness grows in response to cooling. As a demonstration of the impact of including a solidified crust in the flow model, we show that a dome-like shape fed from below with an elastic shell coupled to the basal topography results in more lateral expansion and less vertical uplift than a comparable highly-viscous rind, demonstrating the need for lateral transfer of stress in solid layers to accurately interpret and predict dome deformation.

Bubble growth in silicate melts drives significant volume expansion, which has a first order control on magma transport dynamics. When magmas are exposed to external environments, heat and volatile loss at free surfaces can reverse bubble growth, leading to shrinkage and complex feedbacks between diffusion, rheology, and flow. To resolve how magma flow controls, or is controlled by, bubble expansion, we couple a micro-mechanical model for volatile diffusion into individual bubbles, with a macro-scale thermal evolution and fluid flow of the surrounding magmatic suspension. This two-way coupling captures the co-evolution of bubble size, melt viscosity, and pressure gradients, allowing both growth and resorption to emerge naturally from local conditions. We identify distinct dynamical regimes governed by (i) bubble growth limited by (a) viscous resistance or (b) diffusion at the bubble scale, (ii) viscous transport of the suspension, (iii) outgassing through permeable porous networks and exposed magma-fluid interfaces, and (iv) thermal quenching. Across these regimes, thin, high-viscosity boundary layers arising from temperature and volatile concentration gradients play a central role in modulating flow and bubble evolution. The model is implemented in a flexible, modular numerical framework (Multiscale Vesiculation, Fluid flow, Failure, and Interaction Nonlinear model: MVFFIN) enabling extension to a wide range of systems and applications, including conduit flow and pyroclast evolution. By resolving the interplay between internal bubble dynamics and external boundary conditions, this approach provides a unified framework for understanding multiscale degassing and its impact on magmatic transport and fragmentation.

An analytical solution for a wave velocity field scattered by a submerged permeable vertical plate-type breakwater under the linear monochromatic wave is obtained and the applications of the solution are presented. The water has an infinite depth, and the flow is assumed to be incompressible, inviscid, and irrotational, which leads to the two-dimensional potential wave theory. The permeable breakwater vertically occupies a finite interval beneath the water surface and the water flows through the breakwater. The resulting nonlinear boundary condition is resolved by the perturbation method with a small parameter representing the permeability. The solution was expanded up to the first order so that the leading-order term can represent the wave scattered by the impermeable breakwater and the first-order term can give the correction to the solution considering the wave scattered by the permeable breakwater. Each order of the wave velocity potential is determined by a reduction method and this leads to the homogeneous Riemann-Hilbert problem for the leading-order problem and the nonhomogeneous Riemann-Hilbert problem for the first-order problem. \rev{The effects} of wavelength, breakwater length, and breakwater permeability conditions on the reflection and transmission coefficients are discussed in detail as an illustrative example of the application of the solution. \rev{An exact energy identity is also derived; it verifies the first-order solution and yields a closed-form boundary $\varepsilon_{\max}(kb)$ of the validity range of the expansion.

We demonstrate, by studying precession-driven flows, that inertial wave hydrodynamic turbulence can drive a robust magnetic dynamo action. Motivated by the stronger damping of large-scale geostrophic vortices in rapidly rotating planetary and stellar interiors, we introduce a controlled damping of the vortices, which usually accompany inertial wave turbulence and feed on wave energy. It is shown that even a small vortex damping results in a significant increase of the growth rate of the dynamo due to inertial waves in the kinematic regime, allowing it to persist for magnetic Prandtl numbers as low as $Pm \sim 10^{-3}$ and Poincaré numbers $Po\sim 0.025$. These critical values of $Po$ and $Pm$ for the dynamo onset decrease with increasing Reynolds number. The onset and growth of the dynamo appear to correlate with the coherent fluctuations of kinetic helicity. Spectral analysis shows that magnetic energy growth is primarily due to inertial-wave-induced induction over a broad range of scales. These results establish inertial waves as an efficient mechanism for magnetic field amplification in rapidly rotating low-$Pm$ flows relevant to planetary and stellar interiors.

Charge separation during the breakup of water drop has been recognized since the early studies of waterfall and spray electrification, yet the role of controlled drop fragmentation at structured liquid-repellent surfaces remains unclear. Here we show that water drops impacting superhydrophobic meshes generate charged secondary droplets as liquid penetrates and fragments through the mesh pores. By combining Faraday-cup charge measurements with high-speed imaging, we identify how the charge depends on the Weber number and on the pathway of spray formation. No measurable charge is detected below the penetration threshold. At low Weber numbers, recoil jet formation gives a high charge per unit spray mass, whereas at intermediate Weber numbers both recoil jets and impact-induced jets contribute to charging. At higher Weber numbers, pancake bouncing suppresses recoil jet formation, so charging is dominated by impact induced penetration and the total charge approaches a saturated value. We further show that smaller mesh pores enhance the charge-to-mass ratio and that conductive meshes provide stable charging under repeated impacts by dissipating residual surface charge. These findings provide design principles for superhydrophobic mesh platforms for spray charging and rain-driven energy harvesting.

Multiphase electrohydrodynamic (EHD) flows play a crucial role in various engineering applications. However, existing numerical studies on three-phase electrohydrodynamic systems predominantly rely on phenomenological models, often neglecting thermodynamic consistency and critical surface charge convection mechanisms. To address these fundamental gaps, this paper proposes a thermodynamically consistent three-phase EHD model derived strictly from the Onsager variational principle. This theoretical framework intrinsically guarantees thermodynamic consistency and accurately captures complex multiphysics interactions without requiring a priori assumptions. Furthermore, a mesoscopic lattice Boltzmann method is developed to solve the proposed model, enabling the natural capture of interfacial evolution and charge transport. The accuracy of the numerical framework are rigorously validated against several benchmark cases, including electroosmotic flow in microchannels, the spreading of a three-phase liquid lens, the equilibrium of static compound droplet, and the deformation of compound droplet under uniform electric field. Using this validated framework, we investigate EHD applications, specifically simulating the complex dynamics of double droplet coalescence and separation under electric field, as well as the behavior of droplets subjected to combined EHD and shear flow. Overall, this work provides a robust, thermodynamically reliable numerical tool for exploring the highly nonlinear behaviors of multiphase EHD systems.

We demonstrate that the area rule of velocity circulation -- traditionally associated with the turbulent inertial range but shown not to be exact -- is strictly satisfied in the large-scale absolute equilibrium of two-dimensional (2D) homogeneous isotropic turbulence under enstrophy equipartition. We also derive a novel perimeter rule from the 2D inviscid loop equation, which posits that the probability distribution function (PDF) of velocity circulation depends solely on the loop perimeter rather than its area. This perimeter rule holds strictly in the large-scale absolute equilibrium characterized by energy equipartition. At the intermediate states determined by both enstrophy and energy, these two regimes are separated by a characteristic equilibrium scale $l_\text{eq}$: the area rule governs loop statistics when $l\ll l_\text{eq}$, while the perimeter rule emerges for $l\gg l_\text{eq}$. These statistical laws remain robust even for loops with extreme aspect ratios as low as $0.03$, a value that inertial-range studies never achieved. Our findings provide a new steady-state solution to the 2D loop equation and suggest additional solutions, paving the way for exploring previously undiscovered geometric invariants of turbulence.

Alternate bars are ubiquitous bedforms in alluvial rivers, and excessive bar-height growth can increase flood risk and disrupt ecosystems. Predicting bar-height variability requires quantifying the dependence of bar growth rate on water discharge, yet this has rarely been achieved because conventional flume measurements interrupt the flow and cannot continuously capture bar evolution. Here we conducted laboratory experiments under four discharges and four channel slopes (16 conditions) and continuously mapped bed topography using Stream Tomography, a nonintrusive, flow-through measurement technique. Bar height exhibits sigmoidal growth and is well described by the Landau equation, allowing robust estimation of the growth rate and equilibrium height. The inferred dimensionless growth rate tends to increase as discharge decreases, but its sensitivity is weaker than that predicted by stability theory for a single alternate-bar mode. This discrepancy becomes more pronounced at lower discharge, indicating limitations of linearization and the influence of interactions among multiple bar modes. Furthermore, numerical flow simulations over the measured bed topography reveal that, during bar development, lower-discharge conditions produce a relatively larger bar height-to-depth ratio, making the flow more prone to deflection. In such cases, sediment transport is restricted downstream of depositional areas, thereby limiting bar migration. Consequently, flow and sediment transport become concentrated in the scour zones, enhancing local scour and promoting the growth of bar height. These results provide benchmark constraints for bar stability theories and help improve predictions of how bar height responds to changes in discharge.

Viscoelastic filament thinning is classically described by elastocapillary dynamics in extensional flows, yet in confined microchannels the combined effects of wall-induced shear, elasticity, and capillarity remain poorly understood. Here, we experimentally investigate the breakup of a shear-thinning viscoelastic liquid coflowing with an immiscible Newtonian fluid in a rectangular microchannel, focusing on the formation, stretching, instability, and breakup of the thin filament connecting the primary droplet to the upstream liquid. Four regimes: stable coflow, squeezing, dripping, and jetting are identified and mapped using the capillary numbers of the dispersed and continuous phases and an elastocapillary parameter. Although elasticity weakly affects the onset of primary droplet formation, it strongly alters later filament dynamics by delaying capillary breakup and stabilising long-lived filaments. Scaling analyses based on capillary, viscous, and elastic force balances predict the primary droplet size, critical filament thickness at instability onset, maximum filament length, and critical jet length. Particle tracking shows that confinement creates a non-uniform wall-induced shear field along the inclined filament, producing spatial variations in interfacial velocity and initiating the first bead-on-a-string instability at the location of maximum shear. A Rayleigh-Plateau analysis incorporating an effective viscosity derived from the Oldroyd-B model predicts the instability wavelength and growth rate to the correct order of magnitude. These results show that confined viscoelastic breakup is governed not solely by classical elastocapillary thinning, but by a coupled wall-shear-elasticity mechanism controlling filament stretching, instability, and secondary droplet formation, thereby providing a predictive framework for filament-mediated breakup in confined viscoelastic multiphase flows.

We investigate the exponential growth of uncertainty energy in 3D Navier-Stokes turbulence, emphasising the intermittent and highly localized amplification/production of uncertainty, a critical factor in understanding the predictability of turbulent systems. From the Navier-Stokes equations one can identify some key fields contributing to the growth/decay of uncertainty-production term $P_{\Delta}$: strain rate, vorticity, and vortex deformation. The dynamics of these fields are examined in the $Q-R$ plane, where $Q$ and $R$ are the second and third invariants of the velocity gradient tensor, to understand their role in the evolution of uncertainty-production term $P_{\Delta}$. We proceed by estimating committor functions across the entire spatiotemporal domain of direct numerical simulations (DNS) of turbulence in a periodic domain at different Reynolds numbers. Our estimates of the probability of rare extreme events of local uncertainty-production term as a function of uncertainty energy, strain rate, vorticity, and vortex deformation confirm the role of strain rate in driving uncertainty. Where strain rate and vorticity are too close to their space-average values, stable probabilistic forecasts appear impossible solely on the basis of the fields considered here.

We study the simultaneous vanishing-viscosity and vanishing-resistivity limit of steady incompressible MHD flows in a disk. The boundary velocity is a small nonaxisymmetric perturbation of a rigid rotation with mean angular speed \(\alpha\), while the prescribed tangential magnetic trace has mean \(\beta\). Assuming \(\alpha\neq0\) and the non-Alfvénic condition \(|\alpha|\neq|\beta|\), we construct solutions converging on compact interior subdisks to a rigidly rotating ideal MHD core with constant vorticity and out-of-plane current density. A new MHD--Wood law determines the two core rotations from the boundary data: the velocity core is selected by a coupled kinetic--magnetic balance, whereas the magnetic core is fixed by the imposed mean circulation. Consequently, zero circulation gives complete interior magnetic expulsion, while nonzero circulation leaves a uniform magnetic rotation after the nonaxisymmetric modes are confined to a thin boundary layer. This provides a fully coupled realization of Prandtl--Batchelor selection and flux expulsion; unlike classical kinematic models, the magnetic field actively changes the flow and need not be weak. The proof combines a non-Alfvénic coercive theory for a periodic MHD boundary layer, global matching of the two fields, and a coupled stability estimate adapted to the magnetic boundary condition. A separate conditional rigidity argument, using exact viscous identities and local convergence but no interior asymptotic expansion, explains the same core structure for a broader single-eddy family.

Estimating positive largest Lyapunov exponents from data is comparatively natural because neighboring trajectories separate, whereas stable dynamics require resolving contraction before measurement noise or finite precision erases the signal. We introduce a period-aware forecast-error contraction procedure for estimating a dominant negative Lyapunov exponent from ensembles of short scalar trajectories without using governing equations or an analytical Jacobian. A k-nearest-neighbor predictor is trained on trajectory histories, the geometric-mean absolute forecast error is evaluated at phase-consistent horizons, and the exponent is obtained from the slope of the logarithmic error profile. Unlike data-driven approaches that reconstruct local evolution matrices or differentiate a learned surrogate, the proposed method extracts the contraction rate directly from out-of-sample forecast errors. Two adaptations are essential: the forecast step is synchronized with the detected orbit period, and candidate slopes are accepted only when they form a stable consensus across several transient lengths. On the logistic map, the method recovers 92 of 112 negative-exponent parameter values with a mean absolute error of 0.0253 and $R^2=0.886$. On a two-dimensional map without fixed points, independent scalar pipelines based on the three observables $x_n$, $y_n$, and $z_n$ give mean absolute errors of 0.00879--0.01145 and $R^2=0.983$--$0.986$. Because the estimation stage uses only observed trajectories, the framework provides a basis for repeated-relaxation experiments in which short sensor responses are available but the governing equations and analytical Jacobian are unknown. Experimental validation remains a subject of future work.

Magnetic field-line transport in tokamaks is governed by the interplay between chaotic dynamics and invariant phase-space structures that act as partial transport barriers. We investigate the conservative Tokamap, an exact symplectic mapping for magnetic field-line dynamics, using a unified geometrical, dynamical, and statistical framework. Phase-space portraits and Lyapunov exponents characterize the mixed Hamiltonian dynamics, while ensemble-averaged transport exhibits universal dynamic scaling with growth, crossover, and saturation regimes connected through a homogeneous scaling theory. Poincaré recurrence statistics reveal that decreasing the magnetic-shear parameter systematically slows transport, with the characteristic transport time following the algebraic scaling $\tau_c\propto x_q^{-0.213}$. This behavior reflects increasingly dominant stickiness associated with KAM islands, resonance chains, and cantori. Our results establish a direct connection between the geometrical organization of Hamiltonian phase space and macroscopic transport properties, providing a comprehensive framework for understanding long-time magnetic field-line transport in tokamaks and other Hamiltonian systems with mixed phase space.

Using official government data sets of USA and France we analyze the occurrence/frequency/popularity distributions of given names on a time scale of more than 100 years. These distributions are characterized through the Lorenz and Pareto curves broadly used in the analysis of wealth inequality in the world. These curves remain stable during the considered time period with the Gini coefficient remaining in the narrow range 0.85-0.95. As for the case of wealth inequality, we show that the distributions of names are well described by the Rayleigh-Jeans (RJ) thermalization and condensation phenomenon well studied in various physical systems. The RJ thermalization results from two integrals of motion being analogous to energy and probability norm conservation in physical systems with energy states corresponding to popularity levels of names. Time correlations between names are also determined showing their stability until the middle of the twentieth century and a significant change after that.

In this paper, we give a memorial tribute to Prof. Erik M. Bollt (1967--2025).

We report nonlinear edge waves in a 2D mechanical topological insulator. A bulk lattice consists of pendulums with on-site cubic nonlinearity connected by linear springs realizing quantum spin Hall effect. We show that the nonlinear interaction between two edge modes with equal group velocities (EGV) is described by a 1D two-component coupled nonlinear Schrödinger (CNLS) equation. On the interface separating two bulk lattices with opposite spin Chern numbers, we construct linear springs such that the dispersion relation exhibits EGV points with favorable CNLS coefficients. Thus, we realize nonlinear edge waves propagating along the interface, including bright-bright (BB) edge solitons for focusing CNLS coefficients, and dark-dark edge solitons, edge domain walls, and dark-bright edge solitons for defocusing CNLS coefficients. In terms of the site amplitudes, these solutions resemble bright and dark breathers. These solutions should be topologically protected when both carrier frequencies lie within a band gap, which we explicitly show by passing BB edge solitons through compact defects on the interface. We also show energy transfer in BB edge soliton collisions with potential application to collision-based computing. Generally, vector edge solitons exhibit a large parameter space for soliton collisions, which endows mechanical devices with greater potential for information processing and other functionalities.

We investigate pseudovorticity generation in Gaussian beams undergoing self-focusing under amplitude and phase noise, using the cubic-quintic nonlinear Schrödinger equation. Pseudovorticity, defined as the curl of the optical momentum flux, characterizes local rotational flow in the absence of phase singularities. Our numerical simulations show that thermal amplitude and phase noise induce a multipolar pseudovorticity pattern. Unlike the pure cubic case, where noise asymmetries are radiated away during collapse, the quintic saturation arrests collapse and traps the noise in the resulting soliton. Hence, pseudovorticity multipoles persist, oscillating at the focusing-refocusing period. These results suggest a potential pathway for controlling local optical torque through noise engineering.

Whereas conventional Gaussian focusing gradually concentrates optical energy around the focal plane, abruptly autofocusing waves maintain a low peak intensity over most of their evolution before undergoing a sudden, high-contrast intensity surge at a prescribed focus. Since their introduction in 2010, their two-dimensional spatial realizations have enabled applications ranging from particle manipulation and material processing to terahertz generation and nonlinear optics. The recent work of Cao et al. marks the transition from (2+1)-dimensional spatial autofocusing to the full space-time domain through the experimental synthesis of spherical Airy wavepackets. This advance opens new opportunities for ultrafast structured light, tightly localized energy delivery, and nonlinear photonics.

For more than three centuries, Newton's Second Law (F=ma) has governed mechanics with undisputed success, yet its epistemic authority has rested on empirical adequacy alone. That empirical contingency vanishes under two physical principles - the Principle of Excluded Perpetual Motion (PEPM) and the Weak Equivalence Principle (WEP) - from which the law emerges as a structural necessity of admissible mechanics. Under the PEPM constraint, Suppes' operational measurement protocol grounds gravitational mass and force as independent primitives. The fusion of Stevin's static and Galileo's kinematic inclined-plane analyses establishes F/a as a well-defined, object-intrinsic quantity - the operational definition of inertial mass. The WEP compels the equivalence of inertial and gravitational mass without presupposing Newton's Second Law. Substituting this equivalence into the definition of inertial mass yields the law as a theoretical identity between independently defined quantities. The derivation is anchored in gravity because weight uniquely bridges statics and kinematics, yet the result is independent of the underlying force mechanism. The derivation carries structural consequences: modified-inertia formulations of MOND are inadmissible under the PEPM-WEP constraint; the location-invariance of the Kibble-balance realization of the SI kilogram is secured on first principles; and under the PEPM alone, torsion-balance and free-fall experiments constitute equally direct tests of the WEP. More fundamentally, Newton's Second Law is not an irreducible axiom of mechanics, but a structural consequence of deeper physical principles: energy conservation and the Einstein Equivalence Principle.

We investigate Hamiltonian curl-force systems with indefinite kinetic energy. We first reconsider Berry's polynomial Hamiltonian curl-force model, whose numerically observed closed trajectories motivated an integrability conjecture. A Painlevé analysis yields a non-principal resonance spectrum, so that the corresponding Laurent series cannot accommodate the required number of arbitrary constants of the general solution. The model therefore fails the standard Painlevé test. We then introduce a four-parameter curl-force family and identify the parameter locus on which this system is integrable. We construct a second Hamiltonian, compatible Poisson tensors, separated complex characteristic variables, and a Lax representation. More generally, the separated form yields polynomial integrable curl-force Hamiltonians of arbitrary degree. We also show that the same construction admits a higher time-derivative potentialisation whose free limit is the degenerate Pais-Uhlenbeck oscillator. Finally, we analyse zero-curl invariant reductions and elliptic periodic solutions, and exhibit an isolated periodic orbit outside the integrable regime. This illustrates that closed trajectories alone do not imply Liouville or Painlevé integrability.

We introduce a notion of completeness for two-dimensional second-gradient elastic continua and propose a microstructural route toward its synthesis. A continuum is said to be complete if the Hessian of the stored energy with respect to the second-gradient variable is locally positive definite, so that every nonzero admissible increment of the placement second gradient is quadratically controlled in the highest-order part of the energy about each configuration. Starting from the Principle of Virtual Work, we derive the constitutive relations, equilibrium equations, and admissible boundary interactions for a broad class of fibrous second-gradient continua whose stored energies depend on fiber stretch, stretch gradients, and curvature. The theory is then applied to several continua motivated by pantographic microstructures. Classical pantographic sheets are shown to be incomplete, while bi-pantographic fabrics enlarge the class of components of the second gradient detected by the energy but remain incomplete. Finally, we formulate a tri-pantographic continuum associated with a proposed three-family architecture and prove that it is complete. The examples illustrate how microstructural architecture influences both the completeness properties of an effective continuum and the pointwise form of its higher-order boundary interactions.

Antifreeze materials prevent ice-formation by disrupting the ice-formation by binding to certain ice-planes. Cellulose, the most abundant biopolymer, has shown the ability to bind to ice-planes but the exact mechanism of this binding is far from being understood. Molecular dynamics simulations are used to investigate the hydration water of chains of cellulose-type glycans and its significance in the expression of the antifreeze behavior of sugar-derivatives found in some antifreeze materials. We find that glycans are able to prevent water from freezing near its surface by preventing their rearrangement to achieve a highly tetrahedral structure at temperatures well-below the freezing point of water. This validates our hypothesis on the role of tetrahedral coordination based on previous $\textit{ab initio}$ calculations that demonstrated cellulose prefers to bind to ice basal and prismatic planes using a tetrahedral geometry. Our findings suggest that the tetrahedral ordering of water around glycans is the key to understanding and designing cellulose-based antifreeze materials.

The mechanisms governing triboelectric charging between insulating particles of the same material remain an open question in nonequilibrium physics, with several competing models proposed to explain observed charging behaviour. Here, we investigate charge evolution in a minimal system consisting of two acoustically levitated particles undergoing repeated binary collisions. To quantify particle charge transfer, purpose-built Faraday cage picoammeters were developed and calibrated. The MultiLev acoustic levitation system was used alongside Ultraino simulations to generate transducer control signals, enabling controlled collision and separation of polystyrene (PS) particles. Although individual collision events exhibit stochastic charge transfer, described by skew-normal distributions, we demonstrate for the first time that the cumulative charge evolution of an individual acoustically levitated particle pair follows the saturation behaviour predicted by the condenser model of triboelectric charging, with fits achieving $R^2 > 0.99$. Under identical conditions, conductive graphite-coated PS particles also undergo charge transfer, but accumulate substantially less charge, consistent with the distinct charging behaviour expected for conductive materials.

In recent years, non-reciprocity has been explored as a ubiquitous manifestation of non-equilibrium activity at the microscopic scales for various active matter systems, from mixtures of chemically active enzymes, colloids, and droplets, to engineered light-controlled active colloids and robotic meta-materials. A commonly used minimal model to describe the dynamics of a binary mixture of conserved species with non-reciprocal interactions is the non-reciprocal Cahn-Hilliard (NRCH) model. The model is characterized by a temperature-like tuning parameter, which can trigger phase separation, and a non-reciprocal coupling, which can lead to the formation of spatio-temporal patterns, as it represents an intrinsic source of non-equilibrium activity and breaks parity and time-reversal symmetries. Here, we study the scaling behavior of the NRCH model near the critical point using perturbative dynamical renormalization group techniques. We find that structural and dynamical correlations are controlled by different correlation lengths, both of which diverge at the critical point, but governed by different scaling laws. In particular, while the structural correlations are always controlled by temperature and the classical Wilson-Fisher critical exponent, the dynamical correlation length exhibits multiple scaling regimes in which either temperature or non-reciprocal coupling can dominate as the key tuning parameter, with a new critical exponent characterizing the divergence. The critical point corresponds to a conserved equilibrium-like dynamics with odd mobility, which we denote as the odd Cahn-Hilliard (OCH) model. Our findings may have important implications on how living systems can control phase separation and spatio-temporal pattern formation using the rates of catalytic reactions, and in general metabolism, as control parameters.

We study the prediction of plastic activity in the confined channel flow of two-dimensional amor- phous soft particles around a circular obstacle. Using datasets generated with a particle-based bubble model, we formulate the prediction problem within two supervised-learning frameworks: re- gression of the non-affine displacement and binary classification of neighbor change events. A key technical challenge is that the obstacle and the confining walls explicitly break translational and rotational symmetries. We address this issue by introducing additional structural descriptors that encode the positions of particles relative to these boundaries. Starting from simple linear models, we systematically increase the complexity of the learning framework by considering a logarithmic transformation of the target variable, the incorporation of particle-size information, the addition of symmetry-breaking obstacle and wall descriptors, the coarse-graining of local structural descrip- tors, and nonlinear neural-network models. We find that the obstacle and wall descriptors provide the largest improvement in predictive performance. Nevertheless, the models considered here cap- ture mainly the overall localization of plastic activity near the obstacle and do not fully reproduce its detailed heterogeneous pattern in individual configurations. A perturbation analysis indicates that this heterogeneity is robustly encoded in the initial structure, suggesting that further progress requires more expressive structural representations and machine-learning architectures.

We investigate the structural and dynamical behavior of methane water systems under nanoconfinement using molecular dynamics simulations across pore widths from 1 to 5 nm. Structural analysis reveals a strong and nonmonotonic dependence on confinement: while tetrahedral ordering partially recovers as confinement is reduced, cubic like order associated with clathrate precursors is maximized at intermediate pore sizes. Radial distribution functions show that three dimensional correlations are suppressed under strong confinement, whereas lateral ordering persists, indicating a reduction in the effective dimensionality of structural organization. Transport properties reflect the same structural competition. Parallel diffusion is nonmonotonic with pore size, while perpendicular motion is subdiffusive due to confinement induced trapping and heterogeneity. Methane exhibits stronger subdiffusion and remains dynamically coupled to the water matrix. A characteristic confinement length scale emerges at which structural ordering, dynamical heterogeneity, and solvent solute decoupling are simultaneously maximized. At strong confinement, three dimensional correlations are suppressed, leading to dimensional reduction, frustrated ordering, and inhibited nucleation.

> Dense non-Brownian suspensions exhibit complex resuspension dynamics governed by hydrodynamic interactions, particle microstructure, and gravity. While viscous resuspension in spherical suspensions is known to be strain-controlled, its applicability to anisotropic particles remains unclear. Here, we investigate dense suspensions of spherical and rod-shaped particles under steady and oscillatory shear. The results reveal two strain-controlled transitions: particle detachment from the sediment bed and the transition to a fully suspended state. Both particle shapes exhibit the same critical strain for detachment, approximately 6, indicating that resuspension onset is largely independent of particle morphology. In contrast, complete resuspension requires a critical strain of approximately 120 for spheres and 180 for rods, demonstrating a strong effect of particle anisotropy. A fluid-strain scaling collapses the onset of resuspension across particle concentrations and shapes while highlighting the distinct influence of particle shape on complete suspension. These findings establish a unified strain-based framework for viscous resuspension and clarify the role of particle anisotropy in dense suspension dynamics.

Stress relaxation in transient polymer networks often shows extended power-law behavior, $G(t) \sim t^{-\beta}$, where the exponent $\beta$ frequently departs from the value $1/2$ predicted by the sticky Rouse model and its variants. We introduce the fractional inhomogeneous Rouse model (FIRM), which uses a generalized Langevin equation driven by fractional Gaussian noise of exponent $\alpha$, while retaining heterogeneous bead friction to represent sticky cross-links. Thus, FIRM unifies subdiffusive sticker dynamics and chain heterogeneity within a single framework. We show that the relaxation modulus $G(t)$ can be represented as a linear combination of Mittag-Leffler functions. For homogeneous chains, it recovers two power-law regimes, $t^{-\alpha/2}$ and $t^{-2\alpha}$, on either side of the terminal relaxation time. Fitting FIRM to stress relaxation data for an imine-based polystyrene vitrimer shows that $\alpha < 1$ is required to capture the shape of the terminal relaxation. It also accommodates both Arrhenius and non-Arrhenius temperature dependence in the rheological activation energy. We derive expressions for dynamic properties such as mean-squared displacement and dielectric response and outline how generalized memory kernels extend the framework to real materials. Together, these results suggest novel ways in which data from rheology, dielectric spectroscopy, scattering, and other experimental methods may be incorporated into a chemistry-specific molecular model.

Extreme flows realize the largest possible growth, either instantaneously or in finite time, of certain quantities of interest which is achieved by a suitable choice of the initial condition or the applied forcing. The quantities of interest usually measure some small-scale properties and therefore provide information about the regularity of the flow. Extreme behavior is at the heart of several open problems in fluid mechanics including the dissipation anomaly in turbulence and formation of singularities in various models of fluid flow. In this essay we describe a framework making it possible to study such extreme behavior systematically by combining mathematical analysis, scientific computation and physics. As a first step, one aims to deduce rigorous upper bounds on the growth of the quantities of interest in the solutions of a given model. These inequalities express fundamental limitations on the most extreme behavior possible among {\em all} admissible solutions. However, given how they are obtained, these bounds may be conservative and overestimate the growth actually realizable in the system. In order to probe this possibility, as the next step, we set up variational optimization problems where the growth of the quantity of interest is maximized under suitable constraints. Solution of such problems is enabled by modern methods of numerical optimization. When properties of the thus obtained maximizers match the bounds, the bounds are declared sharp and therefore cannot be fundamentally improved. Finally, properties of the solutions saturating the bounds reveal insights about the physical mechanisms realizing the extreme behavior. We survey problems where this research program has produced sharp bounds together with extreme flows saturating these bounds. A collection of open problems is then presented and we close the essay with a discussion of possible methodological improvements.

Pipe flow at intermediate Reynolds numbers, between the laminar and fully turbulent regimes, takes the form of several spatially and temporally intermittent phases in which turbulent and laminar states coexist. In the lower range, $Re\in (1750,2300)$, turbulence appears in the form of localized traveling structures called "puffs", which form long-lived chaotic dynamical states, whose stochastic decays and splits control the steady state intermittency. At the other end, $Re\in (2300,3000)$, puffs are replaced by an extended turbulent state, with laminar pockets intermittently forming and disappearing within it. Using direct numerical simulations of pipe flow at $Re = 2400, 2450, 2500, 2550$, we provide evidence that these laminar gaps form a distinct dynamical state analogous to puffs: a traveling laminar pocket in a turbulent surrounding, stabilized by a shear-dependent self-tuning mechanism. We analyse the mean spatial profile of these gaps and show that their lifetimes are exponentially distributed, suggesting that gap closing corresponds to an escape from a chaotic saddle. Finally, we suggest these laminar gaps become unstable and disappear at a finite Reynolds number, $Re\sim 2900$, which can be interpreted as the onset point of spatially and temporally homogeneous turbulence.

Forecasting turbulent flow dynamics requires a balance between predictive fidelity and computational efficiency. Diffusion-based generative models can represent complex spatiotemporal dynamics, but their application to high-dimensional turbulent flows remains computationally expensive. In contrast, proper orthogonal decomposition (POD) provides compact, physically interpretable reduced-order representations, although aggressive modal truncation can remove relevant flow structures. This work introduces a hybrid reduced-order generative forecasting framework that combines POD with Generative Learning of Effective Dynamics (G-LED). The method performs temporal prediction in a physics-based modal space and uses diffusion-based reconstruction to recover physically meaningful flow-field representations. It is assessed using experimental measurements of the turbulent wake behind a circular cylinder. Three configurations are compared: full-field G-LED, global POD-G-LED, and localized POD-G-LED. Full-field G-LED provides the highest fidelity, preserving richer vorticity fluctuations and more consistent turbulent kinetic energy distributions, but requires approximately 17 h for diffusion-model training, 7 h for Transformer training, and 3 min to predict 100 future snapshots. By transferring prediction to a reduced POD space, global POD-G-LED reduces these costs to approximately 8 h, 2 h, and 50 s, respectively, while retaining dominant wake organization and coherent energetic structures. A localized POD-G-LED formulation assigns different modal resolutions to distinct wake regions and improves vorticity statistics and energetic distributions relative to the global reduced-order configuration. These results show that coupling physics-based modal representations with diffusion-based generative reconstruction offers an effective route to efficient turbulent-flow forecasting.

The free surface atop a turbulent liquid flow is deformed by the underlying fluid motion, with the turbulence imprinting its geometry on the surface. Here we develop a theoretical framework to model such deformations based on the Euler equation with gravity and surface tension, and evaluate it against simultaneous high-resolution measurements of surface topography and subsurface velocity fields in a zero-mean-flow turbulent water tank. We consider a range of Reynolds and Froude numbers, focusing on regimes in which the surface is unbroken. Over a range of spatial and temporal scales, we find close quantitative agreement between the measured surface curvature and that which is modeled based on the velocity field a few millimeters beneath the surface, both from the statistical and the local/instantaneous standpoints. Importantly, we verify a strong correlation between the magnitudes of the surface curvature and the divergence of the near-surface horizontal velocity, which in turn is directly related to gas and heat transfer at the air-water interface. We discuss how the sub-surface motion at increasing depths decorrelates from the surface shape, and does so more rapidly at smaller spatial scales. These findings demonstrate that measurements of surface deformations may be used to sense the state of the flow beneath the surface and provide a foundation to make optically-based inferences of processes controlled by near-surface turbulence.

The mechanism of turbulence modulation in particle-laden flow over erodible beds remains an open question. Using particle-resolved direct numerical simulations, this study realises a longitudinal-to-transverse bedform transition by varying the Shields number, revealing non-monotonic modulation of near-wall turbulence. At low Shields numbers, streamwise sediment ridges generate form-induced streaks that produce a distinct secondary peak in the premultiplied energy spectra, exceeding the conventional near-wall turbulent peak and enhancing the turbulent kinetic energy. As the Shields number increases, saltation intensifies and disrupts these structures, causing the secondary peak to vanish in the streamwise direction and weaken in the spanwise direction, thereby suppressing turbulence. Proper orthogonal decomposition of the bed surface reveals a redistribution of modal contribution from a single dominant mode to higher-order modes, with longitudinal features persisting as remnants, directly linking bedform evolution to turbulence modulation.

We extend the Carter-Govan multiple-scales analysis of weakly viscous, narrowband deep-water wave packets beyond Dysthe order within the potential-flow reduction of Dias, Dyachenko, and Zakharov (DDZ). We seek to determine whether this framework generates the complex multiplier $(1 + i\beta)$ used phenomenologically to modify the nonlocal Dysthe mean-flow interaction. Although order counting places a direct viscous carrier-mean interaction at sixth order, it does not exclude an indirect fifth-order contribution arising from viscosity dependent lower-order harmonics and nonlinear interactions. We therefore derive the first correction to the induced mean flow and the complete fifth-order first-harmonic solvability condition. The resulting nonlocal terms are derivative--dependent and contain no explicit viscosity, excluding the proposed indirect mechanism within the DDZ framework. At sixth order, a restricted calculation of the nonlinear viscous block isolates a direct carrier-mean contribution with the same operator structure as the imaginary component of the prescribed mean-flow correction. Independently, a finite-adjustment-time model yields an exact, frequency dependent mean-flow response. Its low-frequency expansion produces the multiplier $ 1 + i\beta_{\mathrm{eff}}(\Omega)$, with $\beta_{\mathrm{eff}}(\Omega) =\Omega\tau.$ When $\Omega\tau = \mathcal O(\epsilon)$, the resulting phase-lag correction enters at fifth order, one order beyond the leading Dysthe mean-flow interaction.

We investigate interfacial dynamics and multiscale energy transfer in immiscible Rayleigh-Taylor turbulence using numerical simulations with varying surface tension coefficients $\sigma$. Capillarity is shown to control characteristic length scales, interfacial area, and global energy and enstrophy budgets. The flow exhibits self-similar evolution with respect to surface tension, with the maximum kinetic energy scaling as $\sigma^{1/2}$ and the flow duration as $\sigma^{-1/4}$. A scale-by-scale budget shows that surface tension removes kinetic energy at large scales while injecting it at small scales, with the crossover occurring near the Hinze scale. We further recast and verify a local kinematic relationship between surface-tension power and interface stretching, up to conservative transport, $ \boldsymbol{f}^\sigma\cdot\boldsymbol{u} = - \sigma\mathcal{S}~|\nabla c| + \mathrm{Transport}$, where $\boldsymbol{f}^{\sigma}$ is the surface-tension force, $\boldsymbol{u}$ the velocity, $c$ the heavy-fluid volume fraction, and $\mathcal{S}$ the interface stretch rate. This relation links kinetic-energy transfer to the scalar-variance cascade and shows that energy transfer to the interface is governed by local strain. Statistics of individual bubbles and droplets reveal vertically elongated filaments with diameters of about three capillary scales, yielding a linear volume-area relation. Their vertical velocities scale with the square root of equivalent diameter, consistent with drag-buoyancy balance. These findings, particularly the direct link between surface tension power and resolved interface stretching, provide a rigorous physical framework for developing subgrid-scale closures for large eddy simulation of immiscible turbulent flows.

Neural surrogates offer a promising route to accelerating computationally expensive simulations governed by partial differential equations across science and industry. Their practical deployment, however, is limited by unreliable predictions under out-of-distribution (OOD) conditions. We develop a solver-coupled surrogate-Newton framework that uses surrogate predictions as high-quality initial guesses for Newton-Krylov iterations, thereby combining rapid global flow-field prediction with high-accuracy numerical convergence at the terminal stage. On an OOD benchmark comprising geometries sampled from actual transonic airfoil optimization trajectories, the framework lowers the median residual L_2 ratio by over seven orders of magnitude while substantially reducing field and aerodynamic errors. In practical supercritical airfoil optimization, it improves online prediction reliability while achieving a 15.5-fold generation-level speedup over CFD. We further test the framework's extension to three dimensions using a flying-wing dataset. Together, these studies demonstrate the potential of surrogate-Newton coupling to deliver accurate, efficient and scalable steady CFD across industrial workflows.

Experiments on highly viscous polymeric films show that punctured holes expand exponentially in time, without sustained accumulation of liquid near the rim. This response departs from the Taylor--Culick description, in which displaced liquid accumulates in a growing rim that moves at constant speed. Although these differences were initially attributed to viscoelasticity, they were later rationalized using a purely viscous theory, leaving the role of viscoelastic stresses unresolved. We analyze the expansion of an axisymmetric hole in a freely suspended viscoelastic liquid sheet described by the Oldroyd-B model. Exploiting the separation of length scales between hole radius and film thickness, we derive extensional thin-film equations on the scale of the hole and an effective boundary condition from an asymptotic force balance in the tip region. Analytical solutions are obtained for weak viscoelasticity, $Wi\ll 1$, and the ultra-dilute limit, $\mu_p\ll\mu_s$, where $Wi$ is the Weissenberg number, while $\mu_s$ and $\mu_p$ are solvent and polymeric viscosities, respectively. For weak viscoelasticity, the dimensionless hole radius grows approximately as $e^{(0.5+\alpha Wi \beta_p)T}$, where $\alpha=(12 - 6\log 2-\pi)/21\approx 0.224$ and $\beta_p=\mu_p/(\mu_s+\mu_p)$. In the ultra-dilute limit, the radius grows approximately as $e^{(0.5+\alpha^{*}\beta_p )T}$, where $\alpha^{*}(Wi)>0$ is evaluated numerically. In both regimes, viscoelastic stresses increase the exponential growth rate relative to the Newtonian limit and induce film-thickness variations, with thickening near the retracting edge. This acceleration arises from azimuthal stretching and radial compression of the polymers, which redistribute stresses in the film and modify the stress balance at the tip, leading to a stronger outward radial extensional flow.

Fog harvesting efficiency with mesh collectors is governed by complex interactions between droplet inertia and geometry-induced flow structures. Although previous studies have primarily relied on mean-flow metrics, the present work introduces a spectral-dynamic framework to examine an important but often overlooked control on droplet capture. A two-way coupled Eulerian-Lagrangian model is used to simulate droplet-laden flow (2-40 microm) across five representative mesh geometries. The results show that capture efficiency correlates not only with the magnitude of velocity fluctuations, but also with their spectral distribution and persistence. Frequency-domain analysis indicates that mesh geometry redistributes fluctuation energy across pore and obstruction regions, thereby defining a characteristic flow timescale. By comparing this flow timescale with the droplet response time, a dynamic matching parameter, {\Pi}= droplet response time/flow time scale, is introduced. The highest capture efficiency occurs when {\Pi} is order unity, corresponding to sustained droplet-flow interaction in the near-mesh region. Geometries that generate broadband, moderately amplified spectral content (e.g., triangular mesh) increase droplet residence time and interception probability, whereas geometries with either weak or highly localized fluctuations reduce performance through insufficient forcing or premature bypass. A physics-inspired correlation for capture efficiency is proposed based on this condition. The study therefore provides mechanistic design guidance, rather than a definitive optimum, for geometry optimization in fog-harvesting meshes.

Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly. However, most existing studies remain in 2D, while 3D turbulence has fundamentally different physics and is far more costly to simulate. Existing 3D resources also typically provide only one realization per configuration, making it difficult to distinguish learning the dynamics from fitting the statistics of a single flow. In this paper, we introduce TIDE (Turbulent Incompressible DNS Ensembles), a 256^3 DNS corpus and benchmark for 3D incompressible turbulence, with 15 configurations on eight controlled axes, independent ensembles, pressure fields, and equation-level verification. The benchmark includes five tasks, standardized learned baselines, controlled generalization splits, and physical-fidelity metrics alongside pointwise error. Across the main forecasting configurations, current learned models barely outperform persistence and still make about twice the error of a spectral solver given the true equations. Moreover, lower pointwise error can coincide with severely distorted small-scale dynamics, showing that accuracy alone does not ensure physical fidelity. Generalization results further show that most regime shifts reflect limited training coverage, whereas forced-to-decay transfer exposes a missing conditioning variable: operators trained under forcing continue to predict driven evolution when the external drive is removed. Closing these accuracy, fidelity, and conditioning gaps is the central open problem made measurable by TIDE.

We study a physics-informed neural network (PINN) for the unsteady, two-dimensional incompressible Navier--Stokes equations in which the stiff divergence-free constraint is replaced by an artificial-compressibility (AC) relaxation governed by a single scalar parameter $\eps$. The relaxation reintroduces a pressure time derivative, converting a differential-algebraic constraint into an ordinary residual that a PINN can minimise directly. On the Taylor--Green vortex, which admits a closed-form unsteady solution, we quantify the effect of $\eps$: the residual divergence scales as $\eps\,|\partial_t p|$, so larger $\eps$ raises both the divergence and the velocity error, and both decrease monotonically and saturate as $\eps$ is reduced. On the $Re=100$ cylinder wake the plain forward AC-PINN collapses to the steady symmetric branch and does not reproduce von Kármán shedding; assimilating a few hundred sparse velocity sensors from a boundary-layer-resolved finite-element reference (whose Strouhal number, $0.176$, we bring close to the $0.164$--$0.172$ literature band by resolving the separating shear layer, though it remains just above it) recovers the unsteady vortex street to $7\%$ over the wake and its shedding frequency to within $3\%$ of that same reference --- a bound set by the reference's own fidelity rather than an independent validation against the true flow.

We investigate the linear stability of particle-laden pulsatile channel flow using Floquet analysis within a two-phase dusty-gas framework. Uniformly distributed spherical particles are coupled to an incompressible Newtonian fluid through Stokes drag, and the governing equations are linearized about a time-periodic base flow driven by a sinusoidally varying pressure gradient. The effects of Reynolds number, Womersley number, pulsation amplitude, particle relaxation time, and particle mass fraction on temporal instability are examined. In the steady limit, particles with very short relaxation times destabilize the flow, whereas finite relaxation times introduce interphase slip and drag-mediated damping that stabilize disturbances. Under pulsatile forcing, increasing pulsation amplitude destabilizes the flow at low Womersley numbers but stabilizes it at sufficiently high Womersley numbers. This transition is governed by the penetration depth of oscillatory motion and is systematically shifted by particle relaxation time and mass loading through interphase momentum exchange. A critical corresponding value remains small throughout, indicating strong particle-fluid coupling and ruling out resonance-like particle dynamics. These findings provide a unified physical framework for the stability of pulsatile particle-laden flows relevant to physiological and periodically forced multiphase systems.

Effects of wind direction in realistic urban canopies remain difficult to characterize systematically because local flow patterns, building-height variability, and turbulent statistics within a realistic urban canopy may respond differently to changes in the approaching wind. To investigate these multi-scale directional impacts, we conducted high-resolution large-eddy simulations of the atmospheric boundary layer over the Zona Universitaria Pedralbes district in Barcelona. The computational meshes employ fourth-order spectral elements, yielding pedestrian-level resolutions below 1 m and resulting in approximately 5.0e8 degrees of freedom. Sixteen wind directions uniformly distributed over 360deg are simulated to capture the full directional response of the urban fabric.

Data assimilation (DA) uses Bayesian inference to update the state of a numerical forecast model with observed data. In this study, we propose a fundamentally different, unified approach to atmospheric data assimilation. We use latent video flow-matching to sample temporally consistent trajectories from a prior trained using ERA5 reanalysis (69 variables over an 8-day window). We also use posterior sampling to assimilate real observation sources, such as those from the NOAA Integrated Global Radiosonde Archive and the Integrated Surface Database. Because the prior generates a continuous trajectory, it naturally propagates information between observed and unobserved frames. Therefore, we can perform various DA tasks, such as filtering and smoothing, simply by changing the observed frames. Moreover, we generate full-state ensemble forecasts directly from sparse observations, achieving performance competitive with state-of-the-art observation-to-forecast models.

Transport in fluids is generally reduced to continuum laws parametrized by bulk coefficients and effective interfacial parameters, such as viscosities, diffusivities, slip lengths, and interfacial resistances. This description becomes incomplete at the nanoscale, where spatial heterogeneity, molecular structure, and finite relaxation times are inseparable from the transport process. Here we formulate coupled transport in nanoconfined fluids as a space--time-resolved Onsager response matrix and extract it from equilibrium molecular dynamics simulations. Applied to a confined charged fluid, the framework resolves the nonlocal and transient pathways coupling particle, solute, heat, and charge transport. Momentum transport appears as a long-lived, nonlocal hydrodynamic mode, whereas charge transport relaxes rapidly through localized ionic friction. Off-diagonal responses reveal distinct projected dynamics, providing a microscopic basis for nonlocal, history-dependent transport laws.

Long-term instabilities in astrophysical fluids are inherently nonlinear, where even small-amplitude perturbations can trigger dramatic instability. However, owing to the complex interactions among non-normal modes, the perturbation structures responsible for the greatest growth remain poorly understood. In this paper, we employ the nonlinear optimization method known as the conditional nonlinear optimal perturbation (CNOP) to identify the most dangerous initial velocity perturbation, i.e., the perturbation that maximizes the kinetic energy growth in the two-dimensional compressible Rayleigh-Taylor instability in astrophysical hydrodynamics. Compared with random perturbations, the optimal perturbation forms a coherent wave-packet structure localized around the density interface. We investigate its dependence on spatial resolution and optimization time horizon through two sets of numerical experiments. For a fixed optimization time, increasing the spatial resolution produces a more sharply localized wave packet, whereas for a fixed spatial resolution, increasing the optimization time causes the wave packet to become progressively more dispersed. Furthermore, we analyze the optimal perturbations in Fourier space using the fast Fourier transform (FFT), which provides a clearer characterization of the spectral distribution. Higher-resolution simulations concentrate most of the perturbation energy into only a few dominant modes, while longer optimization times distribute the energy over a broader range of modes. These results indicate that short optimization time horizons involve relatively weak modal interactions and remain closer to the linear regime, whereas longer optimization times enhance nonlinear modal interactions, broaden the spectral distribution, and reduce the predictive capability of linear stability theory.

Although controlling chaos can be regarded as a form of chaos synchronization, conventional chaos synchronization does not provide a practical framework for controlling high-dimensional open chaotic systems, such as weather. In high-dimensional open environmental systems, it is simply impossible to make the difference between drive and response systems asymptotically approach zero over the entire domain. Instead of conventional global chaos synchronization, here I define regional chaos synchronization, in which state variables within only a small target region are synchronized with a target trajectory using actuators located in the target region. Theoretical considerations and numerical experiments show that the performance of regional chaos synchronization is substantially degraded by the injection of errors from exterior regions that the controller is not intended to modify. Even under the same actuator specifications, the performances of regional chaos synchronization differ among trajectories, which is not the case of conventional global chaos synchronization. An appropriate target trajectory differs substantially from the natural trajectory only in the target region. This choice of target trajectories can minimize the injection of errors from exterior regions and thereby enable successful regional chaos synchronization. The implications of this new framework for realistic control problems such as weather control are discussed.

Analytical expressions for the phase variance in a nonlinear fiber optic system based on phase-shift keying are developed. The Gauss-Hermite functions are used as the orthogonal basis to represent the noise field. Number of degrees of freedom (DOF) to accurately model the phase variance is estimated. The amplifier noise excites higher order Gauss-Hermite noise modes and the nonlinear mixing of a signal pulse and higher order Gauss-Hermite noise mode leads to new noise fields which enhance the nonlinear phase noise. The higher order noise modes propagate linearly and enhance the linear phase noise if the matched filter is not used at the receiver. Analytical expression for the optimum launch power is developed taking into account the linear and nonlinear phase noise.

We propose a phase field model of a macrocracked single crystal in which the crack and the geometrically necessary dislocations descend from a single energy functional. Energy minimization alone then decides dislocation nucleation, through an integral criterion evaluated in closed form along slip chords. The criterion yields a size effect inaccessible to point-wise strength conditions: a grain-size-dependent yield stress. With slip suppressed the model reproduces Griffith fracture; with fracture suppressed, the nucleation load measured by the full non-smooth solver agrees with the closed-form nucleation criterion to four percent. The coupled computations produce a two-stage response: at loads an order of magnitude below cleavage, dislocation bands emitted from the notch tip blunt and shield it, raising the initiation load; once the crack grows, the bands heal; a compact cluster of like-signed dislocations travels with the tip, its canceling partner walls pinned at the grain boundary, and the dissipated fracture resistance equals the elastic one. In the purely energetic, dissipationless limit, emission shields the crack but does not toughen it; toughening requires dissipation, incorporated in the sequel through the threshold resistance to dislocation motion.

The centre-mode elastic instability, prevalent in rectilinear flows of dilute polymer solutions, allows dynamic states to emerge even in the absence of inertia. Here, we show that this instability can be significantly enhanced when the base flow has a nonuniform spatial-distribution of polymers. Specifically, we consider a polymer-laden stream sandwiched between streams of pure solvent. In such a flow, the polymeric stress not only depends on the conformation tensor (determined here by the Oldroyd-B equation) but also varies proportionally with the polymer concentration field, which satisfies a scalar transport equation. We consider the Stokes limit and first focus on the simple setting of periodic Kolmogorov flow. A linear stability analysis shows that the centre-mode instability is strongly promoted when the base flow has polymers localized near the maximum of the base-velocity profile; concentrating polymers near the maximum shear suppresses the instability. As the polymer loading is increased, the neutral stability curve of the nonuniform system develops a double-lobe form, which results in a sudden decrease in the critical Weissenberg number (product of the elastic relaxation time and the typical strain-rate). An energy analysis attributes this destabilization to elastic feedback forces arising from gradients in the polymer concentration. We end by demonstrating the relevance of these findings to channel flow, where localizing polymers about the centreline is shown to strongly promote the centre-mode instability.

Local detailed balance restricts transport by self-propulsion in static activity landscapes. We show that a delayed speed adaptation (``delayed motility/kinesis'') generically breaks this symme try, inducing directed transport in asymmetric periodic motility profiles and enhancing diffusion in symmetric ones. Both effects occur for run-and-tumble, active Brownian, and inertial active particles, without requiring potential interactions, walls, imposed gradients, higher dimensions, or translational diffusion. Their magnitudes, and even current reversals, are conveniently tuned via the delay time, which establishes delayed motility as a versatile generic and experimentally accessible mechanism for autonomous self-steering and transport control in motile-active-matter circuity.

The motility of microswimmers in confined environments is a fundamental problem in active matter physics, with direct implications for microfluidic applications and the understanding of microorganism behavior in complex natural habitats. Although the run-and-tumble dynamics of flagellated microalgae such as Chlamydomonas Reinhardtii (CR) are well characterized in bulk suspension, the extent to which elementary geometric confinements alter their swimming remains insufficiently understood, particularly regarding the relative contributions of steric contact versus hydrodynamic interactions. Here, we experimentally investigate the trajectories of individual CR cells in a diversity of PDMS microfluidic geometries of growing complexity using single-particle tracking and statistical analysis. We show that cells in straight channels accumulate near walls and align along the channel axis, a behavior qualitatively reproduced by steric Active Brownian Particle simulations, yet showing a confinement-dependent velocity enhancement consistent with hydrodynamic wall coupling. In circular cavities with diameter below the persistence length L_0 ~350 microns, cells transition from bulk active Brownian exploration to quasi-circular wall-following trajectories. In dumbbell geometries, inter-compartment dwell length reflect purely geometric predictions, evidencing no measurable hydrodynamic contributions even for strong confinements. Together, these results demonstrate that environmental geometry can selectively amplify or suppress motility modes in active biological suspensions, opening avenues for the passive control of microswimmer transport in engineered microfluidic networks.

Developing synthetic materials that exhibit life-like behavior, such as internally driven cycles, remains a central challenge in active matter. Here, we introduce a minimal colloidal model of chemical signaling in which particles produce diffusing signaling molecules that selectively promote or inhibit attractive interactions among neighboring particles. This bio-inspired, paracrine-like signaling mechanism generates context- and history-dependent many-body interactions that break time-reversal symmetry and drive the system far from equilibrium, leading to the spontaneous emergence of autonomous, internally sustained limit cycles in the composition of particle clusters. Using computer simulations, we map the resulting nonequilibrium phase behavior and identify distinct dynamical regimes controlled by the rates of signal production and degradation, together with the diffusion range of the signaling molecules. Among these, we find a robust oscillatory state in which particle clusters autonomously assemble in a cyclic fashion, driven entirely by internal feedback loops. Our results establish paracrine-signaling colloids as a minimal, physically realizable platform for programmable nonequilibrium materials with life-like functionality and provide a general route toward synthetic active matter with self-regulated collective dynamics.

Helices are among the most common ordered structures in biological and synthetic polymers, but their formation involves more than local conformational preference. A finite helix must nucleate, grow, resist breaking, and maintain a selected handedness against thermal fluctuations. We develop a three-state Ising-like transfer-matrix theory in which each segment is coil-like, right-handed helical, or left-handed helical. This formulation separates ordinary helix--coil cooperativity from the persistence of handedness. The right--left symmetric problem decomposes into symmetric and antisymmetric sectors, giving two characteristic lengths: the helical correlation length $\xi_H$ and the chiral persistence length $\xi_\chi$. In the strongly helical rare-wall limit, $\xi_\chi\simeq (1/2)\exp[\beta(K+J)]$. A local chiral bias, motivated by the Ramachandran landscape, is then amplified over finite helical domains.

Motility-induced phase separation occurs in assemblies of self-propelled units when activity is coupled negatively to density. In contrast, the consequences of a positive coupling between density and activity on the collective behaviour of active matter remain unexplored. Here, we show that collective activity can emerge from such a positive coupling among non-motile building blocks. We perform experiments with self-sustained oscillators powered by contact-charge electrophoresis. Although the oscillators are non-motile by design, they spontaneously form an active gas when confined together. The super-elastic nature of collisions constitutes a positive density-activity coupling and underlies the active gas properties. Elucidating the origin of binary collisions allows us to precisely control the structure of the active gas and its eventual crystallization. Beyond considering the overlooked positive coupling between density and activity, our work suggests that rich collective properties can emerge not only from the symmetry of interactions between active building blocks, but also from their adaptable and responsive behaviour.

Cell adhesion to viscoelastic substrates is mediated by focal adhesions (FAs), which dynamically couple actomyosin contractility to the extracellular matrix. Although substrate stress relaxation is known to regulate adhesion stability and cell migration, a predictive physical framework linking viscoelasticity to force transmission and adhesion dynamics remains lacking. Here we review briefly what is known about the active wetting and de-wetting of FAs on viscoelastic substrates and synthesize existing experimental and theoretical work into a two-timescale physical framework to describe the phenomena reported. At short timescales, oscillatory actomyosin-driven displacements are transmitted through molecular clutches, leading to frequency-dependent energy transfer to the substrate. We show that this transfer is maximized at an optimal frequency set by a balance between elastic energy storage and viscous dissipation, establishing a resonance-like mechanism that selects both the effective FA stiffness and traction force amplitude. At longer timescales, this mechanically optimal state couples to adhesion remodelling through an effective surface tension, enabling FA growth and disassembly to be interpreted as active wetting and de-wetting processes. The model predicts that adhesion stability and steady-state size are controlled by substrate stiffness and viscoelastic timescales, as well as mechanosensitive feedback mediated by Piezo1-dependent calcium signalling.

We develop a continuum theory for proliferating active matter starting from a microscopic stochastic model of self-propelled particles undergoing birth, death, and nonlocal competition. Beginning from the master equation, we derive mean-field evolution equations for the particle density and polarization fields and close the resulting hierarchy through a von Mises ansatz, providing a coupled hydrodynamic description applicable to a broad class of proliferating active systems. As an application, we study the recently introduced Active Brownian Bug model, in which the form of flocking emerges despite the absence of explicit alignment interactions. Linear stability analysis predicts both Turing and Hopf instabilities, whose analytical thresholds agree with numerical simulations. The continuum model reproduces the principal dynamical regimes of the underlying particle system, including homogeneous states, stationary periodic clusters, and coherently propagating flocking states. These results establish a general continuum framework for proliferating active matter and provide a physical interpretation of collective motion driven by the interplay between activity and population dynamics.

The synchronization and phase-locking behavior of oscillators with smooth dynamics is well captured by continuous phase-models à la Kuramoto. However, these models do not apply seamlessly for hybrid oscillators, where discrete events occur along their otherwise smooth dynamics. Consequently, the synchronization and phase-locking mechanisms of hybrid oscillators remain overlooked. Here, we combine experiments, theory, and simulations, to investigate and rationalize the coherent motion of pairs of hybrid oscillator. Using contact-charge electrophoretic (CCEP) oscillators as an experimental realization, we show that in-phase oscillations can occur, despite oscillators repelling each other. We rationalize this behavior by introducing a discrete-time framework that explicitly accounts for discrete events and elucidates the origin of phase-locking. Our model highlights the roles played by inertia and the decay of interaction strength along the oscillation cycle in promoting phase-locking of CCEP oscillators. More generally, it provides a phase-locking criterion that holds for a broader class of coupled hybrid oscillators, and reveals that various mechanisms can lead to their coherence.

A finite density of mutually avoiding directed polymers in a quenched random medium is a minimal model of glassy line matter. The dilute theory, solved by replica Bethe ansatz, predicts an interaction free energy proportional to $\rho^2$ and disorder cumulants with distinct power-law dependences on the density $\rho$, but direct numerical tests have been hindered by the combinatorially large many-polymer transfer matrix. We recast the problem as filling logarithmic eigenvalues of a single-polymer transfer-matrix product, obtaining the quenched free energy, its cumulants, and a disorder-induced linear spectral edge consistent with the replica prediction.

We develop a thermodynamic theory of electric double layers in binary liquid mixtures by allowing the Stern-layer capacitance to depend on the local solvent composition. This coupling produces an additional negative contribution to the inverse differential capacitance. As a result, the surface potential can become a nonmonotonic function of the surface charge density, leading to negative differential capacitance and a voltage-induced first-order transition between two electric-double-layer states. We determine the coexistence condition using a common-tangent construction for the surface-charge-controlled grand potential and obtain phase diagrams in terms of the Stern-capacitance contrast, surface charge density, bulk composition, and surface potential. We also compare the theory with capacitance data for tetrabutylammonium chloride in water/1-propanol mixtures, finding semi-quantitative agreement in the continuous-response regime. These results suggest that solvent exchange inside the Stern layer can strongly control the capacitance and interfacial phase behavior of binary mixtures.

Exotic nanoparticle superstructures can be accessed by harnessing nanoparticle softness and charge regulation, features often viewed as obstacles to structural control. Here, we show that regulated charge mismatch in polymer-grafted nanoparticles enables the assembly of high-stoichiometry cubic superlattices. By co-tuning grafting density, particle size, and bulk composition, we realize ionic-lattice analogues such as CaF2 and Th3P4, as well as single-component A3 and A7 superlattices without atomic counterparts. The A3 lattice has recently been identified theoretically as a photonic band-gap lattice. These phases emerge from a 1:1 "parent" lattice when local charge neutrality cannot be satisfied, driving either progressive interstitial filling or reorganization into a larger basis. For instance, the systematic occupation of ZnS tetrahedral sites yields CaF2, while ligand-swapping symmetry breaking converts CsCl into Th3P4. Upon heating, the assemblies exhibit reversible lattice contraction and pronounced negative thermal expansion. Furthermore, the energetic penalty for defects increases with nanoparticle size, facilitating the scalable production of high-quality, open superlattices for photonic applications.

An alternative explanation is presented for recent reports that attribute sustained chemiluminescence (CL) and electrochemiluminescence (ECL) from electrogenerated microbubbles on steel or copper electrodes in aqueous luminol solutions (over 2-30 V range) to the spontaneous formation of hydroxyl radicals at the gas-water interface. Our experiments with a broad set of electrodes, viz., steel, copper, aluminium, and platinum, reveal that while microbubbles can be electrogenerated on all electrodes, CL is exhibited by steel and Cu only and not by Al and Pt. These observations establish that the gas-water interface of microbubbles is not the site for hydroxyl radical generation (else CL would be recorded in all cases). Complementary quantification of H2O2 in these experiments reveals its electrode dependence as follows: Al > Cu > Steel > Pt. This establishes that depending on the electrode, H2O2 forms first, and in some cases, hydroxyl radicals are observed (i.e., where CL/ECL is seen). Experiments with NMR and EPR spectroscopy revealed that: (i) H2O2 formation occurs only when O2 is present in water; and (ii) while steel and copper generate hydroxyl radicals through 1-electron reduction of H2O2, Al does not promote one-electron reduction of H2O2 to generate hydroxyl radicals, and Pt preferentially promotes disproportionation of H2O2 to H2O and O2. In fact, we demonstrate that H2O2 and hydroxyl radicals can be observed at specific metal-water interfaces even without microbubbles, confirming that the solid surface is the reactive site. Therefore, this work affords electrode-based predictions of whether or not electrogenerated microbubbles would yield CL in luminol solutions and calls into question the notion of spontaneous formation of hydroxyl radicals at gas-water interfaces.

Predicting the transition of wind-forced, gravito-capillary surface waves from smooth to corrugated states remains a longstanding problem in nonlinear wave mechanics. Solving driven-dissipative, nonlinear potential flow equations we map these waves ($4-13$ cm) onto a Reynolds number -- wave energy phase-space. We identify a transition band separating smooth from corrugated wave states - the wave steepness exhibits a non-monotonic dependence on Reynolds number within this. Subharmonic (in)stability analysis reveals that the fastest-growing mode intensifies corrugations on alternate faces of the carrier wave, offering insights with broad implications for interfacial pattern-formation and oceanic remote-sensing.

Stochastic Differential Equations (SDEs) have become a cornerstone of scientific machine learning, though they are predominantly utilized as algorithmic tools for uncertainty quantification or distribution matching. In contrast, leveraging SDEs fundamentally to model macroscopic, nonlinear physics as stochastic processes remains largely unexplored. This work introduces a probabilistic, non-intrusive reduced-order model (ROM) for chaotic dynamical systems. We argue that projecting high-dimensional nonlinear dynamics onto a low-dimensional manifold introduces irreducible uncertainty, compounded by the chaotic attractors and multi-admissible futures inherent to turbulent flows. Consequently, a chaotic system governed by a partial differential equation can be effectively modeled by an SDE in a suitable latent space. To this end, a nonlinear autoencoder is employed to map the flow field into a low-dimensional representation, within which the temporal evolution is explicitly governed by an SDE. The predictable component of the dynamics is captured by a learned drift term, while state-dependent stochasticity is absorbed by a diffusion term. We demonstrate that this probabilistic framework successfully propagates highly nonlinear states, offering a robust alternative to traditional deterministic methodologies for chaotic regimes. Ultimately, our model generates new chaotic flow trajectories that remain locally and globally consistent with the true transition kernel learned from Direct Numerical Simulation (DNS) data. Even though these generated trajectories are unique and distinct from the training set, they preserve the underlying statistics and manifolds, validating the strong generative performance and robustness of our methodology.

This study presents a systematic manufacturing approach that combines metal additive manufacturing and subtractive machining to construct flexible wing models for transonic wind tunnel testing. Two wing designs were fabricated and evaluated in terms of geometric accuracy, structural characteristics, and aeroelastic behavior. Three-dimensional scanning, static load tests, ground vibration tests, finite element analyses, and transonic wind tunnel tests were conducted. The fabricated models reproduced the designed geometries and structural properties with good accuracy. The average surface roughness was below 1.0 micrometer, and the average surface deviation was below 0.3 mm, improving geometric precision over previous skill-dependent polishing methods. Independently manufactured models also exhibited highly consistent flutter behavior, with measured flutter frequencies of 157.0 and 158.0 Hz. The results demonstrate that the combined additive and subtractive manufacturing approach enables efficient and reproducible production of flexible wing models for reliable aeroelastic wind tunnel experiments.

This study investigates the droplet size distribution (DSD) and atomization characteristics of a liquid jet injected into a crossflow (LJICF) under varied momentum flux ratios, Weber numbers, and flow conditions. Numerical simulations are performed using the validated compressible Volume of Fluid-Lagrangian Particle Tracking (VOF-LPT) coupled framework to capture both the primary and secondary atomization processes. Key parameters, including momentum flux ratio, Weber number, crossflow pressure, and velocity, were analyzed to assess their impact on droplet size characteristics, including Sauter mean diameter (SMD) and standard deviation (STD) in the downstream region. The discrete size distribution of droplets comprising probability density and cumulative distribution reveals a shift toward finer, more uniform droplets under enhanced breakup conditions. The findings emphasize the critical role of aerodynamic forces and instabilities in driving efficient atomization, with higher momentum flux ratios and Weber numbers leading to finer and more uniform droplets. Increased crossflow pressure promotes finer droplet formation but is found to reduce droplet density in the downstream domain due to a confined spray plume, delayed particle conversion, and reduced droplet residence time. The log-normal and Rosin-Rammler distributions effectively capture droplet size trends, with the former closely representing the skewness and tail behavior and the latter accurately representing intermediate and larger droplets. However, both have limitations in replicating sharp peaks and the smallest droplet sizes, respectively.

This study employs swirling hot coflow to ensure improved fuel-air mixture and stable flame, which are essential for designing low-emission, swirl-stabilized combustors. The present study introduces a swirling confined hot coflow around an air-diluted methanol spray. We have used the Eulerian-Lagrangian approach for multiphase simulation, resolving the dispersed liquid phase via the Lagrangian framework while addressing the continuous gas phase through the Eulerian framework. The Modified Flamelet Generated Manifold (FGM) model facilitates accurate and computationally efficient simulation of gas-phase reactions. The swirl numbers (SN), which are 0.2, 0.6, 1.0, 1.4, 2.0, and 3.0, are employed in this study to evaluate their impact on flame stability and auto-ignition. A higher lift-off height is observed as the swirl number rises from lower to moderate (SN = 0.2, 0.6, and 1.0). It decreases after the lift-off height reaches the critical swirl number (SN=1.0). These large swirl numbers also cause the time-averaged flame structure to change from a sharp columnar flame to an evenly spread combustion region. It also produces a more compact and widely dispersed flame for higher swirl numbers. Particle statistics, Flame Index, proper orthogonal decomposition (POD), and the mean gas-phase flow field distribution are used to study these impacts on flame dynamics in detail.

We study the motion of inertial particles in two-dimensional inviscid and viscous vortex crystals, where vortices are placed at the tips of a regular polygon, and determine the conditions under which long-term trapping of particles can occur. In crystals with a central vortex, we find that trapping points in addition to those found in a previous analysis may exist finding, furthermore, that particle trajectories may approach a limit-cycle which can be described by means of asymptotic methods. We show that these newly discovered fixed points persist temporarily in the presence of viscosity, and study the different transitions following viscous vortex mergers. We find that for moderate Reynolds numbers, the annular merger of the vortex crystal form an annular vortex layer that can keep particles trapped within a disk centered at the origin. For larger Reynolds numbers, pairwise vortex merger leads to crystals with a smaller number of vortices, with particles clustering at the fixed points of the newly formed vortex crystal.

This work introduces a robust deterministic framework for approximating solutions of the Boltzmann equation with binary collisions by discretizing their dependence on time, position, and velocity using Galerkin methods. By employing a family of parametric Galerkin closures based on $\varphi$-divergences in velocity space, we derive rigorous hierarchies of moment equations that govern fluid dynamic variables. Addressing the limitation that these closures alone do not guarantee dissipation of a $\varphi$-divergence entropy for the true binary collision operator, we restore this property by formulating a compatible approximate collision operator tailored to each closure. This constructed operator intrinsically retains fundamental physical properties essential for high-fidelity flow simulations, including Galilean invariance, exact conservation of mass, momentum, and energy, and strict dissipation of a $\varphi$-divergence entropy. Furthermore, we show that the resulting closed moment systems are symmetric-dissipative, yielding Cauchy problems that are well-posed locally in time. To translate this mathematical foundation into an efficient computational tool, we discretize the position and time variables with an entropy-stable discontinuous Galerkin (DG) finite element method. The fully implicit, entropy-stable space-time approach enables time steps far beyond typical CFL-limited step sizes and the direct computation of steady states. The robustness and accuracy of the methodology are verified and validated through numerical simulations on the supersonic nozzle flow of argon, mass flow through a channel, and heat transfer between parallel walls, demonstrating agreement with analytical benchmarks, experimental measurements, and stochastic particle simulations.

High-dimensional sensitivity analysis and uncertainty quantification for multiscale gas dynamics, spanning the continuum to rarefied regimes, require computationally efficient and mathematically consistent gradient evaluation. This paper develops a discrete adjoint method for the unified gas-kinetic scheme (UGKS) based on a dual-consistent formulation. The adjoint system is derived directly from the discrete microscopic velocity-distribution equation coupled with the macroscopic-moment compatibility conditions. To resolve the stiff cross-scale coupling, we propose an asymptotic-preserving (AP) adjoint formulation constructed via macroscopic-moment projection and microscopic lifting. Under this framework, the AP adjoint formulation eliminates the stiff collision coupling and removes the collision-time step restriction in the continuum regime. Numerically, a memory-efficient residual-evaluation algorithm that mirrors the forward UGKS cell-vertex data structure is implemented to bypass the memory bottleneck in velocity space. Furthermore, a macroscopic--microscopic predictor--corrector implicit marching scheme is designed to accelerate convergence without solving a globally coupled system. The accuracy, consistency, and robustness of the proposed AP-adjoint scheme are rigorously verified against an independent linearized UGKS solver across a wide range of Knudsen numbers, including lid-driven cavity heat conduction, microchannel thermal creep flow, and hypersonic flow past a circular cylinder.

Intermittency represents a fundamental route to chaos in nonlinear dynamical systems. In this work we introduce an adaptive control strategy in which the control parameter of an intermittent system is promoted to a dynamical variable that evolves autonomously under an auxiliary nonlinear map drawn from the same functional hierarchy as the system itself. The construction eliminates the need for orbit identification, local linearization, and trajectory-triggered perturbations, which are central ingredients of conventional feedback schemes. The theoretical framework is developed within a class of one-dimensional nonlinear ergodic maps with exactly known invariant (Sinai--Ruelle--Bowen) measures, for which we derive in closed form (i) the dynamics and invariant measure of the evolving control parameter, (ii) the invariant measure of the coupled system, and (iii) the $q$-generalized Lyapunov exponents before and after control. The generalized Lyapunov spectrum serves as an analytical order parameter for the control process: the collapse of its positive regions provides a quantitative and initial-condition-independent signature of chaos suppression, and yields the sensitivity to initial conditions in explicit form. To establish the physical relevance of the approach beyond low-dimensional maps, we apply the same construction to a cluster of three interacting ultrasound-driven microbubbles described by the Keller--Herring model, promoting the experimentally accessible acoustic driving frequency to a dynamical variable. Systematic bifurcation and Lyapunov analyses, performed over wide ranges of driving pressure, frequency, and equilibrium radii, demonstrate that intermittent chaotic radial oscillations are progressively suppressed and replaced by stable periodic motion.

Physical reservoir computing (PRC) leverages the intrinsic dynamics of physical systems to perform information processing while requiring training only in a linear readout layer. Here, we introduce a geometry-programmable metabeam inspired by the hierarchical overlapping architecture of biological scales as a physical reservoir. Contact-mediated interactions between embedded scales induce tunable nonlinear dynamics, enabling controlled transitions between periodic, multi-periodic, and chaotic responses under external excitation. The computational capability of the metabeam reservoir is evaluated using static nonlinear function approximation, Lorenz-63 prediction, and the NARMA-2, NARMA-5, and NARMA-10 benchmarks. Input signals are encoded through the excitation amplitude, whereas computation is realized through the vibrational amplitude of the metabeam followed by a trained linear readout. Across all benchmark tasks, the proposed metabeam consistently outperforms an equivalent linear beam reservoir, yielding lower normalized root-mean-square errors (NRMSEs) and improved computational performance. Different dynamical regimes of the metabeam exhibit distinct computational advantages, with the periodic regime providing the highest prediction accuracy for memory-intensive tasks and the multi-periodic regime achieving the best performance in static nonlinear function approximation. These findings demonstrate that simple interacting surface textures can simultaneously enrich reservoir dynamics and information processing capability, establishing scale-covered metabeams as tunable and mechanically programmable platforms for embodied physical intelligence and PRC.

We investigate the nonlinear dynamics of a thermo-electro-mechanically coupled memristive resonator comprising a doubly clamped Euler--Bernoulli microbeam, an RLC circuit, and a TiO$_2$ memristor with temperature-dependent ionic mobility governed by Mott and Efros--Shklovskii hopping conduction. The dynamics are analyzed using two-dimensional parameter-space maps, bifurcation diagrams, Lyapunov exponents, reconstructed attractors, Poincaré sections, Grassberger--Procaccia correlation-dimension analysis, empirical mode decomposition, the Hilbert--Huang spectrum, and electro-memristive hysteresis. Parameter-space maps reveal predominantly quasi-periodic and deterministic chaotic regimes without stable phase-locked periodic states. Bifurcation analyses show that the beam length and excitation frequency govern the dynamics through the frequency ratio $r_\omega=\omega_0/\omega_b$, whereas the excitation current mainly controls the oscillation amplitude and chaotic intensity. Under fixed operating conditions, the asymptotic regime depends on the initial conditions, and complementary diagnostics identify the thermo-memristive subsystem as the primary source of the nonlinear complexity, subsequently transmitted to the microbeam through electromechanical coupling. Temperature continuously reorganizes the electro-memristive hysteresis through the chain $T \to \sigma(T) \to M(w,T) \to i_m(t) \to w(t)$. The hysteresis area evolves non-monotonically with temperature, revealing a configuration-dependent optimal thermo-memristive operating point. These findings highlight temperature, beam length, and electrical excitation as complementary control parameters for tailoring thermo-memristive memory, deterministic chaos, and nonlinear dynamics in thermo-active MEMS, with potential applications in neuromorphic sensing and chaos-based secure communication.

This paper presents purely convex programs for passively safe impulsive rendezvous and proximity operations in cislunar orbits. Approach, arrival, and abort maneuvers are all designed and validated in the context of maneuver execution error and navigation uncertainty, and formulated for efficient onboard execution in the autonomous scenario. The outlined methods form the baseline onboard guidance routines for NASA's CAPSTONE 02 mission planned to demonstrate autonomous rendezvous and proximity operations capabilities in the southern 9:2 synodic near rectilinear halo orbit. High fidelity closed loop Monte Carlo simulations using the planned relative navigation sensor suite and measurement cadence verify the intended maneuver design performance.

We present the first demonstration of transition to spatiotemporal chaos with multiple colliding pulse sequences in systems described by perturbed cubic nonlinear Schrödinger (NLS) equations. For this purpose, we consider propagation of multiple sequences of optical pulses in two distinct types of nonlinear waveguide arrays with cubic gain and loss. By employing a perturbation theory for NLS solitons, we show that the dynamics of pulse energies in the waveguide array systems is described by generalized Lotka-Volterra (LV) models, which exhibit dissipative chaos in a wide region in parameter space. We test the LV models' predictions for chaotic dynamics of pulse energies by extensive numerical simulations with perturbed systems of coupled-NLS equations. We find excellent agreement between the results of the LV and coupled-NLS models for energy dynamics in both types of waveguide array systems, despite the strong pulse pattern distortions and the strongly nonlinear nature of the dynamics.

Universal hallmarks of quantum chaos---such as the ramp and plateau in the spectral form factor---and the ramp's gravitational duals involving wormholes are widely interpreted as consequences of spectral or ensemble averaging. In this paper, following an earlier proposal of~\cite{Liu25c}, we develop an alternative approach: these phenomena arise as macroscopic smooth structures hidden within erratic microscopic data, which can be isolated through a smooth filter projection. Using the semiclassical Gutzwiller trace formula as a paradigmatic example, we illustrate how many features characteristic of random matrix models---including the ramp, the plateau, the spectral curve, and single-eigenvalue instantons---can be derived in the semiclassical limit without invoking ensemble or explicit spectral averages. We postulate the existence of a minimal Gutzwiller-like structure in the large-$N$ limit of holographic systems and explore its consequences. Beyond deriving the ramp and the plateau, this Gutzwiller-like structure predicts universal rapid macroscopic oscillations in the density of states and the possible existence of hyper-instantons, both of which involve double exponentials in $1/N^2$. On the gravity side, we demonstrate how spacetime wormholes enable the construction of emergent hyper-non-perturbative objects---such as baby-universe and wormhole condensates---which yield double exponential effects in $G_N$. This mirrors the postulated boundary Gutzwiller-like structure and provides a dual gravitational derivation of the universal rapid macroscopic oscillations in the density of states and the spectral plateau.

Kepler's first two laws state that a planet moves on an ellipse with the Sun at a focus and sweeps out equal areas in equal times (constant areal speed). In the Principia, Newton showed how these laws connect to universal gravitation. Since then, the equivalence between orbital laws and force laws has remained a central topic in celestial mechanics. We present fully geometric proofs, built from explicit Euclidean straightedge-and-compass constructions, of this equivalence in both directions. The proof system combines finite-step constructions, tangent and triangle geometry, affine transport, local displacement ratios, conic invariants, and several hodograph realizations. Within this broader framework, one contribution is to use the auxiliary circle as the primary hodograph proxy in configuration space rather than the directrix-circle normalization of radius 2a. Our emphasis is a Principia-style argument that avoids differential equations while remaining close to Euclidean methods.

By investigating the origin of the evolutionary discrepancy between the H-function and entropy, we elucidate that the H-function fails to serve as a valid arrow-of-time criterion in the rigorously derived Boltzmann equation for the hard-sphere gas model under the Boltzmann-Grad limit.

Multi-phonon resonance conditions underpin kinetic theories of phonon transport and lattice thermalization. We show that exact resonance matching, nonzero interaction coefficients, and network connectivity do not guarantee persistent energy diffusion. Symmetry-enforced balance relations drive exact-resonant collision currents to nonthermal zero-flux states, producing kinetic arrest from individual resonant sets to connected networks. Complete energy spreading is sustained by quasi-resonances. The thermodynamic and weak-nonlinearity limits do not commute: the leading kinetic behavior is recovered in the former, whereas at fixed finite size the thermalization time diverges through higher-order crossovers as the nonlinearity vanishes. Exact-resonance existence and connectivity are therefore kinematic, not sufficient dynamical, criteria for phonon energy diffusion.

This book has one primary goal: To get you moving quickly from learning basic principles of colloid science, to designing colloidal systems for function or motion in the lab. It is not intended to provide encyclopedic knowledge about all aspects of colloid and surface science; rather, I have chosen not to include many topics of genuine importance. In reaching the intended goal, I use two parallel strategies. First, I give practical results that can be used immediately. If there is a cumbersome calculation, I have worked to reframe it into a table or figure. This is the case for Hamaker constants and hydrodynamics of spheroids, for instance. Second, I describe the physics of various colloidal phenomena, so that you as a researcher can think about alternative strategies. In balancing algorithms with explanations, I provide plug-and-chug example problems to familiarize you with units, constants, and typical values. The practice problems provide extensions to the most basic theory that open new possibilities, while also giving results that are useful in practical and research studies. Throughout the book, I provide data we commonly use for viscosities, zeta potentials, ionic phenomena, and other parameters. Rather than providing every reference and every technique, I have provided those references and techniques that we most often use in our lab. In the end, this book aims not to be an exhaustive study of colloids, but rather to be a doorway to producing desired colloidal systems as quickly as possible.

Understanding how the mechanical properties of liquids confined within nanometer-scale gaps differ from bulk behavior is central to biophysics, lubrication, catalysis, electrochemistry, and surface science. Yet the characterization of ultrathin confined liquids remains challenging, as many existing approaches rely on destructive or intrusive contact-based techniques, mostly measuring the liquid flow in the low frequency regime. Here, we present a non-invasive, all-optical technique based on ultrafast laser ultrasonics that probes confined liquids at equilibrium in the gigahertz frequency range. The method measures the phase and amplitude of time-domain Brillouin scattering signals transmitted through liquid layers whose thickness is varied step by step with subnanometer effective sampling. Supported by numerical modeling of acoustic propagation and optical detection, these signals allow us to extract the thickness-dependent acoustic velocity and attenuation of confined liquids. We show that nanometric confinement modifies the GHz acoustic response of glycerol, the liquid crystal 8CB, and a butyl-based ionic liquid over unexpectedly long spatial scales. These effects extend from a few nanometers to several tens of nanometers and reveal bound interfacial layers, acoustic stiffening, and enhanced solid-like behavior under confinement. Our results open a route to probing liquid confinement in a scarcely explored regime: dynamically measured at gigahertz frequencies, yet sufficiently weakly perturbative to preserve the equilibrium confined state.

Ferroelectric nematic liquids exhibit complex ferroelectric domains shaped by competing elastic and electrostatic interactions. Using fluorescence and polarizing optical microscopy, we investigate domain formation and evolution under different anchoring conditions. Charged fluorescent ions map the electrostatic potential, revealing that electric fields are localized near domain walls and material surfaces. Upon cooling, domain walls transform from Ising- to Néel-type configurations, lowering the electrostatic potential, and reversibly recover upon heating.

We present a computational study aimed at exploring the different and independent roles of the Weissenberg number and of the ratio between the polymeric and solvent viscosity contributions in a viscoelastic fluid model. The tensorial model under investigation, recently proposed, is based on a logarithmic relation between the elastic (or recoverable) strain and the elastic stress. In this model, the elastic strain plays the role of a conformation tensor and its evolution equation inherently preserves its determinant and positive definiteness. These properties are also enforced in the computational method employed in the study. A finite-difference discretization in time is combined with a stabilized mixed finite element formulation based on the Variational Multiscale method for the spatial discretization and with a generalized Lie derivative approach for the advection terms. The behavior of the model is analyzed in paradigmatic pressure-driven flows and we find that the value of the viscosity ratio is crucial in determining to which extent non-Newtonian flow profiles are observed upon increasing the Weissenberg number. By comparing the solutions of the log-strain tensorial model with those of a suitable Generalized Newtonian Fluid model, we show that flow-type dependence plays a significant role even in the simple planar flow past a cylinder.

Foam scraping exhibits a dynamic transition between a slip state, in which the foam moves beneath a plate, and a scraping state, in which the foam is expelled from the confined region. Although this transition has been associated with the propagation of local T1 rearrangements, the physical parameter controlling their propagation remains unclear. Here, we investigate the dependence of the critical scraping velocity on the liquid fraction, bulk viscosity, and surfactant system. For all examined conditions, the critical capillary number follows $\mathrm{Ca}_c\propto\phi^{-1}$, apart from a solution-dependent prefactor. We propose a local fluid--structure-coupling model in which viscous work transmitted through the Plateau-border network competes with the effective energetic cost required for one T1 event to trigger the next. The observed scaling implies an effective energetic cost governed by the Laplace pressure and is consistent with a small local compressive component of the bubble deformation. These results identify local coupling between interstitial flow and bubble deformation as a mechanism controlling the macroscopic slip--scraping transition.

I derive the impedance response of an ideal electrolyte containing an arbitrary number of mobile ionic species between blocking planar electrodes, described by the Poisson--Nernst--Planck equations. By transforming the linearized equations to a charge--salt basis, the response is written in terms of a multi-component diffusion--migration matrix and its eigenvalues/eigenvectors. When all diffusivities are equal, the charge mode decouples from the neutral concentration subspace and the classical binary-electrolyte result is recovered. In contrast, unequal diffusivities couple charge relaxation to one or more neutral composition modes. For a ternary electrolyte with two cations and one anion, this coupling produces additional diffusive features and broadens the crossover between resistive and capacitive regimes. The results found in this paper provide a minimal continuum explanation for why mixed electrolytes can display impedance spectra that cannot be interpreted as a simple binary electrolyte with an averaged diffusion coefficient.

Over the past decade, Machine Learning Interatomic Potentials (MLIPs) have emerged as a powerful technique for performing molecular dynamics (MD) simulations with nearly ab initio accuracy. Alongside the development of new descriptors and advanced machine learning architectures, sophisticated procedures for the generation of diverse and accurate reference datasets have been established. To date, research has focused primarily on MLIPs for crystalline or amorphous inorganic and small molecular systems; however, large macromolecules such as polymers remain underrepresented in the literature, despite beeing an important class of materials. In this work, we investigate several aspects of developing MLIPs for polymers, utilizing polyethylene as a representative, yet simple model system. First, we compare various local atomic descriptors, identifying the Atomic Cluster Expansion (ACE) as the most effective for this application. Second, we implement and automatized active learning scheme to efficiently generate diverse training data and demonstrate that ACE potentials fitted on small oligomers are transferable to larger polymers. Given that the accurate reproduction of the density depends critically on a correct description of intermolecular interactions, which are far more complex to learn than intramolecular interactions, we carefully evaluate the performance of the ACE potentials with respect to non-bonded interactions. By utilizing the computationally efficient OPLS-AA force field as a ground truth reference, we are able to perform a direct comparison of nanosecond-scale MD trajectories resulting from the ACE and reference potential. We find that the ACE potential accurately reproduces key thermodynamic, structural and dynamical properties.

Active matter generates nonequilibrium fluctuations that mediate effective interactions between immersed objects. While fluctuation-induced (FI) forces in active fluids depend on activity, density, and geometry, their dependence on confinement remains poorly understood. We study FI forces between fixed intruders in two-dimensional active fluids composed of self-propelled circular or rodlike particles using Langevin dynamics simulations. We find that the FI force exhibits a pronounced nonmonotonic dependence on intruder separation, reaching a maximum at an optimal gap size well beyond the depletion regime, in contrast to the commonly assumed monotonic decay. This optimal confinement is robust across parameters and is more pronounced for elongated particles. The effect arises from a confinement-controlled balance between particle transport and crowding: narrow gaps hinder exchange between inner and outer regions, whereas large separations effectively decouple the intruders. At intermediate distances, enhanced crowding around the intruders generates maximal collision-rate asymmetries, leading to the strongest effective interactions. These results identify confinement geometry as a key control parameter for FI forces in active matter.

Polymers synthesized via ring-opening polymerization (ROP) of cyclic monomers represent an important class of materials due to their chemical recyclability and possible insertion in several critical applications. We present a dataset of 1 million synthetically realizable ROP polymer structures generated through a combination of Virtual Forward Synthesis (VFS) and polymer expert language models and qualified by stringent chemical heuristics. VFS is used to generate ROP polymers by applying known reactions to existing monomers. The polymer foundation models polyBART and POLYT5 further enable the generation of ROP candidates, with polyBART exploring its learned latent space and POLYT5 producing candidates via sequence-to-sequence generation. The resulting ROP polymers are subjected to robust filtering criteria to ensure novelty, validity and overall data quality through a combination of automated validation pipelines and a comprehensive set of chemist-informed heuristic rules introduced in this work for the first time. We hope that this dataset will serve as a valuable resource for downstream sustainable applications.

Physical learning rules such as equilibrium propagation (EP), coupled learning (CL), and adjoint coupled learning (AL) train resistive networks through local measurements. In the small-nudge limit EP and CL exactly conserve the conductance mass K = (1/2) sum_e kappa_e^2, a property that stabilizes training. We show that conservation also governs the inductive bias of these rules. For a single output we prove that EP and CL are trajectory equivalent, so single-output experiments cannot distinguish what the two rules learn. We prove that AL does not conserve the mass but dissipates it at exactly twice its own loss. In linear circuits we prove that the conserved mass has no functional consequence: all three vector fields are homogeneous in the conductances, so the selected solution is independent of the initialization scale. Fixed nonlinear elements break this protection. In diode circuits the learned input-output function depends on the initialization scale by up to about forty percent, an effect absent in linear controls, and the conservative rules retain this memory permanently while the dissipative rule partially erases it. At matched training loss the dissipative rule typically generalizes worse than the conservative rules, although it reaches low training loss faster; the penalty correlates with the mass dissipated en route and fades in larger circuits, where little mass is lost. The conservation structure of a local learning rule thus sets its initialization memory, its training speed, and, where dissipation is appreciable, its generalization; it should be treated as a design parameter of physical learning machines.

This work investigates how locally persistent crystal-like ordering in liquids influences the Debye-Waller factor. We have developed a theoretical framework based on liquid-phonon theory which introduces a phonon relaxation time, expressed as the ratio of shear viscosity to infinite-frequency shear modulus. These values are obtained using the Yukawa one-component plasma model. Within this framework, we establish expressions for the heat capacity at constant pressure and the Debye-Waller factor for the liquid state. These expressions explicitly introduce additional temperature dependence arising from the finite phonon lifetime. Anharmonicity is accounted for within the quasi-particle approximation. We compare our heat capacity results with values measured by Gathers for aluminum and copper, finding good agreement when assuming partial local crystal-type order. Comparisons with experimental heat capacities serve to validate the approach prior to its application to the study of electrical resistivity, the principal objective of this work. Using liquid-phonon Debye-Waller factors in the methodology developed earlier in [Phys. Rev. E 102, 053209 (2020)] for electrical resistivity in dense matter, and comparing with experimental resistivities from Gathers, we elucidate the character of the locally persisting crystal order in liquid aluminum and liquid copper. These results indicate that the electrical resistivity measurements can serve as a valuable probe for determining both the extent and the nature of crystalline order in the liquid state.

A conformation tensor is positive definite for every physically realizable polymer microstructural state. Numerical discretization can move the conformation tensor outside the positive-definite domain. This raises a question: can the least eigenvalue alone identify the first unstable direction? We answer it by linearizing Oldroyd-B, equilibrium-normalized FENE-P and Giesekus models about uniform frozen states. All include solvent viscosity and stress diffusion. We examine every non-zero planar Fourier mode, assuming each model's uncoupled constitutive tangent is strictly stable. The margin $1+r\chi$ measures the balance between solvent damping and the zero-frequency polymer response. The complete velocity--conformation system is stable if and only if this margin is positive. At zero margin, a simple stationary root appears; finite inertia changes growth rates but not the neutral boundary. At fixed wavenumber and other parameters, decreasing $\lambda_1$ identifies the first neutral direction. Oldroyd-B and equilibrium-normalized FENE-P first become neutral along principal directions; Giesekus mobility can instead make an oblique direction neutral first. For the reference case, onset is $\lambda_{1,c}=-1.933$ at $\theta_c=23.94^\circ$, before the principal-axis prediction. Along this family, the all-direction threshold approaches $-2.319$ as the other principal stretch grows, whereas the formal principal-axis extrapolation tends to negative infinity. A rational-parameter counterexample, matrix spectra and uniform forced-base calculations test the neutral boundary and both sides. These results concern one linear, uniform, planar Fourier mode, not nonlinear or inhomogeneous-flow stability. Within this scope, onset depends not on indefiniteness alone but also on constitutive-tangent geometry and wavevector direction.

Soft cells are shapes without sharp corners that can fill the space without gaps and overlaps [2]. A sharp corner is a point on the surface of the solid through which no smooth curve passes. In the paper introducing the concept of soft cells [2], the authors proved that there exists an algorithm that can soften tilings consisting of convex polyhedra, preserving the lattice points and combinatorial structure of the original tiling. Although the algorithm guarantees (with a few restrictions) that there exists a soft tiling that is combinatorially equivalent to the convex polyhedral tiling, the proof does not address how to find all such tilings. For a polyhedral tiling based on a truncated octahedral cell, paper [3] shows how to find all soft tilings for a fixed symmetry group. In this paper, we extend this method and apply it to the cubic lattice, imposing only natural conditions, rather than symmetry constraints. The natural conditions being, the directions of edge half-tangents of the tiling are restricted to lattice directions, and the edges of the tiling are planar. This results in 26 soft cubic cells with different geometries. A total of 68 fundamental domains can be created from the cells, which can be classified into 8 groups based on their lattice symmetry. The paper also presents an algorithmic process (with a corresponding program in language Python) for classifying the 26 non-equivalent geometric cell types.

Quasicrystals have revolutionized our understanding of order in solids by demonstrating exotic structural and physicochemical properties with diverse potential applications. Despite the development of various theoretical models and experimental techniques to describe quasicrystal structures, the precise determination of local three dimensional (3D) arrangements of constituent atoms, or of secondary building units such as clusters or micelles, remains elusive. This challenge is particularly acute in self assembled soft matter quasicrystalline systems, where the complex assembly of molecular groups introduces additional defects and structural modulations. Herein, we report the first complete structural determination of self-assembled mesostructural dodecagonal quasicrystalline particles. Employing advanced electron tomography, combined with dedicated structural tracing and processing workflows, the 3D coordinates of all nodal sites were extracted. This approach reveals that the actual structure deviates from the conventionally assumed tetrahedral close packing geometry, exhibiting diverse coordination environments and displacive fluctuations. We identified and quantified rotational intergrowths arising from node exchange, as well as various defects and disorder, with these features discernible only through 3D analysis. Additionally, we propose a simplified two-layer stacking of isomorphic hexagonal model to form dodecagonal quasicrystal. This work advances our understanding of soft-matter dodecagonal quasicrystals and paves the way for detailed structural elucidation of self-assembled systems.

An electron crosses the cold Fermi sea. The sea recoils, screens, remembers. It returns the electron dressed: a quasiparticle with a mass, a lifetime, and a Green function. This was Nozières' lesson. We carry it to water. Electrons become dipoles; the Fermi sea becomes a hydrogen-bonded polar liquid. We ask the same question: can the collective modes of water live long enough and reach far enough for molecular machines to interact and synchronize?

We derive predictive formulas for the scattering mean free path $\ell_s$ of statistically homogeneous two-phase dielectric media in dimensions $d=1,2,3$. Unlike Mie-based estimates limited to identical circular or spherical scatterers, the formulas apply to arbitrarily shaped and polydisperse particulate media as well as nonparticulate media, with microstructure entering through the spectral density. The formulas are based on the exact strong-contrast expansion for the effective dynamic dielectric constant. We apply them to five nonhyperuniform and hyperuniform models and validate selected cases using finite-difference time-domain simulations. For $k_1/s \lesssim 1$, where $k_1$ is the incident wavenumber and $s$ is the specific surface, the predictions agree well with simulations and are consistent with Mie theory where applicable, while improving accuracy for two-dimensional transverse-magnetic polarization. Mie estimates become more accurate for $k_1/s \gtrsim 1$. For hyperuniform media with $\widetilde{\chi}_V(k)\sim k^\alpha$ at small $k$, the theory predicts $\ell_s\sim k_1^{-(d+1+\alpha)}$; stealthy hyperuniform media are transparent over a finite wavenumber interval. These results provide a microstructure-based route to predict and design wave transport in general disordered dielectric materials.

We study the stochastic dynamics of a rotating Brownian particle in a non-Markovian fluid. Experimentally, we find that rotation enhances the long-time diffusivity of the particle and generates time-antisymmetric cross-correlations between orthogonal displacement components in the plane perpendicular to the rotation axis. To rationalize these observations, we introduce a minimal linear model in which a tracer is coupled to a slow bath degree of freedom and rotation enters through an advective coupling. Eliminating the bath variable yields a generalized Langevin equation with a non-reciprocal memory kernel. This kernel rotates in time, forming a logarithmic spiral, and it obeys Onsager-Casimir symmetry under reversal of the rotation vector, and the corresponding fluctuation-response relation. From the latter we obtain a geometric construction that links two-time cross-correlations to the transverse response of the particle in bulk. Unlike the ordinary Einstein relation, this relation involves the antisymmetric sector of the response. Our experiments and theory are in qualitative agreement, establishing rotating colloids in viscoelastic fluids as a minimal realization of Onsager-Casimir symmetry in time-nonlocal stochastic dynamics

Flying insect swarms exhibit cohesion without the local velocity alignment observed in flocks of birds or schools of fish. The interaction rules and channels of communication between insects that lead to collective behavior have not yet been determined. We propose a theoretical model based on acoustic communication between swarm members, where each individual is attracted to a weighted mean field of its neighbors. We demonstrate that this simple framework can describe a wide range of swarming dynamics, including a phenomenon where pairs of insects break free from the swarm in a helical orbit around each other. Counterintuitively, our numerical model suggests that stochastic noise enhances the stability of an insect swarm, as it interferes with pair formation. Finally, we demonstrate that a specific species of malarial mosquito produces swarms that reside on the edge of a transition to instability. Our study shows that fairly simple local interaction rules can be sufficient to describe the collective behavior of swarming biological systems.

In Newtonian fluids, impact of a droplet on a liquid pool births a cavity, crown, capillary waves, and Worthington jet. The corresponding hydrodynamic events for elastic or Boger fluids, however, remain an uncharted domain of comprehension and exploration. We thoroughly investigate, via experiments, theory, and simulations, how elastic energy storage, fluid relaxation, and competitive inertio elasto capillarity govern the spatio temporal evolution of the cavity, the crown, and the ensuing Worthington jet in polymeric elastic fluids. The events are systematically explored over a wide range of impact Weber and Deborah numbers, considering varied Newtonian and elastic fluid droplet pool combinations, and revealing new, and distinct morphological regimes compared to Newtonian counterparts. We illustrate that these new findings are purely driven by fluid elasticity, and not by viscosity or interfacial tension. We derive a theory for cavity radius evolution, using energy conservation within potential-flow framework. We show that 30-40 % of the droplets kinetic impact energy may be stored as elastic energy by the stretching polymer chains during cavity expansion. Appealing to the FENE P model, we derive a theory for the temporal evolution of the radius of the elongated Worthington jet. We show that in elasto capillary regime, competitive elastic and capillary stresses lead to exponential decay of the jet radius. The role of elastic stresses and the local velocity field in governing cavity evolution, morphology, and jet formation are further elucidated through computer simulations. Our findings significantly advance the uncharted paradigm of interplay between inertia, capillarity, and elasticity in droplet-pool interaction elastohydrodynamics.

We study dynamical effects during nucleation in thermal first-order phase transitions in field theory. Focusing on the classical regime of the decay of a metastable state, we present the general formula for the thermal decay rate including the dynamical prefactor and give a recipe for its systematic evaluation. We describe the physical mechanism which reduces the actual thermal decay rate with respect to the statistical rate obtained in equilibrium theory. We also discuss the thermality conditions ensuring the existence of a steady-state thermal rate, in which case our formula is exact up to exponentially small corrections. We show that it reproduces the known results for the nucleation rate in stochastic mechanics and field theory, and allows us to unify and go beyond them. We illustrate this in real-time numerical simulations of simple field theory models. We observe significant non-perturbative contributions which can dominate the dynamical prefactor in weakly-coupled field theories at moderate exponential suppression of the decay rate. We explore the connection of these non-perturbative effects to oscillons. Notably, our numerical method requires exponentially less computing time than direct simulations of decays and is thus applicable to systems with arbitrarily strong exponential suppression. Finally, we discuss small or poorly thermalized systems when the thermality conditions are violated and the steady-state rate does not exist.

Airborne pollen transport is a key concern for urban air-quality assessment, allergy-risk forecasting, and smart-city planning. However, conventional dispersion models generally assume smooth spherical particles, neglecting how pollen dehydration alters particle morphology and impacts aerodynamic and thermal behavior. To address this gap, this study presents, for the first time, advanced CFD simulations evaluating the aerodynamic drag forces and convective heat transfer of realistically dehydrated (dry) pollen particles. Investigations are conducted at Reynolds numbers ($0.1 \leq Re_p \leq 15$) at the particle's scale corresponding to realistic atmospheric wind speeds ranging from 0.27 to 30 km/h. The findings reveal that dry pollen particles exhibit drag coefficients 8% to 15% higher than those predicted for hydrated pollen spherical particles. Conversely, their Nusselt numbers are 5% to 15% lower than those for hydrated pollen particles. These considerable deviations confirm that conventional spherical correlations are inadequate for simulating dry pollen Lagrangian transport and evaporation. These findings highlight the need to account for realistic dehydrated shapes when modeling airborne allergen transport in urban environments.

Drag reduction is achieved by a steady square-wave forcing of the spanwise wall velocity, based on the experiments in Knoop et al. (Phys. Rev. Fluids, 10, 2025). Particle tracking velocimetry data are analyzed for a non-actuated reference case and actuation at forcing amplitude $A^+ = 12$ ($+$ denotes viscous scaling) for three streamwise forcing wavelengths, which correspond to sub-optimal ($\Lambda_x^+ = 471$), near-optimal ($\Lambda_x^+ = 942$), and post-optimal ($\Lambda_x^+ = 1884$) drag reduction conditions. Conditionally averaged fields on large-scale bursts of turbulent kinetic energy show that forcing suppresses near-wall ejections across all cases, while outer-layer sweep suppression strengthens with $\Lambda_x^+$. Post-optimal forcing exhibits streamwise-periodic attenuation and recovery of turbulence. The recovery phenomenon is caused by an enhancement of very small scales, significantly smaller than those typically energetic in wall turbulence, and is linked to the emergence of small-scale bursting events. While these small-scale bursts are statistically insignificant in the non-actuated and sub-optimal cases, their frequency increases by a factor of four between the near-optimal and post-optimal cases. The small-scale bursts exhibit uniform signatures and intensities, hinting at the possible universality of the recovery phenomenon. A wavelet analysis shows that, in the post-optimal case, very small scales increase progressively in the streamwise direction in regions where the wall velocity remains constant, driving a cyclic pattern of small-scale re-energization and suppression consistent with earlier statistical analysis. This turbulence modulation mechanism is scale-selective: while small-scale structures emerge periodically, large-scale motions are more effectively suppressed as the forcing wavelength increases.

Three-dimensional particle-tracking velocimetry (3D-PTV) measurements were used to compute the spectral transport of the Reynolds-stress tensor. The experimental framework is validated for a zero-pressure-gradient (ZPG) turbulent boundary layer (TBL) at a friction Reynolds number $Re_\tau = 1020$, demonstrating that the dominant non-linear energy transfer mechanisms are adequately resolved to draw flow physics-based conclusions. For the streamwise Reynolds stress in the ZPG TBL, a component-wise decomposition of the non-linear transport term is considered for the first time, which reveals distinct energy transfer mechanisms associated with the spanwise and wall-normal advection. The same experimental framework was applied to a drag-reduced ($\approx 38\%$) TBL flow, achieved by imposing a steady streamwise-alternating spanwise wall velocity. This wall forcing causes a strong attenuation of non-linear energy transfer and its shift away from the wall. The energy transfer mechanisms remain qualitatively similar to those of the canonical ZPG TBL, suggesting that the existing mechanisms simply readjust to their new low-turbulent-energy state.

A volatile droplet gently deposited on a superheated substrate can sit on a thin film of its own vapour, which prevents contact between the drop and surface. This phenomenon is called the Leidenfrost effect. In this paper, through direct numerical simulations, we analyse characteristics of Leidenfrost water droplets with a single computational model over four decades of droplet radius, stitching together previous works in the limit of large and small droplets. Using the model, we show that the ambient humidity, an underappreciated factor in the Leidenfrost system, in combination with the flow in the drop has a significant impact on the geometry and drying kinetics. Our results imply the inadequacies of commonly made assumptions of a pure vapour phase and an isothermal droplet. When modelling large Leidenfrost droplets with an axisymmetric model, large discrepancies between experiments and the computational results occur. Through azimuthal stability analysis, we show that this is due to the unrealistic constraint of axisymmetry. This finding is supported by 3D simulations of a simplified model. Finally, some hypotheses are explored to account for the remaining discrepancies with experimental data.

The aeroacoustic resonance of round supersonic jets impinging on concave surfaces is investigated using compressible large-eddy simulations, vortex-sheet modelling, and Powell's feedback-loop analysis. The choked jets operate at an ideally expanded Mach number of $1.56$ and a Reynolds number of $6\times10^4$. Six geometries are considered: two flat plates at $L/D=2.08$ and $2.58$, where $L$ is the nozzle-to-wall distance and $D$ the nozzle exit diameter, and four Gaussian concave surfaces of fixed depth and indentation spread $\sigma\in\{0.4,0.8,1.6,4.0\}$. As the indentation narrows, the primary-tone amplitude increases by up to $23\,\mathrm{dB}$ relative to the flat-wall reference at $L/D=2.6$, together with larger wall-pressure fluctuations and moments. A Powell-Tam source-transfer budget attributes this amplification to increased Mach-disk source amplitude and more efficient return of the upstream feedback wave to the nozzle. The stronger upstream-propagating waves are consistent with acoustic focusing by the concave wall. For the helical cases, the measured frequencies and radial eigenfunctions agree closely with the guided jet mode predicted by the vortex-sheet model, supporting its role in closing the upstream feedback path. The same selection is recovered for concave and flat walls alike, so this tone is governed by the shear-layer profile of the equivalent ideally expanded jet rather than by the wall geometry. The axisymmetric frequencies, by contrast, coincide with no guided-mode branch and appear instead to follow Powell's classical loop-length criterion. The results identify distinct frequency-selection mechanisms for helical and axisymmetric screech and demonstrate that wall curvature provides effective control of screech amplitude and surface loading.

The weak wall-normal pressure variation in pressure-driven rarefied Poiseuille flow is a stringent test of higher-order constitutive models: it is almost invisible in the total-pressure norm, yet it is generated by anisotropic molecular stress. A tangent-form nonlinear coupled constitutive relation (NCCR) reproduces its convex topology, but the physical reason for its quantitative success remains unresolved. We ask whether the constitutive stress relation and reduced streamwise forcing are independently accurate or whether their effects compensate. A direct simulation Monte Carlo (DSMC) campaign is analysed using two-dimensional momentum budgets, a pressure-error norm based on the transverse signal, a matched-outlet-Knudsen comparison and componentwise tests of the pre-elimination NCCR balance. The non-equilibrium wall-normal stress over-supports the measured pressure defect, while streamwise transport of shear stress supplies an opposing correction. The state map, momentum budgets and forcing diagnostics show that neither outlet Knudsen nor outlet Mach number alone organises the pressure amplitude; along the fixed-ratio sequence, rarefaction is accompanied by larger changes in the constitutive diagnostics than in pressure amplitude. The DSMC-inferred stress relation departs from the fixed reduced coefficient, and even the best common scalar closes the dominant shear component far more accurately than the normal components that carry the pressure field. Correcting the coefficient alone can therefore worsen the reconstruction, whereas restoring omitted streamwise-momentum terms reduces the amplitude bias in strongly accelerated cases. The reduced law can remain accurate through stress--momentum compensation, showing that agreement of a weak non-equilibrium observable need not imply correct internal closure mechanics.

One-way spatial marching methods separate upstream- from downstream-propagating disturbances using a rational approximation of a spectral projector. Among existing one-way Navier--Stokes (OWNS) formulations, the recursive variant, OWNS-R, is the most economical, evaluating the approximation as a product of $N$ resolvent factors. This product amplifies rounding errors multiplicatively, imposing a flow-dependent upper limit on the approximation order that cannot be known in advance. We reformulate the same approximation as an additive partial-fraction sum (OWNS-Summation, OWNS-S). In exact arithmetic, the recursive and summation evaluations are equivalent when supplied with identical weights and poles; in floating-point arithmetic, they are not. Each of the $N$ resolvent solves acts on the same input state and contributes independently to a weighted sum, preventing multiplicative error amplification. The approximation order $N$ therefore becomes a pure convergence parameter, and the solves can run in parallel. Using the same auxiliary poles as OWNS-R, OWNS-S remains accurate in every configuration tested, showing that the recursive evaluation, rather than the poles, is the dominant source of instability. A paired greedy parameter-selection procedure is also introduced, with candidates drawn from analytic estimates of the upstream and downstream spectral regions, avoiding eigen-decomposition during the numerical march. OWNS-S is validated on incompressible, hypersonic and transonic boundary layers. In the transonic case, the disturbance spectrum reorganises from a subsonic to a supersonic topology during the march. The one-way computation proceeds continuously through this transition at a streamwise resolution unattainable by the parabolised stability equations.

This study applies $\textit{4D topology optimization}$, a framework for simultaneously optimizing the morphology and motion of a system, to a rigid body that induces fluid flow. The rigid body shape is represented on a design grid that is independent of the analysis grid, and at each time step, it undergoes rigid-body motion before being mapped onto the analysis grid. The shape is represented using a pseudo-density method, while the motion is directly parametrized by the positions at discrete time steps and smoothed using a temporal filtering technique. The fluid dynamics are evaluated through the lattice kinetic scheme, an extended version of the lattice Boltzmann method. Design sensitivities with respect to both shape and motion are derived via the adjoint variable method, and the shape and motion are intentionally updated simultaneously during the optimization process. Finally, two- and three-dimensional numerical examples are presented and discussed from a physical perspective. Furthermore, the effectiveness of the proposed method is demonstrated by comparison with cases in which only the shape or motion is optimized, as well as through several parameter studies.

The dispersion of reactive solutes in shear flows is governed by the interplay between advective stretching, transverse diffusion, and boundary exchange kinetics. While classical analytical methods and grid-based numerical solvers have extensively characterised these transport mechanisms, accurately resolving the spatiotemporal evolution of solute plumes in asymmetric reactive environments remains computationally demanding. In this study, we introduce a physics-informed neural network (PINN) framework to simulate two-dimensional wall-reactive solute dispersion in canonical shear flows (Couette, Poiseuille, and Couette-Poiseuille) bounded by absorbing walls. By embedding the governing convection-diffusion equation and Robin boundary conditions into a unified loss function, the mesh-free PINN reconstructs the spatiotemporal concentration field. The network predictions are validated against an alternating-direction implicit (ADI) finite-difference benchmark, showing close agreement across non-reactive, symmetric, and asymmetric reactive regimes. The computations are carried out at $\mathrm{Pe}=10$ for impermeable walls, symmetric absorption $(\beta_1,\beta_2)=(1,1)$, and tenfold asymmetric wall-reactivity contrasts $(\beta_1,\beta_2)=(0.2,2)$ and (2,0.2). Leveraging the differentiable nature of the trained PINN, we extract wall-resolved transport diagnostics, including the apparent axial dispersion coefficient, cumulative wall-removal dynamics, and localised uptake fluxes. The results show that the imposed shear profile governs the streamwise organisation of reactive uptake, while unequal wall reactivities induce transverse asymmetry that modifies the macroscopic spreading rate. Overall, this framework establishes PINNs as an interpretable mesh-free tool for analysing boundary-coupled reactive transport in shear flows.

Reliable estimates of the melt rate of tidewater glaciers require accurate knowledge of salt and heat fluxes at the near-vertical ice-ocean interface and such knowledge is currently lacking. In this paper, we present a theory for salt and heat fluxes in the idealized system of turbulent double-diffusive convection in an infinite vertical channel and show how this theory can be extended to give theoretical estimate of the buoyancy-driven melt rate of a vertical ice surface in seawater. Our theoretical results are shown to be in good agreement with direct numerical simulation data and measurements from laboratory experiments.

Capturing the multiscale statistics of turbulence in compressed form remains a central challenge for reduced-order modeling. We introduce a hybrid Tensor Train (TT) approach for a highly intermittent passive scalar. The hybrid TT matches Galerkin, wavelet, and standard TT decompositions for the structure functions while improving the representation of intermittent, non-Gaussian fluctuations. These results open a route toward evolving the linear dynamics of passive scalars directly in compressed tensor form, with potential applications to quantum algorithms for fluid transport.

Here, we investigate the motion of a thin circular quantum vortex filament near the infinite planar surface. The fluid surrounding this surface moves with a non-zero velocity $\bf{v}$, which is parallel to the surface. We study the specific features of this quantum system and show that they are quite suitable for the boundary layer theory. The developed model allows us to calculate the vortex energy spectrum, $E = E({\bf p})$, where ${\bf p}$ is the total momentum of a vortex ring. We have demonstrated that this function has complex non-trivial dependence on the velocity $\bf{v}$. It is stated that the inverse effective mass of a vortex under consideration is of a tensorial nature. In certain quantum states, the system shows the possibility of both negative and positive effective mass existing. This study employs a novel quantization method for classical closed vortex filaments, developed by the author earlier.

We present FESOM2-JAX, a Python re-implementation of the Finite-volumE Sea ice-Ocean Model (FESOM2) in JAX. The model retains the unstructured-mesh, cell-vertex finite-volume formulation of the original, runs unchanged from a laptop CPU to 256 GPUs, and is end-to-end differentiable. FESOM2-JAX is a code shadow of the Fortran model: a projection onto the Python ecosystem, translated with large language models and verified kernel by kernel against the original. It is built to lower the barrier to experimentation, from new numerics and parameterizations to gradient-based calibration and hybrid physics-machine-learning components, while remaining close enough to the original so that what is developed in the shadow can be transferred back. In a 1958-2019 hindcast at 1$^{\circ}$ equivalent resolution with identical physics and forcing, the mean states of the JAX and Fortran versions differ from each other by two orders of magnitude less than either differs from observations, and the two runs agree for six decades in global temperature, salinity, heat content, and sea ice. The complete 1$^{\circ}$ configuration fits on a single GPU, a node of four GH200 superchips integrates $\sim$113 simulated years per wall-clock day, and meshes of up to 7.4 million surface vertices ($\sim$5 km) scale to 128 GPUs. What limits the model is communication rather than arithmetic. What the shadow adds to the original is the gradient: a single reverse-mode pass through the full time loop returns the sensitivity of a model diagnostic to a parameter at every mesh vertex, verified against finite differences. To our knowledge, FESOM2-JAX is the first global ocean-sea-ice model of CMIP-class complexity written natively in a differentiable framework, and the first on an unstructured mesh.

The enthalpy method was introduced in the late 1970s to simulate phase-change problems on fixed grids without explicitly tracking the moving phase-change front. It remains one of the most widely used approaches in academic and commercial software for the simulation of industrial melting and solidification processes. For pure phase-change materials (PCMs) that melt or solidify at a single temperature, the enthalpy method introduces an artificial mushy region bounded by the solidus temperature, $T^{\rm sol}$, and the liquidus temperature, $T^{\rm liq}$. As the numerical parameter $\Delta T=T^{\rm liq}- T^{\rm sol}$ approaches zero, the solution obtained with the enthalpy method is generally assumed to converge to that of the classical Stefan problem, in which the phase-change front is infinitesimally thin. This assumption is largely based on benchmark studies performed under the simplifying assumption of equal solid and liquid densities. In this work, we systematically investigate the accuracy and spatio-temporal convergence properties of the enthalpy method for both low- and high-density-ratio phase-change problems. Because the limiting behavior $\Delta T\rightarrow0$ is difficult to realize numerically, owing to the diminishing thickness of the mushy region, we formulate and analyze the finite-$\Delta T$ mushy Stefan problem solved by the enthalpy method. We show that this problem possesses a self-similar structure that reduces the governing equations to a boundary-value problem involving two unknown parameters. The theoretical analysis also enables improvements to our previously developed low-Mach enthalpy method, enhancing its stability and accuracy as the density ratio between the two phases increases from $\mathcal{O}(1)$ to $\mathcal{O}(3)$.

Physics-informed neural networks (PINNs) have emerged as a versatile approach for solving nonlinear partial differential equations (PDEs), yet achieving high accuracy efficiently using these techniques remains challenging for high-dimensional or multiscale systems. Here, we present a hybrid quantum-classical framework that enhances Quantum PINNs (QPINNs) through adaptive collocation point sampling and loss-aware attention mechanisms. By dynamically prioritizing points in regions with large PDE residuals or steep solution gradients, our method mitigates the spectral bias inherent in conventional PINNs. Current Quantum Physics-Informed Neural Networks are commonly assumed to be limited by the expressive power of quantum circuits. In our work, we observed that, across diverse differential equations, optimization - not only expressivity - can be an important bottleneck. Furthermore, a trainable loss-weighting scheme balances contributions from physics residuals, boundary conditions, and data fidelity during training. Integrating these strategies with quantum computing techniques (including variational quantum circuits and quantum gradient estimation) can yield at least a 60% improvement in solution accuracy under specific regimes for benchmark fluid flows and reaction-diffusion systems. Finally, we argue that merely increasing model expressivity is insufficient for resolving complex PDEs via QPINNs, as they remain constrained by the structural optimization limitations of classical PINNs. This framework provides a scalable pathway for quantum-enhanced scientific machine learning, bridging physics-based modeling with emerging quantum computational capabilities.

In the present study, we propose a consistent and bound-preserving finite-volume WENO scheme that satisfies the requirements of consistency, conservation, equilibrium, and bound preservation for compressible multiphase flows with the Phase-Field mechanism. The proposed WENO scheme is developed based on a new calculation of WENO weights determined by relative smoothness between stencils and on a coupled reconstruction of the masses and volume fractions. Consistency of reduction and volume fraction summation to unity are considered during the development so that fictitious phases, local voids, or overfilling are not produced numerically when there are $N$ ($N \geqslant 1$) different immiscible phases. The proposed WENO scheme is applied to the consistent and conservative Phase-Field method with adaptive mesh refinement enabled. Various benchmark compressible two- and $N$-phase flows are performed to verify the properties of the proposed WENO scheme as well as its variant with the consistent limiter. We finally demonstrate the capability of the proposed WENO scheme in shock-induced cavity collapse and shock-vessel-bubble interaction problems, with discussion of the necessity of bound preservation for high-order schemes and comparison of different compressible multiphase flow models.

A new semi-implicit, two-phase, double-point formulation of the Material Point Method (MPM) for soil-water interaction with seepage and free-surface flows under large deformation is presented in this paper. The approach advances the water phase implicitly while keeping the soil phase explicit, enabling stable, efficient time integration in problems that involve rapid seepage and strong free-surface motion. The proposed framework models high-Reynolds-number interphase drag through a non-linear Darcy's law implemented for the first time within an incremental fractional step MPM formulation without enlarging the implicit solve. This methodology also enhances the numerical stability for fast flows and wave breaking via a hyperelastic constitutive treatment of slightly compressible viscous water, and mitigates spurious oscillations through a new stabilisation approach for the velocity. Robustness of soil-water interface is achieved by combining nodal-based, free-surface detection, suited for higher-order spline functions with smooth porosity-permeability transitions that avoid constitutive divergence at sharp material boundaries. Validation against laboratory benchmark cases reported in the literature, including pure-water dam break, dam-break seepage through a porous barrier, two granular-collapse tsunami experiments, and a dam-break wave over a movable granular bed, shows accurate and stable free-surface evolution, pressure time histories, seepage fronts, and wave-gauge records. Using an advanced critical-state soil model (NorSand) further improves the reproduction of granular flow kinematics. The results demonstrate that the proposed formulation is a reliable and computationally efficient tool for geotechnical hazards involving intense soil-water coupling, seepage, sediment transport and free water.

In this work, a ensemble-of-subproblems strategy with stochastic discrete velocities is extended to deterministic methods for mitigating ray effects in rarefied flow simulations. The strategy involves performing multiple independent subproblems, each using a small set of randomly sampled velocity points, and then averaging their solutions to obtain the final result. The core idea is to ensure that the distribution function at any velocity can contribute to the final result, approximating highly refined velocity-space resolution without increasing the memory requirement in any single subproblem. We incorporate this strategy within the DUGKS framework, and the resulting method is denoted as SDV-DUGKS. To evaluate the performance of the proposed method, we compare SDV-DUGKS with the original DUGKS on several test cases: (a) the Sod shock tube problem, (b) the one-dimensional Riemann problem, (c) the two-dimensional lid-driven cavity flow, and (d) the two-dimensional Riemann problem. The results show that, in the collisionless limit $\mathrm{Kn} \to \infty$: (1) for one-dimensional compressible flows, SDV-DUGKS reduces memory usage by approximately 2/3 compared with that of the original DUGKS while achieving good agreement; (2) for two-dimensional compressible flows, SDV-DUGKS requires one to two orders of magnitude less memory than the original DUGKS while achieving good agreement. Based on these results, it can be concluded that the proposed method serves as a reliable and effective tool for mitigating ray effects in rarefied flow simulations.

This note presents an axisymmetric model of a tornado-like vortex with internal vertical wind shear. By employing a prescribed incompressible circulation-strain flow that captures the horizontal variation of the vertical wind, we show that the model admits an exact viscous Feynman-Kac representation for the tornado structure. In the presence of vortex vertical shear, the tilting term induces radial phase mixing that rapidly deforms the vortex structure, thus causing the radius of the maximum azimuthal wind to broaden and shift upward. At the long-time limit, the vortex approaches the Burgers radial scale while both the wind and vorticity decay exponentially. This class of solutions may help explain why tornadoes often weaken rapidly once an internal vertical shear structure emerges after touchdown.

Sheared-flow Z-pinch stability has been studied within ideal MHD primarily through growth rate calculations, which find that even trans-Alfvénic sheared flows apparently fail to suppress the kink instability. Trans-Alfvénic sheared flow does stabilize the MHD kink but also excites shear-driven instabilities characteristic of high-Reynolds-number supersonic flow. This distinction is evident from the dispersion relations underlying the growth rates, computed here as the analytic dispersion function in the complex-frequency plane. Regularization splits this function into adiabatic and resonant parts describing how discrete modes emerge from and interact with the continuous spectrum. The Doppler-shifted flow continuum interacts with the interchange and kink instabilities in distinct ways. For interchange, the continuum overlaps the instability branch at all wavenumbers, so even sub-Alfvénic sheared flow stabilizes profiles modestly beyond the interchange threshold. The kink, by contrast, is shielded from the continuum by a frequency gap, and trans-Alfvénic flow is required to Doppler-shift the continuum into resonance with it, giving a geometric picture of the stabilization threshold. But shear-driven instabilities arise at this same threshold, including reflection modes and an acoustic kink. It is these shear-driven modes, not the original MHD instabilities, that dominate the ideal-MHD spectrum in trans-Alfvénic conditions. The ideal analysis thus describes the stabilization mechanism while showing that the stability of the sheared-flow Z pinch ultimately rests on non-ideal physics, including finite orbit width and dissipation.

Atmospheric thermal convection drives boundary-layer dynamics and vertical exchange of heat, moisture, and momentum, yet fundamental questions about thermal structure remain open due to limited in situ observational coverage. We introduce a novel high-resolution observational dataset for atmospheric convection based on paragliding flight logs collected over metropolitan France during 2017-2024. Paragliders probe thermal updrafts by circling within them while carrying GPS variometers that record position and altitude; each climbing segment samples the vertical velocity field within a thermal column. Aggregated across 1.47 million climbing segments from 110,730 flights, this dataset provides unprecedented spatial coverage and temporal resolution. To demonstrate the value of this observational resource, we extract three physically distinct observables from climbing segments and characterize their dependence on terrain, season, time of day, cloud state, and soil moisture. Coupling the paragliding observations with global atmospheric reanalysis data (ERA5, 0.25 degrees hourly) through an orthogonalized regression framework against 118 physically interpretable predictors, we identify leading atmospheric predictors of these observables. The empirical relationship between ceiling height and temperature-dewpoint depression matches the theoretical lifting condensation level scaling with striking precision supporting our methodology. Boundary-layer height emerges as the leading independent predictor of both ceiling height and thermal strength across all terrains and seasons, while vertical-velocity variability is controlled by surface heat-flux and wind variables. Taken together, our results highlight the utility of crowdsourced flight-log data for investigating atmospheric convection.

We quantify viscous energy loss for two-dimensional Delort vortex sheets. Let $u^\nu$ be Leray-Hopf solutions on $\mathbb{T}^2$ with uniformly bounded kinetic energy and total vorticity variation, and write $\omega_0^\nu=\mu_0^\nu+f_0^\nu$, where $\mu_0^\nu\geq0$ and $f_0^\nu$ is bounded in $L^p$, $p>1$. For every fixed $0<\delta0$. Previous estimates covered only $T_\nu=o(\exp(|\log\nu|^\kappa))$, $\kappa<1/2$, so this gives a polynomial lower bound on the energetic lifetime of the inviscid vortex-sheet model. If instead $f_0^\nu$ is bounded in $L(\log L)^\alpha$, the rate is $O(|\log\nu|^{-q_\alpha})$, $q_\alpha=\min\{2\alpha,1\}$, and the loss vanishes when $\log T_\nu=o(|\log\nu|^{q_\alpha})$. On $\mathbb{R}^2$, exact radial solutions attain these exponents for $0<\alpha\leq1/2$. At the endpoint, a bounded-energy $L^p$ family attains the rate $1/|\log\nu|$, while every fixed radial datum dissipates $o(1/|\log\nu|)$ and can lose a fixed amount of energy only on the diffusive scale $1/\nu$.

Fully suspended thin films can decouple substrate effects and provide additional tuning degrees of freedom compared with their substrate-supported counterparts, making them unique platforms for next-generation thin film devices. Here we report one-step, transfer-free and substrate-free fabrication of centimeter-scale ultrathin fully suspended metal and metal oxide film structures via liquid metal capillary forming. We show that, analogous to soap film formation, the instantaneously developed few-nanometer-thick native surface oxide can laminate various liquid metals into micrometer-thick metallic films. Surprisingly, the surfactant-like metal oxide bilayer can survive dewetting-induced liquid metal drainage, forming suspended two-dimensional films featuring an enormous lateral size-to-thickness ratio on the order of 10^7. We further demonstrate rapid prototyping of metallic minimal-surface thin-walled structures and ultra-sensitive acoustic wave detection with these suspended thin film platforms.

The influence of the time-delay parameters on the bifurcations of "non-classical" maximal attractors in the Sommerfeld-Kononenko non-ideal dynamical system "spherical pendulum-electric motor" is investigated. Regular and chaotic maximal attractors of this system, as well as their bifurcations, are described. It is established that the presence of time delays can fundamentally change the type of limit sets of the considered dynamical system and significantly alter the scenarios of transitions to deterministic chaos.

Coupled oscillators often experience two distinct influences: an internal input transmitted through coupling from a driver subsystem, and an external periodic forcing applied directly to the response. Here we ask how these two influences interact and whether their combined action can organize the response dynamics. We show that coupling and forcing can cooperate to produce a localized organization in parameter space, where the response displays simultaneously enhanced steady-state amplitudes and increased spectral concentration at the forcing frequency; we term this effect coupling-forcing induced coherence. In delay regimes where the driver approaches a steady state, the coupling acts as an effective bias that shifts the response operating point, providing a resonance-like mechanism that helps anchor the onset of the coherent band. When the driver is also externally forced, coupling-forcing induced coherence can coexist with transmitted resonance (amplification conveyed from the driver to the response through the coupling pathway). We use frequency- and time-domain diagnostics to identify parameter regions dominated by coupling-forcing induced coherence, by transmitted resonance, or by their combined action.

We investigate traveling fronts in a lossy nonlinear transmission line. By prescribing a hyperbolic-tangent profile with dimensionless width $m$, we solve the inverse problem of determining the voltage--charge relation for which this profile is an exact solution. The exact relation is expressed in terms of the Gauss hypergeometric function. We also construct an approximate solution by assuming a cubic voltage--charge relation and replacing the resulting quadratic damping function with its optimal linear least-squares approximation. This construction determines the cubic coefficients and yields a modified governing equation that admits the prescribed profile as an exact solution. In both constructions, physical admissibility selects a shock front. In the broad-front limit, the approximate normalized force agrees with the exact result through order $m^{-2}$; numerical comparisons show that the agreement remains good even outside the asymptotic region of large $m$. Finally, a characteristic analysis of the original partial differential equations distinguishes compressive shocks from noncompressive kinks without recourse to the mechanical analogy.

We bridge two sides of singular perturbation theory: the classical theory of slow-fast systems and the semi-classical approach to quantum mechanical systems. For a specific but physically important class of dynamical systems, we show that purely classical and exotic objects, so-called canard solutions, are shadows of instantons in the corresponding quantum system. We demonstrate that canard solutions exist in a domain of parameter space whose boundaries are determined by an instanton action. We illustrate our statements analytically for the relevant example, the overdamped Josephson junction, and confirm them numerically. For the Josephson junction, the canard window is the exponentially narrow gap between consecutive Shapiro steps.

We study two types of mechanisms of state transitions for vector Kuznetsov-Ma breathers (KMBs) in the coupled Fokas-Lenells framework on unequal backgrounds. The amplitude imbalance breaks spectral reflection symmetry and generates richer breather morphologies. In the degenerate sector, KMBs approaching a non-self-conjugate degeneration curve from opposite sides yield different limiting solitons, revealing a discontinuous KMB-to-soliton transition. In the nondegenerate sector, the background plane waves become frequency matched at a special wavenumber, converting the KMB into a single- or two-soliton state. We determine the exact transition threshold and characterize how nearby solutions vary with the parameter. We further investigate special limiting mechanisms arising on the self-conjugate degeneration curve and on the real spectrum at the state-transition wavenumber. Numerical excitation provides further evidence for these results.

We investigate the quantum interference and energetic phenomena associated with classical caustics in the quantum bouncing ball problem, we refer to as quantum caustics. By considering an initial Gaussian wavepacket, we show that caustics associated with the underlying classical trajectory families are exhibited. We connect the associated phase singularity chains in the vicinity of the caustic with the semiclassical Pearcey function built on the cusp catastrophe lines. We also quantify the amount of superenergy exhibited in these solutions - regions of space where the local energy exceeds the largest constituent energy eigenvalue. We give a complimentary description of the caustic and superenergy behavior using the Madelung/Bohm trajectories, which gives additional insight about the energy of the trajectories and how they traverse the phase singularity chains.

The deformation algorithm based on conservation laws can lift (1+1)-dimensional integrable systems to higher-dimensional counterparts while preserving Lax integrability, yet its generalization to (2+1)-dimensional models has remained an open problem. This paper establishes a unified deformation framework for two (2+1)-dimensional integrable equations: the anisotropic Kadomtsev-Petviashvili (KP) equation and the isotropic Nizhnik-Novikov-Veselov (NNV) equation. By introducing a set of mutually commuting field-dependent deformation operators, we systematically construct infinite families of ($m+3$)-dimensional integrable KP and NNV hierarchies, derive their closed-form Lax pairs, and rigorously verify integrability via the vanishing commutator condition of Lax operators. For each high-dimensional hierarchy, concrete finite-dimensional master systems are obtained by truncating auxiliary spatial variables: a (3+1)-dimensional KP system and a (4+1)-dimensional generalized NNV system. Further symmetry reductions recover the original (2+1)-dimensional KP and NNV equations, and more importantly produce two distinct Harry-Dym (HD)-type reciprocal integrable systems. The KP reduction yields an anisotropic (2+1)-dimensional HD model, while the NNV reduction generates the first spatially isotropic two-space-dimensional HD system reported so far, filling a notable gap in existing literature. Parallel comparison of the KP and NNV branches reveals that the spatial symmetry of the original two-dimensional parent equation directly governs the symmetry properties of its high-dimensional deformations and HD dual subsystems. Our work not only extends the conservation-law deformation conjecture beyond (1+1)-dimensions to accommodate both strong Lax and weak Lax structures, but also provides a universal route to construct reciprocal links for multi-dimensional integrable systems.

This minireview provides a brief summary and a discussion of directions for further development of theoretical and, chiefly, experimental studies of bright solitons in optical couplers, i.e., dual-core waveguides which combine the linear inter-core coupling (tunneling of light between the parallel cores with the intra-core group-velocity dispersion and self-focusing Kerr (cubic) nonlinearity. Following a short introduction to the field, the article focuses on a brief review of relatively recent experimental results for the switching of solitons in dual-core nonlinear optical fibers and the spontaneous emergence of stable asymmetric two-core solitons in the couplers with the symmetric dual-core structure.

A solution procedure is formulated and solved for treating the nonlinear Dissipation Inequality as a constraint equation within continuum mechanics, and allowing for incomplete knowledge of constitutive behavior. The scheme is demonstrated in the context of the rate-dependent, elastoplastic response of a bar, resulting in a nonlinear problem of constrained optimization. Both closed form and computational results are developed. The computational solutions utilize a sequence of convex optimization problems, and are shown to be accurate. In the example considered, the approach is shown to automatically correct an (intentionally) faulty constitutive specification, resulting in the solution to be in accord with the fundamental postulates of continuum mechanics.

Temporal interfaces enable wave manipulation through broken time-translation symmetry, but conventional formulations generally assume that spatial-translation symmetry is preserved across the interface. Here we consider temporal interfaces between periodic media with mismatched spatial symmetries. It is discovered that the reciprocal-lattice vectors of the pre- and post-switching media enter a generalized quasi-momentum-matching condition, giving rise to reciprocal-lattice-assisted wave-vector conversion. We then develop a multichannel temporal-scattering theory and validate it in one- and two-dimensional elastic lattices. A single incident Bloch mode can thereby excite multiple post-interface Bloch modes with distinct wave vectors and frequencies, a response inaccessible at conventional temporal interfaces. These results establish symmetry mismatch as a new degree of freedom for simultaneous control of wave vector and frequency in time-modulated periodic media.

This paper presents a mathematical derivation for three new conserved quantities in the motion of spacecraft on optimal continuous-thrust trajectories in a central gravitational field. The process presented in this paper is rooted in Noether's theorem that connects the point symmetries of a dynamic system with the associated conservation laws of the system. In the approach presented in this paper, the system's Lagrangian is modified to account for the non-conservative control force. Using this generalized Lagrangian, the action functional to be minimized is written. Then, Killing equations are formulated to find the dynamic symmetries for this system. In this paper a process is laid out for how to solve the Killing equations; Noether's theorem is applied to this solution of the Killing equations to write the conserved quantities of the system. Conserved quantities are presented for both the two-dimensional and the three-dimensional trajectories in several different coordinate frames. Numerical simulations and mathematical proofs are used to demonstrate that the computed quantities are conserved.

The conducting bar sliding on rails through a uniform magnetic field is a standard textbook illustration of Faraday's law, almost always solved assuming the magnetic field produced by the induced current is negligible. We extend this classic problem by retaining the self-induced field: modelling the circuit as a rectangular loop of round wire of radius $d$, we compute in closed form its geometry-dependent self-inductance $L(x,l)$ and its gradient $dL/dx$ from the Biot--Savart law, including the flux inside the wire and at the corners. The bar then obeys coupled mechanical--electrical equations of motion containing, besides the familiar braking force $-B_0lI$, the inductance-gradient force $\tfrac{1}{2}I^2\,dL/dx$ familiar from electromagnetic launchers. In the absence of resistance the total energy $\tfrac12Mv^2+\tfrac12LI^2$ is exactly conserved; with resistance the system becomes an electromechanical damped oscillator that, in an appropriate regime, maps onto a series resistor--inductor--capacitor (RLC) circuit with equivalent capacitance $C_{eq}=M/(l^2B_0^2)$, the bar's momentum playing the role of the capacitor charge. Numerical integration of the full equations confirms these analytic approximations in their respective regimes and locates the crossover between over-damped and under-damped behaviour.

Generalised continuum theories couple the macroscopic deformation and the micro-/meso-scopic deformation of an underlying micro-structure. They can account for internal length-scale effects and higher-order mechanical loadings absent from classical Cauchy elasticity and has shown its efficiency in modelling metamaterials. This has led to a proliferation of higher-grade and higher-order models (e.g. strain-gradient, micromorphic, micro-polar) whose underlying kinematic reduction strategies, in particular to reduce the number of material parameters, are rarely identifiable from the free energy alone. It leaves two open issues: the lack of a systematic criterion for selecting an appropriate model, and a persistent ambiguity regarding the physical status of the local frames (''directors of matter'') used in their kinematic description. Are they physical quantities describing the change of state of the given micro-structure or arbitrary kinematic descriptors of its deformation\,? This work addresses both questions through a gauge-theoretic formulation of generalised continua in finite strains. While relying on tools and modelling choices consistent with the existing geometric literature on continuum mechanics, the present approach departs from it in its objectives, aiming at a unifying classification of available mechanical models rather than the description of a specific microstructural phenomenon such as defects. In this work, generalised configurations are defined as moving frames over classical configurations, and invariance with respect to the reference generalised configuration is shown to be a necessary and sufficient condition for a gauge invariance, recovering the micromorphic theory as the general-purpose theory of the deformation of arbitrary directors of matter. A systematic classification of first-order generalised media follows from structural group reduction, while strain-gradient continua are recovered through convected frames, and finally constrained media (e.g. couple-stress) are addressed.

Dissipative equations admit distinct variational descriptions in the Bateman and Caldirola--Kanai (CK) formalisms. The classical correspondence between them is extended to a homogeneous canonical scalar field on a prescribed spatially flat Friedmann--Lemaître--Robertson--Walker (FLRW) background, where the expansion produces the time-dependent damping coefficient $3H(t)$. A multiplier action yields the Klein--Gordon equation and a complementary anti-damped equation containing the term $-3\dot{H}(t)\chi$. A first-order Bateman Lagrangian derived from the same multiplier action reproduces this physical--auxiliary pair for a general potential. Specializing to a free massive field gives the Bateman and doubled CK Lagrangians and Hamiltonians used in the canonical comparison. The factors $a^{3}(t)$ and $a^{-3}(t)$ generate the damped and anti-damped CK sectors, respectively. An explicit time-dependent canonical transformation, generated by a function linear in the Bateman momenta, maps the complete doubled CK system to the Bateman system. For this point transformation, the terms proportional to $\dot{H}(t)$ are required for Hamiltonian equivalence. In rotated variables, the Bateman scalar-field Hamiltonian takes the difference form $H_{B,\mathrm{SF}} = E_{u} - E_{v}$. It is conserved for constant $H$ and generally varies with time otherwise. For the power-law background $a(t) \propto t^{p}$, however, a correlated family at $p = 2/3$ has conserved $H_{B,\mathrm{SF}}$ despite the time dependence of $H(t)$. These results concern classical homogeneous fields on a prescribed FLRW background and exclude the gravitational phase space.

We present a derivation at a level suitable for undergraduates of the Ostrogradsky formalism for Lagrangians in classical mechanics that depend upon an arbitrary number of time derivatives of the configuration. From the boundary term in the first variation of the Lagrangian we derive the Ostrogradsky formulas that define the Hamiltonian formulation of mechanical systems. Worked examples, exercises, and applications to the literature are also provided. An accompanying computer program that implements the formalism is discussed in the Supplementary Materials, and code for computing Hamiltonians via the Ostrogradsky formalism is provided in the Supplementary Materials and in a GitHub repository.

Self-assembly of constituents determines structure formation in the microscopic world. Attractive forces can assemble active particles into colloidal machines, but they do not fix the particles' orientations, which limits control over the machine's function. We demonstrate that non-reciprocal turn-towards torques not only assemble active particles into clusters, without requiring attractive forces, but also link particle orientations to the cluster configuration. Symmetry then dictates whether the cluster is static, rotates, or translates. In small systems, the particle number uniquely determines the stable configuration and function. In larger systems, there are multiple stable configurations with distinct functions, and tuning the torque strength allows us to bias towards the desired function, such as a run-and-tumble motion. Because the interactions driving assembly can be switched on and off, the clusters self-assemble when needed. For such a "just-in-time" self-assembly to be practical, fast assembly is necessary. We show that stochastic resetting, implemented by briefly turning off propulsion and torque, significantly speeds up self-assembly by avoiding slow pathways. Together, our findings demonstrate that non-reciprocal torques can rapidly assemble active particles into colloidal micromachines with controllable function.

Condensates formed by oppositely charged intrinsically disordered proteins provide model systems for understanding how transient electrostatic interactions govern structure and dynamics in biomolecular assemblies. Here we investigate a nearly charge-neutral condensate composed of 50 Prothymosin alpha (ProTalpha) and 40 Histone H1 molecules using a single-bead-per-residue coarse-grained model combining the HPS hydropathy model for disordered regions with a Go model for the globular domain of Histone H1 under NPT conditions at pressures from 2 to 12 bar. We find that chain dimensions, including the radius of gyration (Rg), end-to-end distance (Ree), and their ratio R, are insensitive to pressure, indicating that chain conformations remain largely unchanged over the pressure range studied. Histone H1 exhibits systematically larger values of R than ProTalpha because of its globular-core plus disordered-tail architecture. Translational diffusion coefficients decrease monotonically with pressure, from approximately 0.22 to 0.06 nm^2/ns, with substantial chain-to-chain heterogeneity comparable to the mean diffusion coefficient. Chain relaxation follows a stretched exponential with beta less than 1 that decreases with pressure. ProTalpha relaxation times of approximately 12 to 40 ns obey Rouse scaling, whereas Histone H1 deviates because of the internal constraint imposed by its globular domain. ProTalpha-Histone H1 contact lifetimes of approximately 0.43 to 0.56 ns are much shorter than the Rouse relaxation time, placing the system firmly in the fast-exchange regime where transient electrostatic contacts renormalize chain friction rather than acting as permanent cross-links, consistent with the moderate stretching exponent beta of approximately 0.55 to 0.70 observed across all pressures.

Superselective multivalent binding enables sharp receptor-density discrimination in targeting and sensing, but what its logarithmic response measures microscopically remains unclear. Here, we derive an exact response decomposition of the selectivity into receptor-state reweighting and a direct occupation response. In the dilute quenched Poisson limit, the direct term vanishes and selectivity is exactly the mean receptor excess beneath bound particles, which can be measured at a single density from a sufficiently large co-registered receptor-particle image. Beyond Poisson statistics, the excess is normalized by the Fano factor for a linear count response, while changes in distribution shape require the full count-resolved response. Lattice simulations verify these relations across distinct receptor statistics, while off-lattice simulations show that particle crowding enters through the direct term. These results establish a fluctuation-response framework linking multivalent selectivity to the local receptor fluctuations preferentially sampled by adsorption.

The Poisson-bracket (PB) formalism is widely used to derive dynamics of coarse-grained (CG) fields to capture large-scale physics, extending the role of PBs in classical particle mechanics to macroscopic fields. It has been applied to fluctuations in critical phenomena, hydrodynamics of liquid crystals, liquid crystal elastomers, tissues, and the emergence of odd viscosity from spinning particles. The PB formalism can be formulated in either the Lagrangian framework, using reference space, or the Eulerian framework, using real space. Conventionally, the Lagrangian formulation is used for elastic solids, and the Eulerian one for fluids. However, growing interest in Eulerian descriptions of solids has emerged for phenomena naturally defined in real space, such as viscoelastic responses, moving interfaces, and field-induced structural changes in particles. Here we develop a systematic formulation for applying the Eulerian PB formalism to elastic systems with potentials typically written in Lagrangian space, and clarify its consistency with the Lagrangian counterpart. We show that the Eulerian formulation generates additional nonlinearities absent in the Lagrangian framework. Such nonlinearities originate from CG volume changes under coordinate transformation and from particle flow across neighboring CG volumes. They must be retained when nonlinear effects are important. To illustrate, we study chiral active solids of finite-sized particles, where active torques drive internal particle rotations and generate geometric nonlinearities. These nonlinearities give rise to the odd elastic modulus, which non-reciprocally couples two different shear modes in stress-strain response. By recovering this modulus directly from the Eulerian PB formalism, we demonstrate its ability to capture emergent nonlinear elastic behavior in driven active solids, whose stresses are naturally measured in real space.

Soft microgels are widely used as deformable building blocks for two-dimensional assemblies, yet solid substrates are often treated as passive supports after interfacial deposition. Here, we show that substrate wettability mechanically preconditions soft microgels before drying. Using in-liquid force-volume atomic force microscopy, we find that the same microgels adopt markedly different hydrated shapes and stiffness profiles depending on substrate contact angle: hydrophobic substrates induce spreading, flattening, and internal stiffening, whereas hydrophilic substrates preserve taller, softer microgels with smaller contact areas. These single-microgel states can explain how Langmuir-Blodgett-deposited monolayers respond during drying. On hydrophilic substrates, the observed assemblies are consistent with soft and weakly immobilized microgels rearranging under immersion-capillary forces, producing distinct corona-corona and core-core contact states and an apparent isostructural transition. On hydrophobic substrates, the flattened and stiffened microgels are more strongly immobilized, likely suppressing capillary-driven rearrangements and largely preserving the transferred interfacial assembly structure. These findings establish substrate-controlled microgel mechanics as the missing link between interfacial self-assembly and the final structures observed after transfer and drying.

Understanding how chemically induced surface transport generates fluid motion in confined geometries is essential for the rational design of microscale pumping devices and active microfluidic systems. Here we develop a theoretical framework for chemically driven phoretic flows in a three-dimensional wedge geometry in the diffusion-dominated regime. We formulate both the diffusion and hydrodynamic problems using a Fourier-Kontorovich-Lebedev spectral representation, exploiting the translational invariance and radial structure of the wedge. Green's functions for the concentration field are derived for reflecting and mixed reflecting-absorbing boundaries, reducing to finite image-like sums or closed-form expressions for commensurate wedge angles. The resulting slip velocity is then used to construct the three-dimensional Stokes flow through the Papkovich-Neuber representation, yielding explicit spectral solutions for the velocity field. These results establish a Green's-function framework for phoretic pumping in wedge-shaped confinement and provide analytical benchmarks for numerical simulations of chemically driven transport in confined microfluidic systems.

An octahedral network has been widely used as a fundamental building block for diverse architected materials. Here, we demonstrate that heterogeneous octahedral materials can achieve complete elastic isotropy at a critical constituent volume fraction, nearly independent of the constituent stiffness ratio. The anisotropy ratio, a, transitions from a > 1 to a < 1 at the critical constituent volume fraction, due to a change in the dominant deformation modes. Microstructural analysis reveals that the geometry and connectivity of the heterogeneous octahedral materials are very similar to those of heterogeneous materials constructed on combined simple cubic (SC) and body-centered cubic (BCC) lattices exhibiting opposite elastic anisotropy. More importantly, we demonstrate that varying the constituent volume fractions in the octahedral materials governs elastic anisotropy, similarly to tuning the BCC-to-SC composition ratio in the SC-BCC materials widely employed for designing mechanically isotropic architected materials. The mechanical isotropy of the heterogeneous octahedral materials is further assessed using 3D-printed prototypes.

We develop a model for the diffusiophoresis of a chemically inert, rigid spherical colloid with fixed surface charge in a monovalent weak electrolyte, in which a neutral solute reversibly dissociates into ions. A weak far-field gradient is imposed in the neutral-species concentration. In the fast-reaction limit, local mass action and bulk electroneutrality determine the far-field ionic gradients, while the bulk zero-current condition determines the diffusion-potential gradient. We solve the coupled Nernst-Planck, Poisson and Stokes equations for arbitrary double-layer thickness, linearising in the gradient strength while retaining the nonlinear Poisson-Boltzmann equilibrium. In the Debye-Hückel limit, the mobility consists of one half of the matched fully dissociated response and a finite-double-layer correction due to neutral-ion coupling; the correction vanishes in both the Hückel and Smoluchowski limits. Beyond this limit, numerical solutions for the representative systems reveal a branch-selective response as the surface potential magnitude increases. When the counterion is slower than the co-ion, dissociation-association weakens a retarding concentration-polarisation layer, allowing the mobility to exceed the fully dissociated value. When the counterion is faster, the response remains close to the one-half scaling set by mass action. This reaction-polarisation coupling cannot be reproduced by adjusting only the bulk ionic strength, and hence the Debye length, in a fully dissociated model.

Alignment of anisotropic particles strongly governs the functional properties of printed materials, yet most studies have focused on particle alignment in single evaporating droplets. In droplet- based printing, however, neighboring droplets can coalesce, generating rapid capillary flows that redistribute material and markedly affect the final morphology. Here, we use mesoscale simulations to investigate how droplet coalescence and subsequent evaporation jointly determine alignment and redistribution in sessile droplets with different contact angles and volumes. During the early stages of coalescence, the mean nematic order along the coalescence direction increases for all combinations of contact-angle and volume asymmetries of the droplets. At later times, the mean nematic order either continues to increase or decreases, depending on the droplet geometry. We derive a geometric scaling based on curvature and volume asymmetry and show that the simulation results collapse onto a master curve, identifying an effective geometric asymmetry parameter that governs the mean nematic order at the end of coalescence. During evaporation, the contact angle strongly influences how the coalescence-induced orientational structure is transferred to the final deposit. For small contact angles, the contact line remains pinned for a longer duration, better preserving alignment. In contrast, larger contact angles promote contact-line motion, which weakens alignment, as reflected by a reduced mean nematic order, while simultaneously generating stronger concentration gradients in the final deposit.

Zero-mean forcing can generate directed transport when a medium responds in a spatially structured way and the relevant symmetries are broken. Liquid-vapor interfaces are a useful setting for this problem because surface-tension gradients, wetting dynamics, vapor exchange, capillary and acoustic waves, electro-ionic screening, thermal noise, and boundary compliance can all carry momentum. We develop a conservative continuum model in which the central object is the covariance between a local response field and a zero-mean tangential drive, $\langle Mf\rangle-\langle M\rangle\langle f\rangle$, embedded in an explicit momentum ledger. In a minimal diffuse-interface realization, this covariance gives the phase-selective drift law $U\propto\epsilon_h\Theta\sin\varphi$ for a Marangoni-driven liquid-vapor interface above a structured wall, with exact nulls when the symmetry is restored. Wetting susceptibility then acts as a bounded gain factor: first-order spinodal conditions provide the useful amplification regime, critical wetting saturates because interfacial unbinding removes the short-range drive, and bulk criticality suppresses the channel as the interface disappears. Additional reservoirs - phase change, waves, thermal transport, electro-ionic coupling, compliance, and fluctuations - are treated as compensating channels to be isolated by sign reversals, scaling laws, and budget closure. The result is neither a new microscopic force nor an apparatus-level claim, but a symmetry-constrained accounting scheme for rectified momentum transfer in water-based interfacial systems. Reduced numerical calculations illustrate the phase-selection rules, bounded spinodal gain, momentum-budget closure, transverse chirality, and grid convergence.

The stress analysis of a three-dimensional elastic hollow sphere subjected to uniaxial compression is revisited, employing an elastodynamic framework. Through the application of the Laplace transform, the scalar and vector potentials of displacement are expanded, facilitating a detailed exploration of the system's mechanical behavior. The static solutions for displacement and stress distributions are derived in the long-time limit, which reveal key insights into the response of the elastic hollow sphere. Notably, on the inner surface, certain quantities exhibit a peak at the point where the angle between the compressive force and the point on the surface becomes perpendicular, indicating localized stress concentration. These findings provide a robust analytical approach for understanding and predicting the behavior of elastic hollow spheres under uniaxial loading, with implications for material science and structural engineering.

A new self-sustaining process (SSP) is identified in an oscillating spatially-homogeneous shear flow using a nonlinear Kelvin mode model. This SSP consists of energetic spanwise-invariant 1D `sheets' and weaker spanwise-dependent 2D fluctuations. It is instantaneously 2D, with a time-dependent invariant direction in the flow-cross-shear plane, and has a varicose symmetry. The sheets oscillate in time and are linearly unstable generating fluctuations which then nonlinearly self-interact to reinforce the sheets. The linear instability of the sheet is shown to be due to a lift-up mechanism acting in tandem with `push-forward', which arises due to the `streamwise' shear of the sheets. As the Reynolds number $Re\rightarrow\infty$, both asymptotics and numerics show SSP lower branches with fluctuation velocity $|\boldsymbol{u}'|\sim Re^{-1/2}$. Implications are discussed for oscillatory wall-bounded flows.

We show that the assumption of a stress-free boundary condition at a finite intermediate depth, namely, at the bottom of the Ekman layer, in the analysis of wind-driven ocean flows necessarily leads to an unphysical current profile. Indeed, if the $z$-derivative of the fluid velocity vanishes at a given depth, then this depth necessarily corresponds to a minimum of the velocity profile, with the velocity increasing beneath it. Using a WKB ansatz based on the small variations of the ocean's water density at great depths, we also argue that a no-slip condition at the bottom of the ocean, if sufficiently deep, still effectively implies (up to a very small error) the orthogonality of the Ekman transport and the wind-stress.

We present an analytical model for the nonlinear growth of a single-mode Rayleigh-Taylor instability (RTI) bubble in spherical geometry. The model captures the bubble growth along the polar axis, spanning the linear to nonlinear regimes, for arbitrary Atwood numbers and under both converging- and diverging-gravity configurations. The model predicts that the bubble acceleration approaches an asymptotic value in the nonlinear stage. The spherical geometry is found to enhance the RTI bubble growth relative to planar and cylindrical configurations with the same effective perturbation wavenumber in the converging-gravity cases, whereas it mitigates the bubble growth in the diverging-gravity cases. The model predictions show favorable agreement with direct numerical simulations.

A mass-preserving low-Mach-number framework is proposed for closed-system real-fluid flows governed by general nonlinear equations of state. The formulation enforces consistency between the spatially uniform thermodynamic pressure, the equation of state, and global mass conservation. Moreover, the numerical algorithm employs a segregated strategy in which the thermodynamic state is updated before the momentum equations, and the velocity field is advanced using a pressure-correction method. This approach enables an efficient solution procedure by decoupling the thermodynamic and momentum updates and retaining the use of FFT-based solvers for the pressure correction. The resulting formulation is implemented with second-order spatial accuracy. The implementation is first verified using the method of manufactured solutions, in which the thermodynamic state is prescribed through analytical density and thermodynamic-pressure fields, enabling verification of the nonlinear equation of state, thermodynamic-pressure evolution, and the low-Mach-number divergence constraint. The framework is subsequently validated against benchmark laminar and turbulent flows for both ideal and real fluids, particularly transcritical CO$_2$ channel flow, demonstrating its accuracy and robustness in the presence of strong thermodynamic nonlinearities.

Interfacial instabilities govern the mixing in confined multiphase flows. Yet, the two mechanisms that drive them are usually studied independently: the pressure-gradient-driven Rayleigh--Taylor (RT) instability, which amplifies long-wavelength modes, and the parametrically forced Faraday instability, which selects shorter-wavelength harmonic or subharmonic modes. When an adverse density contrast and vertical vibration act together, the two compete, and neither alone describes the response. We use Floquet analysis to characterize the onset, growth, modal structure, and velocity fields of Faraday--RT waves in a vertically vibrated cylinder, resolved by azimuthal wavenumber, radial (Bessel) mode, and Floquet harmonic. The formulation recovers the classical RT and Faraday limits and reproduces the instability onset at the frequencies measured experimentally. For a free-sliding interface, increasing the vibration amplitude shifts the dominant instability mechanism from RT growth to subharmonic and then harmonic Faraday responses. Lateral confinement can also stabilize individual RT modes, which is not possible in an unbounded domain, although other Faraday modes may remain unstable. Pinning the contact line couples radial modes that otherwise evolve independently, allowing the unstable mode to be a superposition of RT-unstable and Faraday-stable components. This superposition alters the instability mechanism, producing a richer radial pattern. Reconstruction of the unstable modes shows the (linear) velocity fields that imaging cannot access and demonstrates how the instabilities can change the flow more broadly.

Local-in-time well-posedness is established for a recently proposed diffuse interface model describing incompressible two-phase flows. The result constitutes the first analytical study of a model introduced by ten Eikelder et al. for the motion of a binary mixture of macroscopically immiscible, viscous, incompressible fluids with unmatched densities. In contrast to classic diffuse interface models based on a single mean velocity, this model is derived within the framework of mixture theory, assigning each phase its own momentum and mass balance, which results in a system of two coupled Navier--Stokes equations and two mass transport equations. The proof of the well-posedness result uses a fixed-point strategy, where the main difficulty lies in the analysis of the principal part of the associated linearized system.

We present a framework for studying high Rayleigh number turbulent convection to better understand stellar and planetary convection zones. Utilizing the statistical symmetries of the fully developed turbulent state of Boussinesq convection, we identify relevant mean and fluctuating quantities. After validating these symmetry assumptions through numerical simulations, we formulate the governing equations. Vertical profiles of key physical quantities in the saturated turbulent state are explored in the simulations. To develop a modal theory, we use Fourier expansions, review linear theory, and use the Craya-Herring velocity decomposition. The modal equations we derive describe high Rayleigh-number turbulent convection dynamics self-consistently in terms of nonlinear interactions between three mode types: growing gravity modes, decaying gravity modes, and horizontal modes. Energy extracted by the growing modes from the superadiabatic background subsequently follows multiple pathways toward dissipation, enabled by the mode couplings. Among these, the traditionally dominant pathway is the turbulent cascade of the growing modes themselves. Reduced modal equations capture this pathway, precisely describing (i) mutual interactions between growing modes, and (ii) the excitation of decaying and horizontal modes, which are subordinate to the growing modes. Determining the relative efficiency of the pathways requires investigating their modal spectra using numerical simulations and kinetic models.

Three-dimensional (3D) Particle Image Velocimetry (PIV) measures flow velocities by imaging laser-illuminated tracer particles seeded in a fluid, and is widely used in both academia and industry. Many applications require a compact setup for optical accessibility, ideally with a single camera, while also demanding high seeding densities for accurate velocimetry. These requirements, however, are typically incompatible: monocular methods break down at high densities; high-density measurements instead generally rely on multi-camera tomographic systems. Here, we introduce Point-spread-function-Engineering Training-based PIV (PET-PIV), a compact monocular 3D velocimetry approach that resolves this long-standing compactness-density trade-off through a minimal optical modification and deep-learning-based algorithms. PET-PIV requires only the insertion of a single thin phase mask to an otherwise conventional PIV setup, beneath the objective in microscopy or at the lens iris in macro-scale imaging, and calibrates the resulting imaging system in situ, making the approach straightforward to implement and readily scalable. Computationally, PET-PIV operates in two complementary regimes: a tracking/Lagrangian mode that localizes and links individual particles, and, more importantly, a field mode for ultra-high densities which directly reconstructs 3D velocity fields from 2D image sequences. In realistic experimental validations using a tomographic PIV system, PET-PIV demonstrates strong agreement with ground-truth references, with correlation coefficients (CC) exceeding 0.97, alongside an order-of-magnitude improvement in computational speed. Notably, PET-PIV enables monocular 3D macro-scale PIV at densities previously achievable only with multi-camera setups, dramatically expanding the applicability of 3D velocimetry in space-constrained and optically restricted environments.

We study tidal flows in the convective envelopes of rotating, magnetised fluid bodies, such as low-mass stars and giant planets. In well-mixed convective regions, (magneto-)inertial waves are linearly excited by tidal forcing, and their dissipation can dominantly drive spin and orbital evolution in many close star-planet and binary star systems. We perform linear magnetohydrodynamic calculations of wavelike tides in spherical-shell geometry of a tidally-forced, rotating, incompressible, viscous and non-ideal magnetised fluid. Our calculations consider the widest range of magnetic field configurations to date (including both aligned and misaligned dipole fields, free-decay dipole and quadrupole fields, azimuthal "Malkus fields" and mixed poloidal-toroidal "Prendergast fields") to analyse the effects of magnetic fields on the wavelike response and dissipation. We find that the tidal response at a given frequency depends strongly on both magnetic field strength and geometry. Magnetic fields with strong poloidal components modify the flow more efficiently and introduce high-frequency Alfvénic resonances associated with weakly damped eigenmodes. When an enhanced (turbulent) viscosity is adopted, we find that viscous dissipation remains comparable to Ohmic dissipation for strong fields, in contrast to previous studies in which Ohmic dissipation was argued to dominate. We also explore the variation in magnetic effects as the shell thickness, magnetic Prandtl and Ekman numbers are varied. Finally, the frequency-averaged tidal power is found to be largely insensitive to the magnetic field in most cases, though significant deviations are found for free-decay fields. Our results have important implications for the tidal evolution of magnetised, rotating stars and planets.

Motivated by the experimental observation of electronic Poiseuille flow in graphene [J.A. Sulpizio et al. Nature 576, 75 (2019)] we analyze the linear stability of plane-Poiseuille flow of electrons in a two-dimensional material using a modified Orr-Sommerfeld equation. We calculate the critical current needed to make the flow unstable as a function of the experimental parameters and characterize the most favorable situation, that is the one needing the lowest current density, to observe flow instability. We predict the streamwise wavenumber and frequency at which the instability occurs and discuss the difficulties of an experiment aimed at probing this phenomenon.

Machine learning of Hamiltonian dynamics has driven growing interest in Hamiltonian neural networks (HNNs), which encode Hamilton's equations of motion into the learning architecture. Despite this progress, it remains unknown whether such networks can predict dynamical regimes absent from their training data, in particular the broad chaotic sea that emerges beyond the observed parameter interval. We address this question using a parameter-aware random-feature Hamiltonian neural network (RF-HNN). Trained using data from only a small number of control-parameter values at which invariant tori dominate, the RF-HNN predicts autonomous long-time dynamics at unseen parameter values where mixed phase space develops and chaotic regions expand, with no data from that regime used in training or model selection. The method is demonstrated across four two-degree-of-freedom Hamiltonian families, including the Hénon-Heiles system. Using Poincaré-section geometry and finite-time Lyapunov exponents, we show that the RF-HNN reproduces the breakup of regular structures and the emergence and growth of chaotic regions, whereas conventionally trained HNNs with the same Hamiltonian structure remain too regular. These results show that what decides parameter extrapolation is not Hamiltonian structure alone but how the fitted Hamiltonian continues in the control parameter. To our knowledge, this is the first demonstration that a learned Hamiltonian can qualitatively extrapolate from predominantly regular dynamics into a broad chaotic sea absent from training.

The global phase-space organization of non-linear Hamiltonian systems is traditionally visualized using Poincaré sections. However, rigid choices of sectioning hyperplanes often introduce geometric distortions and coordinate artifacts that obscure or clip fundamental invariant structures. Here, we present a multi-mapping analysis of the planar elastic pendulum to systematically overcome these visual and structural limitations. We implement a comparative framework utilizing inverted phase-space mappings that resolve the dense packing of invariant curves near chaotic boundaries, uncovering an apparent separatrix trajectory hidden in standard views. Leveraging the system's vertical symmetry axis, we derive two novel classes of customized canonical transformations that align the sectioning condition with the underlying force field and invariant trajectories, respectively. We demonstrate that the force-line section balances phase-space density representation near equilibrium and exposes a curvature-driven, hexagon-like boundary deformation. Concurrently, the trajectory-aligned section unrolls highly curved invariant manifolds into a regular grid. When combined with inverted mapping, this trajectory-based approach acts as a structural coordinate zoom, minimizing local metric distortions and shifting delicate, higher-order satellite islands directly into the focal center. Our results demonstrate that relying on a single slice is insufficient to capture complex non-linear dynamics; instead, utilizing at least two orthogonal, field-conforming sections provides a superior, distortion-free diagnostic tool for characterizing structural stability, resonance chains, and global transport barriers in multi-degree-of-freedom systems.

Physical systems can process information through their natural dynamics, offering alternatives to conventional digital computing. Reservoir computing offers a basic framework by using a nonlinear substrate to map inputs into rich dynamical states read out by a simple linear layer. Active matter substrates are striking examples; they continuously consume energy and produce entropy. Theoretically, entropy production (EP) can describe the irreversibility and distance from equilibrium. But it remains unclear whether it can track computational capabilities. We address this conceptual gap by analyzing a driven swarm reservoir model. The system EP is computed from phase-space contraction and the bath EP from heat flow, separately, and put in direct association to prediction performance on a Lorenz-63 task. Via force parameter scans, we show that dynamical regimes with the strongest response to a driver as well as dissipation coincide with peak performance. Therein, the dynamical discrepancy between innate (minimal dissipation) and driven transferred heat (maximal dissipation) is sharpest. Generally, driver work and relative differences of driven and undriven EP closely mirror the performance landscape. The system EP, derived from a generalized Liouville-equation estimator, and heat flow provide complementary diagnostics and metrics, which are most robust in the best-performing regime. These results extend prior expectations that dissipation matters for computation by identifying when and how it becomes predictive. They also relate inference power to innate dynamics, pointing to generic principles for physical computing and where EP offers a screening metric for reservoirs and other base substrates.

Resonant tunneling diodes (RTDs) embedded in an electrical circuit are known for their neuron-like response characteristics, which makes them promising candidates for neuromorphic applications. This paper investigates the dynamical response of series-coupled RTDs and systematically analyzes the impact of coupling and inhomogeneities on the solution structure. We further propose a scheme for controlled switching between coexisting stable states which allows to realize tunable memory elements in these circuits. The coupled RTD system exhibits a rich bifurcation structure, showing different degrees of multistability between symmetric and antisymmetric solutions. Limit-cycle branches and their dependence on the system parameters are analyzed using numerical continuation methods. A central focus is placed on the role of symmetry. For two identical RTDs, the system possesses a $\mathbb{Z}_2$ exchange symmetry, which governs the emergence of symmetry-breaking bifurcations and multistable states. The analysis is further generalized to $N$ coupled RTDs, revealing the underlying $S_N$ symmetry structure and its influence on the organization of equilibrium branches, paving the way for neuromorphic network operation.

Phase-field approaches to fracture, initially designed as regularization of the Griffith model of brittle fracture, are now commonly viewed as gradient-damage models whose regularization length becomes a material property driving crack nucleation. One weakness of this approach is that the strength surface cannot be arbitrary: its shape is dictated by the elastic energy, and its magnitude by the regularization length. We focus on the antiplane version of the model introduced by Bourdin, Marigo, Maurini and Zolesi ( arXiv:2506.22558 ), which handles crack propagation along unknown paths and nucleation governed by an arbitrary convex strength surface by degrading the strength instead of the stiffness. It can be interpreted as a regularization of softening plasticity in which localization bands obey an equivalent cohesive law set by the strength domain and the toughness, while the role of the regularization length, when small compared to the elasto-cohesive length, is purely numerical. Strength, stiffness, and toughness thus become independent material data, and limit analysis, perfect plasticity, cohesive fracture, and brittle fracture merge into a single variational framework. We derive closed-form solutions for a simple shear problem, propose a numerical scheme combining alternate minimization and conic programming, and numerically verify the equivalent cohesive law, its independence of the regularization, and the size effect governed by the elasto-cohesive length. A "surfing" simulation highlights the structure of the propagating crack while a re-entrant V-notch is used to show how the model bridges small-scale yielding, cohesive fracture, and brittle fracture without a priori hypotheses.

The second law of thermodynamics still lacks a general proof applicable to both classical and quantum systems across broad ranges of time scales, interactions, and degrees of nonequilibrium. In this paper, we show that when the macrostate-level probability $f$ of an isolated system increases monotonically with the number of possible microstates $\Omega$ (i.e., $\partial f/\partial \Omega > 0$), the second law emerges naturally from the continuity equation of $f$ in phase space; a special case of $\partial f/\partial \Omega > 0$ is Boltzmann's assumption of equal a priori equilibrium probabilities. Based on this finding, the second law can be readily derived for fully chaotic systems. The derivation does not rely on dynamical details, highlighting the statistical nature of entropy increase. In contrast, for a locally nonchaotic system, the positive correlation between $f$ and $\Omega$ may break down (i.e., $\partial f/\partial \Omega \leq 0$). Consequently, the conventional framework of thermodynamics does not apply, and entropy can decrease spontaneously without any energetic penalty.

In this work, voltage-driven translocation of uniformly charged long linear and three-arm star polymers through narrow nanopores is investigated. Langevin dynamics simulation is performed using a coarse-grained model of the polymer and a semi-implicit representation of the nanopore. The mean translocation time of a linear polymer is found to be inversely proportional to the applied voltage over a wide range of voltages. In contrast, the mean translocation time of a three-arm star polymer of the same molecular weight exhibits a pronounced deviation from this scaling relation below a threshold voltage. The threshold voltage is found to be nearly independent of the molecular weight of the polymer, but depends on the size of the nanopore and salt concentration. Metadynamics simulation is used to estimate the free-energy landscape for the translocation of the three-arm star polymer. Below the threshold voltage, the free energy exhibits a pronounced second barrier resulting from an entropic contribution and electrostatic interactions between segments of the trailing arm inside the nanopore. A Fokker-Planck model developed using the estimated free-energy accurately predicts the deviation from the scaling relation below the threshold voltage and shows a remarkable agreement with the Langevin dynamics simulation results using a voltage-independent fitting parameter. The agreement between the theory and the Langevin dynamics simulation results is seen for different nanopore radii, molecular weights of the polymer and salt concentrations studied. A simple extension of the free energy landscape is suggested to predict translocation kinetics for higher molecular weights of the polymer without performing additional computationally expensive simulations.

Macromolecular self-assembly underlies a plethora of biological processes and provides a versatile route for fabricating functional soft materials. The kinetics of self-assembly in solution are inherently stochastic and are fundamentally governed by the interplay of translational and rotational diffusion of the constituent macromolecules. While most computational studies model macromolecules as patchy spherical colloids, thereby neglecting the influence of polymer architecture and internal conformational dynamics, the role of these factors in macromolecular self-assembly kinetics remains poorly understood. Here, we investigate the self-assembly of two patchy macromolecules with different architectures, namely linear chains and star polymers with four and seven arms. The hydrodynamic radii of the macromolecules are chosen to be nearly identical, thereby matching their translational diffusion coefficients and thus isolating the influence of rotational diffusion on the self-assembly process. The binding probability of the patchy macromolecules is found to depend strongly on their internal architecture. Furthermore, reactive path density analysis reveals that self-assembly pathways are influenced by the rotational diffusion coefficient of the individual macromolecules. Overall, this study establishes a bridge between the equilibrium dynamics of macromolecules and their self-assembly kinetics, highlighting the importance of polymer internal architecture in the process of self-assembly.

Dense suspensions of rod-shaped granular particles are widespread in nature and manufacturing, where their fluid mechanical properties are often paramount. We have developed a particle-based simulation that models such suspensions under simple shear flow, providing predictions of the viscosity and microstructure for a given solids volume fraction and particle aspect ratio. The model tracks the trajectories of spherocylindrical rods under the action of short-range frictional contact and hydrodynamic forces, inspired by similar tools that have generated new insight into suspensions of granular spheres. It incorporates new schemes for the computation of lubrication forces between spherocylinders and the dynamic determination of the timestep. For aspect ratios up to 20, the model predicts a viscosity spike at shear start-up, giving way to steady state viscosities that increase systematically with volume fraction and aspect ratio. Likewise, particle alignment increases with volume fraction up to an aspect-ratio-dependent critical point. Our model corroborates the limited experimental rheology data available for suspensions of granular rods, and offers a tool for fundamental exploration of the fluid mechanics, microstructure and rheology of this widespread material.

Ferroelectric nematic liquid crystals combine fluidity with macroscopic polar order. Although the archetypal NF material RM734 exhibits large nonlinear optical coefficients, most known ferroelectric nematics were designed without consideration of optical nonlinearity. Here, we assess whether electronic-structure calculations can be used to identify promising nonlinear optical candidates within known polar liquid-crystal materials. Frequency-dependent molecular hyperpolarisability tensors were calculated using a range of DFT methods and basis sets, then converted to macroscopic d-coefficients using an oriented-gas model with empirical and values. Calculated values were benchmarked against available experimental d33, d15, and d13/d31 coefficients for representative materials. We find that absolute values depend strongly on method and bulk-parameter assumptions, whereas relative trends are more useful for screening. Explicit conformer averaging does not consistently improve agreement with experiment. Applying the best-performing single-conformer protocols to a broader polar liquid-crystal dataset identifies candidate materials with enhanced predicted nonlinear optical response and reveals simple design rules based on donor-acceptor asymmetry, conjugation length, and linker choice.

The Vicsek Model represents a paradigmatic framework for understanding the collective motion of active aligning particles, traditionally assuming isotropic interaction fields. Inspired by biological systems characterized by limited perception and blind spots, we propose a generalized Vicsek model featuring two distinct, non-overlapping angular vision cones. We systematically investigate the non-equilibrium phase behavior of this system by tuning the aperture area ({\alpha}) and the front-back orientation (\b{eta}) of the cones. Our results reveal that restricting the lateral vision area destabilizes global order, shifts the critical noise, and induces highly dense traveling bands. Furthermore, breaking the front-back symmetry introduces non-reciprocal interactions that profoundly alter the emergent spatial structures: forward-biased vision drives strong clustering through "follow the leader" alignment, whereas backward-biased alignment stabilizes an exceptionally homogeneous flocking state with suppressed density fluctuations. Finally, we incorporate short-range volume exclusion, demonstrating that the structural integrity of these novel tightly-clustered phases is highly sensitive to steric interactions. Our work provides new insights into the interplay between non-reciprocal perception, spatial anisotropy, and physical constraints in active matter.

Mechanical energy dissipation in networked materials is relevant for applications from vibration isolation to impact protection, yet identifying optimal dissipative architectures in large disordered truss networks is computationally prohibitive with conventional finite element methods. We develop an efficient graph Laplacian-based spectral framework for viscoelastic truss networks, in which the full continuum dynamics of each rod are retained exactly and the problem size scales with the number of joints rather than element-level discretization points. Using this framework, we investigate how redistributing cross-sectional areas within a network (without changing material composition) controls energy dissipation. We find that random redistribution typically reduces dissipation relative to a uniform baseline, while gradient-based optimization yields nontrivial architectures whose form is governed by the intrinsic attenuation length of the base material. Focusing on driving frequencies near a global resonant mode of the network, we show that the optimal mass distribution decays from the source (driven joint) with the attenuation length scale, and at small attenuation lengths the optimal architecture is independent of the boundary conditions. These results motivate future studies of dissipation length scale based design principles on more complex disordered architectures and provide an efficient computational framework for exploring such structures at scale.

Elasticity often plays a key role in regulating phase separation in physical systems. Recent experiments have shown that elastic effects can be used to control microphase separation in swollen elastomers. Here, microphase separation arises from a mismatch between the characteristic length scales of elastic and thermodynamic interactions. In this first part of a two-part paper, we show that microphase formation in elastomers can be explained using conventional theories of elasticity through a nonlocal thermodynamic-elastic coupling arising from volume conservation. Our theory reproduces the observed dependence of phase transition temperature and domain size on elastomer stiffness in isotropically swollen elastomers. In the companion paper, we investigate the effects of anisotropic swelling and inhomogeneous elastic moduli.

There are three paradoxes in the modern Colloid and Interface Science supported by large bulk of experimental evidence and contradicting classical theoretical models: - Electrokinetics at high ionic strength; - Nanobubbles having life span on scale of days and weeks without any surface stabilization; - Pristine emulsions having life span on scale of days and weeks without any surface stabilization. We overview many dozens of experimental papers by broad spectrum of scientific groups from many countries. We consider this vast experimental data as unambiguous evidence that these phenomena exist. On other hand, classical theoretical models deny such possibility. This contradiction between experiment and theory justifies introduction of new theoretical models. We overview these models. It turns out that there is one common feature between most promising of them -- assumption regarding structured water layer at hydrophobic interface. That is why we combine these three phenomena in this review. There is extensive literature on century old idea of the structured water layer, experimental and theoretical. We overview this literature, which provides convincing support to this hypothesis. We discuss existing theoretical models that incorporate the structured interfacial water layer for the successful explanation of these phenomena in more detail. Theoretical model of electrokinetics at high ionic strength was developed several decades ago. Theoretical model explaining paradoxical longevity of nanobubbles and pristine emulsions by interaction between structured water layer and electric double layer is more recent.

The Mpemba effect, wherein a system prepared farther from equilibrium relaxes faster than one initially closer to equilibrium, has been extensively investigated in a wide range of physical systems. In contrast, its role in biologically relevant non-equilibrium processes remains largely unexplored. Here, we investigate anomalous relaxation in the six-state chemomechanical network model of the Kinesin molecular motor under both equilibrium and non-equilibrium conditions. We first establish the existence of the Mpemba effect in chemical equilibrium and show that many of its qualitative features can be understood from the underlying free-energy landscape. We then examine the effects of mechanical and chemical driving, showing that breaking detailed balance primarily reshapes the Mpemba phase diagram without qualitatively altering the relaxation phenomenology over the physically relevant parameter regime. Finally, we demonstrate that the relaxation of the motor velocity also mirrors the anomalous relaxation of the underlying stochastic dynamics, thereby identifying an experimentally accessible signature of the Mpemba effect. Our results establish molecular motors as a promising baseline for studying anomalous relaxation in living systems and suggest a broader framework for exploring the Mpemba effect in non-equilibrium biochemical networks.

A variable-density thermodynamic extension is developed for the solved-volatility stochastic-fluid formulation of arXiv:2607.25536 . Source-inclusive stochastic transport separates mass, momentum and total-energy conservation into time-evolution partial differential equations and martingale compatibility constraints. Density and temperature are the primitive thermodynamic fields: mass conservation determines density, internal energy determines temperature, and the equation of state determines pressure evolution along stochastic particle paths. The resolved kinetic-energy identity is combined with a finite-correlation reservoir, Green--Kubo calibration, an equilibrium counterterm and adjoint resolved-unresolved exchange. A stochastic Gibbs identity and Gaussian relative entropy yield a conditional entropy-admissibility result for a Hencky-reservoir formulation. Equation-of-state pressure fluctuations are distinguished from mechanical stress impulses; regular finite-Mach fluctuations produce no independent white-noise bulk pressure impulse, while fast mechanical pressure is represented by a causal finite-correlation carrier. Conservative boundary conditions and a calorically perfect ideal-gas specialization are given. In the zero-volatility limit, the classical compressible Navier--Stokes--Fourier equations are recovered. A frozen descriptor analysis identifies a mixed hyperbolic--parabolic drift subsystem coupled to algebraic martingale constraints, with closure-dependent elliptic blocks and a singular low-Mach pressure limit. Canonical calculations verify the pressure carrier, acoustic dispersion, viscous-thermal energy balance and low-Mach scaling. Nonlinear well-posedness, shock admissibility and developed turbulence are not claimed.

In this work, we describe a new preprocessing tool for mesh adaptation on hybrid unstructured meshes with a target application on immersed boundary methods. The tool has as input an unstructured, hybrid, and conforming mesh generated by an external mesh generation software, and the main goal is to refine this mesh around immersed geometries in such a way that the CFD solver using the immersed boundary method can simulate flow problems in an accurate and efficient manner. The input background mesh can be made of different types of elements, like tetrahedra, hexahedra, prisms, and pyramids, which, unlike Cartesian meshes, permit for a more flexible mesh. Hybrid unstructured meshes enable one to use the immersed boundary technology in a new class of flow problems where the full geometry is decomposed into a fixed geometry part and a changing geometry part. A body-fitted mesh is generated for the fixed geometry while for the changing one is used the immersed boundary method. We simulate several flow problems to test the new meshes, including subsonic flow past a cylinder and subsonic flow past an NACA0012 airfoil, both using finite volume and discontinuous Galerkin methods and solving the Navier--Stokes equations. As an industrial example of our mesh generation, we consider the simulation of a multi-element airfoil: in this case, a mesh generation software generates an unstructured conforming background mesh for the slat and main airfoil, while the flap is placed as immersed geometry in this body-fitted mesh. As accurate and efficient results are sought, this mesh is refined around the flap and then the subsonic flow at high-lift flow conditions is simulated with a finite volume method coupled with an immersed boundary method and using the Reynolds--averaged Navier--Stokes equations. The reported numerical simulations are in good agreement with experimental data.

Subgrid-scale (SGS) models for large-eddy simulations (LES) of geophysical turbulence typically need to balance dissipative regularization with backscatter, the upscale transfer of energy from unresolved to resolved scales. Dynamic mixed models (DMMs) combine functional eddy viscosity and structural closures through dynamically estimated coefficients that are least-squares optimal with respect to the Germano identity error (GIE). We show that this classical DMM least-squares estimation can be dominated by the structural component, thereby limiting the functional component's dissipative regularizing role. To address this limitation, we develop a modified Gram-based framework to construct a novel parametric family of fully-coupled, sequential, and fully-decoupled DMMs with tunable structural-functional balance. We evaluate the resulting closures using an idealized forced two-dimensional and $\beta$-plane turbulence framework with the Leith model and the fourth-order nonlinear gradient model. A priori results show that structurally-dominated models achieve strong agreement with the ideal SGS forcing and accurately reproduce local SGS energy exchange, including backscatter. However, in a posteriori tests, structurally dominated models exhibit noise-like artifacts with high-wavenumber spectral deviations, indicating insufficient net dissipation. In contrast, the sequential DMM in which the functional component is determined first and then corrected by the structural component retains much of the a priori structural accuracy while improving the a posteriori vorticity fields, spectra, and domain-averaged diagnostics. Spectral SGS energy and enstrophy-transfer analyses show that this sequential DMM permits backscatter at scales larger than the forcing scale with enhanced dissipation at smaller scales, thereby improving the balance between instantaneous structural fidelity and long-term accuracy.

We study the non-relativistic limit of Gaussian covariant hydrodynamics [1]. We argue that the condition of incompressibility provides additional symmetries matching relativistic hydrodynamics but incompressibility must break down at a ``microscopic`` scale. We then develop the renormalization group equations for average and fluctuations w.r.t. that scale, to understand its effect on flows at intermolecular distances where hydrodynamics gives way to statistical mechanics. The resulting dynamics naturally incorporates spontaneous stochasticity as a macroscopic back reaction of statistical mechanics fluctuations, as well as features reminiscent of anomalous dissipation and ``wild solutions`` as renormalization group counterterms. We frame these considerations into both a phenomenological discussion of the limits of applicability of fluid dynamics, and a discussion of where physics might shed some light on the mathematical issues associated with turbulence.

Direct numerical simulations are carried out for particle-laden flow over the cylinder to investigate preferential clustering of particles in an unbounded vertical channel flow. The flow is examined at Reynolds numbers Re=100 and 200 for varying particle Stokes number, particle loadings and Froude numbers to quantify the combined influence of particle inertia and gravitational settling on particle motion. The unladen flow exhibits the classical vortex shedding pattern observed in flow over bluff bodies at both Reynolds numbers. Reynolds number dependent wake width, wake recovery, and velocity-deficit evolution are observed, characterizing the coherent flow structures that govern particle dynamics. In particle-laden unsteady wake flows, the non-uniform particle distribution leads to formation of coherent voids and clusters, whose shape are directly correlated with background flow dynamics. Gravity modifies particle-fluid interaction, which leads to an increase in slip velocity, weakens vortex-induced particle clustering and promotes them to travel through vortices, resulting in a transition of the void shape from individual leaf-like structure to snake-like void zone and eventually into a nearly vertical void structure. In upstream region infront of the cylinder, inertial particles form a bow-shock-like structure whose extent increases with increase in Stokes number and finite Froude conditions. Voronoi based analysis combined with local Q values is used to investigate effect of gravity and inertia on particle distribution. The dimensionless settling velocity, St/Fr^2, is identified as the governing parameter controlling the evolution of void shape, normalized void cell area and the probability distribution of Voronoi cell areas. The effect of wake dynamics, particle inertia, and gravity is reported to jointly govern preferential clustering in bluff-body wakes.

Shock waves in high-speed compressible flows contain finite-thickness, high-gradient regions where the continuum assumption becomes questionable and translational non-equilibrium arises, including non-Maxwellian micro-velocity distributions. Classical shock stability analyses rely on Navier-Stokes or moment closures and cannot retain bi-modal velocity distributions inside the shock. We develop and apply, for the first time, a kinetic linear stability theory (kLST) for one-dimensional normal shocks by linearizing the Boltzmann-BGK equation about kinetic BE-BGK base flows. Perturbations are posed in reduced distribution functions, with macroscopic fields recovered by velocity-space moments, so the stability operator acts on the VDF rather than a closed continuum system. Verified against compressible Couette eigenvalue benchmarks near continuum, the framework is applied to argon shocks at $M_\infty=1.2$, $3.0$, and $4.0$. At low Mach number, where BE-BGK and Gilbarg-Paolucci profiles nearly coincide, the spectra recover stable continuous branches. At higher Mach number, comparing Maxwellian and non-equilibrium VDF-based eigenspectra shows that kinetic effects shift the spectrum toward less stable regions, so continuum predictions can miss important changes even when macroscopic profiles appear well resolved. For large high-Mach matrices--$O(10^5)$ unknowns and up to billions of nonzeros--we develop a parallel SLEPc/PETSc infrastructure using shift-and-invert Arnoldi with MUMPS LU for moderate sizes and Jacobi-Davidson (JD) with block-Jacobi ILU for the largest systems. Coupled spatial/micro-velocity sparsity causes severe LU fill-in, making direct solvers memory-limited and motivating JD. We compute kLST spectra for an $M_\infty=4.0$ shock with 281088 unknowns, to our knowledge the highest-Mach kinetic linear stability calculation reported for isolated finite-thickness shock layers.

Ensemble-averaged models of polydisperse bubbly flows require statistics of the evolving bubble population. Prior quadrature-based moment formulations close bubble pressure with a polytropic relation that omits heat and mass transfer at the bubble wall. We formulate constant-transfer equations for bubble pressure and vapor mass within a conditional hyperbolic quadrature method. Second-order conditional inversion produces four joint radius--radial-velocity nodes per equilibrium-radius bin. Bubble pressure and vapor mass are advanced at each node. The node values close the ensemble-averaged flow equations without adding mixed pressure or vapor-mass moments to the transported moment set. The model is implemented in MFC. Monte Carlo calculations verify the evolution of quadrature nodes and the mean bubble variables for a harmonically forced population. Bubble-screen calculations quantify closure error as the equilibrium radius is discretized and the initial distributions vary. The constant-transfer calculation does not exhibit the high-frequency pressure oscillations observed with the polytropic closure under the conditions considered. 3D bubble-screen calculations give a 1.5% relative root-mean-square error between the Euler--Euler center pressure and the mean of 40 volume-averaged Euler--Lagrange realizations.

We present a nonhydrostatic ocean model with a horizontally unstructured, C-grid and a moving, generalized vertical coordinate (GVC) designed for the simulation of nonhydrostatic processes in realistic ocean domains. The GVC system can represent any of the well-known z-level, terrain-following, or isopycnal coordinates while also being able to employ hybrid vertical coordinates. In this paper we outline the specific steps needed to incorporate the GVC system into the unstructured, C-grid, nonhydrostatic, z-coordinate SUNTANS model of Fringer et al. (2006). The approach is adapted from the nonhydrostatic, isopycnal-coordinate method of Vitousek and Fringer (2014), yet our model differs from that implementation through the development of a conservative momentum advection scheme and a positivity-preserving layer height scheme for horizontally unstructured grids. We validate the momentum advection implementation with simulations of a turbulent channel flow and demonstrate the advantages of the hybrid vertical coordinate approach over z- or terrain-following coordinates through simulations of internal solitary waves and the associated bottom boundary layer instability.

We develop two parametric data-driven reduced models: a physics-informed neural network (PINN) and a non-intrusive tensorial reduced-order model (TROM), and apply both approaches to the parametrized one-dimensional shallow-water dam-break problem. Both reduced models do not require time integration and learn a direct solution map from space, time, and dam-break parameters to the physical state. We present a detailed comparison for out-of-sample and extrapolated parameter values. In addition, we demonstrate that it is essential to introduce shock-aware collocation to improve the robustness of the PINN model.

Large Language Models (LLMs) have achieved remarkable performance across a wide range of tasks, yet their internal dynamics remain poorly understood. In this work, we apply the tools of nonlinear dynamics and chaos theory to LLMs. By analyzing both text and hidden state trajectories, we demonstrate that LLMs exhibit hallmark signatures of chaos, including strong sensitivity to initial conditions, manifested as intermittent, jump-like divergence of nearby trajectories combined with bounded evolution, with consistent results across different distance metrics. An exact Jacobian analysis of the Transformer's sub-blocks shows that self-attention and the feed-forward network expand and propagate perturbations, while normalization and residual connections counteract this expansion and promote stability. Recurrence plots show structural similarities between LLMs and canonical chaotic systems such as the Lorenz attractor, while dimension analysis reveals fractal structures in the hidden state space, particularly pronounced in the last layers. We propose that the nonlinear coupling induced by attention mechanisms plays a key role in driving this chaotic behavior.

Chimera states, characterized by the coexistence of synchronized and desynchronized dynamics in identical oscillators, are typically studied in systems with pairwise interactions. Whether higher-order interactions alone can generate such symmetry-broken collective states remains unclear. Here, we show that chimera states can arise solely from triadic interactions. Furthermore, exploiting the intrinsic $\pi$-symmetry of the triadic coupling leads to bimodal phase distributions. We construct a bimodal Ott--Antonsen reduction that incorporates an asymmetry parameter via symmetry-breaking initial conditions, thereby achieving an exact low-dimensional description of the macroscopic dynamics. This allows us to derive an analytic condition for the emergence of chimera states and identify a bifurcation to a breathing chimera regime characterized by persistent oscillations. Furthermore, the reduced dynamics can be expressed as a Riccati-type equation, providing a geometric interpretation of the chimera state as a closed periodic orbit in the complex plane. Our results establish purely triadic coupling as a minimal mechanism for chimera formation and provide a tractable framework for studying symmetry-broken collective dynamics in systems dominated by many-body interactions.

It is known that the generalized coupled nonlinear Schroedinger (GCNLS) equations can be reduced to the basic vector nonlinear Schroedinger models through various symmetry reductions. By using such reductions, soliton solutions of several interesting types can be obtained for the GCNLS system. In this paper, we show how the non-degenerate soliton solutions can be derived using one such reduction and analyze the various special features associated with the resulting soliton solutions. We find that the obtained non-degenerate soliton solutions exhibit breathing behavior, characterized by a breathing frequency. We also show that the vector solitons emerging from the reduction undergo elastic collisions with the standard phase shift, similar to the non-degenerate solitons of other coupled nonlinear Schroedinger models. Further, they undergo interesting energysharing collisions when they interact with the already known bright solitons. These collision scenarios are further confirmed by an appropriate asymptotic analysis. We have also analyzed the stability of the obtained vector solitons and found that they are stable against random perturbations. The results presented here enhance the understanding of the nature and dynamics of non-degenerate vector solitons.

We studied the wave patterns in non-locally, repulsively coupled oscillators on a 2D lattice. The repulsive coupling is tuned by the phase delay $\alpha \pi$ and the wave patterns are found in the regime $\alpha \in \left[0.5, 1\right]$. We focused on the growth of orientationally correlated domains and found that the average total boundary size $\overline{|B|}$ obeys an approximate power law $\overline{|B|}\propto t^{-b}$ for $\alpha = 0.8$ and $\alpha =0.9$. In contrast, at $\alpha = 0.7$, the dynamics is disrupted by defect-mediated domain formation and domain splitting. The fitting-window dependence of the apparent exponent $b$, as well as the mean and standard deviation of the wave speed $c$, decreases with increasing $\alpha$, which is consistent with the linear stability analysis of the wave solution.

Modulation instability provides an important framework for understanding rogue wave (RW) formation on continuous backgrounds. However, the formation mechanism and nonlinear spectral structures of RWs in Bose-Einstein condensate (BEC) matter-wave systems with vanishing boundary conditions remain largely unexplored. Here, we employ the nonlinear Fourier transform (NFT), based on the integrable structure of the focusing nonlinear Schrödinger equation and the Zakharov-Shabat scattering problem, to investigate two representative classes of first-order RWs in BEC systems. Through nonlinear spectral analysis and Darboux reconstruction, we demonstrate that both Gaussian-wave-packet-induced extreme localization events and experimentally observed Peregrine solitons are governed by the coherent dynamics of discrete soliton modes encoded in the nonlinear spectrum. For Gaussian initial states, increasing the initial width leads to an increasing number of discrete eigenvalues, resulting in a transition from fundamental solitons and bound states to Christmas-tree-like RW structures. For experimentally observed Peregrine solitons, localized perturbations reshape the discrete spectral configuration and phase evolution, enabling coherent focusing of multiple bound soliton modes. Furthermore, we reveal the spectral mechanism of higher-order RWs and propose an inverse spectral-engineering approach based on discrete-spectrum phase matching. Our results provide a nonlinear spectral perspective for understanding and controlling RW formation in matter-wave systems with vanishing boundary conditions.

We derive and analyze a mean-field theory of the chiral Ising model recently introduced by Wang, Pietzonka, and Jülicher in "Edge Currents Shape Condensates in Chiral Active Matter", arXiv:2603.20064 . Starting from the master equation for clockwise and counterclockwise rotations of 2x2 spin blocks, we first obtain spatially discrete evolution equations for the spatially resolved average magnetization. On this discrete level, we show that a chiral bias strongly affects phase coarsening: domains coarsen anisotropically, develop nearly rectangular shapes, and eventually display chirality-induced arrested coarsening. Taking the continuum limit of these equations yields an active field theory that has the structure of a relaxational Model-B-type dynamics supplemented by a chiral current that permanently drives the system out of equilibrium. The coarse graining explicitly shows how microscopic rotational bias generates tangential currents localized at interfaces. Using this continuum theory, we perform a linear stability analysis of radially symmetric clusters and identify a chiral fingering instability in which angular perturbations of the interface are amplified and eventually lead to radially asymmetric rotating states or disordered states.

Conway's Game of Life shows that simple rules can generate a rich diversity of emerging structures. This cellular automaton has been translated to continuous space by Rafler (2011) in a simulation called SmoothLife. The isotropic rule of this continuous Game of Life generates patterns whose beauty has attracted the attention of a growing community at the intersection of science and computer art. We study a minimal variant of this model, continuous in space and time, that generates cell-like patterns capable of self-replicating, gliding and disappearing. The phenomenology of these unit patterns is reported and related to homogeneous-state bifurcations, symmetry breaking, observed shape instabilities, finite-amplitude morphological changes, and a dilute-to-dense transition associated with cell proliferation. Its mapping onto a large reaction--diffusion system is interpreted in terms of homeostatic concentrations of morphogens, regulated by the nonlinear survival rule and generated through a cell-sourced cascade of auxiliary reactions. Introducing a global conservation law that limits resource availability causes the system to self-organize at this dilute-to-dense transition, which we call the edge of growth. A further exploration of parameter space reveals a variety of phases and the richness of life-like morphologies organized around this edge. Resemblance to biological processes such as division, motility, and death, together with a concise formulation and numerical implementation, makes the continuous Game of Life an appealing model system for investigating the emergence and self-organization of life-like patterns.

Parametric resonance underpins the operation of a wide range of physical systems, from nanomechanical resonators to quantum-information systems and Ising machines. As an archetypal class of driven-dissipative systems, parametric oscillators are generally expected to exhibit a single pair of stable period-two states with opposite phases. This bistable behavior enables both the simulation of spin Hamiltonians and the preparation of superconducting cat states. Whether multiple pairs of such states can coexist in a single oscillator, however, remains an open question. Here, we show experimentally and theoretically that conventional controlled nonlinear friction can induce the coexistence of two distinct pairs of period-two states in a micromechanical oscillator. The friction is implemented via a canonical approach, utilizing a drive-induced resonant coupling that transfers two vibrational quanta from the oscillatory mode to a faster decaying mode. We demonstrate that the onset of multistability is governed by a swallowtail catastrophe and quantitatively map the associated bifurcation structure. Our results broaden the understanding of parametric resonance and establish micro- and nano-mechanical oscillators as a versatile platform for studying catastrophe theory and multistable nonequilibrium dynamics.

350 years from the 1676 announcement of the Roemer's discovery that light propagates with finite speed, we present our observations using eyes with telescopes having similar resolution compared to those in the late 17th century. We confirmed that Roemer's method is valid and gives reasonable values for the speed of light c, within about 10 per cent of the modern value for our measurements, even with the simplest modelling technique, using uniform circular motions. We found that increasing the complexity of the model, e.g., by taking into account the elliptical orbit of Jupiter, does not necessarily bring the results closer to the value of c due to the influence of other perturbations. Using modern ephemerides yields a noticeably accurate result of c=(298200+-1900) km/s. This experience can have great didactic value by showing the interconnections between formulation of hypotheses and the consequent predictions, making observations, reducing data, and searching for alternative explanations for the same phenomenon. Lastly, we also found, in the correspondence between Roemer and Huygens, that Roemer in 1677 searched for an independent confirmation of what he found during previous years observing Io's eclipses by making observations and reducing the data of the meridian transits of the Great Red Spot on Jupiter.

Liquid Crystal elastomers (LCEs) deform anisotropically along a prescribed nematic director field, making them promising candidates for programmable shape change. Existing studies have primarily focused on either director patterns on flat sheets or simple patterns on curved geometries, leaving the case of a non-trivial director on a non-trivial geometry still largely unexplored. Many biological systems, however, have both complex geometries and complex helical fiber architectures. To explore the interplay between director and underlying geometry, we use a non-Euclidean plate theory for nematic elastomers with a through-thickness twisted director to develop an effective 2D model. With a fixed twist angle, our model shows an anomalous coupling between mid-surface curvature and director twist. This emergent term arises from the interplay between orientational order and elasticity, and dominates traditional bending contributions. To illustrate the general theory, we study the stability of cylindrical shapes with through-thickness twist. We find that the cylinder is unstable to a long-wavelength helical flattening mode and determine the critical parameter for the onset of instabilities.

Deployable shape-morphing structures that transform from flat sheets into stable three-dimensional configurations are highly desirable for applications ranging from soft robotics and biomedical devices to adaptive architecture and aerospace systems. Existing kirigami-based morphing systems primarily rely on isotropic deployment, compliant soft materials, or external constraints to maintain deployed shapes, which limits geometric programmability, structural integrity, and applicability in rigid-material systems. Here, we present an inverse design framework for anisotropic bistable kirigami structures that enables programmable shape morphing through controlled geometric frustration and instability-induced deployment. The framework combines a semi-analytical mechanical model with geometry to establish a direct connection between geometric transformation and the underlying energy landscape. We show that instability-induced shape morphing leads to tunable bistability and directional deployment in anisotropic kirigami structures. The results are validated through finite element simulations and experiments, demonstrating stable deployed configurations and programmable anisotropic morphing. The proposed framework further provides a general design strategy that can be integrated with various active actuation systems, enabling broader engineering applications.

Swimming microorganisms often operate in complex confinement, where an interplay of long-ranged hydrodynamic interactions and a short-ranged repulsive interaction can give rise to interesting dynamical behaviors. Here, we theoretically investigate the trajectories of microswimmers - modeled as squirmers - in the presence of periodic boundaries. The latter modify their swimming velocity, leading to behaviors that differ qualitatively from swimming near planar walls. Using a perturbative approach based on bispherical coordinates and the Lorentz reciprocal theorem, we characterize the interaction between a squirmer and a periodic surface in the limit of small surface amplitude and systematically explore its dependence on the boundary corrugation wavelength, squirmer type, orientation, and swimmer-surface distance. Most importantly, our results reveal that pullers become trapped in the valley of the surface corrugations, in contrast to their sliding motion near planar walls. Furthermore, the near-surface dynamics of pushers display oscillations, reflecting the periodicity of the surface structure. A tilt of the swimmer orientation with respect to the surface corrugations results in a wave-length dependent drift that sorts pushers from pullers. These findings highlight the impact of hydrodynamic interactions in shaping microswimmer transport near structured boundaries with potential implications for microbiological phenomena, such as biofilm formation, and technological applications.

Light scattering provides direct access to polymer conformations and thermodynamics. However, trace large-mass scatterers such as aggregates and nanobubbles form unavoidably in polymer solutions and dominate the scattered intensity, obscuring the intrinsic polymer signal. We demonstrate that resolving the static scattering intensity by molecular mobility cleanly separates the polymer and large-scatterer contributions. Applying this mode-resolved analysis to aqueous poly(ethylene glycol) solutions, we isolate the polymer scattering even when these scatterers account for more than 90 % of the total intensity. The resolved polymer intensity recovers the universal osmotic equation of state from the dilute to the semidilute regime over 288 to 358 K. This approach establishes a reliable basis for measuring the thermodynamics of interacting macromolecules in solutions where irreproducible large-mass scatterers have precluded quantitative analysis.

Dipolar magnetic skyrmions can assemble into chains with alternating helicity that act as one-dimensional polymers, yet their statistical mechanics violates the universal harmonic scaling observed in actin, DNA, and microtubules. From first principles, we compute the inter-skyrmion pair potential and find a bi-exponential form of competing interactions with two characteristic decay lengths that encode the distinct microscopic mechanisms of repulsion and attraction. Multiscale simulations reveal a power-law temperature dependence with exponent $1$ in the worm-chain limit of a single bond, and exponent $1/2$ in the three-bond limit. We find that the power-law behavior is remarkably independent of magnetic field strength, and the crossover is due to competing radial interactions responsible for the bonds, resulting in a quartic transverse confinement. We show that the precise form of the competing interactions (e.g., Morse or double-Yukawa) does not affect the temperature dependence.

Topology governs finite-size violations of local electroneutrality in confined electrolytes. Within Poisson-Boltzmann theory, we show that this topological control gives rise to a universal hierarchy of deviations in spherical, cylindrical, and planar confinement. We quantify this effect through an electroneutrality deviation ratio that captures the global electrostatic constraints associated with compactness and boundary multiplicity in the three topological classes corresponding to slit, cylindrical, and spherical cavities. Although local electroneutrality is asymptotically restored in the limit of infinite cavity size, finite-size deviations follow a robust topological hierarchy, being strongest in spherical cavities, weaker in cylindrical confinement, and weakest in planar slits. These results prove that topology is the organizing principle underlying confinement-induced charge redistribution and that violations of local electroneutrality constitute a general electrostatic constraint governing overcharging, charge reversal, and long-range charge correlations. More fundamentally, they demonstrate that changing the topology modifies the global electrostatic constraints without altering the local Poisson-Boltzmann equations. As a counterintuitive manifestation of nonlinear confinement in a point-ion model, we report the existence of inside confinement charge reversal (ICCR) in charged hollow cylindrical and spherical nanoparticles. Since physically consistent, more general electrolyte theories must recover the Poisson-Boltzmann description in the appropriate limiting case, the present results establish a benchmark against which topological effects should be assessed beyond the Poisson-Boltzmann description.

A wide variety of biological functions are driven by feedback between sensing and actuation. A paradigmatic example is cellular navigation. During navigation, the sensory system maps the environmental input signal onto a sensory output, which then drives an actuation response, changing the future sensory input. How the accuracy of this bidirectional information transmission controls navigation is not currently understood. Here, we study how information controls navigation by analytically solving two generic models that describe two major classes of biological navigators: spatial- and temporal-sensing cells. We find that, in the linear-response regime of shallow gradients, navigation performance is fully determined by the strengths and timescales of bidirectional information transmission, without any explicit dependence on the elementary parameters of the navigator. We call these relations Behavioral Equations of State (BESTs): equalities that map information to function in a system-independent way. BESTs predict an experimentally testable data collapse for the performance of navigators with different sensing and actuation parameters. We test the validity of our theory by performing stochastic simulations of chemotaxis of the bacterium Escherichia coli, computing transfer entropies exactly with the TE-PWS algorithm. The observed performance obeys the BEST without fitting or scaling parameters. Thus, our theory identifies bidirectional information transmission between sensing and actuation as an organizing principle for navigation.

The replicated liquid theory provides a microscopic mean-field description of the glass transition by combining the density functional theory of liquids with the replica method originally developed for spin glasses. In the conventional replica liquid theory, a glassy state is described by assuming that particles in different replicas undergo vibrational motion around common centers of mass, thereby forming molecules that contain one particle from every replica. Here we revisit this assumption by allowing each molecule to contain only a subset of replicas. This generalized formulation describes particle-level replica mismatches, which may be associated with non-vibrational motions such as particle hopping. We apply the theory to high-dimensional hard and harmonic spheres, where the mean-field description is expected to become exact. For hard spheres, replica mismatches destabilize the glassy metastable state and shift the dynamical transition to a significantly higher packing fraction, while leaving the leading thermodynamic glass transition unchanged. The resulting transition density agrees, at leading order in high dimensions, with the recent rigorous lower bound for random sphere packings obtained by Campos, Jenssen, Michelen, and Sahasrabudhe by using a discretized version of greedy Random Sequential Absorption, suggesting an algorithmic interpretation of the transition: grandcanonical dynamics is more efficient in high dimensional spaces than canonical one. For harmonic spheres at finite temperature, the glassy state contains a finite replica-mismatch fraction even at the thermodynamic ideal-glass transition, thereby shifting the transition point from that predicted by the conventional replica ansatz.

This work is devoted to the mechanisms of dielectric response and electric conductivity of suspensions consisting of the nematic liquid crystal 5CB with different concentrations (from 0 to 10 wt.%) of ferroelectric BaTiO_3 nanoparticles with an average size of 24 nm. We revealed that the incorporation of nanoparticles influences significantly the dielectric permittivity magnitude and anisotropy, as well as dielectric losses of the suspension. A pronounced temperature dependence of the anisotropic dielectric permittivity of the suspensions was found at lower temperatures corresponding to the mesophase state; but it is also present at higher temperatures corresponding to the isophase. The dependence of the mesophase-isophase transition temperature on the concentration of BaTiO_3 nanoparticles appeared nonmonotonic. With increasing temperature, both the capacitance and the electrical resistance of the pure liquid crystal increase, as well as it increases in the suspensions with small concentration of BaTiO_3 nanoparticles. Due to space charge accumulation in the shells of nanoparticles, larger concentrations of BaTiO_3 nanoparticles influence strongly the ionic transport by promoting the formation of ionic-electronic screening. This effect modifies the dielectric properties and conduction mechanisms of the suspension, leading to the nonmonotonic dependence of the mesophase - isophase transition temperature versus the nanoparticle concentration.

The aerodynamic design of turbomachinery is critical to the performance of the overall energy system, yet it is challenging due to the complex non-linear flow physics and the presence of multiple-target design compromises. Denoising diffusion model, as one of the leading approaches in generative machine learning, has shown its advantages of high design solution accuracy and diversity in many engineering applications. In this study, we bring it to the 3D inverse design problem of turbomachinery, using centrifugal compressors as a classic representative, to demonstrate the new methodology for complex geometry designs. A diffusion model-centred design framework has been developed in this study. By specifying the desired design condition (mass flow rate and rotational speed) and targeted performance (pressure ratio and efficiency), the trained diffusion model returns directly the 3D compressor geometry that satisfies the condition inputs. Compared to traditional deterministic forward design approaches, the proposed method not only generates accurate geometry solutions to inverse design problems, but also enables effective exploration of the entire design space, providing a diverse set of candidate solutions. In addition, this paper presents the first study to directly train on 3D blade geometry coordinates rather than parametrised representations, demonstrating the feasibility of coordinate-based learning while enabling a highly flexible framework applicable to a wide range of designs. The trained diffusion model achieves excellent design capability, with solution accuracy up to 99% and unfeasible designs less than 1%. Furthermore, the solution diversity of the trained diffusion model is also quantitatively verified by means of comparing the distribution of the solution sets generated from the diffusion model and from direct sampling of physical parameters.

Intermittency in turbulence manifests as intense vortices and sharp peaks of dissipation. Causing the breakdown of Kolmogorov's simple self-similar theory, it leads to anomalous scaling, multifractality and so far remains beyond the scope of a complete theoretical description. How intermittent flow structures influence these different measurements is not known quantitatively. With a simple filtering procedure-thresholding vorticity and inverting the Biot-Savart law to generate filtered velocity fields-we show the effects of intermittent flow structures can be disentangled. As extreme vorticity contributions to the velocity field are filtered out, the energy spectrum scaling persists, while the bottleneck is flattened, and structure function scalings tend towards their Kolmogorov values. The approach is more rapid for transverse exponents, revealing the selective importance of intensely swirling flow regions. Similarly, the extent of multifractality reduces as intermittency is filtered, shrinking the range of roughness singularity exponents. The residual fields are curiously more multifractal, but their structure begins to break away from an underlying turbulence skeleton. The effects on vortex stretching and strain self-amplification are quantified. Our work shows that a Biot-Savart approach can selectively remove the effects of intermittency from turbulence, and hence from its scalings.

We address the problem of locating a chemical source in a flow. Based on the duality between the concentration field and Lagrangian tracer trajectories, we interpret concentration detections as evidence of paths connecting the source to the detection points. This Schrödinger bridge formulation between plausible emission positions and detection points leverages the backward propagator of passive tracers to frame source localization as the sampling of candidate emission locations via Langevin dynamics. The associated drift reveals classical chemotaxis and cast-and-surge as complementary behaviors emerging from a single transport-based principle. Applied to olfactory search in two-dimensional turbulence, the proposed backtracking framework outperforms classical strategies across varying wind regimes using a single, Galilean-invariant learned propagator.

Data-driven subgrid-scale closures for large eddy simulation are of significant interest in many engineering and geoscience applications. In this context, several important questions remain about the role of rotational equivariance as an inductive bias for learned tensorial mappings. We investigate whether equivariance improves accuracy, parameter efficiency, and generalization for subgrid-scale modelling at realistic filter ratios. For turbulent channel flow, we compare data-augmented non-equivariant architectures to those with equivariance as an inductive bias. We compare both pointwise and nonlocal versions of these two model classes. All models are evaluated at matched parameter counts across spatiotemporal, anisotropy, and Reynolds number generalization. We show that non-augmented models learn a small degree of equivariance directly from turbulence data, especially when that data is more isotropic. The equivariant nonlocal architecture attains the highest correlation coefficient on every generalization test at approximately half the parameter count of its non-equivariant counterpart, while the pointwise architectures do not improve on the analytical Clark baseline. Additionally, the equivariant model is more data-efficient than a non-equivariant model. The benefit of equivariance grows with the receptive field of the model, indicating that equivariance and nonlocality are both useful for the subgrid-scale closure task at realistic dataset size, parameter counts, and filter size.

We present an experimental investigation of mixing dynamics within a laboratory-scale 3-liter stirred tank reactor (STR) equipped with two Rushton turbines and three baffles. Using time-resolved, four-dimensional particle tracking velocimetry, we successfully capture trajectories of up to 40,000 tracer particles in the full reactor volume despite obstructions by stirrer and baffles, providing unprecedented time-resolved flow and mixing information. From these Lagrangian data, we analyze velocities, accelerations, and spatial dispersion, revealing anisotropic mixing. By utilizing novel network-based analysis methods on the experimental particle trajectories, we identify coherent fluid compartments that exhibit strong internal mixing but weak exchange with neighboring compartments. We uncover five distinct compartments acting as transport barriers, which have a high impact on substrate distribution in chemical and biochemical processes. Our approach thus realizes and extends early thought experiments from Danckwerts and Levenspiel by providing detailed insight into the behavior of single fluid parcels and Lagrangian mixing withing chemical and biochemical reactors, offering a valuable approach for evaluation and optimization of chemical and biochemical processes. The trajectory data are made freely available to serve as an experimental reference for further research.

We study the effect of surfactant adsorption kinetics on water electrolysis performance using Surfynol 465, an ultrafast-kinetics surfactant. High-speed optical diagnostics reveal that Surfynol 465 reduces bubble residence time by an order of magnitude. Compared to the slower surfactant Triton X-100 and the surfactant-free baseline, it also prevents the growth of large bubbles ($>200\ \mu$m). We validated these results on an anion-exchange membrane electrolyzer (AEMEL) test bench. Adding Surfynol 465 to the $1\text{ M KOH}$ electrolyte decreases cell overpotential by 140--150 mV. It nearly triples the current density (from 0.13 to 0.37 A/cm$^2$ at 2 V) and increases average power by 40\% during a week-long test. Furthermore, downstream corrosion analyses reveal a strong alloy-dependent response. The surfactant reduces degradation in stainless steel and brass but accelerates corrosion in carbon steel.

This study considers extracting causally important vortical structures from the extreme vortex gust-airfoil interaction at a chord-based Reynolds number of $5000$. This extraction is achieved by decomposing a given vortical flow snapshot into its informative and residual components based on the contribution to an arbitrary future target variable with convolutional information-theoretic learning. For the current vortex-airfoil interactions that exhibit transient and multiscale flow characteristics, we first examine the important vortical structures with respect to a future lift coefficient. While the vortex cores are primarily highlighted before vortex impingement, the emerging shear layers are additionally captured after the massive separation, which is evident from a comparison to an instantaneous force-element analysis. We further take the scale-dependent energy transfer as a future variable of interest to examine its impact on the extracted informative structures compared to the lift-associated structures. They are distinct from the lift-based structures in the early stage of the gust encounter yet become similar after impingement, revealing an analogy between informative structures across different transient aerodynamic mechanisms. The present data-driven approach selectively extracts the specific important flow structures responsible for the physics of interest, which can support studying a range of transient aerodynamic flows from the causal, data-driven perspective.

Recent experimental observations revealed that clean spherical bubble chains generate a nearly uniform upward liquid flow. The physical origin of this liquid flow, however, remains unclear. Hydrodynamic interactions in aligned bubble chains were therefore investigated using high-accuracy embedded-boundary simulations that resolve the interfacial boundary layer while capturing long-range interactions among multiple clean spherical bubbles. The simulations were used to quantify the evolution of hydrodynamic interactions within bubble chains and to identify the conditions under which bubble-induced liquid flow can be represented by the superposition of isolated-bubble far wakes. Based on these findings, a reduced-order model was developed and applied to experimentally measured bubble trajectories. The model successfully reproduced the nearly uniform upward liquid flow observed in the experiments. To clarify the role of bubble dispersion, the predictions were compared with those for a uniformly dispersed bubble arrangement having the same overall dispersion width. While the uniformly dispersed arrangement produced a center-peaked velocity distribution, only the experimentally observed bubble trajectories reproduced the nearly uniform upward liquid flow. These results demonstrate that the liquid flow is governed not simply by the dispersion width but by the bubble trajectories that establish the spatial distribution of far wakes. The present study provides a physical framework linking hydrodynamic interactions among bubbles, bubble dispersion, and bubble-induced liquid flow, together with a reduced-order model for predicting the liquid flow generated by bubble chains.

We study by means of direct numerical simulations the influence of the dimensionality of convection on flow properties. We call attention to a few general principles from considering in totality the results from 1D, 2D, 3D and 4D. In particular, we explore two practical aspects: (1) The transient time, or the amount of time it takes for the flow to reach the steady state; and (2) possible implications for the so-called ultimate state.

In reciprocating flapping-like motions, wing-wake interaction plays a crucial role in fluid force generation. While this effect's existence has been acknowledged, particularly in explaining discrepancies between measured forces and quasi-steady approximations, fundamental research on the mechanism underlying this interaction and its scaling remains limited. To address this, we investigate the excess drag force, relative to quasi-steady estimates, acting on a flat plate during the reversal phase of a forward and back translational motion. The flow produced by this motion, studied at insect-flight-relevant Reynolds numbers, serves as a simplified analogue to biological flapping. We demonstrate that interaction with pre-existing wake flow indeed generates excess drag. The main parameter governing this interaction is the distance travelled before reversal, which influences both magnitude and temporal dynamics of the peak drag. We link our observations to optimal vortex formation, as the time trace of the additional drag during reversal is qualitatively altered by the detachment of the starting vortex ring: vortex detachment and re-formation lead to two distinct wake-force peaks. Furthermore, as the pre-reversal distance traversed increases, the wake interaction force post-reversal decays more slowly. Flow observations reveal a similar spatial decay of the streamwise velocity in the wake at the moment of reversal, suggesting a direct link. Representing the starting vortex as a point vortex indicates that the wake's spatial scaling, and commensurately the temporal scaling of the wing-wake interaction effect, is primarily governed by the vortex ring position, shape, and circulation. This simplification reveals a dependence on the pre-reversal translation distance that can be described by a combined fourth-root and linear scaling.

Consider a material point in finite dimensions moving under the influence of a potential force according to Newton's laws. Suppose the potential energy function is a generalized well, strictly convex transverse to a smooth submanifold $M$ on which it is minimal. If the potential is steep, one expects the particle will oscillate rapidly about this submanifold and, if the initial displacement is not too great, should approximately move along $M$ as if it were ideally constrained (e.g. geodesic). This expectation is true if the initial conditions are very well prepared but may fail otherwise - additional potential forces determined by how the Hessian of the potential varies along $M$ may be present. The origin of this force is that the transversal motion acts as a simple harmonic oscillator with a slowly varying frequency, which approximately conserves action, not energy. In this work, we regard continuum mechanical systems such as the elastic thread or compressible fluid as material points moving in an infinite dimensional space according to Newton's laws for appropriate potential energy functionals. We show how to arrive at ideally constrained systems such as the inextensible thread and incompressible fluid as a limit of a strong potential force, computing also corrections to the naive predictions when the data is not very well prepared. For example, for the thread we find a resistance to bending emerge from a strong resistance to compression/expansion. For the fluid, the effective incompressible dynamics may be driven by a remnant acoustical wavefield. Both of these emergent features are nonlinear and non-local. Finally, we give examples of some limits for which the naive models robustly hold because the additional force is trivial. These include the homogeneous incompressible Euler, anelastic Euler, as well as the lake and great lake equations.

We construct quantum Turing patterns in Lindblad lattice dynamics and establish a rigorous theory of their nonlinear order and quantum fluctuations. For an explicit completely positive family with finite-range couplings, the first-moment equations undergo a supercritical instability at a nonzero wave number and admit analytic site- and bond-centered commensurate stripe branches. These branches are locally asymptotically stable in their reflection-fixed period-cell spaces, and projected coherent states exhibit extensive Bragg order on every bounded time interval in the semiclassical limit. We prove $O(N^{-1/2})$ convergence of microscopic covariances to a nonautonomous Gaussian Lyapunov flow, transferring strict partial-transpose uncertainty violations to sufficiently large $N$. In the homogeneous Gaussian sector, a single dimensionless ratio controls both the Turing stability determinant and the logarithmic negativity of opposite momenta, relating wavelength selection directly to quantum entanglement. Differential transport shifts the strongest opposite-momentum correlations from the infrared to the selected Turing scale. Numerical continuation and two-dimensional simulations display stripe, spot, and labyrinth morphologies whose Fourier modes and fluctuation spectra concentrate at the same selected wave numbers.

We exhibit a configuration of five point charges in Euclidean space whose electrostatic potential admits at least 24 critical points all of which are non-degenerate. Maxwell's conjecture that the field of \(n\) point charges has at most \((n-1)^2\) critical points which are all non-degenerate is therefore false.

Transport in crowded media is governed by the interplay of multiple physical mechanisms. Quantitatively disentangling their individual and coupled contributions remains a longstanding challenge because the evolving microstructure continuously modifies their relative influence. Here, we develop a physics-guided interpretable machine-learning framework that couples Brownian Cluster Dynamics simulations with surrogate machine-learning models and SHAP-based interpretation to quantitatively disentangle the individual and coupled effects of total volume fraction, explorer fraction, and template bond flexibility on explorer-particle transport. We demonstrate the framework using binary colloidal systems in which explorer particles diffuse through a template network formed by irreversible bonds with tunable flexibility. Structural descriptors, mean-squared displacement, intermediate scattering functions, and displacement distributions reveal that network formation localizes explorer particles through enhanced transient caging. Bond flexibility emerges as an independent regulator of post-network relaxation by promoting local bond rearrangements that facilitate the release of transiently caged particles without altering the irreversible network topology. Although crowding and composition dominate the overall transport response, quantitative attribution reveals how the relative contributions of crowding, composition, and template bond flexibility evolve as the confining environment develops. Beyond establishing bond flexibility as a distinct control parameter for relaxation in heterogeneous colloidal networks, this work provides a general physics-guided interpretable machine-learning framework for quantitatively disentangling coupled physical mechanisms in complex transport phenomena.

Soft elastic solids are highly deformable materials where fracture is driven by the complex coupling of geometric and material nonlinearities. While geometric nonlinearity (GNL) arises kinematically from the intrinsic capacity of solids to undergo large deformations, material nonlinearity stems from the constitutive behavior unique to each class of materials. Because GNL is a universal feature of all highly deformable solids, establishing its standalone impact is a prerequisite for understanding nonlinear fracture. Here, we focus on brittle soft solids to study the role of GNL alone on the near-tip fields of a static crack under mode I plane-strain conditions, providing a canonical baseline for integrating material nonlinearities in future investigations. By utilizing a compressible St. Venant-Kirchhoff material model, we analyze crack behavior under large deformations in the absence of material nonlinearity. We propose a robust postprocessing methodology based on the crack-tip opening displacement (CTOD) profile and derive asymptotic analytical solutions. Our results reveal a distinct near-tip region where the CTOD departs from classical linear elastic predictions, transitioning into a nonlinear regime dictated by Poisson's ratio. Using a matched-asymptotics approach, we define a physical nonlinear length scale $\lambda_\mathrm{nl}$ that bounds this region and scales quadratically with the far-field stress intensity factor $K_I$. We show that GNL acts as an intrinsic strain-stiffening mechanism sufficient to trigger energy partitioning, effectively shielding the crack tip and imparting an apparent toughening. Ultimately, we conclude that the geometrically nonlinear material model serves as a foundational framework for the broader study of nonlinear elastic fracture mechanics.

Vacuoles have been observed in liquid droplets across variety of experimental systems, ranging from biomolecular condensates composed of proteins and RNA, to synthetic coacervates formed by charged polymers or synthetic nanostars. These vacuoles are long-lived domains depleted of droplet material, and their formation is puzzling because the associated increase in interfacial area is thermodynamically unfavorable. Using theory, we show that vacuoles form through a generic mechanism: a local spinodal instability within the droplet. We demonstrate this mechanism in several experimentally relevant scenarios, including temperature quenches and droplets coupled to chemical processes occurring either inside or outside the droplet. Using non-equilibrium thermodynamics, we develop a theoretical framework that identifies the physicochemical conditions controlling whether vacuoles form and how big vacuoles can become. Our results suggest molecular designs and chemical pathways that promote vacuolation, enabling multi-compartment formation with engineered functions such as enhanced surface catalysis and compartment fission.

Using three-point bending, this study investigates surface-crack formation in photo-aged polypropylene (PP) that has a depth-dependent aging gradient. PP undergoes embrittlement under ultraviolet (UV) irradiation, and because the photo-oxidation proceeds inward from the irradiated surface, the embrittlement develops non-uniformly across the specimen thickness. PP specimens were mildly photo-aged by UV irradiation and had not yet developed visible surface cracks. Each specimen was bent in two configurations: with the UV-irradiated ("aged") surface on the tensile side, and with the opposite ("reverse") surface on the tensile side. When the aged surface was on the tensile side, the stress-strain curves exhibited several discrete stress drops, and in-situ side-view observation confirmed that the formation of each new surface crack coincided with a stress drop. In contrast, no clear stress drops were observed when the reverse surface was on the tensile side. These results show that the through-thickness gradient of embrittlement is directly reflected in the bending stress-strain response. Uniaxial tensile testing, the standard method for evaluating mechanical properties, formally assumes a nominally uniform deformation across the cross-section and therefore reflects the spatially averaged response. Three-point bending, by contrast, imposes the largest tensile strain at the specimen surface and thus selectively probes the embrittled surface layer, making it an effective method for detecting the surface embrittlement of photo-aged polymers.

Lipids and liquid crystals provide a useful platform for addressing how molecular-scale organization is translated into mesoscale shape transformation. Variations in hydrocarbon-chain packing can modify interfacial order, anchoring conditions, and elastic stresses, potentially coupling molecular organization to droplet morphology. Here, we investigate the temperature-dependent structural evolution of monoolein-doped 4-octyl-4'-cyanobiphenyl (8CB) droplets dispersed in aqueous phospholipid solutions. Using polarized optical microscopy, we show that the internal monoolein concentration and the external lipid environment jointly regulate phase transitions, thin filamentation, and larger deformations during heating. The droplets undergo coupled smectic-nematic-isotropic transitions, with extended thin filaments observed exclusively in the smectic regime. At the smectic-to-nematic transition, we observe an abrupt and discontinuous onset of droplet shape deformation, revealing a shape-change transition coupled to the bulk mesophase transition. To our knowledge, this is the first report of a discontinuous droplet-shape-change transition coincident with a smectic-to-nematic phase transition. Varying the internal and external lipid contents redirects the reconfiguration pathway between filament-dominated smectic responses and more amorphous nematic shape changes. Interfacial tension measurements further show that stronger reductions in liquid-crystal-aqueous interfacial tension do not necessarily produce filamentation or deformation. Instead, the observed morphodynamics arise from the coupling between bulk elasticity, mesophase structure, and lipid-mediated interfacial organization. These findings establish lipid composition and hydrocarbon-chain architecture as key parameters governing thermally induced shape transformations in liquid crystal droplets.

Sol-gel transitions are ubiquitous in soft matter and biological systems, yet their thresholds are often poorly captured by classical Flory-Stockmayer theory because spatial organization and loop formation are neglected. Here, we combine molecular dynamics simulations with random graph and random geometric graph models to determine the respective roles of topology and geometry in reversible associative polymer solutions. We show that a coordinate-free random graph recovers the mean-field Flory-Stockmayer limit, whereas a random geometric graph quantitatively reproduces the shifted percolation thresholds observed in molecular dynamics simulations when the detection radius is chosen according to the polymer conformational size. This geometric mapping remains quantitatively valid for linear chains with regularly spaced binding sites over a broad range of chain stiffness. At the microscopic level, we identify primary loops formed already in the pre-gel regime as the dominant source of the deviation from mean-field predictions. Near the gel point, the cluster-size statistics obtained from simulations and random geometric graphs are consistent with the universality class of three-dimensional percolation. These results establish random geometric graphs as a minimal predictive framework for describing topological transitions in reversible associative polymer solutions and show that gelation and network formation can be inferred directly from single-chain conformational information.

Dynamic light scattering (DLS) is a versatile technique for probing microscopic dynamics in soft condensed matter. However, applying DLS to supercooled molecular liquids and glasses demands exceptional experimental performance due to weak depolarized scattering, slow relaxation near the glass transition, and the need for quantitative comparison with complementary spectroscopic techniques. In this tutorial we discuss, how a depolarized dynamic light scattering (DDLS) setup can be tailored to meet these challenges. By combining conventional fiber-optical photon correlation spectroscopy, and multispeckle photon correlation imaging with high-frequency DDLS, such a setup allows to capture rotational dynamics across more than 20 orders of magnitude in time. We detail the experimental design required for high signal-to-noise ratios and long-term optical stability, alongside the treatment of coherence and partial heterodyning effects. As we demonstrate, after proper treatment the different detection schemes yield the same electric-field autocorrelation function, enabling the construction of continuous, ultra-broadband DDLS datasets. Furthermore, multispeckle detection enables time-resolved correlation measurements without temporal averaging, extending DDLS to non-equilibrium systems such as aging molecular glasses. This methodology establishes a unified experimental framework for quantitative investigations of equilibrium and non-equilibrium molecular reorientation dynamics over an exceptionally broad time range.

We describe a generalization of the reciprocal theorem for particles suspended in electrolyte solutions and subjected to an electric field that could be either applied or emerged spontaneously. Attention is focused on catalytic colloids that release ions. The power of the generalization is to capture the effect of formation of a secondary cloud around a catalytic particle, which is equivalent to accounting for an excess charge $Q$ of a system. Our results show that the propulsion speed of catalytic particles has an extra contribution proportional to $Q$ and an external field $E_{\infty}$. The derived equation for $Q$ reveals that its sign is defined by the difference in the ion diffusivity and the magnitude is controlled by the average flux of ions from the surface. We demonstrate the application of the generalized theorem to electro- and diffusiophoresis of homogeneously releasing ions passive particles, as well as to a self-propulsion of inhomogeneous active particles (microswimmers). It is shown that whilst in some situations the extra term in the reciprocal theorem vanishes or has a little effect on the particle mobility, in many others it may dramatically change its magnitude, and even sign. In addition, the relevance of our results for microswimmer interactions is discussed briefly.

We present a fast Stokesian dynamics (FSD) framework for the dynamics and rheology of suspensions of rigid aggregates. The method extends the sphere-level formulation of Fiore and Swan (2019) to multi-bead rigid bodies. Rigidity is enforced implicitly through geometric constraints, enabling stable and efficient time integration. We develop a block-triangular factorization preconditioner for the resulting saddle-point system. The approach combines an approximate inverse of the far-field mobility with a block-diagonal approximation of the Schur complement, enabling independent inversion of each aggregate sub-block via LU decomposition. The method is implemented as an open-source plugin for the HOOMD-blue software suite, and validated against benchmark problems, including doublet dynamics in shear flow, pair sedimentation, Brownian diffusion, and suspension rheology across dilute and structured regimes, accurately capturing both deterministic and stochastic behavior. The framework is further validated against experimental rheology of carbon black slurries, explicitly accounting for van der Waals cohesion, Hertzian contact, and tangential friction via enhanced lubrication. The simulations accurately reproduce the shear-thinning and high-shear viscous regimes. The method exhibits favorable GPU scaling for small system sizes, with decreasing runtime per bead prior saturation. A size-dependent Ewald splitting parameter accelerates simulations at low volume fractions, yielding up to an order-of-magnitude speedup compared to constant Ewald splitting. For larger systems, a constant Ewald splitting produces linear scaling with particle number, whereas the size-dependent choice leads to quadratic scaling due to increased far-field cost. Overall, the proposed framework enables accurate and scalable simulation of rigid aggregate suspensions in Stokes flow.

The discovery of ferroelectric nematic phase opened new directions in the field of soft matter chemistry and physics. In this paper, we have modified a previously reported ferroelectric nematogen based on molecular structure with dimethylamino-terminated part. We have prepared two new homologues by prolonging a side chain and investigated the effect of its length on the mesomorphic properties. While previously reported homologues exhibited a direct phase transition from the isotropic (Iso) to the ferroelectric nematic phase (NF), for prolonged alkyl chain there is a narrow nematic phase (N) in between. For new compounds, we have established their mesomorphic and material properties. We have confirmed ferroelectricity of the NF phase by the polarization, SHG signal and permittivity. Finally, we have compared these parameters with respect to the side-chain length and discussed new effects, discovered for prolonged homologues due to the presence of an additional N phase.

In Artificial Colloidal Ice (ACI), paramagnetic colloidal particles are confined in double-well traps and interact via repulsive, isotropic, magnetic dipole-dipole interactions that can be controlled by an external magnetic field. In this paper, we dynamically introduce anisotropic interactions to ACI by rotating the external magnetic field, which, in equilibrium, makes the system go from a charge-free 2-in, 2-out ice rule state, to a charged 4-in, 4-out state. We observe a strong dependence of the final configuration on the field's rotation rate $\omega$: at high angular velocity, the system achieves a defect free final state via a difussionless transformation from the initial ground state. However, counterintuitively, at slow rotation rates, ergodicity breaks down, trapping the system in a partially ordered metastable state.

Motivated by experiments on light-patterned, quasi-2D active suspensions that exhibit large density variations, we develop a continuum theory of compressible active nematics--suspensions of apolar rods whose orientation is invariant under pi rotations. Under spatially patterned activity, the extensile isotropic active pressure expels material from high-activity regions and accumulates it in low-activity ones; an exactly solvable 1D reduction shows that the resulting density contrast is governed by a single dimensionless parameter, linear in the compressibility. Using compressibility as a tuning knob, we then steer active turbulence from high- to low-activity regions and, at sharp activity interfaces, stabilize an analytically tractable dynamical steady state: a one-dimensional chain of vortices held by soft, activity-induced confinement. Our results establish compressibility as a control parameter for density variations and turbulent flow in active nematic suspensions.

The variational approach based on the Bogoliubov inequality using the fluid of hard spheres as a reference system is implemented to evaluate instantaneous shear, bulk and longitudinal elastic moduli, as well as related sound velocities of Yukawa fluids. The remarkable accuracy of this method is documented. In addition, we evaluate the adiabatic sound velocity from an appropriate equation of state and discuss its relation to the longitudinal and bulk sound velocities obtained from the corresponding instantaneous elastic moduli. The transition between weakly coupled and strongly coupled regimes is analyzed in detail.

The excess energy, entropy, and pressure of a strongly coupled Yukawa fluid are calculated from the variational approach using the fluid of hard spheres as a reference system. As in the case of the one-component plasma, the Percus-Yevick virial entropy is appropriate for such calculations and delivers remarkable agreement with available results from molecular dynamics simulations. The agreement with the molecular-dynamics results is particularly impressive in the strongly coupled regime, making this approach a useful predictive tool when numerical data are scarce or not yet available. As an application of the variational approach, we estimate the location of the melting curve in the regime of sufficiently strong screening.

Topological classification of physical vector fields conventionally relies on field normalization and homotopy-based invariants. However, when field amplitudes vanish, normalization becomes ill-defined, preventing a direct topological characterization. Here, we introduce a general framework for the topological classification of non-normalizable $n$-dimensional vector fields with compactifiable base spaces by transforming them into $(n+1)$-dimensional normalized vector fields. This construction extends homotopy-based classification to fields containing amplitude zeros. We explicitly demonstrate the approach for one-, two-, and three-dimensional non-normalized vector fields and derive the corresponding topological invariants. The resulting topological charges are robust under continuous deformations and can change only when the embedding structure becomes singular. Our framework provides a unified route to the topological characterization of non-normalizable fields and opens the door to the study of topological phenomena in a broad range of systems, including magnetic textures, ferroelectrics, electromagnetic fields, and wave systems.

We investigate the non-equilibrium Casimir pressure in an isothermal binary liquid mixture maintained in a spatially constant and stationary concentration gradient parallel to gravity and confined within a three-dimensional slab of thickness $L$, bounded by two infinite plates parallel to both the gravitational field and the imposed gradient. We assume that the liquid mixture, under the same non-equilibrium conditions, occupies both the interior and the exterior of the slab. Using fluctuating hydrodynamics, we show that the resulting finite-size excess pressure on the plates is described by a scaling function of the dimensionless variable $k_{\mathrm{RO}}L$, where $k_{\mathrm{RO}}$ is the gravity-induced roll-off wavevector. At large separations, this Casimir pressure decays as $1/(k_{\mathrm{RO}}L)$. Depending on the thermodynamic properties of the mixture, the corresponding force can be either attractive or repulsive, while it vanishes for ideal solutions. Since the mixture is assumed to be far from its consolute critical point, the Casimir pressure investigated here is entirely of non-equilibrium origin and it vanishes in the absence of the imposed concentration gradient. Finally, we propose an experimental setup where this force might be measured, consisting of two optically trapped colloidal particles immersed in a dense aqueous colloidal suspension diffusing into an overlying layer of pure water, estimating the expected magnitude of the resulting force.

Most stochastic closures prescribe a covariance tensor, a noise basis or an eddy-viscosity field. This paper develops a different framework in which the displacement-volatility field is solved together with the resolved velocity. The starting point is a one-channel Itô configuration map. A local matrix-logarithm expansion gives distinct material and spatial Hencky increments, their quadratic-variation drifts and the exact pathwise volume constraint. Under constant density, one Brownian channel, pathwise isochoricity and no independent martingale in the resolved Eulerian drift, the material pull-back momentum equation is shown to be the on-shell form of the full stochastic Reynolds transport balance when the momentum-source covariation is retained. The resulting velocity--volatility--pressure system has an index-one differential--algebraic structure. Virtual power fixes the mechanical type of the stress impulse and separates work from quadratic covariation. A finite-correlation precursor then gives a Green--Kubo realisation of the solved displacement covariance. State dependence adds a Lyapunov noise-induced drift, while dynamic boundaries add reaction work and active/passive covariance compatibility conditions. The analysis also gives four limits: a non-zero Brownian transport limit cannot retain finite ordinary unresolved kinetic energy; total energy alone does not fix entropy production; wall tangency limits covariance rank rather than the number of stochastic modes; and a homogeneous decoupled Helmholtz--Stokes equation has only the trivial periodic solution. The result is a theory-complete, testable closure architecture. Developed turbulent statistics, logarithmic wall scaling and computational-fluid-dynamics validation are deliberately left to the expanded fluid-mechanics study.

We propose a universal diffuse-interface modeling framework for surfactant transport in two-phase flows, applicable to all solubility scenarios and to any conservative phase field method. The foundation of our framework is a general three-scalar non-equilibrium model governing the surfactant concentrations in each bulk phase and at the interface, which builds on our prior consistent scalar transport framework and is locally and globally conservative, leakage-free, Galilean-invariant, and reduction-consistent. Assuming thermochemical equilibrium, we derive two one-scalar models: one for a surfactant in full equilibrium between both bulk phases and the interface, and one for a surfactant confined to a single bulk phase and the interface. All models are coupled to the Navier-Stokes equations through a surface tension force that incorporates the Marangoni stress arising from non-uniform interfacial surfactant distributions. While diffuse-interface surfactant models have been developed for the Cahn-Hilliard equation and, more recently, for the conservative Allen-Cahn (CAC) equation, existing models for CAC address only the insoluble and single-phase-soluble cases, leaving the general scenario of partial solubility in both bulk phases unaddressed; furthermore, these models lack Galilean invariance and reduction consistency, and are not applicable beyond the CAC setting. The framework is validated against analytical solutions in one-dimensional transport tests, assessed for convergence in two-dimensional advection-diffusion simulations, and demonstrated in fully-coupled drop-in-shear flow simulations covering insoluble, soluble, and partially-soluble surfactant scenarios.

In this work we propose a local geometric wetting boundary condition for a conservative Allen--Cahn-based lattice Boltzmann framework. The prescribed contact angle is imposed through ghost phase-field values constructed from a locally reconstructed wall normal and a donor-fluid extrapolation. The ghost-node wetting update is local, geometrically consistent, and compatible with thread-safe large-scale implementations, while phase-field mass is controlled through a separate global volume correction. Validation includes static contact-angle tests, short-time droplet spreading, impact on a hydrophobic surface, and gravity-driven motion through a sharp-edged orifice. The simulations recover the imposed equilibrium angles, reproduce contact-angle-dependent spreading exponents between approximately 1/2 and 1/4, and follow the classical W e1/4 maximum-deformation scaling. The model also captures the transition between capture, release, and release with breakup. The proposed approach provides an accurate and scalable framework for wetting-controlled flows in complex geometries.

Air entrainment often plays a crucial role in determining impact loads exerted by free-surface wave flows interacting with structures, yet its modelling is often oversimplified in numerical approaches. In this study a two-phase numerical model, based on the Lattice Boltzmann Method coupled to a conservative Allen--Cahn interface-capturing equation is employed to perform direct numerical simulations of dam-break waves propagating over a dry bed and impacting on vertical walls. Access to high-resolution simulations enables a detailed assessment of how accurately resolving both air--water and solid--water interfaces affects local and overall dynamics, as well as quantities of extreme engineering interest. Indeed, the magnitudes and locations of the pressure peaks are strongly affected by wave front deflection and local aeration induced by a small corner vortex. Additionally, comparisons between no-slip and free-slip implementations suggest that the large air cavity formation, commonly observed as trapped inside the reflected jet falling back onto the incoming flow, may be the result of modeling assumptions rather than intrinsic flow physics, again highlighting the key role of near-wall shear in jet breakup dynamics.

This study investigates dilute bubbly decaying homogeneous isotropic turbulence at high Reynolds number using theory, direct numerical simulation, and experiments. The turbulent kinetic energy and dissipation rate follow power-law decay, while the bubble population reorganizes relative to the evolving Hinze scale. When the dissipation decays sufficiently rapidly, the Hinze scale grows faster than the characteristic bubble diameter, driving the population from super-Hinze toward sub-Hinze sizes. The system passes through a mixed regime in which coalescence dominates but breakup remains active, followed by a pure-coalescence regime. Residual breakup in the mixed regime increases the number of small bubbles and enhances coalescence, leading to faster growth of the characteristic bubble size. DNS of dilute bubble-laden turbulence shows decay exponents close to single-phase turbulence and a bubble-size distribution that shifts toward smaller diameter relative to the Hinze scale. Before the transition, the distribution exhibits two power-law ranges associated with capillary effects and inertial breakup; after the transition, it approaches a single capillary-dominated scaling. Theory and DNS predict distinct growth laws for bubble diameter in the mixed and pure-coalescence regimes, together with corresponding scalings for number density, interfacial area, and coalescence rate. These predictions are further assessed in a spatially developing pump-driven bubbly duct flow at higher Reynolds number. Despite confinement, inhomogeneity, and wall production, the measured trends agree with the theoretical and DNS-based scalings. The results identify Hinze-scale drift as the organizing mechanism for bubble interactions in both idealized and practical decaying turbulent flows, and provide guidance for population-balance and interfacial-area-transport models.

Hele-Shaw flows with an interface are known to give rise to complex pattern formation, whereby the Saffman-Taylor instability triggers a viscous fingering process accompanied by tip splitting and branching. The most popular of these experiments involves a radial configuration with a less viscous fluid injected into a more viscous fluid. In an attempt to characterize the resulting complexity in such an experiment, Beeson-Jones and Woods (2019) have proposed a type of simple empirical model that aims to predict the saturation profile of the invading fingers as a function of a radial coordinate. We revisit the proposed saturation model and test its validity over a broad parameter range using fully nonlinear numerical simulations computed with a level set method. We find that the saturation model is very effective at predicting some near-universal properties of the viscous fingering patterns for one-phase flows, where the invading fluid is neglected, with a sufficiently small surface tension parameter. For larger values of this parameter and for two-phase flows, there are discrepancies between the model and our observations. We explain these differences by studying the morphology of the advancing fingers, including pinching at the base and the rate of tip splitting. Overall, our study shows that the Beeson-Jones-Woods saturation model serves as a valid description of DLA-like patterns, but is not universal over two-phase flows, where surface tension and viscosity ratio substantially alter finger morphology and the resulting saturation profile.

The von Kármán turbulent swirling flow exhibits intriguing large-scale metastable dynamics, including low-frequency state switching. The study of state switching demands long-duration high-fidelity simulations at high Reynolds numbers that capture the flow generated by the impellers. Blade-resolved Large Eddy Simulations (LES) are computationally prohibitive, limiting access to these slow dynamics. Here, we develop a model for the action of the impellers on the flow using experimental data from Particle Image Velocimetry (PIV) and torque measurements of the von Kármán flow. The impeller-region velocity is parametrized via B-splines and coupled to the LES through momentum forcing. An initial set of B-spline coefficients is inferred using the Optimizing a DIscrete Loss (ODIL) framework constrained by the Reynolds-Averaged Navier-Stokes (RANS) equations, PIV measurements in the optically accessible portion of the device, and impeller torque measurements. The coefficients are then refined by the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), which minimizes the discrepancy between the LES time-averaged velocity and torque and their experimental counterparts. Using the data-driven impeller model, we perform long-duration LES of the von Kármán flow. We find that the simulation reproduces the mean flow in the bulk and displays metastable state-switching dynamics. We further show that these metastable states are not axisymmetric and consist of an alternating four-cell flow pattern that slowly rotates around the axis of the cylindrical vessel. The proposed approach provides a practical and computationally efficient route to investigating large-scale dynamics in impeller-driven turbulent flows.

Wind-power variability is a major challenge for the reliable integration of utility-scale wind energy into modern power systems. Although wind-speed statistics are often described by simple parametric distributions, translating these statistics into turbine-level power fluctuations is nontrivial because the relationship between wind speed and power is highly nonlinear and changes across different turbine operating regimes. Here, we develop a two-regime statistical framework for wind-power distributions. In the aerodynamic operating regime, between the cut-in and rated speeds, the turbine power follows an approximate cubic dependence on wind speed. Starting from a physically motivated Rician model for the wind-speed magnitude, we derive an analytical expression for the corresponding wind-power distribution using a nonlinear change of variables. In the control-dominated near-rated regime, where active blade-pitch and generator control regulate the turbine output, the aerodynamic transformation is no longer applicable. Instead, we characterize the power deficit relative to the rated power and show empirically that its continuous tail is well described by a bounded stretched-exponential distribution for both individual turbines and wind-farm ensembles. These results provide a physically interpretable statistical description of wind-power fluctuations across the full operational range of utility-scale wind turbines.

The statistics of atmospheric wind variations are commonly modeled using Gaussian or Weibull forms, which often trade physical interpretability against statistical accuracy, especially in the distribution tails. Here we derive a Rician distribution for wind speed from a simple physical model based on two orthogonal Gaussian velocity components with a non-zero mean in the preferred direction. Using wind-speed records from four geographically distinct wind farms, we show that the Rician model consistently outperforms the Gaussian model and remains competitive with the Weibull model. The same behavior persists when the data are partitioned into monthly windows, where the Rician parameters also provide a transparent description of seasonal and geographic variability, compared to Weibull parameters. In addition, the model naturally connects Gaussian-like and Weibull-like regimes through the Rician parameter ratio $\mu/\sigma$, making the Rician distribution a compact and physically interpretable two-parameter model for wind-speed statistics.

Deep-sea observations are reported of horizontal waterflow differences with typical amplitudes of 0.02 m s-1 over 50-m small scales so that relative vorticity reaches values of the inertial frequency f. The timeseries observations are made using a complex mooring system deployed in the 2500-m deep Mediterranean Sea, where vertical density stratification is extremely weak, with buoyancy frequency O(f), and the slow waterflow with total speeds <0.07 m s-1 is dominated by inertial internal waves and sub-mesoscale eddies. Horizontal waterflow differences increase when polarization, i.e. direction of traversal of elliptic oscillatory motion, switches sign. Common anticyclonic polarization of inertial motions is predominantly found under near-homogeneous conditions. It alternates with uncommon cyclonic polarization under stratified-water conditions, varyingly over 50-m distances. The alternation is in line with predictions from non-traditional inertio-gravity wave theory, but only when relatively strong turbulent convection causes local reduced stratification, as observed.

Coastal Louisiana is sinking, amplifying flooding and land loss, yet the seasonal component of this motion remains difficult to attribute. Satellite geodetic records from Baton Rouge spanning 2004-2024 reveal long-term subsidence of -2.69 +/- 0.69 mm/yr, with a superimposed annual oscillation of 10-15 mm that is in phase with river stage and confined-aquifer hydraulic head. This positive correlation is diagnostic of poroelastic deformation rather than surface loading. A poroelastic model of a semi-confined aquifer driven by hydraulic-head variations reproduces both the long-term and seasonal signals. The seasonal amplitude decreases logarithmically with distance from the intersection of the Baton Rouge Fault and the Mississippi River, as expected for radial pressure diffusion from a flux source. Fault-river intersections therefore act as seasonal conduits into deep aquifers, representing an underappreciated control on coastal land motion that is likely to strengthen as hydrological extremes intensify.

Curvature effects are expected to smooth flame-front wrinkles and thereby reduce turbulent flame speed. We construct a smooth three-dimensional periodic shear flow for which introducing Markstein curvature diffusivity instead increases the effective flame speed predicted by the level-set G-equation. This gives the first counterexample, within this model, to monotone slowdown under curvature smoothing and contrasts with the rigorous monotonicity result for two-dimensional shear flows. The example reveals a genuinely multidimensional mechanism in which local curvature smoothing can enhance, rather than suppress, large-scale front propagation.

We report the experimental realization of minimal chimera states in a system of three uncoupled oscillators driven solely by frequency-modulated forcing. Unlike conventional scenarios where chimera states emerge due to interactions among oscillators, here the coexistence of coherent and incoherent dynamics arises entirely from a common external modulation of a system parameter. By tuning the modulation amplitude and frequency, the system exhibits transitions between global synchronization, global incoherence, and minimal chimera states. The stability of these regimes is quantified using the maximal Lyapunov exponent, while a synchronization order parameter is employed to characterize the degree of coherence. A systematic exploration of the parameter space reveals well-defined regions associated with distinct dynamical behaviors. To provide analytical understanding, we employ a phase-reduction approach and derive the corresponding phase dynamics, which elucidate the mechanisms underlying phase locking and desynchronization. The robustness of the proposed mechanism is further demonstrated in a time-delayed chaotic system. Finally, experimental results obtained from an electronic circuit realization confirm the emergence of minimal chimera states under frequency-modulated driving. These findings establish external modulation as a viable route to chimera formation without coupling, offering a new perspective on collective dynamics in driven nonlinear systems.

We consider a harmonically forced linear impact oscillator, where impact events are instantaneous with energy loss. We study the dynamics at the grazing bifurcation of the non-impacting periodic solution in the limit that the damping coefficient of the oscillator is zero. Through numerical computations we show that a recurring sequence of bifurcations exists between points of resonance. Specifically, resonance creates a stable periodic solution that subsequently loses stability in a secondary grazing bifurcation, then regains stability in a saddle-node bifurcation, then transitions to a chaotic attractor through a period-doubling cascade. The dynamics persist under mild parameter variation, so apply to weakly-damped impact oscillators near grazing.

We investigate the properties of the largest eigenvalue of correlation matrices within the framework of Wishart ensembles. In this work, we propose the largest eigenvalue as an effective empirical order parameter for detecting phase transitions in chaotic and spin systems, drawing an analogy between its derivatives and thermodynamic response functions derived from the free energy, however not necessarily linked to a critical divergence originally observed in the context of phase transitions theory.

In the present work, we explore the self-focusing and resulting collapse of two-dimensional waveforms involving multiple pulses in a nonlinear Schroedinger equation with a general power-law nonlinearity. We find that a wide range of multi-peaked states bifurcate from the critical threshold of the cubic nonlinearity, thus representing ``bifurcations from infinity'', i.e., the relevant pulses start at infinite distance in the critical limit and draw nearer, as the nonlinearity exponent increases past that threshold. We identify the resulting ``interacting particle system'' as amounting to a force balance between the exponentially interacting tails (modulated by a suitable power law) and a linear phase-induced force. The equilibria emerging from this force balance are found to be in excellent agreement with the identified steady states of the partial differential equation. The spectral stability of multi-peaked configurations is analyzed, leading to the conclusion that all the relevant states are less stable than the single-peak collapsing solution whose stability was analyzed earlier. Indeed, we reveal both symmetry-breaking, as well as motion-inducing destabilizing dynamics, with the former ones among them being dominant and ultimately leading to a single dominant collapse spot. Moreover, we characterize systematically both the real and imaginary eigenvalues of multi-peaked configurations, partitioning them in groups of different sizes, described by powers of the solution's blowup rate G.

Despite the variability in gene regulation and environmental conditions, development of an organism occurs through a sequence of highly coordinated patterning processes. Cells integrate different signals to accurately infer their position in order to adopt an appropriate identity. Using a model of epigenetic landscape originally proposed by Waddington to describe cell-fate determination, we establish the critical role played by juxtacrine signaling between cells in determining tissue patterns. Subsequently we systematically coarse-grain the model at the tissue scale to map its patterning to transition between states in a binary spin model having a free energy landscape. We show that such landscapes serve as a powerful unifying framework for describing development of biological systems across distinct spatio-temporal scales.

This work develops well-posed homogenized strain-gradient models for linear elastostatics and elastodynamics in periodic media, with a primary focus on elastic wave propagation. Using the classical two-scale asymptotic expansion method, we carry out second-order periodic homogenization for media in $\mathbb{R}^d$ ($d = 2, 3$), with no restriction on the periodicity cell geometry or material distribution. Reciprocity identities applied to suitably chosen pairs of cell solutions provide alternative expressions for the effective stiffness and inertia tensors arising at the leading, first and second orders, substantially reducing the number of cell problems that must actually be solved. Since direct two-scale homogenization beyond leading order generically yields ill-posed effective operators, a Boussinesq-trick procedure is introduced, involving a tunable scalar weight, to recast the resulting fourth-order partial differential equation as a valid strain-gradient elasticity (SGE) model possessing the requisite symmetry, sign-definiteness and coercivity properties. These properties are then used, via the Hille-Yosida theorem, to establish the well-posedness of the corresponding transient initial-value and forced-response problems. Several practically relevant special cases are examined, including centrosymmetric cells, homogeneous mass density and homogeneous elasticity, each yielding simplified model structures. Numerical illustrations on three two-dimensional periodicity cells (square, hexagonal and a non-centrosymmetric chiral lattice) compare the resulting dispersion relations against reference Floquet-Bloch computations and assess transient wave propagation, demonstrating the model's capacity to capture anisotropic and dispersive effects beyond classical elasticity while preserving mathematical well-posedness.

We reconsider the analysis of the Classical Painlevé Problem developed by F. Génot and B. Brogliato ([1] New results on Painlevé paradoxes. - European Journal of Mechanics-A/Solids, 18(4):653{677, 1999), focusing on the consistency of their results with Galilean invariance. We show that certain conclusions concerning the dynamical evolution of the mechanical system are not invariant under changes of Galilean observer and therefore cannot, in their present form, be interpreted as intrinsic properties of the system. In particular, we show that the classi?cation of motion states depends on the observer through the velocity{dependent characterization of the frictional constraint, and we trace the origin of this dependence to the Galilean velocity-addition theorem. We present and discuss possible reformulations of the model aimed at restoring observer-invariant descriptions of the problem.

We develop from first principles the hydrodynamics of a two-dimensional chiral fluid, i.e. one carrying a net microscopic angular-momentum (spin) field. Enforcing angular-momentum conservation without imposing stress-tensor symmetry, we derive the full form of the stress tensor and of the spin flux, and we show that the entire chiral response is generated from the classical Newtonian one by a single operation of direct physical origin --- the $90^{\circ}$ rotation through which chirality acts, mirrored at the particle level by transverse forces (Caprini & Marini Bettolo Marconi 2025). Applied to the irreducible (deviatoric) decomposition, the rotation assigns to each classical channel a chiral partner --- pressure to chiral pressure, bulk and shear viscosities to their odd counterparts, the spin-flux gradient to its rotated image --- one coefficient and one mechanical action per channel, with no further cross-couplings. In this representation the steady base states become elementary. Quiescent states are organised by a holomorphic chiral complex potential, the mechanical and chiral pressures forming a conjugate harmonic pair subject to a topological existence condition; inhomogeneous activity forces azimuthal flows; and a boundary-driven confined flow, the chiral Stokes cavity, obeys a modified Helmholtz--Poisson system, solved in closed form in a circular domain and numerically in a square one. A single dimensionless group controls both geometries and sets the crossover from a screened, single-vortex regime to a sequence of sign-reversing vortical structures. The theory yields quantitative predictions, amenable to direct comparison with experiments on air-fluidised chiral disks (López-Castaño et al. 2022), and recovers the phenomenological frameworks of the chiral-fluid literature as particular cases.

Hyperuniformity in active matter is usually treated as a property of a prescribed density or continuum field. This view misses a basic feature of hydrodynamic active matter: an incompressible fluid does not respond equally to every microscopic force. Longitudinal forcing is absorbed into pressure, whereas transverse forcing drives flow. The relevant question is therefore not only whether particles are uniformly arranged or whether the total activity is small, but which sector of the active forcing is selected by the physical response. Here we introduce response-selected hyperuniformity, in which long-wavelength order is a property of a source-response pair. In a reversible valence-one fluid with no prescribed partners, locally neutral clusters screen the signed active-moment sector that controls transverse flow, producing a first-moment spectrum that vanishes quadratically at low wavenumber. Locally unscreened moments instead generate a nonzero infrared plateau. The resulting transverse-force spectrum has a universal crossover from fourth- to sixth-order scaling, with the crossover set by the ratio of the unscreened residual to the screened analytic contribution. Complete partner renewal preserves this normal form, establishing exchangeable multipole inheritance, while turnover tunes the residual through an independently measured local defect density. The zero-residual limit yields strictly hyperuniform velocity fluctuations; any finite residual causes defect-controlled infrared leakage and sets a finite screening length. Thus microscopic exchange need not destroy hidden hyperuniform flow order, but rare unscreened moments determine how far the quiet-flow regime survives.

Systems composed of interacting bistable elements are commonly described by transition graphs that determine which state changes are accessible under an external drive. Under quasistatic loading, accessibility is constrained by the equilibrium structure of the system, often resulting in sparse transition networks and unreachable stable states. Here, we show that dynamic loading of dissipatively-coupled hysteron networks enhances accessibility by enabling transition pathways that are forbidden under quasistatic driving while preserving the underlying equilibrium states. In particular, we consider pulse actuation and derive a control map linking pulse amplitude and duration to state transitions. For suitable dissipative couplings, individual hysterons become independently addressable using a single scalar input, increasing transition-graph connectivity and enabling access to otherwise unreachable states. We validate the framework experimentally using pneumatic hysterons and find good agreement with theory. More generally, the framework applies to dissipatively coupled networks of bistable elements across fluidic, mechanical, and electrical domains.

Mechanical instabilities provide a general design principle for shaping developing organs and engineering soft materials. However, in slender structures, simple elastic buckling tends to erase rather than preserve shape complexity: structures relax to the simplest possible shape, erasing finer detail. Living systems nonetheless build complex, reproducible morphologies from continually remodeling material, while remaining robust to noise arising across scales. Using analytical theory and numerical simulations of a minimal model of growing visco-elasto-plastic rods, we show that remodeling plays two opposing roles: At low plasticity, patterns coarsen through elastic relaxation, while high plasticity converts fluctuations into geometric disorder. This sets a trade-off between shape complexity and reproducibility with an optimal intermediate plasticity, which protects initial patterns. Growth breaks this trade-off by suppressing both failure modes, enabling complex shapes to be reproducibly generated. Our results identify remodeling and growth rates as two knobs governing whether an encoded pattern is remembered, degraded, or transformed.

We present a method that enables efficient simulations of coarse-grained electrolyte solutions inside a narrow slit pore with an anisotropic dielectric permittivity tensor. The electrostatic equations for polarizable surfaces are solved using a 2D periodic Green's function method combined with a slab-corrected anisotropic 3D Ewald summation. We apply this approach in Monte Carlo simulations to study 1:1 electrolytes confined between both polarizable dielectric and metallic surfaces. Our results show that dielectric anisotropy aggressively reshapes the double-layer structure. While a coordinate stretching transformation demonstrates that individual ion-image interactions depend strictly on the bulk-like parallel permittivity, the suppression of the perpendicular permittivity dramatically amplifies direct in-plane ion-ion correlations. Under strong anisotropy, these lateral correlations dominate the thermodynamics completely, rendering the structural profiles of mutually opposing dielectric and metallic boundaries practically identical by forcing the smaller cations directly into the contact plane of the larger anions.

We present an analytical theory for the flash temperature for viscoelastic solids sliding on rigid and randomly rough surfaces. The theory takes into account the surface roughness on all relevant length scales.

We analyze the conformational and dynamical properties of the kinetoplast DNA (kDNA), a massive sheet-like structure made from thousands of circular DNA molecules, found in the mitochondrion of certain parasites. The connectivity between circular DNA molecules is achieved by topological linking, hence, the kDNA may be regarded as a naturally occurring two-dimensional version of Olympic gels, whose physical properties are yet to be understood. We propose that the basic aspects in the large scale behaviors of kDNA could be described by the physics of polymerized membrane. Our analysis indicates the relevance of the hydrodynamic interactions in the dynamics of kDNA in aqueous solution. We demonstrate that the predicted dynamical scaling scenario captures various experimental data recently obtained from {\it in vitro} imaging experiments in a unified manner. We also provide an estimate for the in-plane elastic modulus of kDNA, whose magnitude agrees well with recent measurements.

Fluid removal from rubber-substrate interfaces is crucial for maintaining friction during walking and vehicle braking on contaminated surfaces. We study the transient friction of rectangular rubber blocks sliding against tile and glass surfaces lubricated with water, glycerol, mud, or silicone grease. Two block configurations with different lengths in the sliding direction were tested after different stationary waiting times. For water, stationary squeeze-out is nearly complete before sliding begins. For glycerol, both stationary squeeze-out and sliding-induced fluid removal are important. For mud and grease, the steady-sliding state is reached after a sliding distance of the order of the block length, with little dependence on the preceding waiting time, showing that sliding-induced scraping dominates fluid removal for highly viscous substances. Dividing the contact into shorter blocks accelerates fluid removal by reducing the drainage distance and increasing the number of leading edges. Stationary squeeze-out calculations based on the measured surface roughness are in reasonably good agreement with the glycerol experiments. The results provide design guidelines for rubber tread blocks with multiscale drainage channels and sufficient compliance to promote transient fluid removal.

Piezoelectricity (linear coupling between mechanical deformation and electric signal) was originally observed only in solid crystals. Recently, it was discovered that liquid ferroelectric nematic liquid crystals are also piezoelectric. However, so far only their converse piezoelectric signals (applied voltage-induced mechanical deformation) were measured quantitatively. In this work, we have carried out periodic shear-induced electric current and oscillatory rheology measurements on the two archetypic ferroelectric nematic compounds, RM734 and DIO. From temperature, frequency and strain dependent results of the first and second harmonic current signals together with the results from oscillatory rheometry, we were able to quantitatively determine the shear-mode direct piezoelectric coupling constants. These values are similar for both materials and are compared to results of previous converse piezoelectric measurements. We propose a physical mechanism in which the flow alignment of ferroelectric polarization leads to the direct piezoelectric response.

Standard quorum-sensing models in active matter exhibit collective phenomena such as motility-induced phase separation. Here, we show that incorporating competing sensing ranges-- a minimal ingredient inspired by microbial communication --qualitatively changes this behavior, replacing macroscopic phase separation with self-organized microphases characterized by an emergent finite length scale. Starting from the microscopic dynamics, we derive a coarse-grained field theory whose coefficients are explicitly related to the moments of the microscopic sensing function. This mapping enables a direct comparison between particle-based simulations and continuum theory, allowing the characteristic modulation and correlation lengths to be predicted directly from the microscopic interaction parameters. Two-dimensional numerical simulations confirm these predictions and reveal a transition from macrophase separation to finite-wavelength density modulations as the competition between sensing scales increases. For stronger competing interactions, the system develops a peculiar cluster phase with an interstitial percolating network, which is captured by a higher-order gradient expansion. Our results identify competing quorum-sensing interactions as a simple microscopic mechanism for generating tunable active microphases.

Weak magnetic fields have long been reported to either enhance or suppress transmembrane ionic currents, yet the physical origin of these apparently contradictory responses remains unresolved. Here, we develop a mesoscopic equilibrium framework showing that weak magnetic fields primarily modify the equilibrium occupation probabilities of metastable transport states, thereby altering the resulting nonequilibrium ionic current. Rather than acting directly on microscopic ionic trajectories, magnetic fields regulate transport through the statistical redistribution of conducting states. This mechanism naturally explains both magnetic enhancement and suppression within a unified theoretical framework and predicts a universal criterion for magnetic sign reversal governed by a single equilibrium covariance. The theory further identifies experimentally testable signatures, including characteristic magnetic-field dependence and state-dependent transport modulation, providing a quantitative framework for interpreting weak-field magnetic effects in biological ionic transport.

Although confinement strongly influences flows in active materials, it remains unclear how active particles align at rigid boundaries when no thermodynamic anchoring is imposed. We address this question using continuum simulations of active nematics, together with analytical arguments based on a reduced near-wall description. In the flow-tumbling regime, extensile systems align parallel to the boundary, whereas contractile systems align perpendicular to it, consistent with active anchoring observed at active-passive interfaces. In the flow-aligning regime, the preferred orientation depends on the sign of activity and of the flow aligning parameter: either the shear-like flow generated near the wall selects the Leslie angle, or no unique alignment is established. These results provide a unified framework for activity-induced anchoring at rigid walls, demonstrating that boundary alignment in dense active matter can emerge solely from the interplay between self-generated flows and orientational dynamics.

We evaluate machine learning force fields derived from different density functional theory exchange correlation functionals using the full six-dimensional pair correlation function of liquid water, three-body structural descriptors, excess entropy, and transport properties. The predicted microscopic structure and dynamics depend strongly on the underlying functional: neglecting dispersion produces pronounced overstructuring, overly negative excess entropy, and suppressed diffusion. Translational and orientational entropy contributions are tightly coupled and together exhibit a clear relationship with the reduced selfdiffusion coefficient. Among the tested models, RPBE-D3 provides the most consistent agreement with experiment across structural, thermodynamic, and transport properties. The classical SPC/E model serves as an additional reference and displays notable similarities to RPBE-D3, consistent with the comparable Born effective and partial charges of the two models.

In metastable particulate gels, it is tempting to believe that the dynamic similarities between the fluid-to-solid non-linear phase transition of rigidity percolation and the solid-to-fluid transition that occurs during yielding represent mirror images of the same continuous process. Even though these behaviors are clearly dynamically similar, their multi-scale nature makes it difficult to determine if they could also follow a unified structural pathway. We know from model monodisperse colloidal gels that both yielding and the elastic modulus seem to be heavily influenced by a small subset of topologically distinct singly-connected bridges linking mesoscale features. Here we use particle simulations to examine the participation of different classes of particle-level bonds and their contributions to the bulk mechanical response. We find that rigidity is disproportionately supported by singly connected intercluster bridges, whereas yielding localizes at bonds with high edge-betweenness centrality (EBC); strikingly, these independently identified populations substantially overlap and perform comparable mechanical roles. Bimodality exposes this correspondence by concentrating large-particle contacts in both populations, thereby providing a compositional label for the common backbone. Thus, rigidity and yielding are opposing mechanical manifestations of the same mesoscale structure: the intercluster bottlenecks that establish rigidity are also the sites at which rigidity is preferentially lost.

We investigate the Uhlenbeck-Ford (UF) model as a reference system for free-energy calculations in two-dimensional (2D) fluids. The 2D virial coefficients are computed exactly up to tenth order and combined with molecular simulation data to construct highly accurate numerical representations of the equation of state and the excess Helmholtz free this http URL then determine the phase diagram of the model in order to establish the thermodynamic stability limits of the fluid phase and thereby identify the range of applicability of the UF model as a fluid reference system. In the course of this analysis, we identify the solid, hexatic, and fluid phases, and show that the fluid remains the only thermodynamically stable phase, independent of density, for scaling parameters up to $p\lesssim 70$. Finally, we demonstrate the practical applicability of the 2D UF model as a reference system through thermodynamic integration calculations of the free energy of a two-dimensional Lennard-Jones fluid.

We present a tunable mesoscale model to provide a basis for future rheological calculations of of bacterial biofilms, explicitly incorporating reversible crosslinking within the extracellular polymeric substance (EPS) matrix. Using a Dissipative Particle Dynamics framework combined with a Gillespie-inspired algorithm, bonds between polymers and bacteria dynamically form and break, capturing the intrinsically evolving nature of the network. We show that biofilm structure is governed by a competition between polymer-polymer and polymer-bacteria crosslinks, controlled by binding energy, linker availability, and bond stiffness and provide a minimal model that helps to understand the competition between both species.

A recently formulated mean-field model of glasses features an equilibrium, zero-temperature Replica-Symmetry-Breaking (RSB) transition in some parameter range. In this range, the model's solution in the Replica-Symmetric phase is expressed in terms of an effective, self-consistent random potential for uncoupled degree of freedoms, where the transition to the RSB phase is characterized by the emergence of spectral-edge localized modes and a pseudogapped quartic vibrational spectrum, resulting in a finite spin-glass susceptibility. These properties are preserved in numerical solutions of the model under non-equilibrium conditions, i.e., upon an instantaneous quench. Inspired by recent advances in computer glasses, we define a micromechanical response function --- the linear response to local force monopoles --- in the framework of the mean-field model. We establish exact relations between the force monopole stiffness and global susceptibilities, which suggest a close correspondence between the non-equilibrium RSB phase of the model and the above-mentioned effective random potential description. As such, the obtained micromechanical observables constitute a concrete realization of the collective degrees of freedom of the model, offering a bridge between a glassy mean-field model and finite-dimensional glasses. We show that the model's vibrational spectrum can be computed solely from the monopole response statistics and, by employing a marginal stability criterion, we extract a characteristic frequency/stiffness scale of soft glassy modes, which is related to the boson peak in finite-dimensional, laboratory glasses.

We study the chiral dynamics of an intruder immersed in a nonequilibrium bath in two complementary limits: the dilute kinetic regime and the dense hydrodynamic regime. In the dilute limit, starting from a Boltzmann-Lorentz description, we derive an effective Langevin equation whose coefficients are given explicitly by geometry-dependent boundary integrals. This formulation separates the effects of intruder-shape chirality from those of chiral intruder-bath interactions. We find that the chiral interactions generate an odd response and a torque, whereas the chirality of the intruder leads to a ratchet effect. We also show that fluctuation-dissipation-like relations exist and that certain symmetry-allowed couplings vanish in the dilute regime. In the dense regime, we argue that intruder dynamics are governed primarily by bath hydrodynamics and torque-density-driven edge currents not captured by the previous framework. These currents can generate both an antisymmetric drag and a curvature-induced torque, leading to an antisymmetric response when inertia is accounted for. Taken together, these results provide a step toward understanding the mechanisms governing the chiral dynamics of an intruder in a nonequilibrium bath across different scales.

We introduce and simulate an analytically tractable model for an intruder of arbitrary shape in a nonequilibrium bath, with chirality originating from the bath, the intruder, or their coupling. In the dilute regime, a Langevin description derived from a Boltzmann-Lorentz equation shows how intruder geometry governs ratchet effects and odd response. In the dense regime, the dynamics of the intruder are instead governed by the hydrodynamic modes of the bath and edge currents, which are described by a Stokes equation including a chiral torque density. Our results link shape to chiral transport and show that odd response arises from distinct mechanisms in the dilute and dense limits.

Accurate resolution of propeller-hull interaction is essential for predicting the self-propulsion point in ship CFD, yet motion-resolving methods such as sliding interfaces (SI) are computationally expensive, while the classical Moving Reference Frame (MRF) approach cannot capture unsteady interaction effects. Partially rotating grid methods bridge this gap by splitting the propeller rotation into a grid-resolved and an MRF component, but the abrupt transition between the rotating and stationary domains introduces discontinuities in the velocity field. This work presents a modified MRF (mMRF) formulation in which the reference-frame rotation rate is scaled by a spatially varying function that decays smoothly from unity near the propeller to zero at the domain interface, restoring velocity and pressure continuity across the boundary. The governing equations are derived and implemented in the RANS solver FreSCo$^+$, verified against the analytical Taylor--Couette solution, and applied to open-water propeller and Japan Bulk Carrier self-propulsion simulations at model scale. Both MRF and mMRF reproduce the principal integral propulsion quantities ($n$, $K_{\mathrm{T}}$, $K_{\mathrm{Q}}$, $1-t$, $1-w_{\mathrm{T}}$, $\eta_{\mathrm{R}}$) accurately, but the mMRF markedly reduces interface discontinuities and non-physical artifacts in the local flow field, particularly at large MRF fractions, at essentially the same computational cost.

Model-based active flow control requires predictive models that are accurate, stable, and fast enough for real-time optimisation. In controlled wake flows, this is often achieved through Reduced-Order Models (ROMs) that first compress high-dimensional velocity snapshots into a latent space and then learn a time- stepping predictor for the dynamics in the latent space. Here, we study how the choice of the spatial encoder affects the predictability of the resulting latent coordinates for wake flows under control inputs. Using two actuated 2D wake configurations, a simplified truck wake and the fluidic pinball, we compare Proper Orthogonal Decomposition (POD) against nonlinear Convolutional Autoencoders (CAEs) and two types of variational autoencoders for compression, and evaluate several temporal predictors based on Long Short-Term Memory networks. CAEs achieve higher compression efficiency and sharper short-term reconstructions, but they produce latent dynamics that are more irregular and with broadband spectral content. As a consequence, long-horizon forecasts degrade faster and show a higher probability of catastrophic divergence than POD-based models. POD yields smoother latent trajectories that are easier to learn and extrapolate, leading to more reliable predictions beyond the short- term regime. These results reveal a clear trade-off between compactness and forecast accuracy, and suggest that the stability of the latent dynamics prediction can outweigh maximal compression. This is particularly relevant for control strategies rooted in forecasts of the dynamics, such as model predictive control and reinforcement learning. The findings provide practical guidance for designing actuation-aware, hardware-feasible predictive ROMs for real-time flow control.

Gas bubbles evolving on electrodes during water-electrolysis are blocking active reaction area, thus hindering mass transfer and raising Ohmic resistance. Unlike earlier models that prescribe a uniform current density on the wetted part of the electrode, we resolve the primary electric field, which allows the current density and the interfacial gas production to respond to the geometry of the electrode and the temporal evolution of the bubbles. Using three-dimensional geometrical volume-of-fluid (VOF) simulations with phase change in Basilisk, we examine the growth of single-bubbles on electrodes of different size and of multiple bubbles growing on arrays of catalytic electrode islands. The non-uniform current density and the associated Ohmic resistance significantly affect the growth dynamics. Unlike the case of a single bubble, the outer bubbles in case of electrode islands tend to drift outward during growth, thus delaying full electrode coverage and sustaining current. Footprint tracking and a theoretical analysis show that this drift is governed by the liquid advection driven by the growth of neighboring bubbles, scaling with their separation 1/d2, and modulated by the current-density asymmetry. These results show how electrode patterning and bubble spacing can be exploited to tailor the electric field distribution and reduce bubble-induced resistive losses during water electrolysis.

This work investigates deformable gas bubbles rising near a vertical wall in ultrapure water, focusing on how the position of the wall leading edge affects their near-wall dynamics. Two configurations are considered: (i) a wall extending from 11--25 bubble diameters below the bubble injection point, so that the bubble rises under the continuous influence of the boundary; and (ii) a wall whose leading edge is located 144 mm above the injector, corresponding to approximately 80--180 bubble diameters, allowing the bubble to reach its terminal velocity before entering the wall-bounded region. The results show that the wall leading-edge position influences both the transition from periodic bouncing (PB) to bouncing--tumbling--escaping (BTE) dynamics and the rebound frequency within the PB regime. When the wall leading edge is placed downstream, the onset of BTE occurs at smaller bubble sizes, corresponding simultaneously to lower Bond ($Bo$), Galilei ($Ga$), and Reynolds ($Re$) numbers. The Strouhal number ($St$) follows a similar decreasing trend in both configurations at low Bond numbers, but the two behaviours diverge for ($Bo \gtrsim 0.15$). For the PB regime, when the wall extends from the injector, $St$ approaches an approximately constant value of $St\simeq0.014$, whereas substantially lower values are measured for the downstream-wall configuration. The larger rebound amplitudes and longer return stages observed in the latter configuration account for lower frequencies. These findings indicate that the bubble dynamics depend not only on the conventional control parameters and wall separation, but also on the wall geometry and the associated pre-interaction bubble hydrodynamic history.

Rotating circular cylinders are employed in a variety of engineering applications, one prominent example being Flettner rotors for wind-assisted ship propulsion. Besides optimizing the aerodynamic performance of the cylinder itself, passive flow-control devices placed in its vicinity offer additional potential for manipulating the resulting aerodynamic forces. The present work introduces a topology-based adjoint sensitivity analysis for rotating circular cylinders over a wide operating envelope covering Reynolds numbers from 1E+01 to 1E+07 and spinning ratios between 0 and 2 pi. Local sensitivity fields associated with drag, lift, and torque are derived using a porous-medium formulation and validated by dedicated forward simulations employing both distributed Darcy-type source terms and a sensitivity-informed passive flow-control structure. Particular emphasis is placed on the combined sign distribution of the drag and lift sensitivities, yielding intuitive design maps that directly identify regions where local momentum extraction simultaneously improves or deteriorates both objectives. A systematic investigation of the resulting sensitivity spectra reveals that the large-scale topology of the sensitivity fields is governed primarily by the spinning ratio, whereas the influence of the Reynolds number remains comparatively weak over large parts of the investigated operating envelope. The resulting sensitivity atlas provides practical design guidance for passive flow-control concepts and demonstrates that robust solutions may exist over moderate operating ranges.

In fluid-fluid displacements in porous and fractured materials, viscous friction in microscale interfacial (Haines) jumps is intimately linked to macroscale energy dissipation and the associated pressure-saturation (retention) hysteresis. The mode of control (flow rate vs. pressure) and the driving rate (from quasistatic to finite) can substantially affect hysteresis. Despite the significance of hysteresis and dissipation in various technological and natural processes, a quantitative understanding of the link between the micro- and macro-scales, and of the impact of the inherent heterogeneity of porous media, remains elusive. An ``imperfect'' Hele-Shaw cell of variable aperture is a simple model system which allows to study all these in details. However, simulating fluid-fluid interface evolution in heterogeneous media, even in such a simple system, is computationally prohibitive, as multiple length and time scales need to be resolved simultaneously. We develop here a spectral computational approach for interface evolution and energy dissipation and validate it via comparison to computational fluid dynamics simulations and experiments. Computational efficiency is demonstrated by following interface evolution in a cell with a single ``defect'', as well as with random roughness; in both, disparate length scales lead to nontrivial dynamics over many orders of magnitude in time. We also show theoretically that while viscous forces during Haines jumps fully account for the energy dissipated between consecutive metastable equilibria, viscosity does not change the total dissipated amount, merely the relaxation time. Our approach provides a stepping stone towards upscaling of fluid-fluid flows in porous media.

This article presents the experimental study and the modelling of the multistable jet in the wake of two side by side square bars separated by a distance $G$ at Reynolds number $R=U_\infty H/\nu=10000$ (with $U_\infty$ the velocity of the incoming flow, $H$ the bar side and $\nu$ the kinematic viscosity). The velocity field downstream of the bars is measured by means of two dimensional two components Particle Image Velocimetry (PIV). We use the weighted transverse position of the jet $Y_m$ and the jet width $w$ to characterise the regimes of multistability as the gap ratio $G/H$ is increased. Three main regimes of multistability are possible: tristability, bistability, and monostability. In our wind tunnel, tristability is observed for $G/H\in [1.15,1.25]$, bistability is observed for $G/H\in [1.5,2.65]$ and monostability is observed for $G/H\in [3.0,3.5]$. Within the first two ranges of $G/H$, there exists gap ratios for which multistability is more complex. In order to analyse the simple and complex multistability regimes as well as the transition from bistable to monostable, we construct an analytical stochastic differential equation (SDE) modelling $Y_m$ for each gap ratio. These SDEs are written with polynomial drift and diffusion. For this matter we use a data based method that finds an trade--off between simplicity of the model (smaller number of monomials) and precision. A first key advantage of the use of the data-based model fitting method is that when the flow is tristable, bistable or monostable, we recover the drifts expected from the theory of bifurcations, but we are now able to correct it with the right multiplicative noise expressed by the diffusion. The second key advantage is that we can also fit atypical drift expressions when the multistability regime is complex that help us make sense of the jet behaviour.

The "butterfly effect", introduced over half a century ago by Edward Lorenz, has shifted from a cornerstone of dynamical systems to a popular metaphor, yet its true physical manifestation in fully developed turbulence spans a spectrum of phenomena from standard chaotic sensitivity to the recently established concept of Eulerian spontaneous stochasticity. This paper presents an attempt at a systematic synthesis that brings these different but interconnected ideas together within the unifying framework of the Finite Size Lyapunov Exponent (FSLE). The FSLE describes the growth rate of perturbations as a function of their scale, enabling a comprehensive characterization of the multiscale physics of turbulent flows. Using the FSLE and the Sabra shell model, extended to include thermal noise, we bridge the classical, small-scale Lyapunov regime with predictability at large scales and its interpretation in terms of Eulerian spontaneous stochasticity. Moreover, using the FSLE and the Kraichnan model, we also illustrate the closely related phenomenon of Lagrangian spontaneous stochasticity. To complete the spectrum of butterfly effects, we also examine the "literal butterfly" scenario of localized, sub-dissipative perturbations. Ultimately, this synthesis clarifies the physical mechanisms that dictate the fundamental boundaries of forecasting in high-Reynolds-number flows.

Quasi-periodic pressure pulses associated with cardiac and respiratory activity generate reciprocating cerebrospinal fluid (CSF) motion in the human ventricles. While weak and more regular during wakefulness, oscillatory fluid motions have recently been found to be much more exaggerated during NREM sleep, appearing as large flushes in successive pulse trains. The present study investigates whether this forcing can induce greater residual streaming through the human ventricles. Transient CFD simulations were performed in the third ventricle under awake and sleep-related flow pulses. Sleep-related forcing produced clear caudal and rostral preferential pathways and less overall recirculation in the cavity. The streaming flux relative to the stroke volume increased from a low value of about \(0.540\%\) to \(28.4\%\) during sleep. Thus, sleep-related forcing changes not only the magnitude of reciprocating fluid displacement but also the relative contribution of residual streaming. These findings demonstrate differences in hydrodynamic organisation in the third ventricle and highlight the importance of this organisation for intraventricular fluid exchange.

We introduce a second-order accurate vectorial lattice Boltzmann scheme for the incompressible Navier-Stokes system, inspired by a discrete-velocity kinetic approximation proposed by Carfora and Natalini [ESAIM: M2AN, 42(1), 93-112, 2008]. Advantages and drawbacks compared to relaxation schemes are investigated by providing spectral analyses in the linearized case, and numerical validations on the genuinely non-linear problem.

A flow surrogate validated on a simple regime is often taken as evidence that the approach will carry to a richer one. We test this assumption on two transient flows under time-varying boundary conditions emulating the process startup: the three-dimensional slurry film in chemical-mechanical planarisation (CMP), a core semiconductor-manufacturing process, and the two-dimensional Karman vortex street (KVS) behind a cylinder. Eight surrogate models are compared on one shared evaluation pipeline, differing in whether they learn the full field or a latent representation, and whether they predict trajectories in one shot or step by step. No single architecture wins both regimes. On the film, a one-shot full-field model reconstructs the process-relevant cumulative wall shear stress to 3.2% relative error. On the wake, a latent autoregressive DeepONet retains 96% of the shedding power that direct and one-shot models damp to almost zero. The deciding axis is the treatment of time. The self-sustained wake requires the phase memory that autoregressive feedback provides, while the boundary-driven film rewards a direct map. Pointwise RMSE picks the wrong model in both regimes, so the evaluation scores five physical questions instead, the field, its structure, invented motion, amplitude, and timing. The trained surrogates answer queries $10^3$ to $10^4$ times faster than the finite-element solver, but the offline cost of the training simulations means they pay off from the first query beyond the training set for CMP and the third for the KVS. The choice of surrogate should follow the dynamical character of the target flow, and its validation should use failure-mode-resolved metrics, since neither the winning architecture nor its validation transfers.

Raw-Hermite sensing and collision on a fixed discrete-velocity set can convert a uniform translation into artificial coupling between nominally distinct nonequilibrium orders. We develop a central-Hermite formulation for a D3Q125 kinetic model with order-resolved log-Gaussian relaxation and compare three variants: raw sensing/raw collision (A), central sensing/raw collision (B), and central sensing/central collision (C). In homogeneous translated second-order perturbations, model C preserves third- and fourth-order modal purity to machine precision, whereas A and B develop boost-dependent cross-order content. Across a grid-CFL-boost matrix, model C reduces the post-transport collision frame discrepancy relative to A by 65.342-98.102% (median 81.131%) in the total relative L-infinity measure. Long-time calculations remain positive and conservative to numerical precision, although the accumulated benefit is configuration dependent because transport continually re-injects frame error. A transport study further reveals a clear trade-off: central-Hermite interface reconstruction strongly suppresses the third-order discrepancy but amplifies the fourth-order discrepancy. The fully central-Hermite collision therefore substantially reduces collision-induced cross-order frame discrepancy, while residual dependence remains due to discrete transport and finite velocity-space representation. This moment-space improvement does not by itself establish a comparable reduction in macroscopic Galilean transport error.

We introduce a Physics-Informed Token Transformer (PITT) methodology for nonlinear hyperbolic balance laws in one space dimension, using piecewise steady-state profiles for the representation of approximate weak solutions. The method combines symbolic equation tokenization, a Fourier neural operator encoder, an explicit Rankine--Hugoniot law for shock motion, and a learned correction term. For clarity, we present it here for the relativistic Schwarzschild--Burgers equation, a scalar model for spherically symmetric fluid flows on a Schwarzschild background. For this model the steady-state invariant and the generalized Riemann solutions are explicit, and they can therefore be built into the neural evolution. In particular, the leading discontinuities are advanced by the analytical jump condition, while the learned part reconstructs smooth regions, rarefaction fans, geometric dependence, and finite-resolution effects. The method is designed to locate wave fronts accurately and to preserve the relevant steady states. We test our PITT method on moving shocks, stationary shocks, rarefaction waves, and compare it with a standard high-order finite-volume approximation. We also analyze the standard Burgers limit (when the Schwarzschild mass tends to zero). The Rankine--Hugoniot prior plays the dominant role in these tests, while equation tokenization gives a systematic additional gain. The method is relevant for problems involving geometric effects and/or complex shock-wave dynamics, and is used here to study the long-time dynamics of perturbations of steady-state solutions. In particular, we exhibit an asymptotic law of propagation for the shock location of perturbed steady-state flows.

Idealized mock Walker simulations are widely used to study the interactions between overturning circulation and convection in the tropics. Previous studies documented a transition from a single-cell to a double-cell mock Walker circulation when the average sea surface temperature exceeds 300 K. Here, we ascribe the transition to the emergence of periodic convection with warming due to stronger convectively-coupled waves. In cold simulations, the warm pool is dominated by steady deep convection, which results in a single overturning cell. In hot simulations, the warm pool is alternately dominated by deep convection and a stratiform mode, resulting in lower and upper cells respectively. This study suggests that the Walker circulation in a warmer climate may feature complex structural changes in addition to a weakening in strength, and highlights the profound impacts of convection on overturning circulation.

Complex dynamical systems often undergo transitions from periodic to chaotic behaviour as bifurcation parameters vary, making timely detection of these changes essential. Conventional approaches based on the maximal Lyapunov exponent (MLE) generally require either knowledge of the governing equations or sufficiently long, uniformly sampled time series. Their performance degrades when the available data are scanty or contain missing observations, making reliable phase-space reconstruction difficult. We propose a methodology that combines Topological Data Analysis (TDA), specifically 0-D sublevel persistence, with Machine Learning (ML) classifiers to distinguish periodic and chaotic regimes directly from time series. Sublevel persistence extracts topological features by analysing the evolution of minima and maxima, revealing repeating signatures for periodic dynamics and more scattered patterns for chaotic dynamics. These features are used to train logistic regression, support vector machine, and k-nearest neighbour classifiers. Hyperparameters are validated using K-fold cross-validation, yielding average classification accuracies exceeding 90%. The trained classifiers provide binary predictions, identifying periodic and chaotic behaviour in previously unseen data. The proposed methodology is evaluated on the Duffing, Rössler, and Lorenz systems, where the detected transitions closely agree with those identified using the MLE, demonstrating the reliability of the approach. It is further applied to real-world ECG signals to classify normal and abnormal heartbeats, producing encouraging performance across standard statistical metrics. The proposed framework provides an effective alternative for analysing sparse or incomplete time series and is particularly useful in experimental settings where conventional nonlinear time-series methods are limited.

We develop a motif-based framework for spatiotemporal chaos in spatial evolutionary games and use it to map the dynamical phase diagram in the payoff plane. Using Boolean linearization of the imitate-the-best rule, we derive analytical instability thresholds for local motifs including invaders, cooperative pairs, stripe interfaces, and cooperative cores. These thresholds are obtained from payoff balance at contested motif interfaces and recover classical invasion thresholds of spatial evolutionary games, which emerge here as boundaries of the chaotic phase. Combining the Derrida slope with the asymptotic Hamming distance, we obtain a four-region cartography: ordered, transient-chaotic, sustained-chaotic, and subcritical-chaotic dynamics. The phase diagram is organized by density-dependent motif selection: different initial cooperator densities activate different instability mechanisms, yet a small set of motif-instability lines consistently bounds the sustained-chaos region across densities. This cartography reveals a subcritical chaotic phase (Derrida slope $s<1$ but asymptotic Hamming distance $d_\infty>0$), where infinitesimal perturbations decay while finite-amplitude perturbations sustain chaos. The motif-based framework is anchored by an exact benchmark: for homogeneous backgrounds, the Boolean Jacobian yields an exact correspondence between the Derrida slope and spectral radius, linking damage spreading to deterministic instability.

Locating periodic solutions of chaotic dynamical systems normally requires an initial guess close enough to the target orbit for numerical continuation or gradient-based search to converge. We show that Physics-Informed Neural Networks (PINNs) trained on sparse, noisy observations \emph{without} initial conditions recover periodic orbits of the gravitational three-body problem, including orbit families absent from the training data. The method rests on a second-order ODE formulation, fixed-frequency Fourier features, percentile-based adaptive refinement, and a trainable scaling parameter, each validated on forward problems. Across two 100-seed ensembles, $23$--$25\%$ of runs converge to families not present in the training data. We then ask what determines which family emerges. Two $\chi^2$ tests give a consistent answer: changing the training data source significantly shifts the distribution of recovered families ($p < 0.001$, Cramér's $V = 0.339$), whereas switching between the two initialization distributions tested does not ($p = 0.620$, $V = 0.094$). The random seed selects which family a given run recovers; the \emph{distribution} the weights are drawn from does not shift the aggregate frequencies, but the training data does. The evidence is empirical: we do not characterize the loss landscape analytically, and PINNs remain slower than conventional integrators on well-posed initial-value problems. What the experiments establish is that the recovered orbits are verifiable rather than merely plausible: the identified ones refine to genuine periodic solutions, a network trained on Lagrange data recovers the figure-eight choreography (Li--Liao class I.A.1, matched to seven significant digits in $T^*$), and one trained on figure-eight data recovers a Broucke--Hadjidemetriou--Hénon orbit closing to $\delta_T < 10^{-9}$.

Photonic reservoir computing is a promising physical machine-learning technique for predicting time-series data. The quantization of the response signal from the reservoir is required for the implementation of photonic reservoir computing, and the number of quantization bits and sampling frequency need to be optimized to achieve high performance and low energy consumption. However, few studies have been reported to investigate the effect of bit quantization and sampling frequency. In this study, we introduce a concept of approximate reservoir computing with a semiconductor laser by quantizing the amplitude of node states in the reservoir and output weights. We evaluate the performance of a chaotic time-series prediction task and energy consumption per sample. We achieve significant reduction of energy consumption by optimizing the number of quantization bits, the sampling frequency, and the injection current of the semiconductor laser, while maintaining the prediction performance.

Photonic reservoir computing has attracted increasing attention as a fast and low-cost approach for time-series prediction. Photonic reservoir computing utilizes the high speed, broad bandwidth, and spatial parallelism of light. However, the effect of the internal connection structure (network topology) on the computing performance has not been investigated for large-scale photonic reservoirs. In this study, we experimentally and numerically demonstrate photonic reservoir computing using a spatial light modulator to systematically evaluate the relationship between the network topology and the performance of reservoir computing. We introduce complex network structures such as small-world and scale-free network topologies of the internal nodes in the reservoir. We perform the memory capacity measurement and the one-step-ahead prediction task of the chaotic time series to compare the performance. We found that the small-world network exhibits the maximum memory capacity and the best prediction performance. Our numerical calculations reveal that the performance of the time-series prediction can be optimized by changing the rewiring probability of the network and the leak rate of the reservoir. We also implement photonic human brain network as a reservoir, which is designed by the connectomes of human brain activities. We found that the network topology strongly affects the performance of reservoir computing, and the small-world network structure outperforms the other configurations.

In this paper, we study an analog of the scalar two-dimensional Fermi-Pasta-Ulam (FPU) lattice. In particular, a variety of dispersive wave structures and localized patterns are numerically identified in the numerical simulations of the FPU lattice, but, to the best of our knowledge, all of these particular wave structures do not admit analytical closed-form expressions. In order to resolve this issue, we perform a dimensional reduction and accordingly derive a modified KdV equation. Based on this reduction, we first take advantage of some of its exact localized solutions to model the associated wave patterns in the FPU lattice. In addition, we explore the two-dimensional generalization of the Riemann problems for the FPU lattice and the corresponding modified KdV reduction, whose evolution dynamics lead to the formation of multiple composite dispersive structures. Moreover, we propose and rigorously derive the KPII limit of the FPU lattice and investigate their associated wedge problems. Finally, all these relevant numerical dynamics are compared to examine the performance of these quasi-continuum long-wave asymptotic limits.

This study presents a data-driven framework for solving nonlinear wave equations, specifically the Gross-Pitaevskii equation (GPE) and the single-component nonlinear Schrodinger equation (NLSE), using Physics-Informed Neural Networks (PINNs). The approach integrates physical constraints directly into the neural network's loss function, enabling efficient training without requiring labelled data. We implement a PINN-based framework for solitons that models a variety of localized wave structures across both equations. Predicted solutions are compared with exact analytical results and show strong agreement with low error. The method effectively captures soliton profiles in both the GPE and NLSE. The accuracy and flexibility of the framework suggest its usefulness for studying nonlinear differential equations relevant to Bose--Einstein condensates and nonlinear optics.

We show that the inclusion of a dimension-six operator in the Higgs potential has a dramatic impact on the stability of oscillons in the $SU(2)$ bosonic sector of the Standard Model, extending their lifetime by orders of magnitude. This happens for the physical value of the ratio between the Higgs and W boson masses, $m_H/m_W=1.556$ and for the dimension-six operator $O_6 = (\Phi^\dagger \Phi)^3$ whose coupling constant is below the current upper bound.

We construct a nonlinear extension of Fermi's electrodynamics by incorporating a Born--Infeld structure that depends directly on the four-potential $A_\mu$ rather than on the field strength $F_{\mu\nu}$. The resulting theory, which we call Fermi--Born--Infeld (FBI) electrodynamics, eliminates the $U(1)$ gauge redundancy by elevating the Lorenz gauge to a dynamical condition. The Lagrangian is built from the determinant of a metric-like tensor $g_{\mu\nu} = \eta_{\mu\nu} + 2\kappa\, \partial_{(\mu} A_{\nu)}$, ensuring that the canonical energy--momentum tensor and the spin density remain unique and free of gauge ambiguities. We derive the field equations, which reduce to $\partial_\nu(\sqrt{-g}\, g^{\mu\nu}) = 0$, and show that the Lorenz condition $\partial_\mu A^\mu = 0$ emerges dynamically from retarded boundary conditions and the requirement of a positive-energy spectrum. The nonlinearities modify the propagation of longitudinal modes; we argue, via a Vainshtein-like mechanism, that the nonlinear self-interactions may stabilize the longitudinal mode, opening the possibility of a stable massive scalar photon under extreme field conditions. We also compute the spin density from the Noether current and discuss its properties. The FBI theory preserves the physical gauge of Fermi's original formulation while incorporating the regularization features of Born--Infeld electrodynamics, making it a candidate for describing electromagnetic phenomena in strong-field regimes.

The Magnusian is a phase-space function that generates finite-time evolution through nested Poisson brackets. It is related to several familiar generators of classical dynamics, including the radial action, the eikonal phase and related quantities. In this work, we extend the Magnusian framework to systems with dissipation and nonlocal-in-time interactions using the in-in formalism, also known as the Schwinger-Keldysh or Galley formalism. This framework is particularly natural for binary dynamics, where integrating out the mediating gravitational field can produce both dissipative radiation-reaction effects and hereditary, nonlocal-in-time interactions. We derive the generalized Magnusian and show that it continues to generate finite-time evolution. As an application, we construct the Magnusian for Newtonian bound motion subject to the leading 2.5PN radiation-reaction force. The resulting generator defines a discrete evolution map from one cycle to the next and describes the evolution of the system in agreement with numerical solutions.

The rheological behavior of polymer melts under high pressure is a critical factor in many industrial processes like injection molding and extrusion, yet it is often inadequately characterized. At operating pressures that can exceed 100 MPa, viscosity can increase by orders of magnitude, making atmospheric-pressure data insufficient for accurate process simulation. This pressure induced viscosity increase is highly dependent on molecular architectures of the materials. This study aims to deconstruct the influence of specific structural features such as short-chain branching (SCB), long-chain branching (LCB), and polydispersity on the pressure sensitivity of the viscosity of polyethylene. Utilizing a high-pressure sliding plate rheometer (HPSPR) to ensure accurate measurements under uniform shear and pressure, we characterized four distinct polyethylene melts. All samples, regardless of their structure, exhibited piezorheologically simple behavior, allowing the application of time-pressure superposition over the entire shear rate range. A key finding is that the long-chain branched sample, known from the literature to be thermorheologically complex, was found to be piezorheologically simple. This dichotomy is explained by the different physical mechanisms of temperature and pressure. The pressure sensitivity of the viscosity, quantified by the pressure-viscosity coefficient, was found to be strongly dependent on molecular branching. Both SCB and LCB significantly increase the pressure sensitivity while polydispersity had a negligible effect. These results demonstrate that molecular branches are the dominant structural parameter controlling the rheological response of polyethylene to pressure, providing crucial insights for the development of more accurate predictive models for high-pressure polymer processing.

Soft porous media often feature a heterogeneous structure. Notably, biological tissues - such as cartilage and the brain tissue - consist of two or more layers, with varying mechanical and fluid-flow properties. Despite the ubiquity of periodic loading in these systems, the physical implications of layering on nonlinear poromechanics and solute transport remain poorly understood. Uncovering these coupled mechanisms could clarify the fundamental physics behind pressing topics, such as brain metabolic clearance. Here, we address this gap using a bilayer model of a generic soft porous medium. To isolate the specific role of layering, we select combinations of material properties (porosity, permeability, and p-wave modulus) that maintain an identical poroelastic timescale, $T_{\mathrm{PE}}$, across four layered configurations and a reference homogeneous case. We demonstrate that while $T_\mathrm{PE}$ is the key parameter governing the response in a homogeneous medium, the same $T_\mathrm{PE}$ leads to non-trivial localization/propagation patterns for strain, fluid flow and solute transport in a bilayer medium. These non-intuitive results suggest that layered architectures may provide functional benefits for cellular homeostasis over homogeneous ones. Finally, we show that pathological alterations to the brain's layered structure significantly disrupt fluid-flow and metabolic waste clearance, offering a possible mechanical explanation for impaired transport in disease.

A confined self-propelled particle exhibits a range of intriguing dynamical phenomena dictated by the interplay between the intrinsic activity of the particle and the imposed confinement. This competition manifests as a crossover in the steady-state position distribution of a harmonically bound active Brownian particle (HBABP) from Boltzmann-like to bimodal, commonly recognized as the passive and active regimes, respectively, upon variations in activity and confinement strength. We present a comprehensive analysis of the resultant dynamics of an HBABP employing analytical calculations and numerical simulations, examining the variations in the position distribution, residual or resultant velocity, mean square displacement, power spectral density, and effective harmonic confinement at varying activities in the characteristic regimes across the crossover. These analyses provide a reliable identification of the signature of residual or remnant activity in ABP dynamics after being impeded by the harmonic confinement. Our results show that the resultant HBABP dynamics in the regime with a Boltzmann-like position distribution is dominated by residual activity, and the motion in the other regime, with a bimodal position distribution, is similar to that of a harmonically bound Brownian particle--devoid of residual activity--at a displaced position, where the activity is balanced by the restoring force field.

Repeated coiling creates a filament hierarchy. We formulate helicalization as an iterated map acting on an arbitrary rod compliance, rather than homogenizing one prescribed construction. A marginal Jordan mode yields an outer-radius inverse-square stiffness class, while pitch disorder creates a Lyapunov threshold between amplified and screened extension--twist response. An exact finite-level rate distinguishes representative amplified and screened cases by level three; direct three-dimensional beam calculations validate the response through level four and convergence through level five.

Interacting hysteretic spins are an appealing model for cyclically-driven athermal disordered matter. Because they provide a basis for storing and processing information from their environment, such models are also being pursued as a framework for intelligent matter. Recent proof-of-concept designs have begun to demonstrate the strong, controlled, pairwise interactions that are necessary for this endeavor. But, it is not yet clear what are the limits---practically or fundamentally---on such interactions. Here we build rotor-based mechanical hysterons that extend the generality of their interactions in three ways: (i) splitting the interaction strength based on the hysteron state, (ii) building a non-reciprocal interaction of mixed sign, and (iii) incorporating tunable three-body effects. We access these effects within a simple, replicable design platform, and we rationalize our results. Our work expands the space of behaviors for designed structures that compute on mechanical inputs.

Red blood cell (RBC) populations are mechanically heterogeneous, yet how this shapes transport, clogging, and rheology in confined environments remains unclear. We combine microfluidic microchannel experiments with dissipative particle dynamics (DPD) simulations to study how reticulocyte morphology, deformability, and cell-cell hydrodynamic coupling govern microconfined blood flow, and link these to acute and chronic mountain sickness. Reticulocyte-rich samples show three subtypes (multilobular, cup-shaped, near-discocytic), parameterized (R1-R3) by fitting microchannel transit and shape-under-flow data. Single-cell simulations show that 5-micron microchannels amplify mechanical heterogeneity (R1 transits 30-50% more slowly than softer cells), whereas bending-dominated splenic slits discriminate subtypes by only 10-20%. Pairwise simulations show that a leading cell never lets a follower pass below its own single-cell threshold - so the order-of-magnitude, wake-"unjamming" reduction is absent - but the leader's compliance shapes crowded single-file passage: a soft reticulocyte leader lowers a trailing stiff cell's critical passage pressure by ~12% relative to a stiff (sickle-trait) leader and speeds its transit by ~10%. The controlling variable is the single-cell critical pressure gradient Delta_P_c, which rises monotonically with membrane stiffness from control discocytes through reticulocytes to sickle-cell-trait cells. Our simulations reproduce the shear-thinning viscosity of control blood, against which the reported chronic-mountain-sickness hyperviscosity reflects predominantly hematocrit-driven crowding rather than a change in single-cell rheology. These results place benign acclimatization, chronic-mountain-sickness hyperviscosity, and sickle-cell-trait splenic syndrome on a single mechanical axis defined by Delta_P_c relative to the splenic operating pressure.

Extreme first-passage events are broadly relevant to biological, chemical, and physical processes in which the first successful arrival determines the outcome. Existing theories are confined to noninteracting searchers. Interacting extreme-statistics problems are notoriously difficult because correlations destroy probability factorization. We establish a general framework for interacting extreme search. A no-go theorem shows that broad classes of bounded interactions cannot beat the $1/\ln N$ extreme timescale of $N$ independent Brownian searchers, and complementary upper bounds prove that this scale is exact for broad classes of repulsive interactions. We then identify two sharp mechanisms beyond the logarithmic class and derive a unified interaction-driven acceleration limit. In particular, deterministic pairwise interaction can at most reduce the extreme search time to order $1/N$, while stochastic pairwise forcing attains $1/(N\ln N)$. Our results separate acceleration due to statistical redundancy from that generated by coherent many-body transport or amplified fluctuations, deepening our understanding of interacting stochastic systems.

Simulating systems with rugged free-energy landscapes remains a central challenge in computational physics and chemistry. We introduce hyperspatial replica exchange (HS-REX), an enhanced sampling method in which the physical system is artificially extended by additional spatial dimensions. In higher dimensions, free-energy barriers can be circumvented through paths that are geometrically inaccessible in the original space. Restricting the penalty to only solute atoms dramatically reduces the number of replicas required for solvated systems compared to standard temperature replica exchange, a feature especially relevant for biological applications. As proof of concept, we demonstrate the method on a double-well model system and on alanine dipeptide in explicit water as benchmark system. In the latter case, HS-REX achieves enhanced conformational sampling of not only the slow backbone dihedral angles, but also both chiral configurations of the molecule, which are sterically inaccessible to standard sampling in three dimensions. This demonstrates enhanced ergodic sampling over conventional temperature replica exchange.

An analytical model to quantify large indentation force curves acquired on elastic thin films and living cells with spherical tip Atomic Force Microscopy (AFM) probes is presented. The model accounts for the bottom effect in the whole indentation range and overcomes the limitations of Sneddon's and Hertz's contact models, which are valid for semi-infinite thick samples, and of paraboloid tip models with bottom effect correction (BEC) that are applicable to spherical tips only for relatively small indentations. The model is experimentally validated with force volume measurements on polyacrylamide (PAA) hydrogel thin films, where an excellent agreement is obtained. The accurate correction of the bottom effect demonstrates that the intrinsic Young's modulus of PAA thin films increases for thickness below a critical value (~15 um). The model also shows excellent agreement with force curves acquired on live macrophages, providing accurate Young's modulus values for these very soft cells (E~200 Pa). Young's modulus values extracted with the proposed model significantly differ from those obtained from Sneddon's or paraboloid models with BEC, whose values deviate by 100% and -25%, respectively. Results show the potential of the proposed model for analysing force curve measurements with spherical tips at large indentations on thin film elastic materials and living cells at the micro and nanoscale.

The equilibrium equations of elastic rods can be obtained by balancing forces and moments, or by rendering a potential energy stationary. For complex filaments the energy route asks less of one's mechanical intuition. However, in the classical Hamiltonian picture, the components of the generalized momenta are postulated a priori and their physical meaning changes at the whim of the coordinate chart. Here, we draw on two ideas from mathematical physics. First, the extended tangent bundle of the configuration Lie group is framed by left-invariant vector fields. Second, we follow a one-dimensional reading of the Cartan--Lepage--Krupka theory of variational forms: in this setting the momenta are not postulated but forced. The Legendre transform becomes a linear change of frame, and a Poisson structure on the extended tangent bundle follows. For an isolated Cosserat rod, the momenta coincide, in every encoding of the rotation group, with the material force and moment familiar from rod theories. In the presence of interactions, two cases arise: interactions that depend only on the configuration, such as gravity, leave this identification intact; interactions that depend on the strains destroy it --- the conjugate momenta and the internal stresses part company. Because energies add, the momenta decompose into the internal stresses and an interaction contribution. Expressing the two factors of the Poisson bivector in different frames --- one adapted to the internal stresses, the other to the conjugate momenta --- then exposes the Hamiltonian flow directly in the internal variables. Applied to a tendon-actuated rod, where the standard passage to the Hamiltonian picture demands a nonlinear inversion, the construction delivers explicit equilibrium equations, the required inversion collapsing to a rank-one correction.

This report explores and compares numerical stabilization methods for transport-dominated flows arising in atmospheric modeling. The Streamline-Upwind (SU) and Streamline-Upwind Petrov-Galerkin (SUPG) stabilization formulations are implemented in Julia's this http URL package and Python's Firedrake package for a test problem with slotted-cylinder initial conditions. These methods are compared for their ability to mitigate spurious oscillations while preserving sharp features against existing hyperdiffusion and quasi-monotone limiter methods, alongside various combinations. For this benchmark, quasi-monotone limiters were most effective at minimizing un-physical extrema, at the expense of diffusing the overall structure. The SUPG method was not found to improve upon the no stabilization case, for this test case in the computed error metrics. However, it performs best at preserving sharp feature and overall structure, among tested stabilized runs. Theoretical properties of SUPG are analyzed, and an asymptotics-based SUPG algorithm is proposed as future work.

Accurate on-device fluid identification is essential for microfluidic applications, yet maintaining reliability under varying flow, pressure, and temperature remains a key challenge. Existing learning-based methods often treat sensor signals as domain-agnostic features, neglecting the underlying physical relationships that govern fluid behavior, thereby limiting generalization and interpretability. To address this, we propose PRIMS, a physics-aware multimodal Transformer that integrates physical knowledge into representation learning and attention mechanisms through three dedicated modules: (1) Physics-based Token Vectorization transforms raw Coriolis and pressure sensor signals into physically meaningful token embeddings; (2) Physical Component Synthesizer models viscosity-related dependencies among flow, pressure, and density; and (3) Physics-guided Fusion captures cross-physical correlations through attention-based integration. By embedding these physics-based relationships directly into the model architecture, PRIMS bridges analytical fluid mechanics and deep learning, enabling interpretable, data-efficient, and resilient fluid classification. Evaluations on a five-fluid benchmark under dynamic flow, pressure, and temperature conditions show that PRIMS achieves 98.92% average F1-score with only 0.46 million parameters, a 14 times reduction compared to state-of-the-art Transformer-based methods. PRIMS also consistently outperforms prior SOTA models under out-of-distribution shifts to unseen temperature ranges and unseen flow-rate ranges, indicating strong robustness to operating conditions not observed during training. These findings suggest that designing architectures that explicitly mirror governing physical relationships can make them learn transferable, environment-independent representations, improving real-world reliability for microfluidic sensing.

Self-excited aerodynamic flows arise across a broad range of systems and can drive nonlinear fluid-structure interactions and aeroelastic instabilities that are challenging and computationally expensive to predict. This paper presents a physics-guided neural differential equation (DE) reduced order model (ROM) combining a nonlinear fluid oscillator, a finite-memory multi-input Volterra series, and a compact neural network correction. The multi-input aerodynamic formulation is generalized to m structural modes, capturing direct and nonlinear cross-modal coupling. The model is identified from a single prescribed-motion CFD simulation with simultaneous excitation of all retained structural modes, and is then coupled with the structural equations of motion for efficient aeroelastic prediction. Applied to transonic buffet over the ONERA OAT15A airfoil, the time-marching ROM predicts aeroelastic stability, frequency lock-in, and limit cycle amplitudes in good agreement with full-order reference solutions. The ROM is used to provide substantial new insight into buffet-induced aeroelastic instabilities involving more than one structural mode.

Compressible multiphase flows involving shocks and material interfaces arise in applications such as bubble collapse and droplet breakup, where strong nonlinear interactions produce complex interface deformation, mixing, and multiscale dynamics. Developing reliable machine learning surrogates for these flows remains challenging due to the simultaneous presence of compressibility, sharp discontinuities, and multiphase effects. In this work, we introduce the first large-scale benchmark specifically designed for shock-driven compressible multiphase flows, comprising 2.4 TB of high-fidelity 2D and 3D datasets \footnote{Dataset repo: this https URL . Dataset sample videos, this http URL , inference rollout plots from autoregressive rollout of the trained baselines are provided in the supplementary\ this http URL } featuring shock-induced bubble collapse and droplet breakup. We evaluate diverse surrogate model families on our benchmarking framework: Neptuna \footnote{Benchmarking repo: this https URL }, including convolutional, spectral, transformer-based, and pre-trained PDE foundation models. Beyond standard MSE training, we investigate composite losses combining MSE with Sobolev, interface-aware, and structure-aware terms, together with adaptive loss balancing using SoftAdapt and GradNorm. Evaluation includes pointwise, spectral, feature-focused, structural, and physics-informed metrics. Results show that no single model performs best across all datasets and metrics, while composite losses significantly improve interface preservation and spectral fidelity. Among adaptive weighting strategies, SoftAdapt provides the most consistent improvements with almost no overhead compared to MSE-only training.

RANS modeling of turbulent heat transfer in liquid metals remains challenging because the very low Prandtl number weakens the similarity between momentum and thermal transport. Several thermal turbulence closures for forced convection in liquid metals are assessed using OpenFOAM v2212. The combinations include the $k$--$\omega$ SST model with the Kays correlation for $\mathrm{Pr}_t$, the four-equation $k$--$\epsilon$--$k_\theta$--$\epsilon_\theta$ model, the logarithmic $k$--$\Omega$--$k_\theta$--$\Omega_\theta$ model, and two algebraic heat-flux formulations for $\overline{u_i'\theta'}$ coupled with either a low-Reynolds $k$--$\epsilon$ model or an elliptic blending Reynolds-stress model (EBRSM). They are evaluated in channel flow, pipe flow, and heated backward-facing step flow against DNS data and results from the original publications, focusing on reproducibility, robustness, and accuracy. Only a limited subset of models proves reliable for low-$\mathrm{Pr}$ flows. The $k$--$\omega$ SST model with the Kays correlation gives the most robust performance and accurate temperature predictions in all cases. The $k$--$\epsilon$--$k_\theta$--$\epsilon_\theta$ model shows good reproducibility and satisfactory agreement with reference data, remaining the most consistent multi-equation alternative. The logarithmic four-equation model exhibits reduced numerical robustness, while the algebraic heat-flux model coupled with the $k$--$\epsilon$ closure fails to reproduce published thermal results despite correct prediction of the momentum field. The EBRSM-based algebraic heat-flux formulation reproduces selected reference results but suffers from significant robustness limitations. The study establishes a unified formulation of the examined closures, correcting inconsistencies in their published forms, and verifies their reproducibility and robustness.

We analyzed experimentally and numerically the bursting of a bubble within a sessile droplet. Our experiments show that both sessile droplet curvature and confinement enhance the energy focusing. In the low-viscosity regime, this effect results in thinner, faster Worthington jets. In the high-viscosity regime, droplets are ejected for values of the Laplace number (the Reynolds number based on the visco-capillary velocity) smaller than the threshold for a bubble in an infinite liquid bath. This is probably the major result of the present work. Numerical simulations show the critical role of the additional pressure gradient arising from the curvature of the sessile droplet interface. The resulting force drives the liquid towards the bottom of the cavity, compressing it and accelerating jet formation. In the low-viscosity limit, the bottom of the cavity becomes smoother before jet ejection. This effect resembles the energy-focusing enhancement that occurs in an infinite liquid bath at the critical Laplace number, where short-wavelength waves are damped by viscosity.

Integral identities relating the skin-friction coefficients and the Reynolds shear stresses in annular cylindrical flows are derived. In the pressure-driven case, an identity for the radial location of the maximum streamwise velocity is obtained and, in the cylinder-driven case, an identity for the bulk velocity is found. The formulas are used to analyse existing numerical and experimental data and simplify to classical channel-flow and pipe-flow identities in the limiting cases of vanishingly small and infinitely large radius ratios.

This work presents a comprehensive numerical validation of the Lyapunov-Liouville theoretical framework and its non-diffusive turbulence closures under freely decaying homogeneous isotropic turbulence (HIT). The closed system of von Karman-Howarth and Corrsin equations is integrated via an autonomous, high-accuracy architecture across three initial states (Saffman-Birkhoff, Loitsiansky, and Gaussian correlation profiles) and Prandtl numbers from Pr = 10^-3 to 1000. The analysis scrutinizes the transient phase, the self-preserving diffusive regime, and the internal structure of turbulence via velocity and temperature increment probability density functions (PDFs). Our findings reveal that the closure accurately captures distinct decay paths. The Saffman-Birkhoff case yields asymptotic exponents m = -1.25 and n = -1.25. The Loitsiansky condition accelerates mechanical decay (m = -1.51) due to higher dissipation but exhibits higher thermal persistence (n = -0.89). Conversely, the Gaussian profile induces ultra-rapid decay (m = -2.7), reaching its operational limit at t = 33 as R_lambda drops below 10. Furthermore, the model replicates the non-equilibrium evolution of characteristic scales. At Pr = 1000, the thermal microscale drops below the Kolmogorov scale, confirming Batchelor's scaling where the Batchelor constant converges to C_B = 3.5 and the Obukhov-Corrsin constant matches C_OC = 1.8. Finally, the synthesized PDFs capture a sharp transition from quasi-Gaussian statistics at low Pr to enhanced, scale-dependent small-scale intermittency at high Pr, validating the predictive robustness of the theory for multi-scale scalar mixing.

In the present study we have assessed the effect of suction through discrete perforations on the transition of the Blasius boundary layer. In particular, the intermittency and the spectra of the streamwise velocity fluctuations, obtained using hot-wire anemometry, were used to evaluate the optimum suction, i.e., one that provides the greatest delay in transition. The displacement thickness Reynolds number at suction was varied between 1400 and 1600, while the number of rows of holes was either four or ten. The suction holes had diameter of the order of the displacement thickness of the boundary layer, a practical size from manufacturing and maintenance perspectives. As the suction strength was increased the transition front moved downstream, with the maximum delay in transition occurring at the optimum suction. When the suction was increased further, the transition front moved upstream again. The results, supported by a scaling analysis, showed that suction volume flow rate is a better indicator of the effects of suction on the transition delay than suction velocity. In particular, suction through different numbers of rows of perforations produces largely similar effects on the boundary layer transition, provided the suction volume flow rate remains the same. However, suction through fewer rows provided a slightly greater delay in transition in addition to a slightly lower optimum suction volume flow rate. The results also showed that suction applied at a lower Reynolds number provides a substantially greater transition delay but at slightly higher values of the normalized optimum suction volume flow rate.

A prevailing consensus holds that flow reversals of the large-scale circulation (LSC) are suppressed in low-Prandtl-number (Pr) fluids, as high thermal diffusivity rapidly dissipates the energy required to fuel the corner-vortex mechanisms. Here, we report Direct Numerical Simulations of liquid metal convection (Pr=0.029) revealing that strong lateral confinement defies this consensus, enabling sustained LSC reversals. We show that confinement triggers a ``plume condensation" transition, reorganizing chaotic thermal plumes into highly coherent, quasi-linear structures. A thermal dissipation analysis demonstrates that this coherence drastically reduces heat loss during transport, allowing plumes to deliver sufficient buoyancy to corner vortices to drive reversals. We map a distinct ``island of reversal" in the parameter space, establishing lateral confinement as a control parameter capable of overcoming the stabilizing effects of high thermal diffusivity.

We develop a coupled model for electroosmotic pumping and passive-solute dispersion of a solvent-free simplified Phan-Thien-Tanner fluid in a compliant slit microchannel. Pressure, wall deformation, axial field, velocity, and dispersion are evaluated self-consistently along the finite-throughput pump characteristic. Lubrication theory, Debye-Huckel electrostatics, an elastic-foundation wall law, and Taylor-Aris macrotransport yield a closed-form flux relation for combined electroosmotic and pressure-driven forcing. Because the shear rate depends cubically on the total shear stress, the two contributions cannot be superposed. The flux decreases monotonically with pressure gradient, ensuring a unique inversion at prescribed throughput. Current conservation couples the axial field to the deformed gap under constant-current and constant-voltage operation. In pressure-free flow, thinning the electric double layer produces a plug-like profile and the Newtonian Taylor coefficient decays as the inverse square of the Debye parameter. Under hydraulic loading, an adverse pressure gradient drives a sheared core counterflow that persists in the thin-double-layer limit, causing the coefficient to approach a finite plateau. At fixed nonzero throughput, partial cancellation between electroosmotic and pressure-driven shear yields a maximum plate number at finite double-layer thickness. This optimum is conditional: joint optimization over throughput and double-layer thickness shifts the overall optimum toward free-flow, thin-double-layer operation. Viscoelasticity can enhance or suppress loaded dispersion, while compliance shifts the pump characteristic and separation optimum. Brownian dynamics validates the reduced model. The resulting load-resolution relation identifies conditions that balance pressure delivery and separation performance.

Machine-learning surrogates of physical systems face a paradox: explainable models facing the challenge of expressivity to capture complex nonlinear flows, whereas expressive deep surrogates match high-fidelity simulations only through massive parameterisations that turn the learned dynamics into a black box. Here, we introduce quantum-compressed machine learning (QCML), which resolves this tension by compressing the latent propagator of a flow surrogate from $524{,}288$ trainable parameters to no more than $8$. This parameter reduction brings the learned dynamical law to the parameter scale of a physical constitutive relation rather than a black-box neural network, making the surrogate directly interpretable and controllable without sacrificing expressivity. The compression is realised by a structured quantum circuit whose unitary propagator constrains the latent spectrum to the unit circle exactly and by construction, replacing exponential error growth with linear accumulation over autoregressive rollouts. Classical regularisation only approximates this constraint: even a quantum-inspired classical baseline penalised towards unitarity collapses within one Lyapunov time on turbulent channel flow, whereas QCML remains stable over the full rollout. Shared phase and coupling angles parameterising the circuit correspond directly to modal frequencies and inter-mode interactions, giving the learned dynamics a physical interpretation in spectral space. On two patient-specific cardiovascular benchmarks, the structured QCML propagator matches the predictive accuracy of its classical counterpart on surface pressure spectra, pressure drop, and wall shear stress. These results establish QCML as a working component of scientific machine learning and a concrete contribution towards practical quantum advantage in real-world prediction.

This work examines the deformation dynamics of dielectric liquid droplet when exposed to a uniform electric field. The experimental investigation involves two-phase configurations, here as silicone oil droplets suspended in castor oil. The droplet dynamics including deformation, elongation, oscillation, and rotation are investigated over a range of electric field strengths using shadow-imaging. In parallel, fluorescent tracer particles were employed to perform threedimensional Lagrangian Particle Tracking (3D-LPT) using the Shake-The-Box (STB) technique, allowing for a detailed characterization of the internal electrohydrodynamic flow within the droplet subjected to a uniform electric field. For silicone oil droplets in castor oil medium (S/R > 1), the droplets initially deform into oblate shape. At sufficiently high electric field strengths, the droplet undergoes an Electrohydrodynamic instability, aligning their axis at an angle to the direction of electric field due to the imbalance in induce electric torque. Upon further increasing the field strength, the droplets display oscillatory deformation before settling into a transiently stable configuration. The current study identifies and characterizes the distinct regimes of droplet behaviour, from initial deformation at low electric fields to oscillatory behaviour at high field strengths depending upon the relative dielectric and fluid properties of the liquid phases.

We introduce a novel coupling of Rulkov neural maps, proposing a heuristic biological interpretation for the transition to non-small values of the perturbations acting on the slow variables. We analytically prove that the coupling preserves boundedness of motion and the existence of a snap-back repeller (leading to Devaney chaos by the Marotto theorem), if they are associated to the original system. For the coupling of two standard chaotic Rulkov maps, we present numerical simulations for the orbits of the system showing the arising of a global strange attractor, whose fractal structure is strongly suggested by the computation of a non-integer Kaplan-Yorke dimension. Furthermore, we perform standard numerical studies concerning time series, Lyapunov exponents spectra, bifurcation diagrams and basins of attraction. Finally, we briefly propose a generalization of the coupling to an arbitrary number of neurons.

A large literature applies a standard pipeline to fractional nonlinear evolution equations -- traveling-wave reduction to a planar Hamiltonian system, addition of periodic forcing, and visual inspection of phase portraits -- to claim bifurcations, quasi-periodicity, and chaos, often without any quantitative diagnostic. This is particularly problematic because the reduced systems are undamped, near-integrable oscillators for which KAM theory confines chaos, if present at all, to thin stochastic layers, so the burden of proof for a chaos claim is high. We analyze these pitfalls and quantitatively re-examine a representative example, Ullah, Ali and Roshid's study of the second fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) model [PLoS ONE 19(7): e0307565 (2024)], using analytical arguments and four independent diagnostics (Benettin largest Lyapunov exponents in two configurations, a separation-growth test over 3x10^6 time units, stroboscopic Poincare sections, spectral analysis). We find that (i) its linear stability analysis concludes "unstable propagation" from a dispersion relation that is real for every real wave number: all modes are neutrally stable, and the reported singularity is a pole, not a temporal instability; (ii) its unforced "quasi-periodic" system is necessarily periodic, being a planar autonomous Hamiltonian system; (iii) all four chaos assertions fail every diagnostic -- exponents bounded by 5x10^{-7}, linear-in-time separation growth, smooth closed invariant Poincare curves -- while the quasi-periodic assertion is confirmed; (iv) its equilibrium classification and phase portraits are correct. We also document a false positive of the Gottwald-Melbourne 0-1 test on a regular orbit and show that stroboscopic parameter sweeps of conservative systems yield "chaotic-looking" diagrams for purely regular tori, closing with a checklist of standards for chaos claims.

Resonance states spatially diverge and are thus not square integrable. Instead, their norm is defined by the biorthogonal scalar product of left and right states. We replace the corresponding volume integral by a convenient boundary integral in piecewise homogeneous systems and apply this procedure to diverse physical settings. For a quantum particle in any number of dimensions we treat hard-wall and piecewise constant potentials. For electromagnetic systems with piecewise homogeneous material properties, we consider three-dimensional and effectively two-dimensional cavities of arbitrary shape. As examples, we treat the spherical scatterer and the circular disk.

We show how large-deviation statistics allows one to obtain reliable estimates of the multiplicity of stable fixed-points in a model of neural ordinary differential equations previously employed in computational tasks. The result is obtained by developing a suitable perturbative method in the amplitude of the disorder. It turns out that for not-too-large coupling strengths there are no qualitative differences between the symmetric case, when the dynamics is a purely gradient evolution, and the asymmetric case, when limit cycles and chaos can, in principle, arise. The selection of this specific model is dictated by pedagogical reasons, but we are confident that the approach can be extended to other many-degree-of-freedom dynamical models characterized by different classes of random coupling matrices.

Scientists increasingly express their ideas as dynamic models of complex processes. It is often much easier to simulate these models than to calculate the probability of their generating a particular outcome, making likelihood-based estimation infeasible. Existing likelihood-free approaches rely either on manually chosen summary statistics or on representations learned by neural networks. The former is error-prone and laborious, while the latter is computationally intensive, leaving many scientists in a difficult position. We show that, for a large class of dynamic models, parameters can be estimated by matching a small number of random features of the observed and simulated data. Specifically, we adapt results from nonlinear dynamics to show that models with a $p$-dimensional parameter can generically be identified from just $2p+1$ random features. We introduce two estimators for stationary and nonstationary processes, respectively, and we establish their consistency under mild regularity conditions. More broadly, our results serve as the foundation for a new class of random feature methods for simulation-based estimation and inference.

Lorentz transformations in time and two space dimensions consist of boosts and rotations, and combinations thereof. In general, the combination of two boosts is not another boost: It is a boost followed by a rotation. The rotation angle is called the Wigner angle. Although it is straightforward to determine the energy and direction of the combined boost, it is difficult to determine the Wigner angle. In this article, the vector, matrix and spinor derivations of formulas for the Wigner angle are reviewed, and the underlying mathematics and physics are discussed briefly. Although the derivations are different, the results they produce are equivalent, as they should be. Like many physics problems, if one looks at the problem in the right way, it is not difficult to solve.

A soft particle driven through a pore narrower than itself must deform to pass, and how quickly it does so is set by how hard it is to squeeze. We propose a mathematical framework for turning rate measurements of this driven, stochastic passage into quantitative mechanical measurements. Treating the entry of the particle as one-dimensional Brownian dynamics across an elastic barrier, we solve the transport problem exactly and identify two dynamical regimes: at low drive the passage is thermally activated and limited by the energy needed to deform the particle, and at high drive it is friction-limited. We propose a framework to extract the particle's deformation energy and relevant geometrical information by combining measurements in these two regimes. This method could be used in the context of nanopore sensing, where the drive is an applied voltage: the framework then provides a self-calibrating route---translocation elastometry---from a current-voltage measurement to the elasticity and shape of individual soft nanoparticles.

Inflatables made of thin sheets constitute a lightweight, scalable alternative to conventional soft robots. Since sheets are essentially inextensible while offering low resistance to bending, the shape of a straight tube should be trivially set by volume maximization. We show that networks of parallel tubes made from two sheets differing in stiffness defy this expectation as their global shape is governed by the binding angle at the junctions of adjacent tubes. Through this angle, the stiffness asymmetry induces a pressure-dependent curling and stiffening of the networks. Modeling a tube cross-section as two coupled rods, we quantitatively describe the geometry and mechanics of this new class of inflatables. Our model captures unexpected mechanical features such as a stiffness scaling as the square root of pressure and a contact-induced stiffening between neighboring tubes -- challenging common assumptions on thin-sheet inflatables. Unlike prior work restricted to the high-pressure regime, the pressure-dependent description further enables multiprogrammable control over a continuous range of curvatures. Discussing a variety of examples, we finally show that networks of asymmetric tubes are a versatile platform for functional shape-morphing objects.

Ballistic aggregation is a canonical non-equilibrium process, relevant across scales from granular gases to planetary accretion. Collisions are driven by differences in velocities, building up persistent correlations between neighbors. Here, we provide the first experimental realization of one-dimensional ballistic aggregation in a train of droplets formed by the breakup of a liquid jet. Experiments and simulations confirm the analytically predicted scaling, with the global process shown to be governed by a single length scale. While air drag inverts the sign of neighbor velocity correlations, a 1D ordering constraint protects bulk characteristics of ballistic aggregation such as the scaling exponent and the shape of the large mass tail. More broadly, our results show that Smoluchowski-like mean-field descriptions fail when collisions carry directional memory -- as demonstrated here for jet-generated sprays.

Two-temperature induced phase separation (2-TIPS) has emerged as a generic non-equilibrium mechanism in scalar active systems with heterogeneous activity, where particles coupled to different thermal reservoirs spontaneously demix into dense cold and dilute hot phases. Unlike equilibrium phase separation or motility-induced phase separation (MIPS), 2-TIPS is driven solely by unequal energy injection and the resulting heat flux between particle species. This review summarizes recent advances in 2-TIPS across diverse soft-matter systems, highlighting both its universal non-equilibrium mechanisms and the emergent ordered phases arising from particle shape anisotropy, chirality, confinement, and topology. We further discuss density-dependent phase-separation kinetics and coarse-grained descriptions linking microscopic dynamics to macroscopic behavior, and outline key directions for future research.

The mechanical and structural properties of dsDNA have been successfully described by models with varying levels of complexity and coarse-graining schemes. Prior work has characterized local stacking/twist effects and force-torque phase diagrams under external constraints. However, the role of base-pairing and torsional elasticity in global morphological transitions remain poorly characterized in the absence of external constraints. Here we investigate the delicate balance required for the strength of base-pairing interactions and the twisting energy to preserve the double-helix structure in a model made up of two semiflexible chains. We found that the model exhibits several distinct morphological phases: flat, random coil, double-helix, and the unwound double-helix. We calculate the Gauss linking number to characterize transitions between these phases.

Diffusiophoretic transport of colloids in pressure-driven channel flow is commonly analysed in two limits: an early-time regime in which the solute field is fully two-dimensional, and a late-time macrotransport regime in which cross-sectional homogenization leaves only a weak axial bias on the particles. For colloids, however, many experiments operate in the broad intermediate window \(a^2/D_{\mathrm s}\ll t\ll a^2/D_{\mathrm p}\): the solute has entered the Taylor-dispersion regime, but the particles remain effectively non-diffusive across the gap. We show that the Taylor-dispersed solute retains a residual transverse gradient that is Péclet-enhanced relative to the axial gradient and decays only as \(t^{-1/2}\). This gradient is small in the solute concentration but large enough in \(\nabla\ln c\) to drive cross-streamline migration of colloids. Attractive fronts (\(c_{\mathrm f}>c_{\mathrm i}\)) move particles toward faster centreline streamlines, sharpening the leading edge and accelerating removal; repulsive fronts (\(c_{\mathrm f}

Unique and rapid classification of knots and links is an open mathematical problem that is relevant to a range of (bio)physical systems, including polymer melts, DNA, and proteins. In this paper, we explore a data-driven approach to the classification problem of link topology. Extending the framework introduced in Ref. 1 (Sleiman et al, 2024 Soft Matter, 20(1), pp.71-78), we show that a feedforward neural network trained on the writhe density matrix classifies thermally equilibrated configurations of the first six prime links with 97% accuracy. We demonstrate that this accuracy remains high across a range of temperatures and lengths of link components, while rapidly deteriorating with the addition of topology-altering Gaussian noise; a result consistent with the writhe density matrix containing features sensitive to topology. Our results show that neural networks based on the writhe density matrix efficiently classify two-component links, establishing machine learning as a promising tool for rapid classification of more complex link topologies, e.g. Borromean rings and multi-component links, as the computational cost of exact numerical calculation of topological invariants becomes prohibitive.

An axisymmetric general synthetic iterative scheme (AxiGSIS) is proposed to simulate rarefied gas flows and charged particle transport under prescribed electrostatic fields. This solver adopts a finite-volume discrete velocity method defined over the two-dimensional axisymmetric meridian plane paired with a three dimensional molecular velocity space. Under the GSIS framework, the kinetic solver computes nonequilibrium stress and heat flux, which are subsequently imported as corrective source terms into the macroscopic synthetic system. Fast iterative updates of low order flow primitive variables are performed on this macroscopic system, whose corrected flow fields are then fed back to the kinetic solver. This bidirectional coupling enables rapid propagation of macroscopic information and substantially accelerates steady state convergence, particularly in near continuum flow regimes. Four benchmark flows are examined: the Taylor Couette flow, neutral nozzle expansion flow, charged particle flow past an electrostatic sphere, and electrostatically accelerated charged-particle nozzle flow. Results show that AxiGSIS reproduces the reference kinetic solutions and accurately captures axisymmetric flow physics and charged-particle responses to prescribed electrostatic fields. Utilizing fewer spatial cells and iteration steps, AxiGSIS substantially cuts computational overhead relative to conventional kinetic iterations, particularly for low and moderate Knudsen number flows.

In this study, we propose a dynamical model for the evolution of velocity gradients in compressible turbulent flows with vibrational non-equilibrium effects, using physics-assisted deep neural networks. Such models provide a powerful framework for understanding the nonlinear physics associated with small-scale structures. In compressible flows, the influence of thermodynamic fields on velocity-gradient dynamics is represented through thermodynamic gradient field (TGF) tensor. The TGF tensor is one of the primary unclosed terms in velocity-gradient evolution equations. The TGF tensor comprises contributions from the pressure-Hessian tensor, $\rho\boldsymbol{H}$, and the baroclinic tensor, $\boldsymbol{B}$. Accordingly, the proposed framework incorporates closures for both $\boldsymbol{H}$ and $\boldsymbol{B}$ tensor dynamics. Building upon existing phenomenological closures for the $\boldsymbol{H}$ tensor governing mechanisms, we develop a neural-network-based closure for the inviscid mechanism responsible for generating the $\boldsymbol{B}$ tensor. Unlike the other recently used tensor bases, the presented work employs a novel tensor basis allowing for the inclusion of non-symmetric features in the model. The framework also incorporates a data-driven closure for vibrational non-equilibrium this http URL resulting framework combines phenomenological and data-driven representations of various $\boldsymbol{H}$ and $\boldsymbol{B}$ tensors governing mechanisms, termed as the \textit{hybrid enhanced homogenized Euler equation} (H-EHEE) model. Model predictions are evaluated across a range of turbulent Mach numbers and compared against direct numerical simulation (DNS) data and existing compressible velocity-gradient models. The H-EHEE model exhibits close agreement with DNS statistics and provides significant improvements over existing models, particularly in highly compressible flow regimes.

Wave scattering by a thin, porous circular plate submerged in deep water is investigated. The problem is formulated as a second-kind hypersingular Fredholm integral equation over the unit disk, solved numerically using the Boundary Element Method. The analysis focuses on calculating hydrodynamic forces, specifically added mass (real part) and damping coefficient (imaginary part). Results demonstrate the influence of the porosity parameter G: less porous plates (G real) increase added mass and hydrodynamic force, while more porous plates (G imaginary) reduce these effects but increase the damping coefficient. The proposed formulation is validated, showing excellent agreement with established literature.

Turbulent boundary layers (TBLs) subjected to adverse pressure gradients (APGs) are common to industrial aerodynamic applications, yet the effect of freestream turbulence (FST) on TBLs developing under moderate APGs remains insufficiently understood. Wind-tunnel experiments were conducted to investigate the effects of FST on a developing TBL over a NACA 0015 airfoil. Varying the angle of attack (2 and 4$^\circ$) adjusted the pressure gradient, and hotwire anemometry measured boundary layer properties at different chordwise positions ($x/c$ = 0.400--0.625, with $\beta = \delta^*/\tau_0 dP/dx$ = 0.2-1.5). The FST level was increased using static grids, resulting in levels ranging from 0.15 to 6$\%$. The chord-based Reynolds number was kept constant at around 250,000 for all configurations. The results show that increasing FST systematically modifies the mean-flow development of the APG boundary layer. Higher FST levels reduce the shape factor and partially suppress the APG-induced wake in the mean velocity profile, while increasing the skin-friction coefficient towards values closer to canonical ZPG behaviour. The streamwise velocity variance is amplified in both the inner and outer regions, and spectral analysis shows that this increase is associated with energetic large-scale motions introduced by the freestream turbulence, with characteristic wavelengths of order $\lambda_x/\delta \approx 13$. These large scale structures penetrate into the boundary layer and contribute to the near-wall variance, with a stronger effect observed as the adverse pressure gradient increases. The results show that FST is a governing parameter in developing APG TBLs over airfoils and that its influence is amplified by the pressure gradient. It must therefore be considered when interpreting mean-flow evolution, turbulence statistics, and scale interactions in realistic aerodynamic environments.

This study examines the formation, quantification, and fractal characterization of corner vortices in slow viscous incompressible flow within a triangular cavity. The governing Navier-Stokes equations are solved numerically using a pressure-based coupled solver, and the resulting vortex cascade is analyzed through the size and intensity ratios of successive eddies in the spirit of Moffatt's theory of corner vortices. The fractal properties of the vortex sequence are then investigated using the area-perimeter method. An empirical relation is proposed to estimate the fractal dimension of any successive vortex in the cascade for arbitrary grid resolution. The results demonstrate that the corner vortices possess non-integer fractal dimensions between 1 and 2, and that this dimension is systematically linked to vortex size and intensity. The influence of Reynolds number on the fractal scaling is also examined. Finally, a comparative analysis of self-similarity in triangular and square cavities confirms that the observed corner-vortex cascade exhibits robust fractal behavior across geometries and flow regimes.

Microfluidic mixing is important for nanoparticle fabrication, where rapid contact between the solvent and nonsolvent streams is needed to control the formation process. Various micromixer geometries have been developed and analyzed to improve mixing efficiency. However, for toroidal micromixers, the role of flow rate ratio and geometric asymmetry has not been examined in detail. In this study, the mixing process of two toroidal micromixer designs is investigated, namely symmetric and asymmetric, with emphasis on the impact of flow rate ratio and geometric asymmetry during the mixing of miscible fluids. Numerical simulations are carried out to examine the mixing behavior of these toroidal micromixers for different flow rates and flow rate ratios. High-fidelity numerical simulations are performed using the stabilized finite element method. The concentration and velocity fields are used to examine how the chamber asymmetry can affect the mixing performance. Experiments are also conducted to provide a validation for the numerical results. We demonstrate that the asymmetric toroidal mixer design generally improves the mixing over the conventional design, especially at low to moderate total flow rates. The results obtained show that improved mixing can be achieved without changing the overall mixer size.

We present an unfitted boundary algebraic equation method for the two-dimensional exterior/interior Stokes equations on a staggered MAC grid. By constructing an explicit free-space pair of velocity and pressure lattice Green's functions (LGFs) from free-space Laplace LGFs, we represent homogeneous fields using sources supported exclusively on thin staggered boundary layers. This formulation imposes physical Dirichlet data at cut points via local interpolation, while sampled-normal rank updates remove hydrostatic null modes associated with single or multiple obstacles. The workflow parallels that of classical boundary integral formulations and requires no artificial boundary conditions for exterior flows, but follows a discretize-then-represent route and does not require singular/near-singular quadrature. The resulting dense boundary system is solved via GMRES, utilizing a componentwise discrete Calderón preconditioner built from the scalar Laplace kernel and padded FFTs for fast volume convolutions. Extensive numerical validation, including multiply connected domains, narrow gaps, and Moffatt eddies, confirms discrete incompressibility to solver accuracy and recovers the expected Moffatt eddy scaling. We achieve second-order velocity and pressure convergence and bound maximum discrete divergence within numerical accuracy. The discrete Calderón preconditioner reduces the condition number by orders of magnitude and yields nearly mesh-independent conditioning in exterior configurations, while remaining effective---though more demanding---for narrow-gap and fine-grid interior problems.

Sand dunes are bedforms that grow due to the action of a fluid flow over a sand bed or pile. Whenever the fluid flow is mainly in one direction and the availability of sand is limited, crescent-shaped dunes known as barchans appear. These dunes are a strong attractor, being found on Earth, Mars, and other celestial bodies, usually in dune fields where they interact with each other, the terrain, and dune-size obstacles. In this review, we discuss the processes and outcomes of the different barchan-barchan and barchan-obstacle interactions, based on grain-scale subaqueous experiments and numerical simulations. We propose that those interactions depend basically on the Shields and Stokes numbers (that are two dimensionless parameters), the transverse position of bedforms, and the size ratio between the interacting objects. In addition, we show in detail the fluid flow, the trajectories of grains, and the resultant force acting on each grain, explaining the mechanisms for the different behaviors observed. Finally, we discuss the implications for the aeolian case, and put into perspective the current findings.

Near-critical dynamics are often linked to enhanced computation, but the underlying mechanism remains unclear. We address this question in reservoir computing, where a fixed recurrent network maps input sequences into high-dimensional states and only a simple readout is trained. We extend fixed-reservoir universality results to discrete-time input-driven reservoirs and connect their key geometric condition, neighborhood separation, to dynamics. To this end, we introduce a finite-resolution neighborhood separability index and an input-conditioned maximal Lyapunov exponent. We find that neighborhood separability, chaotic time-series prediction, and smooth high-dimensional representation geometry are optimized in the same narrow window of marginal driven stability. In this regime, the covariance spectrum approaches the power-law scaling expected for near-optimal smooth representations. Our results link edge-of-instability computation, universality, readout performance, and optimal representation geometry within a common dynamical framework.

Nerve impulses can be modelled as electromechanical density waves within the improved Heimburg-Jackson model. The inclusion of higher-order polynomial nonlinearities leads to a generalized Boussinesq equation with third and fourth order nonlinearities that, under a traveling-wave reduction, reduces to a Liénard-type equation. Applying a factorization method yields exact Lambert W-kink soliton solutions that represent localized nonlinear density waves near the membrane melting transition. Beyond providing exact solutions, the factorization uncovers an underlying supersymmetric structure. The associated operators satisfy algebraic relations analogous to those of supersymmetric quantum mechanics, thereby enabling the construction of a partner soliton. This supersymmetric pairing establishes a novel and previously unexplored connection between nonlinear electromechanical wave propagation in biological membranes and supersymmetric quantum-mechanical methods. The resulting framework offers a theoretical foundation for analysing mechanically induced perturbations and their nonlinear propagation in nerve membranes, with potential implications for understanding the biomechanical mechanisms underlying traumatic brain injury.

Vortices and vortex rings are topological structures that arise in various physical systems. However, the generation of spatiotemporal vortices (STVs) and vortex rings (STVRs) has so far relied on complex, often active wavefront modulation. We theoretically and experimentally demonstrate that spatiotemporal coupling can drive unstructured wave packets to form vortices upon scattering from simple obstacles. The resulting STVs and STVRs possess controllable topological charges and excellent propagation stability. These findings reveal a fundamental mechanism for spatiotemporal singularity formation and provide a universal route to structured-wave generation.