Employing high-vacuum electrospray deposition and scanning tunneling microscopy, we investigated how individual poly(3-hexylthiophene) (P3HT) chains navigated on the periodic energy landscape of a reconstructed Au(111) surface. The resulting polymer conformations were governed by the interplay between the periodically corrugated substrate, in particular the depth and regularity of the modulated surface potential, and thermal energy. On a regularly reconstructed surface, annealing at °C provided sufficient energy for chain segments to overcome energy barriers of the corrugated surface potential landscape, allowing monomers along the chain to experience a strong thermodynamic driving force toward the low-energy valleys on the surface. The adsorbed polymers adopted a state where the polymer conformations were replicating the herringbone pattern. By contrast, on an irregularly reconstructed surface, the correspondingly disordered potential landscape yielded a diverse mix of coiled polymer chains performing a two-dimensional random walk and collapsed chains located in troughs of the energy landscape. Intriguingly, annealing at °C forced polymers to form clusters of many chains. Our results establish that thermal energy and substrate topography represent control parameters for altering polymer conformations, providing a mechanistic framework for rationally designing polymer nanostructures at the molecular level.

Active matter is driven out of equilibrium by a local influx of energy. While classical active matter has been extensively studied, the extension of active matter concepts to quantum systems has been explored far less. In this work we develop a full quantum description based on the Wigner function. By introducing a hybrid Wigner master equation that incorporates classical active motion and quantum degrees of freedom, we compute the quantum mean-squared displacement (MSD) using established techniques from classical active matter. We analytically derive the time dependence of the MSD and clarify the conditions under which the characteristic scaling with time $\mathrm{MSD}\sim t^{6}$ emerges. We further show that, for certain parameter and initial conditions, the MSD can exhibit an even steeper scaling regime $\mathrm{MSD}\sim t^{7}$, and we examine the robustness of these behaviors against quantum fluctuations of the initial state.

Colloidal crystals permeated by mobile ions exhibit a coupling between electrostatic and elastic degrees of freedom that renormalizes the effective screening length and induces wave-vector-dependent elastic softening. Building on a recently proposed continuum model [\textit{Commun. Theor. Phys.} \textbf{77}, 055602 (2025)], we perform a rigorous Gaussian fluctuation analysis to elucidate the stability limits of the homogeneous phase. By integrating out the electrostatic fluctuations, we derive the effective elastic modulus $\Gamma(q)$ as a function of wave vector $q$. We show that the long-wavelength modulus $\Gamma(0)$ remains identically equal to the bare modulus $\beta K$, protected by perfect ionic screening. In contrast, the short-wavelength modulus $\Gamma(q\to\infty) = \beta K(1-\xi)$ softens as the electrostatic-elastic coupling $\xi \equiv 2\beta n_0 v_0^2 K$ increases, vanishing at a critical value $\xi=1$. For $\xi>1$, the fluctuation spectrum exhibits a negative eigenvalue for all wave vectors $q > q_c = \kappa_0/\sqrt{\xi-1}$, signaling an ultraviolet instability of the uniform phase. In a real colloidal crystal, this divergence is regulated by the discrete lattice cutoff $q_{\max}\sim\pi/a$, confining the physical instability to a finite band $q_c < q < q_{\max}$. The macroscopic limit $q\to 0$ remains unconditionally stable for all $\xi$. The transition at $\xi=1$ thus marks the onset of short-wavelength mechanical failure, while macroscopic elastic stiffness remains intact. Our analysis clarifies the proper physical interpretation of the minimal coupling model and provides a consistent picture of how non-DLVO interactions can drive local structural collapse in charged colloidal crystals.

Surface functionalization plays a decisive role in the performance of biosensors, as it governs the efficiency and stability of biomolecule immobilization at the sensor interface and, consequently, the overall performance of the biosensing platforms. In this work, we present a comparative study of three organosilane chemistries - APTES, APDMS, and CPTES - applied to a SiO2 terminated 1D photonic crystal able to sustain Bloch surface waves and designed to operate as optical biosensors in both label free and fluorescence enhanced modes. Each chemistry was evaluated through a standardized label-free protocol based on the interaction between immobilized SARS CoV 2 spike protein and its corresponding antibodies, enabling quantitative assessment of binding efficiency, nonspecific adsorption, and signal repeatability. CPTES exhibited the most favorable balance between specific signals, reduced variability, and low nonspecific adsorption. The three chemistries were subsequently tested in fluorescence mode for the detection of anti SARS CoV 2 IgG antibodies in human serum, demonstrating the suitability of BSW enhanced fluorescence for rapid serological analysis. Overall, the study identifies CPTES as the most robust and reproducible functionalization strategy among the three investigated for BSW biosensing and highlights the potential of the platform for fast, sensitive detection of clinically relevant antibodies.

Active self-assembly can bypass equilibrium bottlenecks through external energy injection. However, generic driving typically distorts target structures and requires sustained energy input even after assembly is complete. Here, we investigate a class of non-reciprocal interactions that accelerates assembly while preserving the equilibrium Boltzmann distribution. The probability currents induced by these odd interactions reshape fundamental processes, including activated barrier crossing, soft-mode relaxation, and transitions between metastable states. In particular, these currents enhance Arrhenius rates by driving particles across otherwise inaccessible free-energy barriers. We show that this acceleration arises from an effective increase in the mobility of the reaction coordinate, mediated by non-reciprocal coupling between mechanical modes. In turn, we discover a trade-off between kinetic acceleration and power dissipation when active forces are engaged. Our results suggest a route to energy-efficient, high-fidelity self-assembly via active catalysts that transiently accelerate relaxation toward equilibrium targets and deactivate upon reaching the desired state.

We investigate the flow of spherical, bulk granular particles down an inclined plane mixed with small-sized spherical lubricant particles using discrete element method simulations. Predefined cohesive interaction is implemented between lubricant and bulk particles, enabling the coating of the former over the latter. The overall flow rate exhibits non-monotonic dependence on lubricant content. Initially, it increases with lubricant addition, reaches a maximum at an intermediate lubricant content, and decreases for even higher lubricant content. The increase in the flow rate is attributed to a lower inter-particle friction coefficient between lubricant-coated bulk particles. The decrease in the flow rate at higher lubricant content, on the other hand, is attributed to enhanced densification and increased damping between crowded particles. Both these occurrences are examined using various flow level characteristics. The simulation results are found to be in qualitative agreement with previous experimental results. Overall, the outcome integrates novel computational insights and prior experimental results to enhance the understanding of the powder lubrication phenomena.

The Onsager principle provides a variational route to the phenomenological equations of dissipative dynamics through the minimization of the Rayleighian. We develop a covariant formulation of the Onsager principle for active systems, ensuring geometric consistency under coordinate transformations. To further incorporate thermal fluctuations, we formulate the Onsager-Machlup principle for active systems by considering the Onsager-Machlup functional and the corresponding path probability for stochastic trajectories. Requiring that the path probability obeys the detailed fluctuation theorem, we show that the extended Onsager-Machlup theory is consistent with stochastic thermodynamics. Moreover, we incorporate inertia into the variational framework and show that the proper covariant equations follow when the covariant acceleration is held fixed during the variation.

Capillary rise is one of the classical problems in fluid mechanics and is traditionally described by Jurin's law, which balances capillary suction against hydrostatic pressure. Here we extend this classical result to active fluids, materials that generate internal stresses through microscopic energy consumption. Using the continuum theory of active nematics, we show that activity modifies the normal stress balance at the liquid-gas interface through an additional active normal stress contribution. This leads to a generalized active Jurin's law, which can be written in dimensionless form as \(H_{\infty} = 1 - \mathrm{Ja}_a \xi_0\), where \(H_{\infty}\) is the dimensionless active Jurin height at equilibrium, \(\mathrm{Ja}_a\) is an active Jurin number comparing active stress to capillary pressure, and \(\xi_0\) characterizes the alignment of active constituents at the meniscus. The theory predicts that extensile and contractile active fluids can either enhance or suppress capillary rise depending on the magnitude of activity and the interfacial alignment state. From this relation we construct a phase diagram in the \((\mathrm{Ja}_a,\xi_0)\) plane that delineates regimes of activity-enhanced rise, activity-suppressed rise, and complete suppression of the classical capillary state. When orientational order depends on confinement and flow, the coupling between activity and capillarity produces nonlinear equilibrium conditions that may admit multiple steady heights; linear stability analysis reveals that the overdamped dynamics selects a single stable state, whereas the inertial extension allows the possibility of activity-induced bistability. These results show that internally generated stresses fundamentally reshape one of the most classical capillary transport problems.

Using molecular dynamics simulations driven by a machine-learned interatomic potential, we investigate at low to intermediate pressures the $\lambda$-transition of sulfur, a temperature-induced polymerization. At ambient pressure, we capture the melting of crystalline cyclo-octasulfur into a liquid of molecular rings. Within this liquid, the concentration of non-S$_8$ rings increases with temperature; we show that these molecules act as reactive centers, which eventually trigger polymerization. We reproduce key experimental signatures of the $\lambda$-transition, including the sharp increase in heat capacity and the pronounced dependence of the transition temperature on the heating rate. Building on this, we reconstruct a phase diagram of polymerization up to intermediate pressures. Our results reveal a moderate decrease of the polymerization temperature with pressure, culminating with its merging with the melting line at a critical point. Beyond this point, we provide direct evidence of polymerization emerging from the crystalline phase. By analyzing temperature-ramp trajectories, we observe the formation of non-S$_8$ rings, open chains, and extended polymeric structures which retain features of the crystalline arrangement; further heating the system leads to disorder taking over through melting. Polymerization is therefore initiated slightly before melting. Altogether, our findings provide a microscopic picture of the $\lambda$-transition throughout the sulfur phase diagram.

Bubbles released from a needle show shape deformations that depend on the surfactant concentration of the surrounding liquid. We develop a model that predicts the surfactant concentration based on experimental early-stage observations of these deformations. Using high-speed imaging, we examine bubbles within the first 144 ms of ascent, corresponding to a vertical rise distance of approximately 40 mm and extract the instantaneous aspect ratio (AR) and analyse its temporal evolution. In clean conditions, bubbles exhibit pronounced shape oscillations resulting from the periodic exchange between surface and kinetic energy. The presence of surfactants leads to an immediate damping of these oscillations, characterised by reduced AR amplitudes and earlier peak deformations. This damping effect intensifies with increasing surfactant concentration until a near-saturation regime is reached, beyond which bubbles remain largely spherical and further increases in concentration produce indistinguishable AR profiles within the early-stage observation window. To develop the prediction model, an aspect-ratio-based analysis methodology is proposed, which yields an empirical relationship capable of estimating surfactant concentrations between 0 ppm and 2.9 ppm. We finally test the reliability of the model on unknown surfactant-laden bubbles. The model successfully detected the presence and relative extent of surfactant contamination as higher concentrations were introduced.

Direct Numerical Simulation (DNS) of a Mach 6 boundary layer over a flat plate is performed to assess the effect of spanwise non-uniform surface temperature on breakdown to turbulence under deterministic forcing. The streamwise location of laminar to turbulent transition in hypersonic boundary layers has a significant influence on viscous drag and aerodynamic heating of external surfaces of hypersonic vehicles. Previous work investigated the stabilization of hypersonic boundary layers by optimally growing streaks. More recently, DNS for a hypersonic boundary layer showed that it is possible to generate streaks through a spanwise non-uniform surface temperature distribution. The laminar computations showed the control method can stabilize the second Mack mode and it is robust across a range of Mach numbers and wall temperature ratios. In this work, two scenarios are investigated where two-dimensional (second Mack mode) and oblique (first Mack mode) disturbances dominate the initial linear stage of transition. It is found that weak control streaks with amplitude below 5% of the freestream velocity can reduce high-frequency shear-stress due to the second Mack mode by approximately 30% relative to the uncontrolled configuration, and delay transition. For first Mack mode dominated breakdown, the control streaks have no effect on transition location, but the peak amplitude of the spanwise-integrated wall heat flux is reduced. For the first and second Mack mode-dominated scenarios, the mean and high-frequency peak heat transfer are reduced approximately by 15% and 34%, respectively. The dominant mechanisms are identified and attributed to the pressure work contribution to turbulent kinetic energy and the second Mack mode dilatation work.

We find that waves develop in a time-decaying mixing layer of viscoelastic fluid, leading the mean-flow to yo-yo. This is in sharp contrast with Newtonian fluids, where laminar mixing layers evolve monotonically. We combine direct numerical simulations with a theoretical analysis of the energy budget for the flow to uncover the underlying physical mechanism. The yo-yoing of the mean-flow is shown to be driven by the elastic polymers injecting energy into the fluid and, in turn, being rotated by the large-scale mean shear. We then provide the mathematical model of the problem and solve it analytically, finding wave solutions with non-linear dispersion predicting the period of the yo-yoing and the parameter range where it occurs. As decaying mixing layers are one of the simplest and canonical examples of unsteady flows, the phenomenon identified here explains the anomalies recently observed in experiments of unsteady viscoelastic flows in complex geometries.

This study derives conservative and skew-symmetric formulations of the incompressible flow equations in a terrain-following sigma-coordinate system that preserve key structural properties of the Cartesian formulation. Unlike conventional formulations based on the direct application of the sigma-transformation to Cartesian equations, in which metric-induced terms disrupt the intrinsic structure of the governing equations, the proposed formulations are designed to avoid these structural inconsistencies. A conservative form is derived in a manner consistent with general conservation laws, and its modified eigenstructure is analyzed relative to the Cartesian counterpart. A skew-symmetric formulation is then derived by introducing a new set of variables, yielding a form that is energy-conserving for the Euler equations and energy-bounded for the Navier-Stokes equations. Finally, we discuss characteristic-based boundary conditions to ensure energy boundedness of the system.

We introduce a modal representation for Lagrangian trajectories in turbulence, termed Lagrangian Proper Orthogonal Decomposition (LPOD). An ensemble of particle trajectories is used to construct velocity time series, which are normalized independently for each trajectory to isolate fluctuations. Principal Component Analysis is then applied to the resulting dataset, with temporal instances defining the feature space. The method is tested on trajectories from both direct numerical simulations of homogeneous isotropic turbulence and three-dimensional particle-tracking experiments, showing that the leading modes exhibit similar structures and energy distributions in both cases. Truncated reconstructions are obtained by combining modes and coefficients, rescaling the fluctuations, and integrating in time. For trajectories of the order of the integral time scale, single-particle dispersion and curvature statistics are accurately reproduced using a limited number of modes (c.a. 10), whereas capturing the tails of acceleration distributions requires a larger set (c.a. 30-60). Longer trajectories require progressively more modes for accurate reconstruction. These results suggest a possible route to data-driven generation of synthetic particle trajectories via stochastic sampling of the modal Lagrangian dynamics.

Direct numerical simulations of an accelerating turbulent boundary layer (TBL) over a smooth wall and a wall fully covered with streamwise-aligned riblets are performed to investigate drag modulation and its underlying mechanisms. The riblet-scale flow is resolved using an immersed boundary method. Starting from a zero-pressure-gradient (ZPG) TBL at Re=6800, the flow undergoes a threefold freestream acceleration over seventy-five boundary-layer thicknesses, matching the development reported by Warnack and Fernholz (1998), and consequently experiences relaminarization followed by retransition farther downstream. The riblets, defined by a sinusoidal spanwise profile with initial s+=15.2 and lg+=10.5, correspond to near-optimal drag-reducing size in ZPG flows. However, even modest acceleration renders them drag-increasing, showing that the conventional ZPG interpretation based on total-drag viscous scaling does not apply directly in this non-equilibrium flow. During relaminarization, the drag penalty arises primarily from geometry-determined concentration of viscous shear near the riblet crest, with negligible direct Reynolds- and dispersive-stress contributions prior to retransition. Despite the drag increase, the overlying TBL remains statistically similar to the smooth-wall case when scaled with the total shear stress at the groove opening, demonstrating that this shear sets the relevant scaling for the TBL, while the additional drag generated within the grooves remains largely decoupled from the outer-layer turbulence dynamics. This partial decoupling persists until the onset of retransition, when spanwise Kelvin-Helmholtz rollers develop near the riblet crest and promote earlier, stronger retransition through their interaction with the residual near-wall streaks. These findings provide a revised physical picture of riblet performance in non-equilibrium turbulent flows.

The linear and nonlinear motions of a damped rigid planar pendulum, driven by vibrating its pivot sinusoidally, are reexamined. The pendulum is known to exhibit periodic, quasiperiodic, and chaotic motions. Floquet analysis identifies regions of instability and stability within the driving parameter space. A new type of nonlinear oscillation may occur at driving parameters where Floquet analysis predicts a stable stationary state. Such non-Floquet oscillations always have periods longer than twice the period of the vibrating pivot. The possible periods of these oscillations may be four, six, eight, or twelve times the driving period. The power spectrum of the pendulum's angular velocity during these oscillations reveals a novel feature: the two dominant response frequencies sum to the driving frequency.

Autonomous and driven transport in chiral active fluids have been shown to exhibit features that cannot be accommodated within the classical formulation of fluid mechanics, due to the role of odd viscosity. We generalize the theory of phoretic active matter to fluid environments with odd viscosity and derive expressions for translational and rotational self-propulsion velocities in the case of a spherical swimmer with arbitrary activity and mobility surface profiles. We discuss specific examples of chemically active colloids with axisymmetric and non-axisymmetric coatings and the resulting interplay between symmetry and chirality. Our results can be applied to study the emergent collective dynamics of phoretic particles in fluid media with broken time-reversal and parity symmetries.

This work presents a unified viscoelastic-viscoplastic continuum framework for modeling rate-dependent granular flows across regimes. The formulation incorporates two distinct rate-dependent mechanisms, namely micro-inertia and viscoelastic dissipation, within a single continuum description. A central contribution is an explicit link between the coefficient of restitution and a continuum viscosity, derived from an analysis of wave attenuation in granular assemblies, thereby establishing a direct connection between particle-scale collision physics and macroscopic damping. This relation is introduced while retaining inertia-dependent plastic flow governed by the classical $\mu(I)$ rheology. The constitutive model is constructed by meticulously partitioning elastic and viscous responses within the model and corresponding stress-update routine, such that viscous dissipation governs wave propagation and collisional processes without altering the plastic flow rule. The framework is implemented within the material point method to simulate transient processes involving large deformations, material separation, and subsequent reconsolidation. A range of numerical examples, including steady, transient, vibrational, and impact-driven flows, demonstrates that the model captures wave propagation, diffusion, and rate-dependent granular behavior within a unified continuum setting.

Unentangled wormlike micelle solutions relax stress through a dynamic interplay of reversible scission and intrachain relaxation involving a hierarchy of molecular timescales whose relationship to linear viscoelastic response remains incompletely resolved. A multiparticle mesoscopic Brownian dynamics framework has been developed in which persistent worms, represented by bead-spring chains with sticky ends, assemble to form wormlike micelles via reversible scission and fusion. Both linear and ring-like micelles are formed across the dilute and semidilute concentration regimes. Accurate predictions of dynamic properties are obtained through inclusion of hydrodynamic interactions using a RPY tensor. We identify and quantify characteristic timescales governing micellar dynamics, including bond lifetimes, self- and non-self-recombination times, breakage times of wormlike micelles of length $L$, relaxation times of various contributions to stress, and the longest relaxation time. The dependence of these timescales on sticker strength, concentration, micellar topology and hydrodynamic interactions is established. The presence of ring micelles is found to moderately prolong recombination and breakage processes, while hydrodynamic interactions are shown to affect some of the timescales by reducing sticker mobility. When appropriately scaled, the dependence on mean length of the non-self-recombination and micelle breakage times collapse onto master curves. Storage and loss moduli exhibit distinctive features in the intermediate-frequency regime that are absent in homopolymer solutions. A clear connection is made between micellar timescales and these signatures in the dynamic moduli at various characteristic frequencies, providing a direct link between microscopic dynamics and macroscopic rheology in unentangled wormlike micellar solutions, in dilute and semidilute concentration regimes.

We study the dynamics of gyrotactic microswimmers suspended in homogeneous and isotropic turbulence by using direct numerical simulations (DNS). The swimmers are characterized by three non-dimensional parameters: their aspect ratio ($\gamma$), a dimensionless swimming speed ($\phi$), and a dimensionless reorientation time ($\psi$). Strong gyrotaxis (smaller $\psi$) promotes vertical alignment of the swimmers, while weak gyrotaxis leads to nearly isotropic orientations. At low swimming numbers, the orientation distribution is largely shape-independent with spheres and spheroids showing marginally greater vertical alignment than rods, whereas at higher activity the peaks of the distributions exhibit largely shape-independent behavior and the tails show a clear dependence on particle shape. However, at large $\psi$ rods exhibit a stronger alignment along the vertical. We observe that at small $\psi$ the rod-shaped swimmers respond to shear by aligning with the stretching direction of the strain-rate tensor, while at large $\psi$ the alignment with the vorticity vector is preferred. The orientation autocorrelation is found to decay exponentially, with a decay rate that scales as $1/(2\psi)$. Analysis of the mean-squared displacement (MSD) reveals a transition from a ballistic motion at short times to a diffusive regime at longer times. To assess the efficiency of vertical migration, we compute the probability distributions of vertical displacement over a fixed time interval and the time taken to migrate a specific vertical distance. Furthermore, we use a simplified two-dimensional model for spherical swimmers that qualitatively reproduces the key trends observed in the full three-dimensional (3D) simulations.

Architected materials can exhibit remarkable combinations of stiffness, strength, and toughness, yet their application is currently limited by an incomplete understanding of how cracks initiate and propagate through their discrete architecture. Elucidating the mechanisms that underpin these processes is challenging because lattice failure is governed by highly localized deformations of slender beams, which fall outside the resolution and assumptions of optical methods developed for continuum solids, such as digital image correlation (DIC). Thus, characterizing crack propagation within lattice materials requires measurement strategies capable of resolving lattice-scale deformations while accounting for both the intrinsic discreteness of lattice architectures and the progressive formation of material discontinuities during failure. This work introduces a global DIC framework tailored to architected materials, in which the correlation problem is solved directly on the lattice mesh and damaged elements are automatically removed during the analyses. Damage detection, which relies on a data-driven residual criterion, enables the robust tracking of localized deformation and crack-tip motion under different testing conditions. The method provides physically consistent displacement field measurements on the evolving intact lattice topology and resolves the crack path over time. Validations on 3D-printed regular and imperfect triangular lattices under mode-I loading demonstrate that the approach accurately captures both damage initiation and crack propagation. Furthermore, we demonstrate that identifying damaged elements provides an estimate of the critical failure strain, which can be used directly in numerical models or adopted as an alternative element-deletion threshold in DIC analyses.

A polar tracer immersed in an active bath is known to be propelled forward and therefore activated. Here we report that the induced dynamics of an inertial tracer can be much richer than expected. We investigate a heavy polar tracer immersed in a bath of independent active Brownian particles. Using the projection-operator formalism to integrate out the bath, we show that the tracer's reduced dynamics can be mapped to a stochastic Lorenz equation. According to the attractors in the Lorenz equation, the tracer motion is classified into several different dynamical regimes, including active Brownian motion, chiral active Brownian motion, complex chaotic motion, and zigzag active Brownian motion. For certain regimes, we derive analytical expressions for the propulsion speed, the velocity covariance, and the effective diffusion coefficient. Numerical simulations corroborate these theoretical predictions.

Bacterial colonies composed of elongated cells form active nematic fluids that spontaneously self-organise into ordered domains of aligned cells and exhibit self-generated chaotic flows powered by cell growth. While their dynamics have attracted significant attention, the role of initial conditions remains largely unexplored due to a lack of precise patterning methods. Here, we harness the precision of capillary assembly to pattern Bacillus subtilis endospores into arrays with controlled positions and orientations at single-cell resolution. Upon germination and growth of cell chains, we quantify the dynamics and morphologies of the resulting bacterial films. While orthogonally seeded spores lead to chaotic dynamics, seeding them with parallel orientations yields films with high nematic order across millimetres, which subsequently synchronously buckle upon further growth. Our observations are captured by numerical simulations and a model that describes the buckling dynamics starting from the mechanical properties of individual filaments. By programming local cell orientation with single-cell precision, we finally harness nematic alignment to create macroscopic bacterial films with local optical anisotropy, via structural colouration and light polarisation. Our findings demonstrate that initial conditions play a key role and offer exciting opportunities to control the spatio-temporal organization of bacterial assemblies towards addressing open biological questions and realizing living materials with tailored properties.

We show that surface waves in a draining-bathtub vortex provide a hydrodynamic realization of both Aharonov-Bohm phase shifts and Lense-Thirring frame dragging within a single system. A static time transformation maps the flat (2+1)-dimensional wave equation onto the convected shallow-water equation, yielding an effective vector potential set by the background flow. In this geometry, the circulation defines a global phase holonomy that controls wave structure. Traveling waves exhibit wavefront dislocations characteristic of Aharonov-Bohm scattering, while standing-wave superpositions produce nodal patterns that rotate at an angular velocity fixed by the circulation, providing a direct analogue of frame dragging. For noninteger circulation, the problem is naturally defined on the universal cover, ensuring single-valued partial-wave solutions. Experiments on a controlled vortex confirm these predictions and establish a laboratory platform in which topological phase and inertial effects, central to gauge and gravitational physics, emerge from a measurable velocity field.

We show that all existing methods quantifying rotational motion in molecular fluids eventually fail in systems undergoing complex rotational motion characterised by slow, heterogeneous, or intermittent dynamics. This impacts in particular the study of rotational dynamics in molecular supercooled liquids near their glass transition, as well as discussions of the decoupling between rotational and translational motion and violations of the Debye-Stokes-Einstein relation. We present a brief overview of existing methods and explain why none of them can accurately capture the evolution of rotational dynamics from a diffusive fluid to an arrested solid, thus resolving inconsistent literature results. We then introduce an empirical method that efficiently solves all issues. We benchmark our method devising a family of continuous time random walk models for rotational dynamics. Our method correctly quantifies the statistics of free and caged rotational motion, as well as non-Gaussian and non-Fickian rotational dynamics, and should allow a better characterisation of dynamic heterogeneity in the rotational motion of supercooled molecular fluids.

Structural glasses prepared by bulk quenching a liquid melt universally exhibit puzzling low-energy excitations commonly known as the ``two-level systems'' (TLSs). Recent studies indicate that ultrastable glassy films made by vapor deposition exhibit substantially fewer TLSs and, at the same time, are more stable enthalpically than conventional glasses made by quenching a melt. A similar phenomenon is observed in very stable glasses of model liquid mixtures prepared using swap Monte Carlo sampling. However, in a separate set of enthalpically stable solids, exemplified by amber matured over geological times, the two-level systems persist. In addressing this seeming conflict, we emphasize that a depletion of the TLSs, if any, means the configurational entropy of the material is lower than that of conventional glasses made by bulk-quenching a melt. Ageing does induce reduction in configurational entropy, but amber, we speculate, achieves enthalpic stabilization through increased bonding, not ageing. We separately comment on the discrepancy among existing predictions for the extent of cooperativity of the two-level systems. Several experiments are suggested to test the present picture.

One of the main challenges in numerically solving partial differential equations is finding a discretisation for the computational domain that balances the accurate representation of the underlying field with computational efficiency. Meshless methods approximate differential operators based on the values of the field in computational nodes, offering a natural approach to adaptivity. The density of computational nodes can either be increased to enhance accuracy or decreased to reduce the number of numerical operations, depending on the properties of the intermediate solution. In this paper, we utilise an adaptive discretisation approach for the numerical simulation of natural convection in non-Newtonian fluid flow. The shear-thinning behaviour is interesting both due to its numerous occurrences in nature, blood being a prime example, and due to its properties, as the decreasing viscosity with increasing shear rate results in sharper flow structures. We focus on the de Vahl Davis test case, a natural convection driven flow in a differentially heated rectangular cavity. The thin boundary layer flow along the vertical boundaries makes this an ideal test case for refinement. We demonstrate that adaptively refining the node density enhances computational efficiency and examine how the parameters for adaptive refinement affect the solution.

A numerical study for a hydrogen (H2) jet in an air crossflow (JICF) was performed using direct numerical simulation (DNS), large eddy simulation (LES), and Reynolds-averaged Navier-Stokes (RANS) approaches, based on a geometry representative of key aspects of port fuel injection (PFI) in a H2-fueled heavy-duty internal combustion engine. The focus was placed on the H2 mixing process and the turbulent species flux model used in the latter two approaches. Based on the DNS data, the performance of LES and RANS on predicting the turbulent flow fields and mixing process was comprehensively evaluated. Results showed that LES performs very well in predicting both the mean velocity and the Reynolds stress. In contrast, RANS significantly under-predicts all Reynolds stress components, while predicting the mean flow field relatively well. Regarding the H2 mixing prediction, LES shows an excellent agreement with DNS, while RANS significantly under-predicts the mixing process. The underlying reasons for the poor performance of RANS were identified by extracting turbulent transport properties used in RANS approach from DNS data. It was found that the turbulent diffusivity used in RANS is much smaller than that derived from DNS, which is attributed to the over-prediction on turbulent Schmidt number (Sct), as well as the under-prediction on turbulent viscosity. By further analyzing the anisotropic components of Sct and the misalignment angle between turbulent species fluxes directly obtained from DNS and those predicted by the RANS mixing model, the commonly used assumption of isotropic turbulent diffusivity in RANS was demonstrated to be invalid for the present configuration. This study provided a unique DNS dataset for H2 jet in a crossflow relevant to H2 PFI engines and generated new insights on improved modeling of turbulent mixing.

Statistical moments of velocity gradients provide fundamental information on the small-scale properties of turbulence. In this work, we propose a systematic method to derive exact expressions for statistical moments of arbitrary order for both longitudinal and transverse velocity gradients in isotropic turbulence. The approach is applicable to both compressible and incompressible flows and expresses the moments in terms of invariants of the velocity gradient tensor. The derivation combines isotropic tensor theory, orientational averaging, and an algorithmic implementation, enabling the computation of high-order moments in a unified framework. We show that longitudinal velocity gradient moments of order higher than three depend not only on $\mathrm{tr}(\boldsymbol{S}^2)$, which is proportional to the dissipation rate, but also on $\mathrm{tr}(\boldsymbol{S}^3)$, which reflects strain self-amplification, where $\boldsymbol{S}$ denotes the strain-rate tensor. The resulting theoretical expressions are validated through comparisons with existing theoretical results and direct numerical simulations.

Elasto-inertial turbulence (EIT) is primarily driven by polymer elasticity, yet the modulating role of fluid inertia is non-negligible and remains largely unexplored. To investigate the effect of inertia, we perform direct numerical simulations of two-dimensional EIT in channel flow over a wide range of Reynolds numbers ($Re$). We show that increasing inertia promotes both the enhancement of dynamic amplitudes and the wallward migration of core structures. Specifically, inertia intensifies the turbulent fluctuations, facilitates the fragmentation of large-scale structures, and amplifies statistical quantities such as the root-mean-square of velocity fluctuations and polymer extension. The peak location of nonlinear elastic shear stress follows a scaling law $y^+ \propto Re_\tau^{1/2}$, closely resembling that of Reynolds shear stress in Newtonian turbulence, indicating a change of the momentum transfer mechanism. Meanwhile, the peak location of energy conversion between elastic and turbulent kinetic energies exhibits a $y^+ \propto Re_\tau^{0.1}$ scaling law migration, remaining mostly confined to the near-wall region. Remarkably, despite the inertial modulation, the probability density functions (PDFs) of velocity and elastic stress fluctuations extracted at the energy-conversion peak collapse convincingly over the range of $Re$ investigated. This reveals a robust statistical self-similarity across a wide range of inertia magnitude. Furthermore, the PDFs of wall-normal velocity and elastic stress fluctuations exhibit pronounced exponential heavy tails.

Data assimilation (DA) improves prediction of chaotic systems by combining model forecasts with sparse, noisy observations. Many DA methods are inherently probabilistic, but accurate probabilistic DA is often computationally expensive because it requires repeated high-resolution (HR) forecasts and large ensembles. In this study, we develop DiffSRDA, a probabilistic spatiotemporal super-resolution data assimilation framework based on denoising diffusion models, and evaluate it on an idealized barotropic ocean jet instability testbed. DiffSRDA is trained offline to generate short HR analysis windows conditioned on (i) a time series of low-resolution (LR) forecast frames and (ii) sparse HR observations. Repeated reverse diffusion sampling then produces an ensemble of HR analyses, providing both point estimates and uncertainty information. Despite relying only on low-cost LR forecasts, DiffSRDA achieves reconstruction quality close to that of an Ensemble Kalman Filter (EnKF) driven by HR forecasts, while improving over deterministic CNN-based SRDA baselines. The sampled ensemble also yields physically meaningful uncertainty patterns, with spread concentrated in dynamically active regions similarly to EnKF. A key practical result is that accurate base DiffSRDA cycling does not require long reverse chains: most of the full-chain accuracy is retained with only a few reverse steps, making diffusion-based SRDA practical for repeated cycling. Finally, by exploiting the score-based structure of diffusion sampling, we demonstrate training-free observation-consistency guidance for deployment-time sensor-layout shifts, enabling improved use of changed observation configurations without retraining. Overall, diffusion models provide a practical, uncertainty-aware, and computationally efficient approach for spatiotemporal SRDA in chaotic fluid flows.

We present a methodology for simulating dilute suspensions of particles settling under gravity, with the main purpose of overcoming limitations of triply periodic configurations, mainly the strong vertical correlation that hinders the study of cluster dynamics. The current approach removes vertical periodicity and employs a moving reference frame, enabling efficient simulations of both single- and many-particle cases. We illustrate the method with two examples of increasing complexity: a single particle in the steady vertical regime, and a many-particle case at a parametric point where collective effects were previously observed and recovered here. A converged, free-of-corrections time interval of approximately $600 D/U_g$ is simulated in the many-particle case, representing the first simulation of this kind to date. New physical insights can be explored thanks to this new configuration, for example the effect of still fluid on the first layer of particles encountered by the fluid, or the turbulent character of the flow after a swarm of particles has passed by. Finally, the method only requires parameter tuning, allowing implementation within existing solvers without changes to their core formulation: for a standard configuration with an imposed free stream velocity at the inlet, only the input velocity (or the viscosity of the fluid) and the time step need to be updated.

A fin-body configuration is tested in a water tunnel to study the hydrodynamic loads and vortex evolution under dynamic fin-flapping motions, which is an idealized approximation of the pectoral fins of fish. The fin flaps about its leading edge, which is attached to the side of the body, at a range of combinations of amplitudes ($0^\circ-30^\circ$) and frequencies ($0.25\,\mathrm{Hz}-2\,\mathrm{Hz}$ or $k=0.16-1.26$), so the Strouhal number ($St=0.013-0.419$). The quasi-steady hydrodynamic loads exhibit significant hysteresis during the upstroke and downstroke phases of the fin flapping. Particle image velocimetry (PIV) measurements show the details of the shear layer and vortex development in dynamic flapping cases. Orbiting behaviors of the fin tip vortices are observed in larger Strouhal number cases. PIV results also reveal the influence of vortices on hydrodynamic loads in terms of lift fluctuations and thrust generation. The strong dependency on the reduced frequency and Strouhal number leads to scalings of the hydrodynamic loads using a data-driven method to select highly correlated terms. The most significant terms selected by the scaling process are quadratic terms of the Strouhal number and its nonlinear combinations with the reduced frequency.

Bubbles entrained by breaking waves rise to the ocean surface where they cluster and burst, emitting sea spray aerosols into the atmosphere. Bubble bursting thereby links seawater biogeochemistry and aerosol chemistry, influencing the ability of emitted aerosols to serve as cloud condensation nuclei or ice nucleating particles. The mechanisms of film drop and jet drop production are modulated by organic material present in seawater, which may affect the size, number, and composition of resulting aerosols. We disentangle the effect of surfactant on collective bursting processes using laboratory experiments with detailed bubble and aerosol measurements down to small sizes, multiple bubble size configurations, and measurements of bubble lifetime. Submicron aerosol emission, linked to film drop production, increased with surfactant up to an optimal concentration, while production of supermicron aerosols emitted through jet drop production was shut down. Our work paves the way to integrate organic composition into sea spray emission functions.

Accurate reconstruction of localized extreme structures remains a critical bottleneck in the physics-informed modeling of electro-thermal-convective flows. Although conventional physics-informed neural networks effectively capture smooth global dynamics, they frequently suffer from numerical diffusion and distortion when attempting to resolve sharp charge boundary layers or abrupt multiphase interfaces. To address these limitations, we propose a Residual-Attention Physics-Informed Neural Network (RA-PINN) that embeds gated attention modulation within a residual feature framework to adaptively enhance local sensitivity to steep physical gradients. The proposed architecture is rigorously evaluated against standard and recurrent network baselines using canonical electrohydrodynamic scenarios, encompassing near-electrode exponential boundary layers and sharply concentrated charge fields. Quantitative analyses demonstrate that the RA-PINN significantly reduces localized errors and faithfully preserves critical interface topologies without compromising the global consistency dictated by the coupled governing equations. Ultimately, this methodology establishes a highly robust predictive framework for resolving complex interfacial and boundary layer phenomena in advanced fluid dynamics applications.

Orientation and relaxation dynamics of rod-like colloids under flow govern the optical and mechanical properties of many emerging soft materials. In polydisperse suspensions, particles of different lengths exhibit distinct rotational diffusion timescales, yet how this polydispersity influences relaxation following flow cessation remains unclear. In particular, it is not well understood how the pre-shear rate determines the subsequent orientation relaxation dynamics. To address this question, we performed simple shear on dilute cellulose nanocrystal (CNC) suspensions in a narrow-gap Taylor-Couette cell and measured birefringence relaxation after flow cessation using high-speed polarization imaging. To interpret the experiments, we formulated a polydisperse Fokker-Planck model parameterized by the measured length distribution. As a result, the average orientation relaxation time systematically decreases with increasing pre-shear rate. Moreover, when organized by the Péclet number based on the rotational diffusion coefficient of the weighted average rod length, the data agree well with the theory over a wide range of shear rates. This trend arises because the rod sub-population contributing most strongly to the orientation shifts from longer rods to shorter rods as the pre-shear rate increases, showing that the flow history governs the orientation relaxation dynamics. In polydisperse systems, the orientation relaxation time is no longer a material-specific constant but is determined by both the flow conditions and the polydispersity. This study provides a quantitative framework for understanding orientation dynamics in polydisperse rod suspensions and for interpreting rheo-optical measurements.

Laddering is the propagation of a topological defect in an everyday-life material: weft knitted fabrics, following a broken thread or a dropped stitch. What is a minor frustration when damaging a pair of tights is a more serious issue for industrial-scale production, but might inspire new solutions to limit and mitigate damage to architected materials. In this work, laddering is investigated in a pre-stressed model knit through experiments and Discrete Element Rod simulations. The control parameter is the initial tension applied on the fabric. A force threshold due to the stitch's natural curvature is evidenced. It controls both the propagation onset and arrest, as tension is relaxed by the thread length freed by ladder growth, and enables damage prediction at moderate tension. Furthermore, we uncovered that the laddering velocity is of the order of the velocity of bending waves and exhibits an unexpected linear scaling with the fabric tension, that arises from a complex combination of elastic and friction forces. Finally, we discuss the implications of our results from the perspective of damage control and mitigation.

Soft composite solids, comprising discrete inclusions embedded within a compliant matrix, are emerging candidates for engineering synthetic tissues and soft robotic materials. Current strategies for controlling their nonlinear mechanics, such as strain-stiffening, have primarily relied on the nonlinear elasticity of polymer matrices. Although direct contacts between inclusions may enhance stiffening responses at high densities, the role of the non-equilibrium and history-dependent nature of disordered contact networks in composite mechanics remains unexplored. In this work, by applying a mechanical training protocol near a shear-jamming phase boundary, we demonstrate that the structural memory encoded in contact networks drives a crossover from granular-like to biopolymer-like strain stiffening. Simulations of a coarse-grained composite model reveal that this biopolymer-like mechanical response emerges from enhanced non-affine reconfigurations of nearly-jammed contact networks. Without relying on matrix nonlinearity, we establish a design strategy that leverages non-equilibrium memory effects intrinsic to granular systems to achieve highly programmable strain-stiffening in soft composites.

The thermosensitive behavior of microgel particles suspended in solvents, i.e. their temperature-dependent swelling properties, has triggered ongoing interest in industry and academia over the past forty years. The most-studied polymer is poly(N-isopropylacrylamide) - PNIPAM -, where the volume phase transition temperature is well known to depend on the detailed molecular architecture of the monomers. In this article, we focus on publications mostly of the past five years in chemical synthesis, aiming at shifting or controlling the volume phase transition temperature (VPTT) of such polymers by copolymerization of a main monomer - often from the PNIPAM family - with either monomers of different hydrophobicity, or with ones bearing ionizable groups. In some cases, hydrophobicity may be modulated by light as external switching parameter, whereas ionic strength or pH may act on the thermosensitivity of the microgels containing charged groups. Due to either differences in reactivity, or specific synthesis routes, particular microgel morphologies, such as molecular gradient, core-shell, interpenetrated, or patchy (multi-lobular) structures may be generated. They may give rise to spatial modulations of thermosensitivity within particles and are highlighted in this review. Our short overview shows that multiple external control of VPTT and morphology is commonly achieved nowadays.

Surface creasing in swelling polymer gels is commonly attributed to compressive strain or interlayer mismatch, yet its general control remains unclear. Here we show that solvent polymerization degree $N_{\rm s}$ provides an independent control parameter for crease onset in surface-bound polydimethylsiloxane gels swollen by silicone oils. Despite nearly identical swelling kinetics and through-thickness solvent concentration profiles, we observe a transition from creased to stable surfaces with increasing $N_{\rm s}$. A theory coupling swelling thermodynamics and mechanical stability reveals that polymeric solvents reduce the mixing entropy and thereby modify the osmotic pressure, allowing $N_{\rm s}$ to tune separately the equilibrium swelling and the crease threshold. This framework captures the stability boundary across solvent polymerization degree and network elasticity. These results identify polymeric solvents as active thermodynamic-mechanical regulators of swelling-induced surface.

In this work, we investigate the unjamming transition in a three-dimensional granular system composed of frictional spheres, in which the packing fraction is systematically reduced by random particle extractions. Using Discrete Element Method (DEM) simulations, we analyze the evolution of key micro-mechanical quantities, such as the interparticle forces, the coordination number and the overall packing density as a function of the interparticle friction coefficient. Our results reveal friction-dependent relationships on structural as well as mechanical observables, and exhibit trends that are qualitatively consistent with observations reported in dense granular systems. These trends persist despite the very different driving mechanism considered here. This paper is part of the thematic issue \emph{``Sand, silos and asteroids: clustering challenges in granular materials research''}.

multisphere is an open-source Python package for generating multi-sphere representations of complex particles for use in DEM simulations. It reconstructs triangulated surface meshes and voxelized volumes as sets of intersecting spheres and provides tools for evaluation, visualization, and export.

We study a stochastic model of collective motion in which individuals update their orientation through pairwise aligning or anti-aligning copying interactions. We analyze both annealed dynamics, where interaction types are chosen probabilistically at each update, and quenched dynamics, where individuals are permanently assigned to aligning or anti-aligning subpopulations. Starting from the microscopic master equation on the circle, we derive an exact mesoscopic description via a Fourier-mode expansion and a systematic large $N$ expansion, obtaining closed Fokker-Planck equations and effective stochastic differential equations for the polarization. We show that competing alignment and anti-alignment suppress long-range polar order in the thermodynamic limit in both cases, while finite systems display nontrivial fluctuation-induced structure controlled by the interaction composition. Our results, validated by Gillespie simulations, establish an analytically tractable framework for collective dynamics characterized by competing copying rules and intrinsic noise.

Self-excited limit-cycle oscillations (LCOs) from Hopf bifurcations are a key feature of nonlinear aeroelasticity and depend sensitively on structural and aerodynamic parameters. Classical center-manifold and normal-form theory describe this local behavior, but can be cumbersome to apply in large discretized models and standard reduced-order modeling (ROM) workflows. A renormalization-group (RG)-based reduction is developed that directly yields a Hopf-type amplitude equation on a local invariant manifold, specialized for polynomial nonlinearities in tensor-based discretizations and compatible with finite-element-type settings. The method provides explicit coefficients governing the Hopf threshold, criticality, and leading LCO amplitude/frequency trends, and admits a companion slow-manifold approximation with selected stable modes retained as static coordinates. Representative nonlinear-aeroelastic examples illustrate how the proposed framework supplies compact, parameter-aware Hopf/LCO descriptors suitable for local ROM construction near flutter.

A particular interest on two-dimensional turbulence is the inverse energy cascade from small to large sales, which leads to an energy condensation accompanied by the formation of large-scale vortical structures. Indeed, such a phenomenon is observed in the two-dimensional channel (2DCH) with large Reynolds numbers, where prominent large-scale wavy structures play a central role in the momentum and energy transfer across the inhomogeneous wall-normal direction \citep{Falkovich2018}. Yet, the instability of these wavy structures remains poorly understood, and it is unknown whether they have the capacity to generate turbulence. To address this, we first conduct the direct numerical simulation (DNS) of Navier-Stokes equations for 2DCH, then extract the large-scale wavy structures through the singular value decomposition, and finally perform a Floquet-based secondary instability analysis. Two bulk Reynolds numbers are examined in particular, i.e. $Re = 3000$ and $Re = 200000$, which lie on opposite sides of the transitional regime near $Re \approx 10000$ and cover the previously reported simulation domain. At $Re = 3000$, the large-scale wavy structure is found to be linearly stable, consistent with the laminar-like DNS flow field. However, at $Re = 200000$, a subharmonic torsional mode is identified, which leads to a definite growth rate ($\lambda_r = 0.18$) for the wavy structures with a half wave-length shift. Temporal reconstruction shows that this unstable mode deforms and splits into multiple wave trains and evolves in the opposite phase. Compared to the TS (Tollmien-Schlichting) wave of laminar flow, the subharmonic mode found here offers a novel understanding for the generation of turbulence in larger Reynolds number two-dimensional channels.

Global-pressure formulations recast multiphase Darcy flow in terms of a single pressure driving the total flux. Their exact equivalence to phase-pressure formulations, however, holds only when the constitutive data satisfy the compatibility conditions required for a total-differential structure and its generalized nonisothermal extension. In this work, we derive the corresponding exactness criterion for temperature-dependent mobilities and capillary pressures. We show that equivalence is governed by the closure of a mobility-weighted capillary one-form on the augmented state space of saturation and temperature. This yields both the classical compatibility conditions within the saturation sector and a distinct mixed saturation--temperature condition that arises only in the nonisothermal setting. We then incorporate this structure into a reduced matrix--fracture model with heat transport, matrix--fracture thermal exchange, and evolving fracture aperture. Numerical benchmarks recover the three regimes predicted by the theory: globally exact, exact on each fixed-temperature slice but not on the full saturation--temperature space, and fully nonexact. In fractured systems, thermal forcing alone can drive transitions between these regimes, while aperture evolution changes the path through state space. When exactness fails, a least-squares projection performed independently on each fixed-temperature slice provides a conservative scalar-pressure surrogate together with quantitative defect diagnostics. The resulting framework unifies nonisothermal exactness theory, fractured-flow dynamics, and conservative reduced closure within a single global-pressure formulation.

Gate-modulated nanopores have emerged as a promising platform for achieving ion selectivity and ionic current rectification (ICR) with the advantage of active field-based control. However, the mechanistic origin of these experimentally reported phenomena, arising from electrostatic coupling between the prescribed radial pore surface potential and the axial transmembrane electric field, remains insufficiently understood. Here, using coupled Poisson--Nernst--Planck and Navier--Stokes simulations supported by asymptotic analysis, we show that a uniform surface potential inherently interacts with the axial driving field to generate a three-dimensional, axially nonuniform electric double layer (EDL). This field-induced EDL heterogeneity effectively mimics a linear axial variation in zeta potential, breaking translational symmetry within an otherwise uniform pore. As a result, the system exhibits coupled electrokinetic responses, including ion selectivity, ionic current rectification, and non-canonical electroosmotic flow, all governed by a single asymmetry parameter $\alpha$ derived from the EDL structure. Critical transitions occur at specific values of $\alpha$; in particular, at $\alpha=0$, the EDL becomes axially antisymmetric, leading to reversal of ion selectivity, significant ICR and the emergence of a peculiar negative electroosmotic flow rectification accompanied by internal vortical structures. These findings establish the electrostatic mechanism for axial symmetry breaking as the underlying principle for transport in voltage-gated nanopores, enabling a unified framework for designing tunable electrokinetic functionalities beyond geometry- and chemistry-based strategies.

We report the first systematic evidence of hallucination in AI models of fluid dynamics, demonstrated in the canonical problem of hydrodynamically unstable transport known as viscous fingering. AI-based modeling of flow with instabilities remains challenging because rapidly evolving, multiscale fingering patterns are difficult to resolve accurately. We identify solutions that appear visually realistic yet are physically implausible, analogous to hallucinations in large language models. These hallucinations manifest as spurious fluid interfaces and reverse diffusion that violate conservation laws. We show that their origin lies in the spectral bias of AI models, which becomes dominant at high flow rates and viscosity contrasts. Guided by this insight, we introduce DeepFingers, a new framework for AI-driven fluid dynamics that enforces balanced learning across the full spectrum of spatial modes by combining the Fourier Neural Operator with a Deep Operator Network to predict the spatiotemporal evolution of viscous fingers. By conditioning on both time and viscosity contrast, DeepFingers learns mappings between successive concentration fields across regimes. The framework accurately captures tip splitting, finger merging, and channel formation while preserving global metrics of mixing. The results open a new research direction to investigate fundamental limitations in AI models of physical systems.

Compressible multiphase and multicomponent solvers require accurate interface representation without spurious pressure oscillations. At material interfaces, pressure and velocity are continuous while density and the equation of state exhibit abrupt discontinuities. Standard approaches reconstruct primitive or characteristic variables to capture these properties, but do not clarify the failure mechanisms of conservative reconstruction or fully leverage the wave-decoupling advantages of characteristic decomposition. This work derives the complete eigenstructure of the Allaire five-equation model for two variable sets. In the fully conservative~(FC) formulation, $\mathbf{U} = [\alpha_1\rho_1,\,\alpha_2\rho_2,\,\rho u,\,\rho v,\,\rho E,\,\alpha_1]^T$, eigenvectors contain a thermodynamic jump term~$\Psi$ that enforces $dp=0$ and $du=0$ at material contacts by compensating for compressibility mismatches. In the semi-conservative~(SC) formulation, $\mathbf{V} = [\alpha_1\rho_1,\,\alpha_2\rho_2,\,\rho u,\,\rho v,\,p,\,\alpha_1]^T$, the volume-fraction eigenvector carries a structural zero in the pressure slot, enforcing equilibrium without thermodynamic correction. Explicit left and right eigenvectors are derived for one- and two-dimensional stiffened-gas flows. Both formulations satisfy Abgrall's equilibrium condition when reconstruction is performed in characteristic space; reconstruction in physical space yields $\mathcal{O}(1)$ pressure and velocity errors at interfaces regardless of the variable set. The eigenvector structure further reveals that the shear wave is decoupled from all thermodynamic and interface fields in both formulations, extending this result from single-species to compressible multiphase flows including gas-liquid configurations. One- and two-dimensional gas-gas and gas-liquid test cases confirm oscillation-free, accurate results.

Due to attractive inter-particle forces, cohesive particles suspended in turbulence undergo a complex process of aggregation, breakup, and restructuring. Despite a growing body of knowledge on the ``flocculation'' of cohesive granular materials suspended in homogeneous isotropic turbulence, little focus has so far been placed on wall-bounded flows where turbulence and shear are inhomogeneous. This study presents a first investigation of a fully developed wall-bounded flow of resolved cohesive particles. Five direct numerical simulations of turbulent channel flows laden with finite-sized particles at successively increasing cohesive strength are performed. A population balance equation (PBE) framework is used to analyze aggregate dynamics. When integrated over the full domain, the PBE is closed by aggregation and breakup alone. However, this balance is found to not hold locally in the wall-normal direction, where regions of net aggregate production and depletion are identified. This imbalance is shown to be compensated by the size-dependent wall-normal transport of aggregates, revealing a mean circulation: larger aggregates are preferentially produced in the channel center and migrate toward the wall where they break, while smaller aggregates are transported away from the wall, grow, and reenter the cycle.

We investigate gas injection into water-saturated porous channels with Gaussian and parabolic axisymmetric centrelines, as idealized models of underground gas storage in dome-shaped anticlines. Exploiting the slenderness of each channel, we derive an evolution equation for the gas/liquid interface using a composite asymptotic approximation that accommodates large channel slopes and has a simplified small-slope form describing spreading in weakly curved channels. In the high gas-mobility limit, in contrast with flat planar channels, buoyancy influences the dynamics through different mechanisms in each geometry. For gas injected steadily into a Gaussian channel, buoyancy can continually affect the flow due to the attenuation of the gas velocity caused by axisymmetry. In parabolic channels, the increasing channel slope ensures that buoyancy eventually influences the flow, at a timescale depending on injection rate and fluid properties. Asymptotic analysis of the parabolic channel flow reveals five temporal regimes, each with multiple spatial regions and a distinct spreading rate, reflecting the evolving spatiotemporal competition between injection and buoyancy. Initially, a thin film of gas spreads along the upper boundary; the channel slope and elongation of the film then generate a hydrostatic pressure gradient, which strengthens until buoyancy arrests the upper contact line and thickens the film. Beneath the film, liquid then drains until the interface flattens under buoyancy. Analytical solutions of reduced-order models capture interface evolution and contact-line motion through each regime and are validated against full numerical simulations. These results have implications for subsurface hydrogen and CO$_2$ storage, where a horizontal interface that advances vertically enhances both safety and storage efficiency.

A Cyber-physical underwater vehicle is equipped with bio-inspired flapping fins positioned on the sides of the vehicle's main body. The proposed control surfaces are inspired by fish pectoral fins, generating forces and moments that can potentially be harnessed for maneuvering, hovering and station keeping. The streamwise and cross-stream forces produced by the fins are characterized for a range of reduced frequencies and Strouhal numbers. The streamwise forces are shown to be predominantly a function of the fin's projected frontal area, while the lateral forces also depend on the Strouhal number. When operated simultaneously, different flapping synchronizations can be employed for specific goals; a symmetric motion suppresses the lateral forces, while an anti-symmetric motion decreases the peaks of the streamwise force produced. The Cyber-physical vehicle demonstrates how the pair of fins can successfully maneuver the vehicle in the lateral direction.

Polytropic models of stellar winds remain to be useful tools because they allow for a simple description of the energy balance of the expanding plasma without explicitly specifying potentially complex energy transport processes like, e.g., heat conduction or extended wave heating. Among recent applications to stellar winds and to the solar wind was a study of the consequences of strongly localized heating in the latter, possibly due to acoustic waves. Such 'nonuniform' heating can result from a time- and space-localized damping of wave modes and allows, as an extreme case, an adiabatic expansion of particular wind streams outside the heating region. The present study generalizes the modeling from the first analytical as well as numerical studies, that were limited to this extreme case, towards a more realistic non-adiabatic behaviour. The additional energy due to heating is demonstrated to be in a plausible range in view of typical flare energies and low compared to the gravitational energy of the plasma in this region. The corresponding solutions may be of interest for stellar winds, in general, and w.r.t. recent observations made with the Parker Solar Probe, which revealed strongly varying wind streams and the presence of acoustic waves near the Sun, for the solar wind, in particular. Potential observational evidence for the solar wind is discussed.

The Murali-Lakshmanan-Chua (MLC) circuit is a well-recognized prominent nonlinear, nonautonomous, and dissipative electronic circuit having a versatile chaotic nature. Unraveling the dynamical synergy responsible for the genesis of extreme events in nonlinear dynamical systems is a prolific and spellbinding research area. The present study unveils the dynamical exposition of emerging extreme events in the MLC circuit concerning two different events being defined in the system. The large expansion of the chaotic attractor following the PM intermittency route plays the crucial role as the precursor behind the emergence of extreme events in the system. Our main finding reveals the prevalence of a force field due to the presence of externally applied periodic force in the system that creates the dynamical synergy that compels the chaotic trajectory traversing in its phase space to be largely deviated from the residing space, and this large deviation shows the signature of extreme events. Apart from the force field explication, we explored another two dynamical aspects that also interpret the mechanism behind the genesis of extreme events as the large deflection of the chaotic trajectory in the system: the decomposition of the phase space in stable and unstable manifolds concerning slow-fast dynamics and using Floquet multipliers. These two different aspects of calculations of the stable and unstable manifolds explicate the large excursion of the chaotic trajectory as extreme events from two different perspectives. We also analyzed the rare occurrences of the extreme events statistically using extreme value theory: the threshold \textit{excess values} follow the generalized Pareto distribution, and the inter-extreme-spike-intervals follow the generalized extreme value distribution.

Scientific machine learning is increasingly being spoken of as universal emulators for classical numerical solvers for multi-scale partial differential equations, but most apparent successes can be explained by facts that also define their limits. Many successful benchmarks live on low-dimensional solution manifolds where any competent reduced model will interpolate well. More fundamentally, neural surrogates systematically under-resolve high-frequency content due to spectral bias, and coarse-graining compounds this problem through irreversible information loss. In many multi-scale problems, no architecture or training procedure can fully recover what the coarse representation discards. Two simple examples are used to characterize spectral bias, coarse-graining and error accumulation. We discuss why medium-range weather prediction on reanalysis data sits in a favorable sweet spot and why this will not generalize to genuinely chaotic multi-scale scenarios. We identify domains where neural surrogates offer genuine value, propose further research on neural-classical hybrids, and call for better reporting standards.

In classical dynamical systems, stochastic feedback can stabilize otherwise unstable periodic orbits, giving rise to distinct controlled and uncontrolled phases as the rate of control application is varied. In this work, we apply these control protocols in classical, semiclassical, and quantum regimes to the kicked top, a paradigmatic model of quantum chaos. The quantum kicked top, modeled as the dynamics of a spin-S object, naturally interpolates between these regimes with the spin size S acting as an effective Planck constant. We show that the dynamics of the kicked top in classical, semiclassical, and fully quantum limits can all be controlled using stochastic feedback protocols. Comparing the full quantum dynamics to a truncated Wigner approximation that captures quantum noise but neglects interference beyond the Ehrenfest time, we find that low-moment observables are largely accounted for semiclassically, while the remaining discrepancy in higher moments is consistent with contributions from interference and possibly nonlinearities in rare trajectories that explore the compact phase space. We also find rapid purification in the numerics studied for all rates of control considered, suggesting that control quenches the top's ability to encode a qubit of quantum information even in the uncontrolled phase.

Kirigami, the art of paper cutting, has been widely used in the modern design of mechanical metamaterials. In recent years, many kirigami-based metamaterials have been designed based on different planar tiling patterns and applied to different science and engineering problems. However, it is natural to ask whether one can create deployable kirigami structures based on the simplest forms of tilings, namely the monotile patterns. In this work, we answer this question by proving the existence of periodic and aperiodic monotile kirigami structures via explicit constructions. In particular, we present a comprehensive collection of periodic monotile kirigami structures covering all 17 wallpaper groups and aperiodic monotile kirigami structures covering various quasicrystal patterns as well as polykite tilings. We further perform theoretical and computational analyses of monotile kirigami patterns in terms of their shape and size changes under deployment. Altogether, our work paves a new way for the design and analysis of a wider range of shape-morphing metamaterials.

Biological microswimmers alter their motility in complex corner geometries, facilitating their survival. However, the dynamical features of low-Reynolds-number swimming at corners remain undefined. Here, we use active droplet microswimmers near a confined meniscus in a microchannel as a model system to study how microswimmer-corner interactions determine swimming patterns. Combining experiments, theory and simulations, we show that pusher-type micrsowimmers are attracted towards a meniscus corner, followed by transient trapping and eventual escape. We demonstrate that hydrodynamic interactions with the wall-interface corner intimately dictate the attraction and trapping or escape of the microswimmer on the basis of its strength. We show that the swimming trajectory at the meniscus corner can be tuned depending on the type of the microswimmer, the corner geometry and the viscosity ratio for the liquid interface. Our study provides a simple way to manipulate microswimmers by exploiting their hydrodynamic interactions near corner geometries.

Knitted fabrics exemplify a broad class of architected materials capable of large deformations, enabling shape morphing, mechanical biocompatibility, and embedded multifunctionality without material damage. Although geometric nonlinearity has been intuitively utilized in their design, a quantitative description of stitch-resolved deformation and its temporal evolution remains lacking. Here, we introduce a geometric quantification framework that reconstructs smooth yarn centerlines and fabric surfaces from sparse yarn-level representations and extracts interpretable descriptors across dimensions. Applied to representative knitted structures, this framework resolves how global deformation is distributed among stitch reorientation, loop bending, surface bending, and dilation. Moreover, it reveals how regions of large geometric variation emerge, persist, and redistribute over time. Rather than directly measuring stress, these geometric descriptors define a unified geometric state space for comparing knitted structures and identifying candidate regions of mechanical localization. The framework provides a quantitative language for nonlinear deformation in knits and establishes a geometry-based representation that can be coupled to constitutive models, experimental measurements, and graph-based inverse-design workflows.

We present a tunable, non-equilibrium oil-in-oil emulsion that serves as a model system for investigating the transition from controlled droplet deformation to multiscale flows reminiscent of turbulence. By utilizing a miscible mixture of silicone and motor oils as the continuous phase and the immiscible castor oil as the droplet phase, we isolate electrical conductivity as a single experimental control parameter, varying it by over two orders of magnitude while keeping viscosity and permittivity nearly constant. This high degree of control allows us to systematically traverse the electrohydrodynamic (EHD) phase diagram with dielectric constant and conductivity as control parameters. We validate small-deformation theory at low fields before driving the system into a regime of multiscale, unsteady flows at high fields. We employ three complementary approaches on the same system (particle image velocimetry (PIV), used to map velocity fields, and rheometry and differential dynamic microscopy (DDM), two techniques used to probe viscosity and diffusion) to quantify the emergence of scale invariance in the energy spectra with increasing field strength. Above a threshold field, we find that the spatio-temporal energy spectra obtained by PIV analysis of droplet dynamics display power-law scaling, $E(k) \sim k^{-\alpha_k}$, where $\alpha_k$ approaches the inertial turbulence exponent of $5/3$ at high fields. Energy spectra from rheometry also yield a power law, $S(\nu) \sim \nu^{-\alpha_\nu}$, with $\alpha_\nu = 5/3$ at high fields. Mean square displacement (MSD) analyses on the same datasets reveal super-diffusive behavior, $\mathrm{MSD} \sim t^{\gamma}$, with $\gamma = 3/2$. These observations provide strong evidence of a conductivity-tunable transition to EHD-driven turbulence in a microscale emulsion.

We explore the edge flows that emerge at boundaries in nonequilibrium passive and active chiral colloidal fluids. We show that these complex interface currents obey an equation of state that relates their fluxes to bulk observables. For confined fluids, the edge flux is given by the average odd stress in the fluid. In phase-separated systems, the flux along the interface is given by the jump of the odd stress across the interface. We then use the equation of state to reveal, and contrast, the microscopic origins of the edge currents in passive and active systems.

A control framework is proposed for inducing non-equilibrium state transitions in confined active matter, where the statistics of self-propulsion serve as the only control parameter. Positivity of the noise amplitudes and fundamental bounds on position-propulsion correlations define the admissible control space and impose speed-limits on transitions between non-equilibrium states. We show that non-stationary initial states facilitate additional speed-ups, corresponding to pre-loading the state with negative correlations. This enables active cooling protocols that outperform their passive counterparts.

Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering. Traditional stability and receptivity (resolvent) analyses are powerful but rely on known equations and linearization, limiting their use in nonlinear or poorly modeled systems. Here, we introduce a data-driven framework that automatically identifies stability properties and optimal forcing responses from observation data alone, without requiring governing equations. By training a neural network as a dynamics emulator and using automatic differentiation to extract its Jacobian, we can compute eigenmodes and resolvent modes directly from data. We demonstrate the method on both canonical chaotic models and high-dimensional fluid flows, successfully identifying dominant instability modes and input-output structures even in strongly nonlinear regimes. By leveraging a neural network-based emulator, we readily obtain a nonlinear representation of system dynamics while additionally retrieving intricate dynamical patterns that were previously difficult to resolve. This equation-free methodology establishes a broadly applicable tool for analyzing complex, high-dimensional datasets, with immediate relevance to grand challenges in fields such as climate science, neuroscience, and fluid engineering.

This article establishes a first-principles statistical field theory of fully developed isotropic turbulence. Applying an exact Helmholtz decomposition to the local angular momentum field ($\Lvec = \rvec \times \uvec$) reveals a segregation into two orthogonally distinct topological phases: a longitudinal condensate of macroscopic coherent structures ($\PhiL$) and a volume-filling, transverse thermal bath ($\AL$). Constructing a Hamiltonian and evaluating the partition function of these decoupled fields demonstrates that their ergodic exploration of phase space is topologically quantized, mandating a strict $1:2$ equipartition of degrees of freedom. Inverting this topological projection back to the velocity domain isolates the radial velocity field ($\uvec_r$) (which strictly resides in the null space of the $\Lvec$ framework) revealing a recursive partitioning scheme across the cascade into a precise $1/3 : 2/9 : 4/9$ fractional hierarchy. This geometric constraint forces the turbulent steady state into a rigorous canonical equilibrium governed by the equalization of phase chemical potentials ($\mu_\Phi = \mu_A$). The radial component acts as a non-equilibrium mechanical piston, continuously injecting energy into the tangential modes to sustain the canonical equilibrium -- a mechanism that mathematically formalizes the classical phenomenology of vortex stretching. Spectral evaluations from direct numerical simulation strongly corroborate this thermodynamic framework, establishing the universality of the partition ratios $1:2$ and $1/3 : 2/9 : 4/9$ as a fundamental signature of three-dimensional isotropic turbulence.

Rayleigh-Taylor Instability (RTI) typically arises when a dense fluid is superimposed on a lighter fluid, where the desta- bilizing gravitational force acting on miscible fluids drives chaotic mixing. We theoretically present an acoustofluidic method utilizing standing bulk acoustic waves (BAW) to counteract RTI and suppress the mixing of fluids. To success- fully achieve this suppression, we demonstrate that two concurrent conditions are to be satisfied: the acoustic energy density (Eac) of the standing waves must exceed its critical threshold (Ecr), and the orientation of the acoustic waves must be perpendicular to the fluid-fluid interface. This acoustofluidic mechanism reduces the mixing index (MI) by up to an order of magnitude compared to the mixing induced solely by gravity. By analyzing the interplay between acoustic and gravitational forces, this study provides a comprehensive understanding of acoustically modulated mixing dynamics in minichannels.

An experimental wind-tunnel implementation of a model-free single-step deep reinforcement learning (SDRL) controller is presented for TS wave suppression in a flat plate boundary layer. The controller is deployed in a feedforward layout. The arrangement comprises an upstream reference microphone, a downstream error microphone, and a DBD plasma actuator located between them. The controller updates its policy online from the measured error signal and, in real time, adjusts the coefficients of a finite-impulse-response (FIR) filter that maps the reference signal to the actuation command. TS waves are artificially introduced by a second, upstream-located DBD trigger actuator identical in specification to the control actuator. The trigger actuator is driven with single-frequency, multi-frequency, or broadband white-noise inputs depending on the control cases. Experiments were carried out in an anechoic wind tunnel facility using flush-mounted pressure microphones for sensing and controller feedback, together with two-component planar particle image velocimetry~(PIV) for flow-field verification. The controller performance is assessed via second-order statistics of the error signal and the spectral attenuation of the TS wave content. Across all tested scenarios, the SDRL-based controller consistently reduces the downstream disturbance level and exhibits robustness to moderate variations in freestream velocity and in the incoming TS wave disturbance spectrum. These results provide an experimental step toward adaptable, data-driven TS wave suppression with compact sensing and actuation, supporting practical strategies for boundary layer transition delay.

In incompressible flow the viscous force is solenoidal, whereas the Madelung transform of a spinless Schrödinger equation produces only gradient forces. The two are orthogonal, so viscosity cannot arise from Hamiltonian quantum mechanics alone; an open quantum treatment is required. Reducing the $N$-body density matrix to its one-body component and closing the dynamics via Born-Markov yields Lindblad jump operators with $k^2$ scattering rates, which we unravel via quantum state diffusion (QSD) into a norm-preserving stochastic nonlinear Schrödinger equation. Dissipation and stochastic forcing are not separate ingredients: both come from the same Lindblad operators, and their amplitudes are locked by the QSD structure. The Madelung transform of this equation, under incompressibility, gives a stochastic Navier-Stokes equation whose viscosity is set by the mean free path and whose noise correlator satisfies the fluctuation-dissipation relation by construction, in agreement with the Landau-Lifshitz framework. The recovery is conditional: the viscous identification holds at the ensemble level via the vortex decomposition of the velocity field; the single-trajectory identification remains open. The zeros of the wavefunction carry quantised circulation; their codimension-2 topology yields the Migdal area law for circulation statistics under a Poisson assumption, here through a different mechanism than the loop-functional saddle point and verified numerically even in the quantum regime where the de~Broglie length exceeds the Kolmogorov scale.

We investigate the Marangoni modulation of coupled Rayleigh-Taylor and Faraday instabilities in a vertically oscillated Newtonian liquid film carrying insoluble surfactants. Linear stability analysis using Floquet theory reveals that an increasing Marangoni number (Ma) selectively suppresses subharmonic modes, driving the system into a harmonic-dominated regime. The interfacial response is found to be highly frequency-dependent. At low forcing frequencies, increasing Ma causes adjacent harmonic tongues to merge into a novel surfactant mode that migrates towards long wavelengths, ultimately coalescing with the RTI branch and fragmenting the dynamically stable window. Conversely, at high frequencies, surfactants monotonically elevate the harmonic instability threshold, significantly widening the stable parameter space. To uncover the underlying mechanisms, a long-wave asymptotic analysis is performed, demonstrating that the critical forcing amplitude factorizes into a static capillary-gravity margin and a dynamic elasto-inertial modulation, yielding a scaling law for the critical mode balance. Finally, nonlinear simulations based on a rigorous weighted-residual reduced model are utilized to dissect the spatial work performed by individual forces, which shows that surfactants modulate stability through phase-controlled Marangoni transport. In the RTI regime, increasing Ma reverses the transport direction and drives fluid into the peaks, inducing a transition from stabilization to destabilization. In the Faraday instability (FI) regime, the response exhibits a strong frequency dependence, governed by Marangoni transport that redistributes fluid away from interfacial peaks at high frequencies but toward them at low frequencies, thereby suppressing or enhancing the instability accordingly.

Three-dimensional experiments are presented on a school of three pitching hydrofoils. Two side-by-side leader foils maintain the same relative positions while the location of a third follower foil is varied. Force and flow measurements detail the mechanisms that drive the school to achieve collective thrust and efficiency that are 58% and 24% higher than isolated foils, respectively. Traditional drafting involves positioning yourself in the wake of an upstream object. In wakes with a net momentum deficit, drafting reduces drag by lowering oncoming flow speed. By contrast, wakes from oscillatory swimmers feature strong momentum surplus regions, which increases drag by increasing the oncoming flow. Despite that, our results show that the best performance benefits occur for compact schools where the follower is directly in the vortex wake of a leader, whereas regions of reduced mean flow do not improve performance. The thrust and efficiency benefits are shown to be driven by vortex-body interactions that increase the thrust and efficiency of the follower and by body-to-body upstream interactions that reduce the power of the leaders. There is an optimal spatial phase to maximize the thrust and efficiency of the follower that depends upon the actual wake wavelength rather than the estimated wavelength used in previous literature. Moreover, wake breakdown, and its associated elimination of vortex-body performance benefits, is not observed within at least three chord lengths downstream of the leaders. Lastly, measurements of the cross-stream stability of the downstream foil indicate that compact, high-performance formations may require active control strategies in order to maintain their organization and maximise the hydrodynamic benefits of schooling.

The main goal of this paper is to demonstrate the application of metric-based mesh adaptation to real gas problems and highlight the benefits particularly when complex geometries are considered. We use the Hessian of the temperature solution as an indicator to dictate where the mesh needs refinement or coarsening. In the context of hypersonic flow simulations, these methods are not widely adopted since unstructured meshes often result in poor surface heating predictions. The present work aims to demonstrate the great flexibility metric-based mesh adaptation provides when it comes to predicting complex flow features while still maintaining comparable surface heating predictions. We consider two test cases: (a) a supersonic flow over a hemisphere and show that comparable surface heating is obtained by applying mesh adaptation and by employing hexahedra instead of prisms in the boundary layer mesh; (b) we consider a more realistic test case of a hypersonic flow of a C02-N2 mixture past a 70 degree sphere cone atmospheric entry capsule. For the second test case, similar surface heating predictions are obtained compared to more conventional block structured DPLR simulations. Furthermore, for the adapted unstructured simulations, the geometries of the eight Reaction Control System (RCS) jet on the back shell were taken into account. This highlights the ability of these methods to deal with complex geometries that are typically out of reach for block structured approaches.

We investigate the competition between two distinct mechanisms generating stable laws in deterministic dynamical systems: slow mixing of the system and heavy-tailed observables. For heavy-tailed observables on polynomially mixing billiards with cusps we show these two mechanisms interact and there is a transition, depending on the mixing exponent and the index of the heavy-tailed observable, such that the limit law is determined by either the observable or the dynamics. We prove stable limit laws for heavy-tailed observables of the form $\phi(x)= d(x,x_0)^{-\frac{2}{\alpha}}, 0< \alpha < 2$, where $x_{0} \in \partial Q$ is a generic point on the dynamical system given by the collision map of a polynomially mixing billiard $(T, Q, \mu)$ with cusps. The observable $\phi$ has a tail of stable index $\alpha$, i.e. $\mu(|\phi|>t) \sim t^{-\alpha}$. The billiard systems we consider have a slow mixing rate so that suitably scaled Hölder observables on the billiard satisfy a stable law of index $1/\gamma$, with $\gamma$ a function of the flatness of the cusps. We establish stable limit laws satisfied by Birkhoff sums of $\phi$ for the parameter range $\gamma \in (1/2,1)$, $\alpha \in (0,2)$ ($\alpha \not =1$) as a function of $\gamma$ and $\alpha$. As an application, in the setting of intermittent maps, we extend the results of~\cite{CNT2025} to cover all parameter values of the map and the observable $\phi(x)= d(x,x_0)^{-\frac{1}{\alpha}}$ (which has stable index $\alpha$ if $x_0\not =0$) in the regime $0< \alpha < 2$, $0<\gamma<1$. We show if $x_0=0$, the indifferent fixed point, then the stable law has index $(\frac{1}{\alpha}+\gamma)^{-1}$.

Trajectories of units moving on networks are relevant for nonlinear dynamical systems as diverse as polymers, ocean drifters, and human mobility. Although RQA is a well-researched tool with applications in many areas, it has rarely been used for spatial trajectories on networks. Here, we explore the use of RQA for paths on networks. We find that path dynamics on networks display recurrence patterns that are not often described in other applications of recurrence analysis. In particular, the combination of diagonal lines and perpendicular diagonal lines, indicates backtracking paths. We find that recurrence analysis for path dynamics on networks can be helpful to a) better understand the network structure if dynamic and recurrence plots are known, b) better understand the dynamics if network and recurrence plots are known, and c) understand the interaction between path dynamics and the underlying network.

Machine learning emulators have shown extraordinary skill in forecasting atmospheric states, and their application to global ocean dynamics offers similar promise. Here, we adapt the GraphCast architecture into a dedicated ocean-only emulator, driven by prescribed atmospheric conditions, for medium-range predictions. The emulator is trained on NOAA's UFS-Replay dataset. Using a 24 hour time step, single initial condition, and without using autoregressive training, we produce an emulator that provides skillful forecasts for 10-15 day lead times. We further demonstrate the use of Mahalanobis distance as loss that improves the forecast skill compared to the Mean Squared Error loss by explicitly accounting for the correlations between tendencies of the target variables. Using spatial correlation analysis of the forecasted fields, we also show that the proposed correlation-aware loss acts as a statistical-dynamical regularizer for the slow, correlated dynamics of the global oceans, offering a better background forecast for downstream tasks like data assimilation.

Excess pore pressure in granular--fluid mixtures can transiently suppress frictional contacts and dramatically enhance flow mobility, yet its evolution is commonly modeled using constant effective diffusivities. Here we show that the apparent diffusivity is not intrinsic but emerges from the coupling between pore-pressure diffusion and granular compaction. Starting from two-phase mass conservation for a deformable, gas-saturated granular assembly, we derive an evolution equation for excess pore pressure that captures deformation of the granular skeleton. In the thin-flow, small-excess-pressure limit, this reduces to a one-dimensional diffusion--compaction equation with a time-dependent source term controlled by porosity changes. A modal analysis yields a reduced basal equation that separates diffusive drainage from compaction-driven forcing and identifies the corresponding timescales. This framework introduces a dimensionless source-to-diffusion ratio, $\Psi_0$, which governs the competition between these processes and collapses effective diffusivities obtained from high-resolution two-fluid simulations over nearly two orders of magnitude in bed height. This scaling implies that the apparent diffusivity, and thus flow mobility, is not intrinsic but depends on flow thickness through the competition between diffusion and compaction. Incorporating this physics into a depth-averaged model demonstrates that the resulting closure reproduces the thickness dependence of pore-pressure decay and runout observed in experiments. These results provide a physically grounded description of pore-pressure evolution in granular--fluid flows and clarify how diffusion--compaction coupling controls their mobility.

We investigate the kinetics of particle aggregation within the framework of the Smoluchowski coagulation equation, extending it to account for electrostatic interactions among charged clusters. Using a stochastic Monte Carlo implementation, we examine how different charge distributions and net system charge affect cluster growth dynamics. Electrostatic interactions are incorporated directly into the classical Brownian collision kernel, yielding charge-dependent modifications of the collision rates that may either enhance or suppress aggregation depending on the signs and magnitudes of the interacting charges. Our simulations reveal distinct regimes of growth: at intermediate times, charge heterogeneity accelerates or delays aggregation depending on the initial underlying charge distribution, while at long times the system tends toward quasi--stationary states whose properties depend on the net charge. Comparisons between Gaussian and Cauchy--Lorentz initial charge statistics highlight the role of heavy-tailed distributions in promoting faster cluster growth. These findings contribute to a unified understanding of coagulation kinetics in charged particulate systems, with potential implications for aerosol and astrophysical coagulation processes, volcanic ash aggregation, and clustering in industrial fluidized granular beds.

Thermodiffusion in aqueous electrolyte solutions exhibits complex dependencies on temperature, concentration, and salt composition, yet its microscopic origins remain incompletely understood. Here, we employ non-equilibrium molecular dynamics (NEMD) simulations to investigate thermal transport and thermodiffusion in aqueous alkali halide solutions over the temperature range 240-300 K at concentrations of 1 m and 4 m. Building on previous studies of NaCl and LiCl, we extend the analysis to systems containing K$^+$ and I$^-$ ions to assess ion-specific effects. Across all systems studied, the thermal conductivity decreases upon cooling and is generally reduced at higher salt concentration. The Soret coefficient generally increases with temperature, shifting the solutions from thermophilic behavior at low temperature toward more thermophobic behavior at high temperature. Clear ion-dependent trends are observed, with Na$^+$ and K$^+$ salts generally showing stronger thermophobic responses than Li$^+$ salts, especially in iodide solutions. We estimate that the shift in the inversion temperatures of the iodide salts relative to experiment corresponds to a small local offset of the effective heat of transport, 4-5 kJ/mol, showing that small changes in hydration thermodynamics or heat-mass coupling can strongly affect the sign change of the Soret coefficient. Structural analyses indicate that lower temperatures and lower concentrations favor more tetrahedrally ordered, LDL-like water environments, which are associated with enhanced thermophilicity. Analysis of inversion temperatures and mass effects further suggests that the heat of transport contains both structural and kinetic contributions. These findings provide molecular-level insight into the interplay between hydration structure, ionic mass, and thermodiffusive transport in aqueous electrolytes.

Magneto-active elastomers (MAEs) are polymer composites consisting of magnetic microparticles embedded in an elastomeric matrix. These materials exhibit strong magneto-mechanical coupling under external magnetic fields, resulting in tunable stiffness, reversible shape changes, and nonlinear magnetic responses. This study presents a multiscale theoretical framework to investigate the origin of magnetic hysteresis in MAEs, with emphasis on the evolution of the internal microstructure during magnetization and demagnetization. The total energy of the system is formulated as the sum of magnetic and micromechanical contributions, while macroscopic deformation of a cylindrical MAE sample is fully constrained. Particle interactions are modeled first via pure dipole-dipole interactions and then extended to include higher-order near-field effects at close particle separations. The results show that hysteresis in MAEs with magnetically soft particles primarily arises from trapped microstructural rearrangements, leading to distinct particle configurations under increasing and decreasing magnetic fields. Parametric studies demonstrate that particle volume fraction, sample aspect ratio, and matrix stiffness strongly influence the microstructure evolution and the width of resulting hysteresis loops. The proposed framework provides a solid foundation for modeling magnetic hysteresis, which is essential for the design and optimization of MAEs in practical applications.

Charged colloidal crystals exhibit a subtle interplay between electrostatic screening and elastic deformation. In an anisotropic elastic medium the coupling between dilation and the local ionic environment becomes direction dependent, leading to a preferential softening of the longitudinal acoustic response along specific crystallographic axes. This article provides a self-contained derivation of the long-wavelength static stability condition for cubic crystals subject to a generic electrostatic-elastic coupling. Starting from an effective static elastic tensor renormalized by a scalar coupling constant $\lambda_g$, we obtain an explicit condition for the onset of a homogeneous instability: the direction $\hat{\mathbf{k}}$ that first loses rigidity is determined by the inverse Christoffel matrix evaluated along that direction. Closed-form expressions for the critical coupling $\lambda_g^c$ are given for the $[100]$, $[110]$, and $[111]$ high-symmetry directions. We further provide a microscopic derivation of $\lambda_g$ from the Poisson-Boltzmann theory in a spherical Wigner-Seitz cell, linking the phenomenological constant to experimentally accessible parameters such as salt concentration, particle charge, and volume fraction. The analysis reveals that the most fragile direction can be identified without full lattice-dynamical calculations, and the associated unstable strain patterns are discussed. Numerical illustrations using experimentally measured elastic moduli of soft colloidal assemblies demonstrate the predictive power of the criterion. The present framework serves as a diagnostic tool for interpreting directional anomalies in static compressibility or low-frequency acoustic softening.

We present a systematic theory of chemically active emulsions in the hydrodynamic limit by constructing a thermodynamically consistent framework in which the equilibrium is broken by chemo-stating of fuel molecules. For ternary solutions with active chemical reactions, we obtain an effective dynamics of the conserved field dynamics at long length and time scales. The effective dynamics takes into account the broken time reversal symmetry that manifests itself by the emergence of gradient terms akin to those of Active Model B+, which is a generic theory of active phase separation. In addition to the active coefficients modifying the interfacial energy coefficient, the theory contains higher order terms in the gradient expansion that are necessary to correctly describe the dynamics of chemically active emulsions, extending thus Active Model B+. We study numerically a Flory-Huggins model with active chemical reactions. Our theory predicts the formation of microphases when the effective interfacial energy coefficient becomes negative. Moreover, including noise, we show the existence of bubbly phase separation. We also identify a new type of phase behavior, a dynamic active filament phase. Finally, we discuss the steady state entropy production rate in the system resulting from the active chemical reactions. We observe that the total entropy production rate increases with the driving chemical potential and exhibits a kink-like singularity at the transition to the dynamic active filament phase. Our work shows that the generic behaviors of active phase separation can emerge in chemically active emulsions.

Quartz Crystal Microbalance (QCM) sensors are widely used to study biological and soft-matter interfaces due to their exceptional sensitivity to mass loading and interfacial mechanical properties. While classical QCM theory assumes predominantly shear-wave coupling into a semi-infinite Newtonian liquid, finite liquid thickness and acoustic reflections give rise to pronounced compressional (longitudinal) wave effects that strongly modulate both resonance frequency and motional resistance. Such compressional acoustic-wave responses should be properly accounted for when sensing in the liquid phase, for instance when working with cell suspensions. In this work, we systematically investigate compressional-wave responses in cell culture media including DMEM and RPMI-1640 across varying droplet volumes using a 5 MHz AT-cut QCM. Time-resolved measurements are analyzed using four parameters: the time period of compressional acoustic waves (Tca), the time associated with a phase shift between resonance frequency and resistance oscillations (Tp), the peak-to-peak shifts in frequency ({\Delta}fpp) and resistance ({\Delta}Rpp). DMEM and RPMI-1640 both exhibit strong volume-dependent periodic oscillations. At lower volumes, they exhibit low-frequency oscillations with a time period of approximately 40 minutes. However, as volume increases, the oscillations gradually evolve into high-frequency oscillations with a time period Tca of approximately 5 minutes. The peak-to-peak shifts ({\Delta}fpp) and ({\Delta}Rpp) are approximately 100-150 Hz and 40-60 {\Omega}, respectively. The resonance frequency and resistance oscillations also exhibit a phase shift Tp of approximately 10 minutes. These results highlight that compressional-wave artifacts occur even in simple cell culture media, necessitating their explicit consideration when interpreting QCM data in the presence of cells.

During cell division active flows occur in the cortex, a thin layer of gel like network of acto myosin filaments, beneath the cell surface. The cortical flow and the associated stresses bring about change in the cell shape, in particular a sharp invagination at the mid cell. Using 3D phase field simulation of an active deformable shell, which captures coupled dynamics of cortical velocity and nematic order, we show how a nematic like actomyosin ring spontaneously emerge at the equator and drive sharp invagination. We further demonstrate how different cortical flow patterns, including counter rotating flows emerge near the division furrow. We show that these flow patterns, often attributed to intrinsic chirality of actomyosin filaments can instead arise from bias in the initial nematic alignment, revealing a memory effect in the system. By analyzing a simpler model of activity gradient driven compressive flow on a flat interface we decipher the main ingredients for surface instability leading to invagination and counter moving flows.

Microorganisms navigating through narrow spaces encounter significant hydrodynamic challenges. To overcome these constraints and sustain efficient motion, they employ adaptive strategies, including adaptive oscillatory body deformations. While artificial microdroplets can traverse channels narrower than their diameter, studies of their locomotion have thus far been largely restricted to steady-shape regimes. In this work, we demonstrate a transition from steady shape to dynamic interfacial undulations in 5CB (4'-pentyl-4-cyanobiphenyl) droplets within aqueous trimethylammonium bromide (TTAB) solutions. We show that while droplets in dilute, additive-free solutions maintain a steady shape, the introduction of solutes or higher surfactant concentrations triggers pronounced interfacial undulations. Notably, both steady and undulating droplets exhibit a comparable velocity dependence on the confinement ratio, characterized by an initial deceleration followed by saturation, governed by the competition between hydrodynamic resistance and phoretic flow within the lubrication film. Furthermore, we find that increased surfactant concentration increases the capillary number, resulting in a thicker lubrication layer that facilitates a symmetry-breaking transition. Upon varying confinement, the droplet interface shifts from bilateral undulations to a mode localized on one side, forming a traveling-wave pattern strongly coupled to flow field fluctuations at the droplet's anterior. Linear stability analysis identifies the Yih-Marangoni instability as the underlying mechanism for these oscillations, revealing a previously unrecognized mode of adaptive locomotion in confined active matter.

In this work, we perform experiments with spherical polyacrylamide (PAAm) hydrogel drops/spheres, spanning a broad range of shear moduli and impact velocities on hydrophilic (plasma-treated glass) and hydrophobic (silane-coated) substrates, yielding an elastic number El variation of five orders of magnitude. Transient spreading morphology and impact force were simultaneously resolved using synchronized high-speed imaging and piezoelectric force sensing. At low elastic numbers ($El < 1$), impacting hydrogels exhibit a hybrid poroelastic response: a liquid-rich contact foot is expelled from the polymer network and spreads independently, while the bulk drop undergoes viscoelastic contact-line pinning into a pancake geometry at maximum deformation. At high elastic numbers ($El > 1$), contact foot spreading is suppressed, and deformation is accurately described by a neo-Hookean energy balance, yielding a maximum spreading factor independent of substrate wettability. Further, we show that the normalized peak impact force $F^*$ collapses to a constant value consistent with the Wagner limit for $El < 1$ and follows a power-law scaling $F^* \sim El^{0.38}$ for $El > 1$, in close agreement with both Hertzian and neo-Hookean predictions, and independent of substrate wettability. Furthermore, we highlight that post-impact retraction is suppressed across nearly the entire parameter space due to adsorbed polymer chains anchoring the receding gel network to the substrate, producing circumferential ridge instabilities; rebound occurs only when elastic restoring forces overcome the work of adhesion.

A simple framework is presented for unified applications in various fields of colloidal research, with minimal additional concepts & definitions. Several case studies concerning glass transition & crystallization are provided under the minimalist version, upon which adaptations can be made to suit more complicated topics. Major factors influencing accuracy are also discussed.

Flexible mechanical structures can undergo large deformations under small loads, enabling large, complex, and nonlinear wave responses under finite-frequency driving. Here, we study a dynamically driven canonical flexible mechanical metamaterial composed of rigid squares connected at their corners by flexible hinges. This metamaterial supports a uniform dilational mechanism and, in the limit of ideal joints, exhibits a Poisson ratio of -1. The presence of this dilational mode of deformation gives rise to a conformal symmetry, in which the dynamics are approximately invariant under a wide class of physical transformations -- conformal maps. We find that the low-frequency response of the system is dominated by conformal deformations consisting of spatially varying rotations and dilations concentrated at the boundary. Even at high frequencies, each conformal map implies a conserved spatially complex momentum. We explore how experimental parameters such as material stiffnesses and the geometry and number of unit cells allow experimental conformal momenta to approach this conservation, varying slowly compared to the non-conformal momenta of same order. These results constitute a new framework opening fundamental avenues for the study of conformal wave phenomena in dilational metamaterials as well as potential strategies for controlling nonlinear waves and vibrations.

Casimir-Lifshitz forces generate an unavoidable, long-range attraction between protocells under prebiotically realistic conditions. This interaction stabilizes mesoscale clusters such as tetrahedra, octahedra, and 13-cell icosahedra. These highly symmetric assemblies act as persistent macrostates whose transitions remain reproducible despite microscopic noise. A physics-guided coarse-graining yields a well-defined mesodynamics that can be represented as an $\epsilon$-machine: a small deterministic automaton whose causal states correspond to cluster attractors and whose transitions encode ordered reconfiguration pathways. The theory of Rosas et al. (Software in the natural world) shows that such systems can become informationally, causally, and computationally closed, thereby forming an autonomous proto-software layer. In this framework, prebiotic information does not arise from polymers but from attractor-based memory and structured transition dynamics in a purely physical cluster process.

Amphiphilic block copolymers self-assemble into diverse nanoscale morphologies with significant implications for drug delivery. This work presents systematic Brownian dynamics simulations of multi-chain diblock and triblock copolymers across dilute and semi-dilute unentangled regimes, hydrophobic fractions, f of 0-1, and shear rates of 0-0.1 1/ns. In the dilute regime, quiescent conditions yield spherical micelles evolving to cigar-like structures at shear rate ~0.01 1/ns and fragmenting at higher shear; varying f produces dispersed chains (f=0), cigar-like (f=0.25), short cylindrical (f=0.5), and gnarled or worm-like (f=0.75) micelles, culminating in sheet-like phase-separated structures (f=1). While, in the semi-dilute regime, shear drives collective reorganisation toward sheet-like morphologies at moderate rates before fragmentation; the f-dependent progression yields cigar-like (f=0.25), sheet-like (f=0.5), and necklace micelles (f=0.75), with larger phase-separated domains at f=1. Rheological characterisation reveals a universal architectural inversion between equilibrium and flow conditions: diblocks show higher equilibrium viscosity while triblocks maintain superior viscosity under flow via bridging networks. Aggregation number scaling exponents of alpha=0.833 in dilute, consistent with star-to-crew-cut bounds of 0.8 to 1.0, and alpha=1.07 in semi-dilute confirm the concentration-driven transition between regimes. Viscoelastic analysis establishes universal non-terminal power-law scaling across all conditions, governed by micellar relaxation dynamics independent of concentration or topology. These findings provide valuable insights into tailoring the injectability and flow behaviour of block copolymers in drug delivery formulations.

Zero-vorticity contours in the collective flows of living cells obey Schramm-Loewner evolution with diffusivity $\kappa = 6$ and thus fall in the universality class of critical percolation. This observation is surprising because the underlying vorticity field has long-range correlations that, according to the Weinrib-Halperin criterion, should alter the universality class. Here we propose a spectral explanation for this apparent paradox in two-dimensional active nematic turbulence. The universal energy spectrum $E(q) \sim q^{-1}$ implies sign-field correlations whose decay exponent $a = 3/2$ matches the Weinrib-Halperin marginal threshold $2/\nu_0 = 3/2$ for two-dimensional percolation. At this marginal point the long-range correlations are irrelevant under renormalization, so the system flows to the uncorrelated percolation fixed point. Gaussian surrogate fields with the same spectrum confirm $a = 3/2$ to three significant figures, and left-passage analysis of their zero-vorticity interfaces yields $\kappa = 5.98 \pm 0.08$, consistent with SLE_6.

Fibrous networks are ubiquitous structural components in biology, spanning cellulose in plant cell walls, fibrin in blood clots, and collagen in the extracellular matrix of animal tissues. Theoretical models predict that network connectivity critically influences their mechanical behavior. However, accurately reconstructing network topology from 3D image data remains a major challenge as current segmentation methods are not designed to preserve network topology and often rely on intensity-based thresholding, which can fragment fibers and distort junction connectivity. Here, we introduce ToFiE, an open-source topology-aware fiber extraction workflow for reconstructing dense and heterogeneous fibrous networks from high resolution microscopy images while preserving connectivity in three dimensions. We validate ToFiE using synthetic fluorescence microscopy images of fiber networks with varying topologies and signal-to-noise ratios. We further demonstrate its performance by reconstructing the fiber networks of a library of collagen gels with various microstructures, imaged using confocal fluorescence microscopy. Altogether, the results establish ToFiE as a practical semi-automated framework for extracting mechanically relevant network information from imaging data across a broad range of fibrous materials.

We determine the fully resolved equilibrium density profiles for two binary hard-sphere crystal structures using classical density functional theory through the White Bear II functional from fundamental measure theory. While for the substitutional crystal, in which some hard spheres are replaced by spheres of slightly smaller diameter, the density profiles are rather similar to the single-component case (narrow Gaussian peaks centered at fcc lattice sites), we observe a more complex behavior for the case of interstitial solid solutions, where the small species is fairly delocalized in the unit cell. Further, we compute the species-resolved inhomogeneous two-body direct correlation functions for these two types of binary crystals. The large-large components are mainly determined by the vacancy concentration $n_\text{vac}$ and show a characteristic magnitude $~1/n_\text{vac}$. Based on this observation, we propose a simple geometric picture of this six-dimensional function. The components of the direct correlation function involving the small spheres substantially differ in interstitial solid solutions from those of the substitutional crystal.

Functional magnetic composites capable of large deformation, load bearing, and multifunctional motion are essential for next-generation adaptive soft robots. Here, we present muscle-inspired magnetic actuators (MMA), additively manufactured from a thermoplastic/permanent magnet polyurethane/Nd2Fe14B (TPU/MQP-S) composite using laser powder bed fusion (LPBF). By tuning the laser-energy scale between 1.0 and 3.0, both mechanical stiffness and magnetic response are precisely controlled: the tensile strength increases from 0.28 to 0.99 MPa while maintaining 30-45% elongation at break. This process enables the creation of 0.5 mm-thick flexural hinges, which reversibly bend and fold under moderate magnetic fields without damage. Two actuator types are reported showing the system versatility. The elongated actuator with self-weight of 1.57 g, magnetized in its contracted state, achieves linear contraction under a 500 mT field, lifting 50 g (32x its own weight) and sustaining performance over at least 50 cycles. Equipped with anisotropic frictional feet, it supports movement of a magnetic crawling robot that achieves up to 100% locomotion success on textured substrates. The expandable actuator exhibits reversible opening and closing under a 300 mT field, reliably grasping and releasing different objects, including soft berries and rigid 3D printed geometries. It can also anchor in a tube while holding suspended 50 g loads. This work demonstrates a LPBF-based strategy to program both stiffness and magnetization within a single material system, enabling remotely driven, reconfigurable, and fatigue-resistant soft actuators. The approach opens new possibilities for force controlled, multifunctional magnetic soft robots for adaptive gripping, locomotion, and minimally invasive manipulation of biomedical tools.

We introduce a parameter estimation method that utilizes microscopic data, specifically averages and correlations of selected microscopic observables, to determine the parameters of a stochastic differential equation governing coarse-grained degrees of freedom. The method is not limited to static parameters found in the reversible part of the coarse-grained dynamics, such as those in the free energy function or potential of mean force, but also extends to dynamic parameters, including friction coefficients. The method couples the stochastic differential equation with free parameters to dynamic equations for the parameters. The coupled system self-averages, according to Anosov-Kifer's theorem, in such a way that the final state of the parameters gives coincidence between the microscopic and mesoscopic averages and correlations of selected observables. The method is validated in two examples: a Brownian particle in a harmonic potential, and a set of Brownian particles interacting hydrodynamically with the Rotne-Prager-Yamakawa mobility tensor. This latter case illustrates how the method can be used not only to determine coefficients but also state dependent transport properties - in this case, the position dependent form of the mobility tensor. The parameter estimation for these two models yields excellent results. Subsequently we use the methodology to study a bimodal-mass Lennard-Jones fluid for which we infer both the potential of mean force between the heavy particles and its hydrodynamic mobility tensor.

An analytical solution is obtained for the problem of the slow movement of a small drop of a fluid in another immiscible fluid in an infinitely large reservoir with the boundary condition of the normal slip and/or tangential partial slip at the interface. That generalizes the conventional Navier and Maxwellian boundary conditions of partial slip. Normal slip is accompanied by the density gradient in the fluid and is applicable only if one of the phases in contact at the interface is a gas. Although tangential partial slip and the associated generalization of the Hadamard-Rybczynski equation (HRE) have been considered previously, they were done using the friction coefficient formalism. Here, this issue is discussed within the more general formalism of slip lengths. It is proven that each of the two fluids separated by an interface has its own slip length. New equations describing the terminal velocity of gas bubble rise and aerosol falling have been obtained. The result is compared with experiment. It has been shown that the gas density within a rising bubble and around a falling droplet in the air is not uniform. The relative magnitude of the density increment increases with the size of the bubble or aerosol. Presumably, the best applicability of the generalized HRE should be expected for the interface of hydrophobic liquid and hydrophilic one (water and hydrocarbons, water and higher alcohols, in general: aqueous emulsions, water, lipophilic organic liquids and oils, etc.). These are quite important emulsions in practical terms, for example, for the oil industry and medicine. Experimental methods for determining the slip length are considered.

We investigate the creep dynamics of a driven elastic line at finite temperature, well below the depinning threshold. We show that creep is governed by two distinct length scales. The first, $\ell_{\mathrm{opt}}$, corresponds to the optimal activated rearrangements that control the dynamics' bottleneck and remains essentially temperature-independent. The second, $\ell_{\mathrm{av}}$, characterizes the spatial extent of thermally activated avalanches and grows as temperature decreases. By combining structural and dynamical observables, we show that $\ell_{\mathrm{av}}$ governs both the crossover in the structure factor and the growth of the four-point dynamical susceptibility, while the relaxation time remains controlled by activation over large barriers associated with $\ell_{\mathrm{opt}}$. We find that the avalanche scale follows $\ell_{\mathrm{av}}(T)\sim T^{-\nu_{\mathrm{dep}}}$, thereby selecting a unique scenario among competing theoretical predictions. These results establish a unified picture of finite-temperature creep in which activation controls temporal scales while depinning criticality governs spatial correlations.

Applications such as digital microfluidics and bio-diagnostics rely on droplet locomotion. A prominent example of such motion is durotaxis, a phenomenon that requires a stiffness gradient along a surface for the transport of liquids, cells, or other nano-objects. Using surfaces with varying properties in specific directions can be exploited as a universal concept for fluid transport with or without external energy supply. Changes in properties may refer to substrate patterns, Laplace pressure changes, wettability gradients, etc., leading to exciting phenomena, which can be employed in novel applications in various technologies. Here, we report on key results and progress in the area of directed droplet motion over the years, and we provide perspectives and implications for anticipated applications.

Phase-field models for anisotropic fracture employ two complementary mechanisms: (i) the anisotropic crack density function, controlling direction-dependent fracture resistance, and (ii) the anisotropic strain energy, governing the fracture driving force. Although the unified framework was presented in Pranavi et al.[Comput. Mech., 73 (2024)], the distinct roles of these mechanisms and their interaction remain uninvestigated. This work addresses this gap by first validating the formulation against mixed-mode fracture experiments on a soft elastomer (Lu et al. [Extreme Mech. Lett., 48 (2021)]), and then conducting systematic parametric studies on single-edge-notched (SEN) and open-hole tension (OHT) specimens to isolate each mechanism. The SEN studies show that the crack density anisotropy controls the crack path and toughness while leaving the elastic response unchanged, whereas the anisotropic strain energy deflects the crack but saturates rapidly. The OHT studies reveal a geometry-dependent role expansion: the anisotropic strain energy governs fiber-orientation-dependent stiffness, peak force, and fracture displacement. When both mechanisms act together, the combined response exhibits nonlinear synergistic interaction exceeding the linear sum of the individual contributions. These results establish that the crack density anisotropy governs the crack path (fracture resistance), while the anisotropic strain energy governs the driving force and, in stress-concentration geometries, additionally controls the elastic strain energy distribution around the stress concentrator.

We introduce an information-theoretic framework that uses variational autoencoders (VAEs) to extract compact, physically interpretable manifolds from high-dimensional flow-field data. To this end, the Kullback--Leibler (KL) divergence in the variational objective is decomposed into three complementary information-theoretic terms: the index-code mutual information, the total correlation, and the dimension-wise KL divergence. These terms explicitly regulate data compression, latent disentanglement, and geometric regularization. This establishes a principled basis for targeted latent-space design, allowing enhanced interpretability without sacrificing information capacity, a common drawback of heavily regularized VAE variants. The approach is evaluated on two synthetic unsteady flow datasets. First, we consider a flow around a cylinder in a channel with variable cylinder position, diameter, and Reynolds number. Later, we also consider the flow around a NACA 0012 airfoil at varying angles of attack and subjected to strong vortex gusts with variable intensity, position, and length scale. Comparisons with Principal Component Analysis, Isometric Feature Mapping, and $\beta$-VAE demonstrate clear advantages in disentanglement and physical interpretability. The learned latent coordinates successfully separate distinct physical effects. Moreover, the proposed method demonstrates strong robustness to variations in the loss-weighting parameters, despite involving a larger number of such parameters.

Coherent structures in aspect ratio 2, axis-switching elliptical jets are studied using direct numerical simulation (DNS). Three different datasets are studied with varying near-nozzle forcing levels. Increasing the forcing level causes the jet to axis switch at an earlier streamwise location. Spectral proper orthogonal decomposition was applied to the dataset to extract the most-energetic coherent structures in the flow, and modes associated with the main symmetries of the flow were identified. The flapping mode was found to decay faster at the high forcing level, a feature that was linked to the axis-switching behavior. The axis-switching phenomenon causes the flapping mode to become a wagging mode relative to the new axis, lowering the growth rate of the structure. Two different coherent structures were found in the SA (dihedral group $D_2$) symmetry for the axis-switching cases: the wagging mode which was dominant in the pre-axis-switch region and a new flapping mode which is dominant in the post-axis-switch region. The new flapping mode was dominant in the low-frequency region of the full-field SPOD spectrum which was overtaken by the wagging mode at $St\approx 0.2$ for the medium-forcing case and at $St\approx 0.4$ for the high-forcing case. This new flapping mode is likely a flapping mode relative to the axis-switched mean flow, which develops due to the slower growth of the shear layer in the major axis.

Air lubrication regimes were studied using simultaneous drag force measurements and multi-plane imaging to characterize the regimes and identify the governing mechanisms of drag reduction. A bubbly, transitional, and air layer regime are identified over a large range of freestream velocities ($U_{\infty}$), air flow rates ($Q_{air}$), and Froude-depth numbers ($Fr_d$). For the lowest $U_{\infty}$, drag reduction lags significantly behind the non-wetted area coverage at all cases and no simple correlation exists. Within the bubbly regime, a drag increase is found for low $U_{\infty}$ with large, slow-moving bubbles forming a single layer over the plate height. For higher velocities, bubbles become smaller and disperse vertically, while the drag starts decreasing. For higher $Q_{air}$, irrespective of $U_{\infty}$, air patches start to form (transitional regime) and drag monotonically decreases, with the onset of the air layer regime at 60\% drag reduction. A new scaling of the associated critical $Q_{air}$ is proposed, combining the air exit velocity, the liquid velocity close to the air layer and $Fr_d$. For a further increase of $Q_{air}$ and low $U_{\infty}$, a thicker and smoother air layer is formed with even lower drag; for higher $U_{\infty}$, marginal differences are observed. The air layer morphology is significantly altered however, depending on $Fr_d$: for $Fr_d>0.7$, it is unbounded, extending beyond the current test section length, and for subcritical conditions (deep water regime, $Fr_d<0.61$) a closure is formed and the air layer transitions to a cavity of a specific length.

We study the hydrodynamic behaviour of a mesoscale numerical model for wetting dynamics based on the immersed boundary - lattice Boltzmann (IBLB) method. This IBLB model features a wetting potential to capture the interaction between a non-ideal droplet interface and a solid boundary; it is designed to prevent abrupt curvature changes near the contact line. As this approach prevents direct contact between the droplet and the solid, it forms a thin film beneath the droplet, which could compromise the hydrodynamic consistency in this region. This paper presents detailed comparisons against two other hydrodynamic solvers, respectively based on a boundary element method (BEM) and a volume of fluid (VoF) method, in order to examine the hydrodynamic behaviour of this IBLB scheme, elucidate its limits of validity in wetting applications, and explore the properties of its contact-line model.

Fan-array wind generators (FAWGs) provide controlled turbulent inflow conditions that cannot be reproduced in conventional wind tunnels. Despite their increasing use in experimental studies, numerical modeling of FAWG-generated flows remains largely unexplored. The present study assesses the capability of Reynolds-Averaged Navier-Stokes (RANS) modeling to predict jet interaction in a 10x10 fan-array wind generator. Numerical predictions are compared against experimental measurements of axial velocity and turbulence intensity from a reference configuration. Individual fan units are represented using a pressure-jump boundary condition based on a reconstructed performance curve derived from manufacturer data. Grid convergence is verified, and the influence of fan representation, operating point and inflow turbulence conditions is examined. The results show that RANS modeling captures the global jet interaction topology and downstream velocity decay with reasonable accuracy. However, systematic magnitude discrepancies are observed in the near-field injection region and peripheral shear layers. Turbulence intensity predictions exhibit larger deviations, reflecting limitations of the eddy-viscosity closure in highly mixing-dominated flows. A low-aspect-ratio flat plate is included as a demonstrative application to illustrate the aerodynamic impact of FAWG-generated inflow. Overall, the study shows that RANS modeling, combined with a pressure-jump fan representation, provides a computationally efficient framework for predicting the mean-flow structure of FAWG systems, while exhibiting clear limitations in resolving localized turbulence characteristics.

Accurate autoregressive prediction of 3D turbulent flows remains challenging for neural PDE solvers, as small errors in fine-scale structures can accumulate rapidly over rollout. In this paper, we propose FlowRefiner, a flow matching-based iterative refinement framework for 3D turbulent flow simulation. The method replaces stochastic denoising refinement with deterministic ODE-based correction, uses a unified velocity-field regression objective across all refinement stages, and introduces a decoupled sigma schedule that fixes the noise range independently of refinement depth. These design choices yield stable and effective refinement in the small-noise regime. Experiments on large-scale 3D turbulence with rich multi-scale structures show that FlowRefiner achieves state-of-the-art autoregressive prediction accuracy and strong physical consistency. Although developed for turbulent flow simulation, the proposed framework is broadly applicable to iterative refinement problems in scientific modeling.

Finite-dimensional state-space representations of unsteady aerodynamics implicitly assume a system with fading memory. However, the impulse response of the two-dimensional inviscid (Euler) equations is characterized by an asymptotic $t^{-3/2}$ power-law decay due to the persistence of shed vorticity. The present work demonstrates that this decay rate constitutes a critical boundary for moment convergence: the second temporal moment diverges logarithmically, causing the characteristic memory time to grow as $\sqrt{\ln T}$ with the observation window $T$. As a result, no window-independent characteristic time scale exists, and finite-dimensional models fitted to inviscid data effectively parameterize the observation horizon rather than intrinsic flow physics. To quantify this behavior, a temporal-moment diagnostic, $\nu_t(T)$, is introduced based on the ratio of the second and zeroth windowed moments of the impulse response kernel. Exponential models exhibit stable memory time plateaus, as their sufficiently fast decay ensures convergence of the moment diagnostic. Compressible Euler simulation results confirm the predicted $\sqrt{\ln T}$ scaling at intermediate times, while numerical dissipation inherent to the discretization acts as an artificial regularizer that enforces convergence at late times. These results establish the two-dimensional inviscid limit as a critical boundary for moment-based system identification, where the absence of a dissipative mechanism prevents the definition of a window-independent characteristic memory time.

Potential flow theory remains a cornerstone of unsteady aerodynamics due to its computational efficiency in modeling complex flow phenomena. This study presents a significant advancement by integrating a viscous unsteady theory with established numerical vortex methods, creating a hybrid computational tool for low-to-moderate Reynolds number flows. We develop a Viscous Discrete Vortex Method (VDVM) by replacing the classical inviscid Kutta condition with a closure derived from triple-deck boundary layer theory, allowing the model to account for Reynolds number dependencies and unsteady viscous effects. The framework utilizes a three-dimensional vortex ring scheme and an unsteady Bernoulli formulation for load calculation. The model is validated against experimental and high-fidelity CFD data, showing excellent agreement in thrust and torque across a wide operational envelope. Using this validated framework, we conduct a systematic parametric investigation into rotor blade design for electric vertical take-off and landing (eVTOL). A sophisticated optimization of the spanwise geometry was performed: twist distributions were calculated by iteratively solving for axial and tangential induction factors to maintain optimal local angles of attack, while chord distributions were derived using the Adkins and Liebeck framework to satisfy the Betz condition for maximum efficiency. Results demonstrate that this tapered chord and nonlinear twist profile significantly mitigate tip losses and manage spanwise loading. The optimized geometry achieved an 8.99% increase in the efficiency compared to the baseline. This work bridges the gap between high-fidelity viscous analysis and fast vortex methods, providing a versatile tool for the performance-driven design of lifting surfaces in unsteady flight regimes.

Simulations of the transitional flow in Taylor-Couette configuration are carried out to study the effect of the gap width on turbulent transition. The research results show that, under the same radius and the rotating speed of the inner cylinder, as the gap width increases, the flow becomes more stable. It is discovered that the average velocity distribution in the gap approaches the free vortex flow as the width increase and the stability of the flow is enhanced. It is found that, as the gap width increases, the maximum of the energy gradient function (from the energy gradient theory) in the gap decreases, which delays the turbulent transition. As such, the larger the gap width, the later the transition occurs. As the gap width increases, the Reynolds number based on the gap width alone is not able to characterize the flow behavior in Taylor-Couette flows, and the effect of the radius ratio should be taken into account.

The velocity field within a steady toroidal vortex is found for arbitrary mean core radius and section ellipticity. The problem is solved by transforming to coordinates that define invariant sets. The method allows the properties of the coordinate system metric tensor to be exploited in the continuity equation in order to obtain the solution. The vorticity is found to decrease monotonically with distance from the symmetry axis. For a given outer radius and outer perimeter velocity, the circulation of the vortex ring can be either smaller or larger than that of Hill's spherical vortex.

Representing turbulent flow fields in a compact yet physically faithful form remains a central challenge in computational fluid dynamics. We propose a continuous parametric representation based on localized Gaussian primitives, in which the velocity field is modeled as a superposition of kernels with learnable positions, amplitudes, and scales. This formulation yields a compact, grid-independent encoding while enabling evaluation of derived quantities such as vorticity and enstrophy. The approach is assessed on three-dimensional Taylor-Green vortex fields spanning stages from smooth flow to fully developed turbulence. We quantify the compression-accuracy trade-off using both primary variables and derivative-sensitive diagnostics. The baseline isotropic formulation achieves high velocity accuracy at compression ratios exceeding 1e3-1e4, but exhibits substantial enstrophy degradation due to loss of small-scale structure. To address this limitation, we investigate structure-aware extensions including adaptive placement, multi-resolution kernels, and anisotropic Gaussians. The anisotropic formulation provides the most consistent improvement, better aligning with elongated vortical structures and recovering intermediate- and high-wavenumber content, while other strategies yield modest gains. A compact-support Beta basis improves enstrophy in some cases but introduces localized artifacts. Overall, the results indicate that the main limitation of baseline Gaussian representations lies in geometric expressiveness rather than parameter count. The proposed framework provides a compact, interpretable, and continuous representation of turbulent flows, and establishes a foundation for structure-aware and physics-informed flow compression.

We present this http URL , an open-source Julia package for solving the incompressible Navier--Stokes equations on staggered Cartesian grids. The package features matrix-free, hardware-agnostic kernels that are compiled from a single source for multi-threaded CPU or GPU execution, and hand-written adjoint kernels for all discrete operators, enabling efficient reverse-mode automatic differentiation through the entire solver. This differentiability allows neural network closure models to be trained a-posteriori while embedded in a large-eddy simulation. Memory optimizations permit double-precision direct numerical simulations at resolutions up to $840^3$ on a single GPU. The software design, numerical methods, hardware performance, and integration of neural network closure models are described, and results for turbulent channel flow are validated against reference data.

We present a fully coupled boundary integral formulation for modeling steadily propagating semi-infinite plane strain fractures in poroelastic media. By combining fundamental solutions of plain strain poroelasticity for instantaneous fluid source and edge dislocations (normal and slip modes) with temporal and spatial superposition principles, we derive boundary integral equations governing the tractions (normal and shear stresses) and pore fluid pressure on the fracture surfaces. Assuming prescribed tractions and pore fluid pressure profiles, we develop a numerical methodology to solve the governing equations for fracture opening, slip, and cumulative fluid exchange rate. The formulation is systematically verified on several relevant problems, including the case of a tensile fracture with exponential normal loading, a stress-free tensile fracture with an imposed exponential pore fluid pressure, and a shear fracture under uniform shear loading over a finite region, demonstrating excellent agreement with analytical solutions. The framework provides a robust tool for analyzing coupled fracture-fluid interactions in permeable poroelastic media and can be adapted to broader classes of elasto-diffusive problems by modifying the underlying physical parameters.

We develop two deep learning surrogate autoregressive models for the prediction of the temporal evolution of two-dimensional ideal magnetohydrodynamic (MHD) Kelvin-Helmholtz instabilities across a range of magnetic field strengths. Using two neural network architectures, a Koopman-based Transformer model and a ConvLSTM-UNet, our approach enables simultaneous prediction of vorticity and current density directly from high-resolution simulations. The models are trained in an autoregressive manner and are able to reproduce key features of the multiscale dynamics over several instability growth and nonlinear saturation phases. Beyond accurate field reconstruction, the surrogates preserve essential physical structures of ideal MHD dynamics, including the conservation trends of global invariants and the propagation of Alfvénic fluctuations. Compared to direct numerical simulations, the proposed surrogates offer substantially reduced computational cost while maintaining good agreement with the reference dynamics. These results suggest that deep learning based surrogate models can provide a promising complementary tool for the efficient and physically consistent exploration of high-fidelity plasma and fluid simulations.

Accurate machine-learning models for aerodynamic prediction are essential for accelerating shape optimization, yet remain challenging to develop for complex three-dimensional configurations due to the high cost of generating training data. This work introduces a methodology for efficiently constructing accurate surrogate models for design purposes by first pre-training a large-scale model on diverse geometries and then fine-tuning it with a few more detailed task-specific samples. A Transformer-based architecture, AeroTransformer, is developed and tailored for large-scale training to learn aerodynamics. The methodology is evaluated on transonic wings, where the model is pre-trained on SuperWing, a dataset of nearly 30000 samples with broad geometric diversity, and subsequently fine-tuned to handle specific wing shapes perturbed from the Common Research Model. Results show that, with 450 task-specific samples, the proposed methodology achieves 0.36% error on surface-flow prediction, reducing 84.2% compared to training from scratch. The influence of model configurations and training strategies is also systematically studied to provide guidance on effectively training and deploying such models under limited data and computational budgets. To facilitate reuse, we release the datasets and the pre-trained models at this https URL . An interactive design tool is also built on the pre-trained model and is available online at this https URL .

We present a physics based numerical model that estimates the seismic radiation generated by water sediment flows in gravel-bed rivers. The model reproduces the trajectories of individual particles, evaluates impact and rolling forces from grain scale dynamics, and accounts for broadband turbulence and vortex shedding in the water column. Synthetic seismic signals are propagated to the receivers using the Rayleigh wave Green s function approach and synthetic ground-velocity signals are estimated. Application to a controlled test case shows how intermittent, size selective sediment transport mechanisms produce distinct spectral signatures. Comparison with seismic data from a flood event in a mountain torrent in the Tuscan Apennines displays general agreement with the observed frequency bands and clarifies the relative width of particle collisions and turbulent flow. These results show that resolved grain scale dynamics provides a framework for discriminating sediment transport and flow induced contributions to river seismic noise.

Machine learning is becoming increasingly important for nonlinear system identification, including dynamical systems with spatially distributed outputs. However, classical identification and forecasting approaches become markedly less reliable in turbulent-flow regimes, where the dynamics are high-dimensional, strongly nonlinear, and highly sensitive to compounding rollout errors. Diffusion-based models have recently shown improved robustness in this setting and offer probabilistic inference capabilities, but many current implementations inherit target parameterizations from image generation, most commonly noise or velocity prediction. In this work, we revisit this design choice in the context of nonlinear spatiotemporal system identification. We consider a simple, self-contained patch-based transformer that operates directly on physical fields and use turbulent flow simulation as a representative testbed. Our results show that clean-state prediction consistently improves rollout stability and reduces long-horizon error relative to velocity- and noise-based objectives, with the advantage becoming more pronounced as the per-token dimensionality increases. These findings identify target parameterization as a key modeling choice in diffusion-based identification of nonlinear systems with spatial outputs in turbulent regimes.

This work aims to address the bottleneck issues of hardware resource limitation and decoherence error in the Hamiltonian simulation of quantum fluids, which are caused by the standard quantum Fourier transform and the evolution of momentum operators, resulting in excessively deep circuits and excessive two-qubit gates. We propose an approximate operator optimization scheme aimed at reducing the circuit depth in Hamiltonian evolution. The proposed scheme successfully reduces the depth of analog circuits from $O(n^2)$ to $O(nlogn)$ or even $O(n)$ by eliminating $O(n^2)$ redundant two-qubit entangling gates. In this work, the numerical experiments are implemented on a supercomputing-oriented quantum simulator, simulating two-dimensional unsteady divergent flow. Experimental results demonstrate that although the truncation of high-frequency qubit coupling terms introduces deterministic theoretical errors, scaling at $O(n)$ for AQFT and $O(n^2)$ for momentum truncation, the optimized simulations successfully preserve the inherent macroscopic temporal evolution characteristics of the fluid in a 10-qubit simulation, achieving high correlation coefficients of $r$=0.933, $r$=0.941, and $r$=0.977 for density, X-momentum, and Y-momentum distributions respectively. Furthermore, we also analyzed the relationship between the algorithm truncation error and the hardware cumulative noise when the qubit number is extended to a higher level. This study proves that rationally adjusting truncation thresholds can establish an equilibrium point, preventing the hardware cumulative error from rapidly approaching 100% at the 20-30 qubit scale, providing a feasible engineering pathway for simulating complex fluid systems on real quantum devices in the future.

We present an experimental study of the Duffing--Holmes oscillator with a double-well potential, implemented as an analog electronic circuit under periodic external forcing. By systematically varying the forcing amplitude and frequency, we characterize the full dynamical landscape of the system through bifurcation diagrams, Poincaré maps, and maximum Lyapunov exponent calculations. The observed phenomenology includes period-doubling routes to chaos, periodic windows with multistability, dynamical intermittency, and antiperiodic orbits in which the trajectory recovers the global symmetry of the double-well potential. These results are synthesized into a high-resolution two-dimensional phase diagram in parameter space. The close agreement between all experimental diagnostics validates the fidelity of the analog implementation and demonstrates that continuous-time hardware provides a powerful platform for the quantitative study of nonlinear dynamics, free from the discretization artifacts inherent to numerical simulation.

Dissipative structures are open dynamical systems that sustain coherent macroscopic organization by continuously exchanging energy and matter with their environment and generating entropy. A recent thermodynamic analysis of the paradigmatic Malkus--Lorenz waterwheel interpreted the Lorenz system as an engine, deriving an exact formula for its thermodynamic efficiency, and showing that efficiency tends to increase as the system is driven far from equilibrium while displaying sharp drops near the Hopf subcritical bifurcation to chaos. Here, we extend that single-engine framework to coupled dissipative structures. We introduce two canonical couplings -- master-slave coupling (series) and symmetric diffusive coupling (parallel) -- and prove two fundamental association laws allowing us to reduce the composite systems to an equivalent engine with a specified efficiency. We then apply these abstract results to coupled Lorenz waterwheels, deriving efficiency formulas consistent with the underlying power balance. We perform numerical simulations confirming that (a) series coupling induces an increase in thermodynamic efficiency, (b) parallel coupling averages the efficiency of engines and increases total energy flow, (c) synchronization is typically neutral or beneficial for efficiency except in narrow parameter regions, and (d) coupling modifies the curvature of entropy-generation trends. Our theorems suggest a mathematically rigorous and transparent route to define and compute thermodynamic efficiency for generalized flow networks, with potential application to complex systems energetics.

Dynamical properties of classical chaotic systems, for instance relaxation, can be understood as emerging from the time evolution of initially smooth long-wavelength densities to ever finer short-wavelength densities with fractal structure. Whether there is any analogous fractality by which one could characterize quantum many-body chaos is not known. By studying the spectral properties of the truncated operator propagator, we provide such structures. Namely, we show that the slowest-decaying operators, i.e., the leading Ruelle-Pollicott eigenvectors, have a nontrivial fractal dimension quantifying their non-locality, visible also in the divergence of their condition numbers. Furthermore, we find that unitarity imposes a constraint, i.e., an (approximate) equality, between the temporal decay rate of local correlations and this spatial operator fractal dimension. With this insight, a scenario for many-body quantum chaos becomes clear: over time, local operators evolve towards increasingly non-local ones with a quantifiable fractal structure, thereby naturally leading to effective non-unitary relaxation on the subspace of local operators - a kind of many-body Kolmogorov cascade in the space of operators. Our predictions are demonstrated in various quantum circuits: the kicked Ising model, brickwall circuits with a random 2-qubit gate, and dual-unitary circuits, where our results are exact.

The general relativistic magnetohydrodynamic (GRMHD) simulations are widely used to study accretion disk and jet dynamics around a black hole. Despite strong observational evidences for intrinsically nonlinear behavior, the interpretations of GRMHD simulation results, more precisely the underlying timeseries, have not been well-explored by nonlinear timeseries analysis. In this work, we characterize the jet and disk dynamics of different GRMHD simulated flows using the nonlinear timeseries analysis. As diagnostic tools, we consider Higuchi fractal dimension (HFD), Hurst Index (H) and spectral slope. We implement them for two model disk frameworks: magnetically arrested disk (MAD) and standard and normal evolution (SANE), across a range of black hole spins with the Kerr parameter spanning from -0.9375 to 0.9375. We simulate the disk/jet systems by two well-documented codes: HARMPI and BHAC, and obtain, respectively, low and high temporally resolved timeseries data. For both jet and disk dynamics, MADs are characterized by higher HFD, lower H and flatter spectral slopes than SANEs. High HFD in MAD could be due to its intermittent variability and indicates that it has lesser long-range temporal correlations than SANE. Moreover, HFD in MAD decreases with spin magnitude owing to increase in collimated, hence ordered, jets. However, in SANE, it increases with spin for positive ones due to interplay of winds and jets. Extending our analysis to observations, we attempt to segregate the classes of black hole: GRS 1915+105, into MAD- and SANE-like clusters based on their spectral properties extracted from X-ray data. The mean HFD of MAD-like cluster is higher than SANE-like cluster, thus, corroborating with the simulation results. Our work highlights the role of nonlinear timeseries analysis to understand the underlying dynamics of accretion flows and their connection to magnetic regulation.

Freshwater scarcity demands desalination technologies that are efficient, scalable, and sustainable. Capacitive deionisation (CDI) is promising but remains limited by inefficient ion adsorption and poor charge utilisation. Here, we show that suitably chosen polyampholytic block copolymer grafting can substantially enhance CDI performance, via a combination of dipolar response and steric effects. Using mean-field classical density functional theory and grand-canonical Monte Carlo simulations, we demonstrate that such polymer grafted electrodes enable strongly improved desalination performance, without altering the pore architecture. Even an electrode grafting by simple neutral polymers can generate an improvement, although a suitably designed block polymer architecture offers an additional performance gain. These results establish interfacial block copolymer grafting as a powerful route toward high-performance, membrane-free desalination.

Active matter systems characterized by the interplay of chirality and self-alignment offer a rich landscape for the emergence of non-equilibrium collective behaviors and the development of autonomous materials. We present a versatile experimental platform for studying these dynamics using augmented commercial bristlebots, where custom-designed housings and elastic couplings induce a self-aligning torque and a stable chiral drift. By mapping experimental trajectories to a Langevin-type model, we characterize the single-particle dynamics. In circular geometries, we show that the stability of edge currents is governed by the interaction between intrinsic particle chirality and handedness of the edge current. Furthermore, we demonstrate that transport can be geometrically rectified using a nautilus-shaped obstacle, which acts as a doubly chirality-sensitive ratchet. Finally, we explore the collective dynamics of rigidly linked assemblies, observing spontaneous mode-switching between translational and rotational states in triangular active solids. Our results provide a robust framework for the passive control of active gases and illustrate how geometric constraints can be used to program complex transport properties in synthetic active systems.

Collective rotations are common in active matter, enhancing cohesion, transport, and mixing. They are typically attributed to chiral non-reciprocal dynamics due to intrinsic particle chirality, torque-generating interactions among units, or geometric confinement. Here, we uncover a different mechanism for rotational order in active matter where a dynamic environment coordinates the self-organization of non-chiral active particles into living crystals exhibiting sustained collective solid-like rotations. At intermediate densities, feedback from a fluctuating landscape of passive Brownian particles stabilizes large living crystals of obstacle-avoiding run-and-tumble agents. Strikingly, this environmental feedback also produces living crystals with qualitatively distinct dynamics: collective solid-like spinning emerges for particles with long persistence times approaching ballistic motion, rather than for particles moving by conventional enhanced diffusion. Beyond revealing a new route to collective rotational order in active matter, these findings highlight the integral role of a dynamic environment in self-organization and suggest environment-mediated design principles for active materials with unconventional dynamical responses.

Electrical discharge at the smallest possible length and charge scales is not well understood. Using optical tweezers, we investigate spontaneous discharges of a single micron-scale particle levitated in air. These ``microdischarges'' have a typical size of $\sim$40 $|e|$, but can be as small as a few $|e|$ and as large as several hundred. The absence of a well-defined trigger charge and the weak dependence on particle size suggest events are not classical gaseous breakdown. Instead, we show that microdischarge events arise from the rapid capture of ions left in the tracks of nearby passing ionizing radiation. Our results highlight the role of natural ionizing radiation in initiating micron-scale discharges and provide a platform for studying discharge physics in electrode-free environments and at the smallest scales.

The temperature increase in the contact regions between solids in sliding contact has a huge influence on friction and wear. Here we test an analytical theory for the flash temperature, valid for randomly rough surface with multiscale roughness, by comparing the theory predictions with the experimental results of Sutter et al \cite{Sutter} for steel sliding on steel. The theory, which is based on the study of stress and temperature correlation functions, is valid for randomly rough surfaces with roughness on arbitrary many decades in length scale. Within the uncertainty of the experimental data (mainly the surface roughness power spectrum and the steel penetration hardness), there is good agreements between the theory and the experimental results.

Plasmonic nanoparticles (NPs) integrated within thermoresponsive polymeric microgels provide a versatile platform for the realization of stimuli-responsive optical materials, where the microgel volume phase transition enables dynamic control of plasmon coupling. This study uncovers a counter-intuitive re-entrant behavior with increasing NP loading in which plasmon coupling initially strengthens and subsequently weakens beyond a critical NP-to-microgel number ratio. By combining light and X-ray scattering techniques with optical spectroscopy and electrophoretic mobility measurements, it is demonstrated that plasmon coupling is governed not only by the interparticle distance between NPs confined within individual microgels, but also by the colloidal stability of the hybrid complexes. At intermediate NP loadings, surface charge inhomogeneities induced by NP adsorption promote aggregation of microgel-NPs complexes, resulting in enhanced plasmon coupling. In contrast, when the complexes remain colloidally stable, coupling is dictated solely by NP organization within the corona of individual microgels. A quantitative relationship between plasmon coupling and interparticle distance reveals two distinct coupling regimes. This behavior is rationalized through a phase diagram linking colloidal stability to optical response. These findings identify colloidal stability as a key parameter for designing soft plasmonic systems with programmable optical properties.

Molecular dynamics is a powerful tool to investigate the properties of fluid systems. However, a correct interpretation of the results of simulations is required. In particular, some simulations show appearance of large voids in liquids, which contradicts our common sense on what is liquid. In the present paper we discuss the origin of large cavities liquids in molecular dynamics simulations. We demonstrate that the cavities appear either if the temperature of the system is above the critical temperature of liquid-gas transition or if the system is in two-phase liquid-gas region. These conclusions are illustrated by several examples from literature and our own simulations.

We develop a kinetic theory of cohesin-driven loop extrusion on a disordered chromatin track with transient barriers. In the stationary state, the mean loop size is shown to obey a universal law determined by the bare processivity and a renormalized obstacle density. Beyond the mean, one-sided extrusion always yields a single-exponential loop-length distribution, whereas two-sided extrusion produces a finite sum of exponential modes and, generically, a peaked distribution. Experimental CTCF-anchored loop statistics exhibit such a peak, thereby providing a direct discriminator of extrusion symmetry. The theory therefore establishes a unified framework for disorder-limited loop extrusion and supports a scenario in which both cohesin arms actively operate in living cells.

The results of a numerical investigation of fluidized beds of spherical particles in a narrow vertical cylindrical pipe, with particular attention to the spontaneous settling along the wall, are reported. Starting from a steady fluidized state, the particles fluctuate because of fluid-particle, particle-particle, and particle-wall interactions. The particles are heavier than the fluid, with diameters d yielding ratios of pipe to particle diameters D/d=4.3 and 4.7. For given ranges of flow velocities and bed sizes, particles settle on the wall, with a decrease in the bed height and particle fluctuations. Either a glass- or crystal-like shell forms along the pipe wall, in qualitative agreement with previous experiments. The polydispersity and the particle-particle friction are varied to test the stability of the particulate shell formation. The shell structure is analyzed by unwrapping it in a plane and locating all particles and their contact points, and we find that it exhibits a hexagonal lattice with a defects density that increases with polydispersity. The shell formation is hindered by polydispersity, and there exists a critical point for polydispersity above which a crystal-like shell is unstable. In a particular case of bidisperse beds, the crystal-like shell only appears when the particle-particle friction is high enough. Finally, we compute the contact forces within particle-particle chains and in particle-wall contacts, which sustain the cylindrical shell, highlighting the dominant role of particle-particle forces.

Detachment and fracture are central to many tissue-level processes, but they are challenging to simulate with Voronoi-type models that typically assume a confluent tissue. Here we analyze the finite Voronoi model, a nonconfluent extension of conventional Voronoi models, in which cell boundaries are composed of straight Voronoi edges and circular arcs of fixed radius $\ell$. When the line tension on cell-medium interfaces exceeds the tension on cell-cell contacts, we find that the model exhibits a strong time-step dependence in the fracture timescale of initially intact active clusters: decreasing $\Delta t$ can unphysically suppress cluster rupture events. We trace this behavior to a divergence of detachment forces in the finite Voronoi model and introduce a simple regularization. Finally, we calibrate the near-detachment mechanics against a deformable polygon model and examine how key physical parameters control the tissue fracture timescale under two different calibration strategies. Our results show that, for studies focused on fracture or intercellular adhesion in nonconfluent monolayers, a physically motivated calibration of near-detachment mechanics in the finite Voronoi model is essential.

While host-guest co-crystals are well established, and co-amorphous solids are recognized in materials science, the concept of a host-guest co-amorphous structure remains largely unexplored. A potential analogue is seen in SiO2 glass under high pressure with helium as a pressure medium; the drop in compressibility in this system is ascribed to helium atoms occupying internal voids. In this study, we investigated a semicrystalline polymer, isotactic poly(4-methyl-pentene-1) (P4MP1), which shares key characteristics with SiO2 glass, particularly regarding the first sharp diffraction peak (FSDP). The FSDP in P4MP1 is attributed to internal voids, as evidenced by its suppression under pressure and recovery upon decompression for molten P4MP1. Notably, the response to helium as a pressure medium is also known to parallel the behavior observed in SiO2 glass. Here, we analyzed two-dimensional X-ray diffraction (2D-XRD) patterns of stretched P4MP1 and found a suppression of FSDP when P4MP1 is immersed in decane. The use of stretched samples enabled the clear isolation of the amorphous FSDP from overlapping crystalline diffractions. Our findings reveal the existence of a host-guest co-amorphous system at room temperature and atmospheric pressure, in which decane molecules occupy the amorphous host matrix of P4MP1. Unlike conventional co-amorphous mixtures, this structure is defined by the specific accommodation of guests within the host's inherent voids. Intriguingly, the signature of this structure in diffraction measurements, manifested as changes in the FSDP intensity ratio, may be regarded to parallel the variations in Bragg peak intensity ratios in host-guest co-crystals. Since selective sorption and guest exchange are well-known in co-crystals, hosts capable of forming co-amorphous structures will be promising materials for molecular sieves, or more generally, liquid-phase molecular sieves.

We investigate the balanced $M=4$, $p=4$ spin-glass model for a one-dimensional long-range proxy for the finite dimensional short-range $p$-spin glass model to examine the nature of the glass transition beyond mean-field theory. We perform large-scale Monte Carlo equilibrated simulations for both fully connected and power-law diluted versions of the model. The critical temperatures extracted from the finite-size scaling (FSS) analysis of spin-glass susceptibility are in good agreement with theoretical predictions for $\sigma = 0, 0.25$, and 0.55. For these values of the long-range exponent $\sigma$ (which is the power of the decrease of the interactions between the spins with their separation), one might have expected that mean-field theory would provide a good description of the system. However, the spin-overlap distribution and the value of the $\lambda$-parameter do not provide numerical evidence for a one-step replica symmetry breaking (1RSB) phase transition. Instead, our results indicate a direct transition from the paramagnetic state to a full replica symmetry broken phase, with a renormalized value of $\lambda\equiv \omega_2/\omega_1 < 1$ suggesting a continuous FRSB transition, despite this ratio being equal to 2 at mean-field level. A value of $\lambda > 1$ is required for the discontinuous 1RSB transition. We argue that strong finite-size effects and closely spaced transition temperatures remove the expected 1RSB transition for the system sizes which we can study. For values of the exponent $\sigma = 0.85$, which roughly corresponds to a three dimensional system, we find that the renormalized value of $\lambda$ is again less than 1, with no signs of either the 1RSB transition or the continuous FRSB transition, suggesting that the Kauzmann temperature $T_K$ in three dimensions might be zero and the complete absence of phase transitions in structural glasses.

Turbulent thermal convection governs heat transport in systems ranging from stellar interiors to industrial heat exchangers. Two-dimensional Rayleigh-Bénard convection serves as a paradigm for these flows, reproducing key features such as thin boundary layers, large-scale circulation, and sustained plume dynamics. While Matrix Product State (MPS) methods have demonstrated significant compression of isothermal turbulent fields, their application to buoyancy-driven flows with active thermal coupling has remained unexplored. We apply MPS to two-dimensional Rayleigh-Bénard convection with dynamical simulations up to $\mathrm{Ra} = 10^{10}$. An a priori decomposition of DNS snapshots up to $\mathrm{Ra} = 10^{11}$ shows that the bond dimension $\chi$ required to represent the flow fields grows without saturation, in contrast to the plateauing of $\chi$ reported for velocity fields in isothermal 2D turbulence. Crucially, however, dynamical simulations solving the governing equations directly in the compressed MPS format at fixed $\chi$ show that the $\chi$ required to recover statistical observables, such as the Nusselt number, scales significantly more favorably with $\mathrm{Ra}$ than the a priori complexity suggests. At $\mathrm{Ra} = 10^{10}$, a relative error of $1.8\%$ in the mean Nusselt number is achieved with a nearly 9-fold reduction in degrees of freedom, using a $\chi$ comparable to that required at $\mathrm{Ra} = 10^{9}$. Spectral analysis confirms the progressive recovery of spatial and temporal scales with increasing $\chi$. These findings establish MPS as a scalable tool for simulating thermally driven turbulence, suggesting the method may remain viable for investigations of the ultimate regime at substantially higher $\mathrm{Ra}$.

We study the onset of two-dimensional secondary shear instability (SSI) in the braid regions connecting primary Kelvin-Helmholtz billows in stratified shear flows. While strain induced by the billows stabilises the braids, it also compresses their tilted isopycnals, enhancing baroclinic shear that enables rapid perturbation growth. By modifying the classical analysis of Corcos & Sherman (J. Fluid Mech. 73, 241-264, 1976) in braid-aligned coordinates and adding an additional stability criterion based on the ratio of strain rate to shear, we develop an inviscid, time-dependent model for the braid and the onset of SSI. We show that the criterion for instability can be achieved significantly earlier than the saturation of the primary billow at sufficiently high initial Richardson number Ri, as increased stratification slows billow growth while accelerating baroclinic shear production in the braid. Two-dimensional direct numerical simulations up to Reynolds numbers Re=10^7 quantify the role of viscosity. At high Re, we find that SSI indeed develops early in the braid, as predicted by the inviscid model, while the primary billow is still growing and before viscosity slows braid thinning. These results provide a mechanistic explanation for field observations of braid-dominated mixing and suggest that, at geophysically relevant Ri and Re, SSI can control the three-dimensional turbulent transition and ensuing diapycnal mixing by preceding and pre-empting both vortex pairing instabilities and secondary convective instabilities in the billow core.

Scale-resolving simulations of high Reynolds number incompressible flows are often limited by the Courant-Friedrichs-Lewy (CFL) stability restriction imposed by explicit time-stepping schemes, resulting in small time step sizes and long time-to-solution. In this work, we systematically compare two implicit formulations of the velocity correction scheme -- a linear-implicit approach and a sub-stepping (or semi-Lagrangian) method -- against a standard semi-implicit formulation within a high-order spectral/hp element framework. The schemes are assessed in terms of stability limits, temporal accuracy, and computational performance for implicit large-eddy simulation of the Imperial Front Wing benchmark, a complex high Reynolds number geometry with curved surfaces that imposes strict CFL constraints. Both implicit schemes extend the stability limit by up to two orders of magnitude in time step size. While increasing the cost per time step, they reduce the overall time-to-solution by up to a factor of eleven. Accuracy analysis shows that time step sizes up to twenty times larger than the explicit limit have only minor impact on resolving laminar-turbulent transition and key flow statistics. The results quantify the trade-off between stability, accuracy, and computational cost for implicit velocity correction schemes on complex geometries and provide guidance for selecting time integration strategies in large-scale scale-resolving simulations.

Particle-resolved direct numerical simulation (PR-DNS) is performed for turbulent open channel flow over a smooth horizontal wall with a vertical cylinder and a dilute set of mobile, heavy, spherical particles. At the chosen parameter point (which matches a previous study without a cylinder) the particles are mostly translating in the horizontal plane while remaining in contact with the wall. It is shown that the presence of the cylinder leads to the generation of intense vortical structures, enhanced turbulence intensity in the wake region, and to strong modifications of the local wall shear stress. These cylinder-induced perturbations have direct consequences for the average particle concentration: preferential accumulation/depletion in different parts of the wake region occurs, while the wall-normal transport of particles (against gravity) is significantly enhanced. A second simulation which adds roughness elements on the wall reveals an additional effect upon the wall-normal distribution of particles. It turns out that the configuration with wall-roughness and a wall-mounted cylinder features the largest fraction of entrained particles, even far from the wall.

This study presents a systematic validation and comparative assessment of computational fluid dynamics (CFD) strategies for centrifugal blood pump simulations using the U.S. Food and Drug Administration benchmark model. A scale-resolving large eddy simulation (LES) with transient sliding-interface (SI) coupling is evaluated and compared against Reynolds-averaged Navier-Stokes (RANS) approaches employing both multiple reference frame and SI formulations. Numerical predictions are validated through direct comparison with particle image velocimetry measurements under two representative operating conditions. The results indicate that LES with transient rotor-stator coupling achieves consistently improved agreement with experimental velocity fields compared with RANS-based methods, particularly in the diffuser region where strong intermittency and wall-bounded turbulence are present. In contrast, RANS-based approaches exhibit noticeable discrepancies in these regions. A mesh sensitivity study and an assessment of temporal averaging effects are conducted for LES. The quality of the LES results is further quantified using three complementary metrics, demonstrating that a mesh resolution of approximately 80 million cells achieves a well-resolved LES regime. Building on the validated scale-resolving simulations, detailed analyses of vortical structures, turbulent kinetic energy distributions, and velocity energy spectra are performed to characterize the internal flow physics of the pump. This study demonstrates that scale-resolving, transient simulation approaches are essential for accurately capturing the highly unsteady, turbulence-dominated flow features in ventricular assist devices and provides practical guidance for future high-fidelity hemodynamic and hemocompatibility studies.

The extreme heat fluxes characteristic of hypersonic flows significantly limit the flight envelope of hypersonic vehicles. The role of hydrodynamic instability and the onset of laminar to turbulent boundary layer transition is of notable importance. The effect of streaks on the suppression of planar (second Mack mode) instabilities has been previously investigated, but a potentially passive and non-intrusive control method has not been established yet. Recent work shows that streaks can be generated through a spanwise variation in surface temperature. This method exploits the aerothermodynamic characteristics of the flow, and therefore promises to be robust. This work uses direct numerical simulations to determine and quantify the effectiveness of this novel control method in the suppression of second Mack mode instability for a hypersonic boundary layer over a flat plate. The computational analyses cover a range of Mach numbers 4.8 to 6 and wall temperature ratios representative of both wind tunnel testing and flight scenarios. Among the range of configurations investigated the energy of the second Mack mode is reduced by up to approximately 60% by the steady streaks. The streak wavelength parameter plays a significant role in the stabilisation benefits. For a Mach 6 configuration, for the most linearly amplified second Mack mode disturbance frequency, nearly optimum performance is achieved for a spanwise wavelength of approximately 8 to 10 times the local boundary layer thickness. These findings open new avenues for controlling hypersonic boundary layers and offer valuable guidance for future experimental campaigns aimed at validating this novel control strategy.

We consider the statistics for the vorticity field in two-dimensional homogeneous isotropic turbulence (HIT). First, we exploit the invariance properties to derive dimensionally reduced governing equations for the one-point and two-point probability density functions (PDFs). These take the form of linear kinetic transport equations, but with an unclosed operator in terms of a conditional average. To solve the PDF equation numerically we suggest a hybrid data-driven method that relies on carefully selected samples of DNS data and a sampling estimator for the conditional average. The method is applied to DNS data for both decaying and forced HIT, demonstrating good agreement with the direct evaluation of the PDFs using the DNS data.

Even with the most advanced computational capabilities, high-fidelity (e.g., large-eddy) simulations of large-scale rocket engines remain far out of reach. In the current work, we develop and establish a component-based reduced-order modeling (CBROM) framework to enable accurate and efficient parametric modeling of large-scale rocket engines by geometrically decomposing a single domain into a combination of several representative components, including injectors, combustor and nozzle. Individual component-based reduced-order models (ROMs) are trained for each component with fabricated system-level responses enforced through carefully formulated boundary conditions during the training, which only require high-fidelity simulations of a much smaller computational domain, thereby significantly reducing the costs of ROM training. The trained component-based ROMs are then coupled together to enable full-system simulations. Specifically, we pursue an advanced adaptive ROM formulation leveraging a model-form preserving least-squares with variable transformation (MP-LSVT) projection to construct the component-based ROMs. The CBROM framework is evaluated using a seven-injector model rocket combustor configuration that exhibits self-excited combustion dynamics with distinct characteristics that vary with flow condition and geometric variations. The framework is demonstrated to provide accurate parametric predictions of the changes in dynamic behaviors, expressed in the spectra from dynamic mode decomposition (DMD) analysis and features in the time-averaged and RMS fields of target state variables.

This study performs a three-dimensional numerical simulation of the coupled flow field in a hydrogen-air rotating detonation combustor (RDC)-turbine system to evaluate the effectiveness of different film cooling strategies for the turbine blades. The results demonstrate that combining the endwall cooling with leading-edge film cooling effectively reduces blade surface temperatures while improving turbine flow field stability and blade protection. For endwall cooling, numerical simulations compare circular and slot hole configurations. Circular holes consume less cooling air than slot holes while maintaining comparable cooling performance, making them the preferred choice. For the leading-edge film cooling, both the vertical and the vertical-inclined schemes are examined. The vertical-inclined scheme demonstrates higher cooling efficiency and improved secondary flow attachment, ensuring greater stability under the oscillatory effects of the detonation flow. Additionally, the flow fields of film-cooled turbine blades with and without the propagation of the rotating detonation wave are compared, revealing that the upstream rotating detonation flow field facilitates the downstream diffusion of secondary film cooling jets.

Flow and transport in fractured geological media are strongly controlled by aperture heterogeneity and uncertainty in subsurface characterisation, yet most upscaling approaches rely on deterministic representations of fracture permeability. This study presents a scalable probabilistic workflow that bridges image-based fracture geometry and uncertainty-aware hydraulic predictions across scales. The approach integrates Bayesian correction of aperture-permeability model misspecification, a deep learning surrogate for predicting spatially distributed permeability statistics, and Darcy-scale flow upscaling to propagate uncertainty to effective transmissivity. The workflow is applied to natural shear fractures from core material in the Little Grand Wash Fault damage zone (Utah) and to simplified geometries derived from the same datasets. The Bayesian component quantifies uncertainty due to measurement errors and imperfect constitutive relations, while a Residual U-Net learns the effects of local heterogeneity and spatial correlation on predicted permeability uncertainty. Together, these components generate ensembles of permeability fields that are subsequently upscaled to probabilistic macroscopic flow responses. Results show that common empirical aperture-permeability relations are systematically biased for natural fractures, whereas the proposed probabilistic workflow yields uncertainty-aware permeability estimates consistent with physics-based behaviour. The method captures the impact of channelisation, connectivity, and complex 3D void geometries on transmissivity while quantifying the resulting uncertainty bounds. Computational efficiency arises from the proposed hybrid strategy for probabilistic upscaling, which combines physics-informed and data-driven approaches, preserves Stokes-flow consistency and supports uncertainty propagation without repeated high-fidelity simulations.

We study the orientational dynamics of superparamagnetic colloidal dimers that carry both an induced magnetic moment, proportional to the applied field, and an effective permanent moment. In a static, uniform magnetic field, dimers that are permanently fixed together hop between two preferred in-plane angles, developing a bimodal steady-state orientation distribution. When the same field is periodically reversed, we observe a sharp, field-controlled change in the dynamical response from small hopping events with $\Delta \theta\ll \pi$ to full $\Delta\theta \approx \pi$ rotations on each field flip. We show that both the static bistability and the switching bifurcation can be rationalised by a magnetic response in the dimer that consists of both a strong induced and weak body-fixed component. This leads to a complex orientational energy/potential landscape, with coupled roll-yaw rotations of the dimer responsible for the bistable dynamics. By combining the misorientation between dimer axis and field, bifurcation field strength and short-time orientational variance, we determine the magnitude and orientation of the net permanent dipole, thereby characterising details of the internal magnetic structure of the particles via microscopy.

We study dense mixtures of passive and active self-aligning disks with isotropic or anisotropic mobility. We find that the passive fraction controls an order-disorder transition that is continuous in the isotropic case and discontinuous in the anisotropic one. A mean-field equation derived from the microscopic heading dynamics captures this dichotomy. Near the transition, both ordered regimes can exhibit multiple metastable oscillating or rotating states, depending on the spatial arrangement of passive particles and lattice defects, but with different transient dynamics: Systems with isotropic mobility visit multiple long-lived attractors during each simulation while systems with anisotropic mobility are trapped by a single attractor. Our results reveal the passive fraction as a physically relevant control parameter in active systems, leading to rich self-organizing dynamics.

DNA-coated particles are promising as building blocks for functional and finite-sized assemblies because they can be programmed with orthogonal interactions owing to the sequence-specific hybridization of DNA strands. To fully exploit this programmability, it is important to develop particles with coatings that incorporate multiple distinct DNA sequences in tunable ratios and to understand how the coating composition influences self-assembly. Here, we compared two strategies to graft multiple DNA sequences in tunable and well-defined ratios on micron-sized colloidal particles. We found that a method based on click chemistry yielded mixed coatings with large batch-to-batch variation in the composition, while a method based on isothermal DNA polymerization produced coatings of predictable composition with a precision of a few percent, but requires reaction rate measurements for each new sequence in the coating. Our self-assembly experiments showed that, even with precise control over coating composition, equilibrium co-assembly of multiple types of DNA-coated particles is limited by the number of interactions that are reversible within the same narrow temperature window. This finding highlights the need to explicitly incorporate sequential assembly pathways into structure design, with coating composition dictating the order of binding events, Together, our results show how systematic tuning of interaction strength and sequential assembly through multispecific DNA coatings is a prerequisite for the experimental realization of finite-sized and dynamic structures that have so far remained largely theoretical.

Interactions between fluids and granular materials are prevalent on the Earth's surface. In the case of fluid flow over a sediment bed, the fluid imparts a shear stress to the granular materials. When the applied shear stress is above a critical value, the grains become entrained in the fluid flow. Prior experimental studies have shown that granular beds subjected to a sub-critical fluid flow can strengthen in the same direction as the sub-critical flow. In contrast, granular beds can become weaker in the direction opposite to the sub-critical fluid flow. To investigate the grain-scale mechanisms that control directional strengthening and weakening, we perform discrete element method (DEM) simulations of granular beds subjected to model fluid flows in two (2D) and three (3D) dimensions with varied inter-particle static friction coefficients and conditioning flow speeds. In these studies, the sub-critical grain motion does not cause significant bed compaction. Instead, we find that the strength of a granular bed in a particular direction is highly correlated with the fraction of {\it surface} grains that can be dislodged by a fluid force applied in that direction. Further, the anisotropic bed strength only persists over a finite time scale that is set by the Shields number. We also show that inter-particle static friction is not required for bed strength anisotropy, but varying the friction affects the magnitude of the anisotropy. This research enhances the grain-scale understanding of erosion of granular beds caused by fluid flows and underscores the importance of tracking the history of the fabric of the bed surface since it couples strongly to bed strength.

Modelling micro- and meso-scopic scale thermodynamic and transport properties of soft condensed matter hinges upon its representation. This is especially relevant for polar solvents such as water, since these require effective representation of their dielectric nature as driven by molecular charge distributions and molecular network structuring. The dielectric nature of a medium leads to complex phenomena such as local polarisability response and restructuring near interfaces in reaction to changes in local charge distributions. Inclusion of such phenomena when using larger-than-atomistic techniques such as coarse-grained molecular dynamics (CG-MD) and dissipative particle dynamics (DPD) is still an open question, to which we provide a novel way to consider and justify the necessary and suitable coarse-graining level, enabling us to compare new polar CG models' performance against that of an underlying atomistic model. We polarise our previous non-polar nDPD water model to prepare it for use in simulations of liquid electrolytes as well as solvated organic membranes and measure its fitness to serve as a dielectric medium by comparing its properties to those of the TIP3P water model, while simultaneously observing changes to properties already represented well by the non-polar model.

Solid phase of dense granular matter is inevitable because of jamming transition when the packing fraction or the pressure suffered is high enough. The experiment suggests that active Brownian granular matter will keep fluid phase even under the highest packing fraction (higher than the packing fraction of crystallization) if crystallization is prevented by mixing granular particles of different sizes. The findings encourage us to reconsider the role of activity in affecting the global dynamical properties of matter.

Chitosan is a highly versatile and sustainable polymer with a broad range of potential biological and materials engineering applications. Despite its versatility, the native brittleness of chitosan limits its broader utilization. This limitation can be addressed by blending chitosan with small-molecule additives to modulate its thermomechanical properties. We employ molecular dynamics (MD) simulations to investigate the mechanism underlying antiplasticization followed by plasticization at increasing water content. Decomposition of the elastic moduli reveals a competition between weakened polymer-polymer interactions and enhanced polymer-water interactions, with their relative strengths governing the resulting properties. We introduce a simple model incorporating dynamically accessible free volume regions as a key driver of polymer mobility, effectively capturing the (anti-)plasticization of elastic properties. We show that accessibility of free volume regions is enabled by connectivity of additive-accessible volume regions. This study provides new insights into the molecular interactions that dictate the properties of chitosan-water mixtures and may inform the rational design of chitosan-based materials and other hydrated biopolymers.

We develop a method for simulating colloidal suspensions using multiparticle collision dynamics (MPCD) with a discrete particle model represented as a rigid body. The key steps for incorporating the rigid-body constraints are to thermalize the velocities of the discrete sites before they participate in the MPCD collision step, then transfer momentum from the sites to the rigid body. We demonstrate that the rigid-body model produces the expected statistics for a single spherical particle and the same transport properties for a hard-sphere colloidal suspension as an equivalent model using harmonic bonds to maintain the site geometry. Importantly, the rigid-body model has less computational overhead and permits a larger simulation timestep than the harmonic-bond model, leading to a nearly order of magnitude speedup in benchmark simulations of hard-sphere colloidal suspensions. Our method is compatible with arbitrary discretization, so it enables more efficient MPCD simulations of suspensions of colloidal particles with complex shapes.

We explore the mechanics of a terminally loaded buckled elastica under frictionless self-contact. With the aid of two integrals associated with the elastica, we propose a scale-invariant condition necessary for the onset of contact. The condition is independent of the boundary conditions, does not involve the position vectors of the material points, and delivers the value of the compressive load at which self-contact initiates. Furthermore, we show that one of the two integrals, namely the \emph{Hamiltonian}, persists after contact. We compute post-contact configurations of modes three through ten for a pinned-pinned buckled elastica. At a given value of the compressive load, we report multiple post-contact configurations for modes eight and nine. Finally, we show that an infinite force is required to transition from a point contact to a line contact in symmetric post-contact configurations of odd modes.

We present a meshless numerical method for simulating the dynamics of axisymmetric vesicles in a viscous medium. Key innovations include: (1) adaptive reparameterization based on local length scales, reducing the number of required harmonics; (2) gauge dynamics for maintaining optimal parameterization; (3) error control near the symmetry axis; and (4) spectrally accurate quadrature schemes for singular integrals. The method achieves high accuracy and computational efficiency for simulating lipid bilayer dynamics and related problems in soft matter physics.

Active colloidal microparticles require reliable actuation to sustain directed motion. Light-based propulsion is particularly attractive as it provides persistent energy supply and enables direct spatiotemporal control. Here, we introduce 3D-printable particles with symmetry-broken refractive index profiles (SBRIP particles) that achieve propulsion through direct momentum transfer from asymmetric light refraction. Internal refractive-index gradients provide optical symmetry breaking independent of external shape, fundamentally decoupling propulsion from particle geometry. Geometrically symmetry-broken particles with a homogeneous refractive index are another special case, where propulsion originates from refractive contrast at the boundary instead of within the particle. Unlike conventional systems relying on absorption or reflection, this transparency-based mechanism minimizes heating and mitigates shadowing in bulk suspensions. We present a theoretical framework for refractive propulsion as well as numerical simulations of the SBRIP particles using raytracing and the finite volume method. This is complemented by experiments, validating the momentum transfer mechanism using particles with geometric symmetry breaking. The high transparency of our particles ensures deep light penetration, enabling the realization of volumetric active matter. This opens pathways toward adaptive nonlinear optical materials where light-driven particle reorganization modulates the local refractive index, establishing a dynamic feedback loop between the optical field and the material structure.

We investigate the thermo solutal transport phenomena and deposition patterns during the evaporation of surfactant laden droplets experimentally and through theoretical scaling based analysis. Experiments were conducted using the sessile droplet configuration in the acrylic chamber for both hydrophilic and hydrophobic substrates. Infrared thermography and particle image velocimetry measurements were conducted during evaporation to illustrate the temperature and velocity distributions, respectively. Sodium dodecyl sulphate SDS surfactant molecules enhanced the evaporation rate with an increase in concentration for the hydrophobic surface. In contrast, the evaporation rate increased up to 0.5 CMC and then decreased for droplets on a hydrophilic substrate. The evaporation rates computed from the shadowgraphy imaging were explained using the average velocities obtained from the PIV analysis. It was found that advection within the droplet is strongly dependent on surfactant concentration and wettability. Further, the theoretically obtained Marangoni velocities were in close agreement with the experimental values. It was found that Marangoni solutal advection dominates other advection mechanisms, such as Marangoni thermal advection and buoyancy driven flow. However, surfactant crowding and viscous resistance with increasing surfactant concentration can dampen the increase in solutal advection. The surface tension and viscosity measurements were also conducted with variation in surfactant concentration to understand the suppression of advection by viscous forces. The computation of contact line velocities showed sudden fluctuations, illustrating stick slip behaviour during droplet drying, complementing microscopic visual observations.

Granular flows are ubiquitous in nature and industrial applications, yet a complete continuum theory remains a long-standing challenge. The leading empirical approach, {\mu}(I) rheology, lacks microscopic foundations and becomes multivalued in dense, slowly sheared flows where nonlocal corrections are required. Exploiting state-of-the-art high-speed X-ray tomography to investigate microscopic dynamics of dense granular flows in a Couette geometry, we establish a new, universal constitutive law spanning quasi-static to inertial regimes based on structural relaxation, resolving the fundamental difficulty in the original {\mu}(I) framework. By further establishing a non-equilibrium statistical framework for granular flows, we demonstrate an intrinsic analogy between driven granular matter and hard-sphere liquids owing to their identical Carnahan-Starling equation of state, naturally explaining our rheological approach and the emergence of glassy behaviors. Our framework unifies granular rheology with the broader physics of disordered systems and provides a complete, microscopically-based theoretical framework for dense granular flow.

Quantitative modeling has become an essential tool in modern biophysics, driven by advances in both experimental techniques and theoretical frameworks. Powerful high-resolution techniques now provide detailed datasets spanning molecular to tissue scales, allowing to visualize cellular structures with unprecedented detail. In parallel, developments in soft and active matter physics have established a robust theoretical basis for describing biological systems. In this context, two main modeling paradigms have emerged: particle-based models, which explicitly represent discrete components and their interactions, and continuum models, which describe systems through spatially varying fields. We compare these approaches across biological scales, highlighting their respective strengths, limitations, and domains of applicability. To keep our discussion biologically relevant, we focus on five systems of fundamental importance: the cytoskeleton, membranes, chromatin, biomolecular condensates and tissues. With this Review, we thus aim to provide a framework for both theorists and experimentalists to select appropriate modeling strategies, and highlight future directions in biophysical modeling.

Ultrasound-guided drug and gene delivery (USDG) is a promising non-invasive approach for targeted therapeutic applications. Mechanical properties of encapsulated microbubbles (EMBs), which serve as contrast agents, strongly affect their specific interactions with ultrasound and are thus critical to the success and efficiency of USDG. Accurate calibration of high-fidelity particle-based models of EMB capsid mechanics is computationally challenging because direct Bayesian inference with dissipative particle dynamics (DPD) is prohibitively expensive. We employ a surrogate-accelerated Bayesian calibration workflow that combines deep neural network (DNN) surrogates, transitional Markov chain Monte Carlo sampling, and hierarchical regularization across EMB diameters. Using this framework, we develop two data-informed DPD models of commercial EMB agents, i.e., Definity and SonoVue, and perform inference of force field parameters based on published compression experiments for Definity and indentation experiments for SonoVue, each spanning three distinct diameters. The inferred posteriors show that key model parameters, such as the stretching stiffness and bending modulus, are consistently constrained by the available data. The presented methodology can be used to derive bespoke, data-informed models for a wide range of ultrasound contrast agents, including encapsulated gas vesicles, EMBs with diverse capsids consisting of lipids, proteins, or polymers, and functionalized with ligands.

A ternary liquid crystalline mixture was designed to obtain a tilted hexatic smectic phase in the glassy state. Structural, electro-optic, and dielectric properties of the mixture are investigated, and selected measurements are also performed for its pure components. In particular, the electron density profile perpendicular to smectic layers is determined from the X-ray diffraction data and compared to the results of density functional theory calculations both for the mixture and pure components. Comparison of the experimental smectic layer spacing and tilt angle in the mixture allows us to assess whether molecular dimerization is likely to occur. On the mesoscopic scale, the helical pitch is determined in the SmC$_A$* phase of the mixture, and selective reflection of light is observed under a polarizing microscope in the SmC*, SmC$_A$*, and SmX$_A$* phases. The glass transition in the smectic X$_A$* phase is observed in calorimetric results. At the same time, the dielectric spectra do not directly reveal the primary $\alpha$-process, although the secondary $\beta$- and $\gamma$-processes are detected. Overall, the results show that the ternary mixture stabilizes a broad SmC$_A$* phase and enables vitrification of the hexatic SmX$_A$* phase, while the structural data suggest a change in the molecular organization between the SmC* and SmC$_A$* phases.

In this perspective article, we discuss bacterial populations as a model system of active matter. It allows for the exploration and characterization of various phases of active matter and brings rich implications for both physics and biology. Specifically, we focus on active gas, active liquid, active glass and active liquid crystal states observed in bacterial populations and describe how these differ from their thermal counterparts. A few future directions are also discussed that will deepen the physical interest in active matter as a new type of material, with its implications for several life phenomena observed in bacterial populations and other biological systems.

The sodium dodecyl sulfate (SDS) surfactant is widely used in various applications, such as household products (e.g., shampoos, toothpaste, detergents, and cleaning products) and food manufacturing (e.g., emulsifiers). To investigate its properties via computer simulation, various models have been developed, including coarse-grained (CG) models that are suitable for capturing a surfactant's self-assembly and fundamental properties for aqueous systems with a surfactant, such as surface tension. Here, we present a CG model for SDS/water systems for many-body dissipative particle dynamics (MDPD), which is based on the MDPD--Martini force field (FF). In the model, charged groups, namely, the SDS sulfate headgroup and the sodium cation, are explicitly modeled following the standard mapping of the Martini force field for molecular dynamics (MD), while the remaining interactions have been obtained from previous MDPD--Martini models for lipid systems, thus demonstrating their transferability. Various relevant system properties, such as the coherent scattered intensity and surfactant distribution at the liquid--vapor surface, are investigated, and results are compared to those obtained by MD simulations and experiments at different surfactant concentrations. Our findings indicate that MDPD--Martini models can offer a credible alternative to MD--Martini models for systems with explicit charges as shown here for SDS. Moreover, MDPD--Martini models reproduce nicely the experimental surface tension isotherm, in contrast to MD simulations. In view of the transferability of the MDPD--Martini interactions, the model parameters of this study can be tested and used to simulate a wider range of soft-matter systems.

Freezing of complex fluids is central to a wide range of natural and technological processes, where the interplay between heat transport, solute redistribution, and interfacial deformation gives rise to complex morphologies. Unlike simple liquids, polymer solutions exhibit strongly coupled transport and rheological properties that evolve dynamically during solidification, making their freezing behavior difficult to predict. Here, we examine the freezing of polymer solution droplets spanning dilute to entangled regimes. We find that droplet morphology and freezing dynamics in viscous solutions are governed by a single dimensionless parameter, the Capillary--Lewis number, which captures the competition between viscous stresses, capillarity, and solute transport. Circularity, radial deformation, and freezing time collapse onto a master curve spanning nine orders of magnitude, revealing a transition near unity corresponding to the point at which solute diffusion can no longer relax concentration gradients ahead of the freezing interface. This collapse holds across distinct polymer chemistries within the viscous fluid regime, while deviations emerge when the material exhibits elastic-dominated response ($G' > G''$), indicating the breakdown of purely transport--capillary control. These results establish a minimal transport--mechanics framework linking solute redistribution to interfacial deformation during freezing polymer solutions.

We study synchronization of two cardiomyocytes mediated by elastic interactions through the substrate. Modeling each cell as an oscillating force dipole governed by a Rayleigh-type equation, we derive an effective mechanical coupling from the elastic response of the surrounding medium. Using phase reduction theory, supported by direct numerical simulations, we obtain a dynamical phase description for two cardiomyocytes that predicts geometry-dependent selection of synchronized states. Depending on the mutual orientation, the cells robustly converge to either in-phase or anti-phase beating, yielding an orientation-dependent state map with a nontrivial state boundary. The synchronization time also depends strongly on the distance and mutual orientation of the cells. These results bridge earlier energetic two-body theory and dynamical single-cell theory, and provide a dynamical framework for elastic synchronization of cardiomyocytes.

The re-solidification of amorphous solids after mechanically driven yielding from a nonequilibrium state is a fundamental soft matter science problem of broad relevance in materials science, with implications for material strength, processing, and printing-based additive manufacturing. We present a microscopic statistical mechanical theory that predicts in a unified manner the coupled time evolutions of structural and stress recovery following shear cessation from a mechanically prepared nonequilibrium state. The approach is built on recent advances in understanding activated dynamics in Brownian systems under both quiescent and startup continuous shear conditions. A particle-level microrheological model framework self-consistently incorporates stress generation, constraint softening due to external mechanical forces and structural deformation. After flow cessation, the theory captures the re-building of kinetic constraints and activation barriers over time that underlie structural recovery, stress relaxation, and re-solidification through dynamic relaxation and an elementary form of convective elastic backflow. The ideas are general for particle-based materials, and quantitatively applied to dense hard-sphere Brownian colloidal suspensions which also serve as a foundational paradigm for glass forming materials where thermal fluctuations are important. The theory properly captures the rich range of stress relaxation behaviors observed experimentally that evolve from exponential, to stretched exponential, to fractional power law in form with increasing packing fraction. A microscopic understanding is achieved of the emergence of apparent residual stresses on laboratory timescales, power-law endless aging, sigmoidal recovery of the elastic modulus, pre-shear-rate-dependent memory effects, and a two-step structural relaxation process that can become decoupled from stress relaxation.

We investigate the thermal responses of a harmonic oscillator chain coupled at its boundaries to heat baths held at different temperatures. This setup sustains a steady energy flux, continuously dissipating heat into both reservoirs. By introducing slow variations in the bath temperatures, we quantify the resulting excess heat currents and thereby obtain the nonequilibrium heat capacity matrix at fixed but arbitrary temperature differences. We demonstrate the existence of a well-defined thermodynamic limit for long chains. The specific heat associated with energy exchanges with a single bath depends on the difference in friction coefficients governing the system-bath couplings. That thermokinetic effect is typical for nonequilibrium response. When the couplings with the thermal baths acquire temperature dependence, the specific heat correspondingly inherits a nontrivial temperature dependence, in sharp contrast with equilibrium. Our results provide the first explicit determination of specific heat(s) in a locally interacting, spatially extended driven system. Beyond its exact solvability, the model may offer a natural nonequilibrium extension of the Dulong-Petit law, capturing the high-temperature behavior of driven molecules.

Porous monolithic photocatalysts based on anatase TiO2 in silica aerogels are promising for air purification. Their bicontinuous spinodal architecture offers high surface area and strong light scattering. However, extracting intrinsic kinetic rates requires accurate optical models. Current methods replace the complex 3D pore network with a homogeneous 1D slab, an approximation whose error is unknown for spinodal geometries. We combine 3D spinodal masks from Cahn-Hilliard simulations with GPU Monte Carlo photon transport to quantify this. We introduce a solid-phase fluence estimator that accounts for catalytic site distribution, comparing it to volume averages and diffusion approximations. The solid phase receives 50% more photons than volume averages at porosity 0.70, rising to 70% at 0.90. This preferential illumination stems from quasi-ballistic paths through pore channels, termed photon channelling. The extracted kinetic descriptor differs by 34% between 3D Monte Carlo and diffusion models. Homogeneous controls show that roughly 50% of the total 73% discrepancy is intrinsic to the bicontinuous structure and cannot be fixed by effective medium theories. These results provide the first quantitative correction for kinetic extraction in such photocatalysts and establish design rules linking synthesis coarsening, pore size, and light efficiency.

Ferromagnetic elastic slender structures offer the potential for large actuation displacements under modest external magnetic fields, due to the magneto-mechanical coupling. This paper investigates the phase portraits of the Hamiltonian governing the three-dimensional deformation of inextensible ferromagnetic elastic rods subjected to combined terminal tension and twisting moment in the presence of a longitudinal magnetic field. The total energy functional is formulated by combining the Kirchhoff elastic strain energy with micromagnetic energy contributions appropriate to soft and hard ferromagnetic materials: magnetostatic (demagnetization) energy for the former, and exchange and Zeeman energies for the latter. Exploiting the circular cross-sectional symmetry and the integrable structure of the governing equations, conserved Casimir invariants are identified and the Hamiltonian is reduced to a single-degree-of-freedom system in the Euler polar angle. Analysis of the resulting phase portraits reveals that purely elastic and hard ferromagnetic rods undergo a supercritical Hamiltonian Hopf pitchfork bifurcation, whereas soft ferromagnetic rods exhibit this bifurcation only within a restricted range of the magnetoelastic parameter, $0<\tilde{K}_{dM}<1/8$. Both helical and localized post-buckling configurations are analyzed, and the corresponding load-deformation relationships are systematically characterized across a range of loading scenarios. Localized buckling modes, corresponding to homoclinic orbits in the Hamiltonian phase space, are constructed numerically. In contrast to the purely elastic case, the localized configurations of soft ferromagnetic rods exhibit non-collinear extended straight segments, a geometrically distinctive feature arising directly from the magnetoelastic coupling.

The dynamics of water in electrolyte solutions exhibits a striking, ion-specific anomaly: the diffusion coefficient of water is enhanced relative to the neat liquid in chaotropic CsI solutions, yet suppressed in kosmotropic NaCl solutions. This phenomenon, long challenging for classical force-field-based molecular dynamics, is studied here using classical molecular dynamics simulations with a many-body machine-learned force field (MLFF) trained within the MACE equivariant graph neural network framework. The force field is trained on energies, forces, and stresses computed at the density functional theory level with the revPBE-D3 exchange--correlation functional, which provides a reliable balance between accuracy and computational efficiency for aqueous systems. Simulations of NaCl and CsI aqueous solutions at ambient conditions over a concentration range of 0.89--3.56 mol/kg reproduce the experimentally observed anomalous diffusion and show a quantitative improvement over previous results obtained with the DeePMD framework, trained on the same theory, particularly for NaCl solutions. This improvement is traced to a stronger Na$^{+}$--water interaction in the first hydration shell and the non-negligible retarding contribution of the second hydration shell of Na$^{+}$. For CsI solutions, the water acceleration is shown to be primarily driven by the anion I$^{-}$, whose diffuse and weakly structured hydration shell facilitates rapid water exchange with the bulk. These results are rationalised through a shell-decomposition analysis of time-dependent water diffusivities and ion--oxygen potentials of mean force providing a coherent microscopic picture of the acceleration--retardation mechanism in the studied aqueous electrolytes.

Inspired by the structure of $srs$ Laves networks in $\mathbb{R}^3$ that underpin the celebrated gyroid surface, we construct a Laves network of identical three-coordinated vertices on $S^3$ with double-twist. This network is a subset of the vertices and edges of the 600-cell, and can be viewed as a bipartite graph of disjoint 24-cell vertices inscribed in the 600-cell. We describe mutually entangled realizations of this network on $S^3$, and describe their relation to the well-known $srs$ Laves network structure in $\mathbb{R}^3$.

Slender magnetic elements provide a versatile platform for programmable shape-morphing under remote magnetic actuation. However, a general and physically interpretable framework for the inverse design of a `magneto-elastica' under prescribed boundary conditions remains lacking. In this work, we develop an explicit analytical formulation for the inverse design of a magneto-elastica based on the integral form of the moment equilibrium equations. This approach yields direct constraints on the admissible curvature and rotation fields, enabling a systematic characterization of the feasible design space. We identify the key dimensionless parameters that govern the competition between magnetic torques and elastic restoring moments and show that the applied boundary conditions are an essential ingredient. We obtain closed-form solutions for the beam tapering profiles required to generate desired actuated shapes in the cases of clamped--free and clamped--clamped configurations; in the latter case, this includes analytical expressions for the boundary reactions. The formulation recovers the classical inverse elastica in the absence of magnetic fields and reveals a linear scaling between curvature deviation and magnetic mismatch. A tessellation strategy based on stiffness tailoring is further proposed for the design of discretized morphing surfaces. The theoretical predictions are validated against discrete elastic rod simulations and experiments across representative geometries. This work establishes a consistent analytical framework for the inverse design of a magneto-elastica and provides new insight into magnetically-induced shape programming in slender structures.

Organelle patterning and its heritability remain central mysteries in cell biology, highlighting the fundamental tension between genetic inheritance and self-assembly. Here, we explore the nonequilibrium assembly and size control of the Golgi complex and endosomes, amid a continuous flux of membrane traffic, within a stochastic framework of mechanochemical fusion-fission cycles that violate detailed balance. Using a dynamical systems approach, we identify distinct, robust regimes, ranging from fixed points to limit cycles with definite phase relations. We identify these dynamical regimes with diverse phenotypes, from stable cisternae to periodic, cell-cycle-dependent dissolution/reassembly to cisternal progression. We analyse its dynamic response to systematic perturbations or driving protocols and make definite predictions that may be tested experimentally. Our analysis reveals that the two competing models of Golgi organization-vesicular transport and cisternal progression - are, in fact, two phases of the same underlying nonequilibrium process. Finally, our framework offers a strategy for controlling cisternal chemical identity and number and by modulating the interplay between glycosylation enzymes and membrane fission-fusion dynamics.

We use a minimal model for a dense suspension undergoing thickening and thinning to investigate microstructural changes in 2d simulations. Our simulations show that in steady flow the contact network contains distinct building blocks which are clearly signaled by sharp peaks in the radial distribution function, similar to what is observed in granular jamming. These structures {deform} during thinning. Non-Gaussian stress fluctuations that only emerge during thickening are associated to power law tails in the distribution of local contact forces, which tend to emerge when the flow-induced building blocks form large spanning assemblies. The subset of the contact network characterized by strong contact forces and connectivity large enough to be rigid or over-constrained is increasingly likely to percolate as the system starts to thicken, and to percolate over larger strain windows during thickening. The tendency of these structures to span the sample and to persist is dramatically reduced during thinning, where instead their deformation allows for a more homogeneous spatial redistribution of contact forces, significantly reducing the fluctuations of the macroscopic stress over time.

Multiscale periodic metamaterials have been designed for numerous applications, such as impact absorption, acoustic cloaking, photonic band gaps, and mechanical logic gates. This prior work has focused on optimizing mesoscale structure for desired bulk isotropic properties. In contrast, we seek to develop materials with highly anisotropic elastic properties. To quantify elastic anisotropy, we introduce two rotationally invariant, normalized quantities that characterize the anisotropic response to shear and compression, respectively, $A_G$ and $A_C$. We find that typical crystalline solids possess average elastic anisotropy $\overline{A}_G \approx 0.15$ and $\overline{A}_C \approx 0.09$. Compared to atomic crystals, jammed granular materials can attain elastic anisotropies that are several orders of magnitude larger. Since grain rearrangements reduce anisotropy in granular materials, to preserve strong elastic anisotropy, we design tessellated granular materials that consist of multiple connected grain-filled voxels, which limit rearrangements and enable highly anisotropic elastic properties. Bulk granular packings with $N$ grains prepared at pressure $p$ have maximal anisotropy for $pN^2\sim1$ and become isotropic in the large-$pN^2$ limit. We show that homogeneously tessellated granular systems can inherit the elastic response of the constituent voxel configurations with elastic anisotropy up to $100$ times that of crystalline compounds over a range of $pN^2$. We show further methods to tune the elastic anisotropy of tessellations by designing heterogeneously patterned voxel configurations and tessellations that allow large boundary deformations.

Many biological systems collectively construct complex, adaptive, and functional architectures, where function emerges from bottom-up building processes rather than top-down planning or centralized control. However, general strategies for programming and controlling such emergent function in engineered systems remain largely unexplored. In this work, we present a systematic framework for designing local behavioral rule sets for simple builders such that, when adhered to, structures with targeted global properties emerge. Using a minimal model inspired by tent caterpillars, we study how simple agents equipped with limited sensing and no memory or global knowledge construct networked structures through local deposition of line segments. We base our framework on tuning local degrees of freedom in a complex system to alter global behavior. By identifying the degrees of freedom that influence a given property and specifying how they are tuned through local rules, we demonstrate that the corresponding global properties can be directed. We explore this through three geometric properties of the agents' resulting networks, in particular area coverage, average line density, and front curvature. We show that agents can reliably achieve targeted values for these properties while maintaining low variability in the presence of stochasticity. These results establish a generalizable approach for programming emergence in decentralized systems and suggest new pathways for designing adaptive materials and autonomous construction strategies in complex, uncertain environments.

Two-dimensional tsumoite (BiTe), a polymorph of Bi2Te3, has emerged as a promising candidate for nonlinear photonic devices owing to its strong spin-orbit coupling, tunable bandgap, and high carrier mobility characteristics. This work presents a thorough examination of the third-order nonlinear optical response of BiTe dispersions using spatial self-phase modulation (SSPM) spectroscopy. The nonlinear refractive index (n2) and third-order nonlinear susceptibility are quantitatively derived from the diffraction ring patterns, demonstrating third-order nonlinear susceptibility values, similar to or surpassing those of advanced 2D materials. The temporal development and distortion of the SSPM rings are examined using the wind-chime model, and thermal factors influencing the SSPM pattern are analyzed. First-principles electronic band structure studies reveal that the elevated nonlinear susceptibility arises from band dispersion. Direct correlation between carrier transport and third-order nonlinear susceptibility is established. Utilizing these qualities, all photonic devices, including a photonic isolator based on a 2D BiTe-2D hBN heterostructure, are depicted to show asymmetric propagation. A photonic information converter and a logic gate are designed using the cross-phase modulation technique. These findings establish 2D BiTe nanostructure as a formidable nonlinear optical platform for advanced photonic signal processing and integrated photonic applications.

Entropy is one of the key thermodynamic variables reflecting changes in the state of matter. Unlike other thermodynamic variables, it is well-defined also for nonequilibrium steady states through its relation to information. Applying this relation to physical systems is an ongoing challenge, as it requires knowledge of microscopic high-dimensional continuous distributions which is generally unattainable. A set of new approaches for the measurement of entropy in nonequilibrium steady or absorbing states have been developed and successfully applied to identify dynamic structures and transitions in diverse systems, ranging from jammed packings to swarming bacteria. We briefly review these approaches, emphasizing why applications to physical systems, including those out of equilibrium, is substantially different from the general statistical challenge of entropy estimation and inference. We point at promising current and future directions.

This article aims to introduce the broad field of soft active matter physics and its relevance to the life sciences in simple, accessible language. Although this area of research is relatively new, it has already demonstrated significant potential in providing a physical understanding of many biological processes. While several review articles by leading researchers exist, they can be difficult to grasp for undergraduate students and even early-career researchers who wish to enter this field. In this article, I cover the basics, introduce the origins of soft active matter physics, and explain how it differs from traditional equilibrium condensed matter ideas at the fundamental level. For the most part, I will avoid mathematical equations and excessive technical precision in several statements. Instead, I will focus on communicating the core ideas and the overall spirit of the argument, using everyday examples to develop a physical intuition. The primary focus will be on the dynamical aspects of these systems. I will conclude by briefly discussing a published experimental study from our research group that examines universal features of the trajectories of homing and migrating organisms.

Polymer crystallization is a process of great interest in both fundamental theory and industrial settings, particularly in polymer processing and applications involving semi-crystalline materials. The effect of processing on the initial stages of crystallization is not fully understood. Our study investigates the influence of pre-shear on monodisperse melts and bidisperse blends of a generic, segmentally coarse-grained polymer model. Through molecular dynamics simulations, we explore how polydispersity affects crystallization, where we found that the addition of short chains to a melt of longer chains increased the final crystallinity by about 10%, and increased the initial growth rate by roughly a factor of two. In contrast, however, pre-shearing the hot melt before quenching only showed a minor increase in both growth rates and final crystallinty, except in monodisperse melts of short chains. Crystal grain shapes were most influenced by pre-shearing monodisperse melts, where both asphericity and prolateness decreased. Additionally, we determined topological connectivity of crystal grains through tie- and loop-chain analysis. Again, only monodisperse melts showed a significant increase of tie chain fractions with pre-shear, while all other systems showed only modest increases. Our findings provide insight into the changes of crystallinity and cluster morphologies that emerge when pre-sheared, offering a deeper understanding of the initial crystallization processes in polymer melts when subjected to pre-shear.

Steady shearing and planar extension are commonly viewed as two distinct types of flow field, especially in the context of probing the rheology of complex fluids. By leveraging the kinematic equivalence between the two flows, we derive an effective extension rate experienced by a material element which removes the rotational component of the shearing flow. This enables reconstruction of the steady planar extensional viscosity of an unknown fluid using only material functions measured in a steady shearing flow, revealing a deep rheological equivalence between the two deformation histories. We demonstrate this equivalency through phenomenological and microscopically motivated frame-invariant constitutive models as well as experiments with a viscoelastic polymer solution.

Tendon-bone enthesis connects tendon and bone, two mechanically dissimilar materials, while effectively minimizing stress concentrations, a capability rarely achieved in engineering materials. Its hierarchical organization and graded variations in composition or mineralization are widely recognized as key contributors to its exceptional performance. Here, we investigate the mechanics of enthesis, focusing on the insertion of interface collagen fibers into bone where hierarchical collagen fibril structures and graded mineralization are present, and translate these insights into bioinspired engineering material design using a convolutional neural network-based field predictor (CNNFP). We first construct a three-dimensional finite element model (FEM) of the interface fiber-bone enthesis, in which local material properties depend on mineralization level, mean fibril orientation, and angular dispersion, informed by a multiscale continuum theory. We introduce a scalar risk factor that integrates local stress states and constituent fibril organizations to quantify local vulnerability. Simulation results demonstrate that graded and spatially heterogeneous configurations markedly reduce stress concentrations, supporting prevailing biomechanical hypotheses. We then train the CNNFP as an accurate surrogate for FEM and embed it within a kernel-based gradient optimization framework to efficiently identify optimal field configurations. The optimized designs are validated against FEM ground truth, establishing a generalizable AI-enabled pathway for the optimization of bioinspired functionally graded materials.

The stretching and pinch-off of a liquid bridge is a simple way to probe when a suspension of particles stops behaving as a continuum. In this study, we consider density-matched suspensions of rigid nylon fibers with aspect ratios (length over diameter) ranging from 2 to 84, and volume fractions $\phi$ spanning the dilute to dense regimes. High-speed imaging of pendant-drop breakup reveals three successive regimes, as previously observed for spherical particles: an equivalent-fluid regime at early times, a dislocation regime corresponding to the separation of the rods, and a final regime controlled by the interstitial liquid once the neck is devoid of rods. The thresholds between these regimes follow the previously proposed scaling for spherical particles, in which the rod length, rather than the rod diameter, is used as the relevant discrete scale. In the equivalent-fluid regime, pinch-off also leads to an effective extensional viscosity that increases with both volume fraction and aspect ratio. This viscosity is not equal to the shear viscosity measured in a parallel-plate rheometer, but both sets of data are well described by Mills' law using a critical volume fraction $\phi_c$. Finally, the critical volume fraction $\phi_c$ decreases monotonically with the aspect ratio and is well captured by an empirical law. These results show that pinch-off is a sensitive probe of continuum breakdown in anisotropic suspensions and that, for rigid rods, the rod length controls the onset of heterogeneous thinning.

We report the motion of individual magnetic Quincke rollers composed of silica particles doped with superparamagnetic iron oxide nanoparticles, whose activity arises from the coupling between Quincke rolling and an externally applied rotating magnetic field. We applied a clockwise (CW) rotating magnetic field of magnitude approximately 11 mT and rotational frequencies ranging from 0.2 to 2.75 Hz. At low frequencies, the dominant mode of motion is a CW helical trajectory. Circular trajectories emerge as a limiting case of this helical motion, in which lateral translation vanishes and the particle traces overlapping closed loops in the xy-plane. At higher frequencies, a second regular mode becomes prevalent, characterized by helical wavy trajectories in which the particle follows a CW helical path with a spatially varying curvature. Under specific conditions, however, we observe the unexpected emergence of anomalous counterclockwise (CCW) trajectories, in which individual particles roll in a direction opposite to that of the applied CW rotating magnetic field. A theoretical model incorporating electrostatic interactions, far-field hydrodynamic coupling, and a magnetic dipole approximation indicates that the anomalous behavior results from the interplay among the magnitude and orientation of the initial magnetic dipole moment, the frequency of the rotating magnetic field, and the magnitude of the initial translational velocity. Together, these factors determine the likelihood of a particle exhibiting regular or anomalous rotational motion.

Applying an impulsive force to a powder layer shaped with a concave surface generates a sharp powder jet. This phenomenon has been proposed as a method for evaluating the flowability of powders from small amount of samples. In this study, we systematically varied the radius of the initial concave shape as a controllable parameter and quantitatively examined the resulting jet dynamics, focusing on ejection velocity and maximum height. Our high-speed observations revealed that increasing the concave radius led to broader jets with significantly reduced velocity and maximum height. These dynamic quantities followed a scaling relation with drop height, while the scaling coefficient decreased with the concave radius, indicating that the surface geometry directly governs the extent of energy dissipation. Furthermore, a minimal mechanical model incorporating the sliding distance and velocity squared type dissipation of the powder flow reproduces the observed linear dependence of the jet height on the concave radius. These findings establish powder jets as a sensitive probe of dissipation in dynamic powder flow and provide a quantitative framework for comparing powder specific interactions such as humidity, particle size and particle shape.

Colloid models have frequently been used to successfully describe the influence of protein-protein interactions on antibody solution properties, but they suffer from inherent problems due to the anisotropic shape of the particles. The net charge required to describe electrostatic interactions is an effective quantity that cannot directly be obtained from the known molecular structure of an antibody, and the solution structure caused by excluded volume interactions is strongly overestimated at high concentrations due to the assumption of hard sphere interactions. As a result, these models have descriptive rather than predictive power. Here we present an improved, soft penetrable sphere model based on analogies to soft colloids and star polyelectrolytes that take into account the Y-shaped antibody form and the corresponding charge and ion distribution. The model not only correctly describes the concentration and ionic strength dependence of thermodynamic and collective dynamics quantities such as the osmotic compressibility and the apparent hydrodynamic radius, but also reproduces the center-of-mass static structure factor obtained in computer simulations using a weakly coarse-grained model, in which the antibody is described at an amino acid level. We demonstrate that this soft penetrable sphere model quantitatively reproduces experimental data from static and dynamic light scattering at low and high ionic strength for two well-characterized monoclonal antibodies (mAbs) using the net charges and the overall mAb dimensions directly obtained from their molecular structure.

Understanding dynamical facilitation in nonequilibrium glass-forming systems driven by active forces remains an open challenge. In particular, it is unclear whether facilitation survives in active glasses, where persistent self-propulsion breaks detailed balance and introduces directional memory. Here, we use large-scale simulations of a two-dimensional athermal Ornstein-Uhlenbeck particle model to investigate how persistent active forcing modifies cooperative relaxation. We analyze the morphology of cooperatively rearranging regions (CRRs) and the spatial transport of mobility excitations. A spatially resolved core-shell decomposition reveals distinct responses of the core and shell to activity: the core undergoes global morphological changes while retaining internal plasticity, whereas the shell acts as a rigid scaffold that supports primarily axial deformation and facilitates transport. Dynamical observables, including modal displacement, shell occupation probability, and facilitation length, exhibit a pronounced non-monotonic dependence on persistence time. This behavior reflects the competition between persistence and effective noise, leading to either coherent or trapping-dominated dynamics at large persistence, depending on temperature. Despite significant morphological changes, the facilitation length shows an approximate scaling collapse when rescaled by the persistence length, $l_p=\sqrt{T_{\mathrm{eff}}\tau_p}$. This is consistent with a diffusive-like time-length coupling, $\xi_{\mathrm{fac}} \sim \tau_{\alpha}^{1/2}$, indicating that activity reshapes facilitation pathways without altering their large-scale transport character. Our results support a generalized facilitation framework for active glass formers.

We present an analytical study for predicting the finger width of the Saffman-Taylor finger in a tapered Hele-Shaw cell. We consider a rectilinear geometry with a constant depth gradient and apply analytical techniques of singular perturbation analysis and WKB approximation to derive an expression for the finger selection mechanism for such tapered Hele-Shaw cells with small depth gradients. We establish \[ \Lambda - \frac{1}{2} \sim f(\alpha) Ca_m^{2/3} \quad \mbox{as} \quad Ca_m \rightarrow 0, \;\;\; \mbox{and} \;\;\; \lvert \alpha \rvert \ll 1.\] Here, $\Lambda$ is the dimensionless finger width, $Ca_m$ denotes the modified Capillary parameter, and $f(\alpha)$ is a linear function of the gap gradient $\alpha$, such that $f(\alpha = 0) = 1$ recovering the results of parallel Hele-Shaw cell (Hong and Langer \cite{hong1986analytic}, Combescot \emph{et al.} \cite{Combescot1986}, Shraiman \cite{shraiman1986velocity}). Our findings indicate that the Hele-Shaw cell gap gradient plays a crucial role in determining $\Lambda$, allowing for control over fingering instabilities such that the single-finger steady state can be stabilised or destabilised depending on the sign of the gradient, compared to the standard Hele-Shaw cell. The theoretical estimates reveal excellent agreement with experimental finger-width data and predictions from linear stability analyses.

Concentration regimes in polymer and polyelectrolyte solutions can be identified by scaling laws for the relation between specific zero-shear viscosity and concentration. Recently, we have shown that the same is true for the infinite-shear viscosity plateau. The shear-thinning range is usually accessed by focusing on the viscosity functions for the respective concentration regime. For salt-free aqueous xanthan solutions, we find power-law dependencies of the specific viscosity on concentration throughout the entire shear-rate range. We distinguish six different concentration regimes. Apart from those already known for the zero-shear viscosity of polyelectrolyte solutions, i.e. dilute, semidilute unentangled, semidilute entangled and neutral semidilute entangled, we identify a linear regime for low shear rates at high concentrations, where the solution gels and a regime at both, higher concentrations and higher shear rates. Within some regimes, the power-law exponents change smoothly with shear rate, particularly, when deviating from the zero-shear viscosity plateau before the power-law of the viscosity function. Some regimes merge as their power-law exponents approach each other. The fact that the regimes extend smoothly from the zero-shear regime into finite shear rates, i.e. away from thermodynamic equilibrium, shows that indicators such as critical concentrations remain valid at finite shear rates. This motivates us to interpret the data in the light of existing scaling laws and current knowledge about shear-rate dependent interaction mechanisms in polyelectrolyte solutions, particularly in xanthan solutions. It allows to follow the shift of relevant interaction mechanisms with shear rate. We think that the consideration of scaling laws under shear can be particularly helpful for identifying, for instance, thresholds for shear-induced disentanglement or disaggregation.

We study how an active bath is transduced into the internal fluctuation spectrum of a semiflexible polymer. Starting from the statistics of active forces exerted by an explicit bath of active Brownian particles, we derive an effective description in terms of temporally persistent and spatially correlated noise, and test it against simulations of both explicit-bath and implicit-noise models. We find that activity reorganizes polymer fluctuations spectrally rather than uniformly: increasing the active force predominantly enhances the lowest modes, while increasing persistence shifts the spectral weight toward progressively longer wavelengths. The theory captures this mode-level reorganization well and explains the strong qualitative correspondence between explicit and implicit active baths over a broad parameter range. In contrast, global size measures such as the radius of gyration are systematically underestimated, which we trace to activity-induced bond stretching and contour-length renormalization absent from the present fixed-contour theory. Our results show that a semiflexible polymer acts as a multiscale probe of active matter, resolving the temporal and spatial structure of nonequilibrium forcing through its mode spectrum.

Porous media underpin absorption, filtration, separation, and high-area interfacial transport in chemical and diagnostic systems, yet sustained directional flow through them remains difficult because tortuous pore networks and strong acoustic losses promote bypassing, weak flow, and counterflow. Here, we show that floating-electrode unidirectional transducers (FEUDTs) convert porous materials into actively pumped transport platforms by generating predominantly unidirectional surface acoustic waves (SAWs) that couple more effectively than conventional interdigital transducers across wet multilayer interfaces. By varying pore size, permeability, sample thickness, and fluid viscosity, we find that transport is strongly enhanced when the SAW wavelength is comparable to the characteristic pore dimension, providing a practical design rule for acoustically activated porous media. Under these conditions, FEUDTs drive directional flow velocities up to 0.6 mm s$^{-1}$ at sub-watt input power, about 600 times faster than diffusion alone. FEUDTs also sustain pumping in prewetted porous media, where capillary contributions are removed, yielding velocities that exceed capillary-driven flow under matched conditions while remaining far above thermally induced transport. A reduced theoretical framework captures the main experimental trends and identifies transducer architecture, pore geometry, and actuation strength as the key parameters governing long-range, tunable transport in porous functional materials.

Reliable transformation between frequency- and time-domain material functions remains a central challenge in linear viscoelasticity due to finite bandwidth, discrete sampling, and experimental noise. We introduce \emph{i\text{-}Rheo-Tempo}, a quadrature-free method that reconstructs the shear relaxation modulus directly from dynamic measurements through an exact second-derivative representation of the complex viscosity. When the spectrum is approximated as piecewise linear, the inversion reduces to a compact interval-slope formulation based solely on local spectral properties, avoiding numerical quadrature, parametric fitting, and predefined relaxation spectra. The method is validated against a set of complex fluids including synthetic models, polymer melts, industrial elastomers, comb polymers, and broadband microrheology datasets spanning nearly nine decades in frequency. In all cases, the reconstructed relaxation modulus is in quantitative agreement with independent time-domain measurements. These results demonstrate that \emph{i\text{-}Rheo-Tempo} provides a robust, model-free solution to the frequency-to-time inverse problem and, more generally, establishes a framework for recovering time-domain responses from experimentally measured complex spectra.

This study presents a computational investigation of self-assembly and rheological behaviour of multichain amphiphilic block copolymers under varying chain length, architecture, composition, and shear rate. Using Brownian dynamics (BD) simulations, we systematically examined bead-spring model multi-chain diblock and triblock copolymers with chain lengths of 12-48 beads, hydrophobic fractions (f) ranging from 0 to 1.0, and shear rates spanning 0-0.1 1/ns. In the dilute regime, results demonstrate that triblock copolymers form extensive 3D networks with bridging architectures through hydrophobic end blocks, achieving solution viscosities up to half an order of magnitude higher than diblock systems, with superior structural integrity under weak shear. At shear rate=0.003-0.01 1/ns, both chain architectures show increased gyration radius of individual chains within each micelle and decreased cluster counts, indicating aggregation of clusters prior to breakdown at higher shear rates. Shape anisotropy analysis reveals that triblocks develop highly elongated prolate structures (L1/L3 = 11) at high shear rates, while diblocks form more discrete micellar assemblies (L1/L3 = 7.5). Chain length analysis shows systematic increases in radius of gyration, with triblocks exhibiting an increase in cluster count, indicative of network percolation. Rheologically, triblock systems maintain lower crossover frequencies with increasing hydrophobic fraction, reflecting slower network relaxation versus diblocks. The terminal relaxation time of triblock copolymer systems increases with hydrophobic fraction due to double-ended hydrophobic bridging, while diblocks maintain stable values. These findings provide fundamental insights for the rational design of polymer-based drug carriers through architectural selection and flow conditions.

We highlight some properties of the Schrödinger-Navier-Stokes (SNS) equation [Salasnich, Succi, and Tiribocchi (2024)] of potential relevance for microfluidics and soft matter. Specifically, we show that the SNS equationwith generic parameters is formally equivalent to the Navier-Stokes-Korteweg equations for capillary fluids, with the equivalence established at the level of an action functional that decomposes naturally into a Korteweg conservative and a Rayleigh dissipative components, respectively. We derive the dispersion relation for sound modes, showing that the dispersive parameter controls capillary stiffness while the dissipative parameter controls viscous damping, and that the Bogoliubov dispersion relation is recovered in the quantum limit. We also derive an effective one-dimensional SNS equation for a fluid confined in a narrow capillary tube. Finally, it is argued that the SNS may facilitate the quantum simulation of complex states of flowing matter.

It is common to study polymer physics through the use of idealized single-chain models, and the most popular of these is the freely jointed chain model. In certain thermodynamic ensembles, statistical mechanical treatment of this model is analytically tractable or sometimes exactly solvable. This enables useful relations to be ascertained, like the expected chain end-to-end length as a function of an applied force. However, most of these relations return ensemble averages, which are values with inherent uncertainty, as opposed to deterministic values with no variance. This is an important distinction to understand and quantify, because the majority of studies to date involving single-chain models effectively treat these values as deterministic rather than fluctuating. To address this issue, thermodynamic fluctuations are examined in the freely jointed chain model. Specifically, the probability densities and standard deviations of the longitudinal, lateral, transverse, and radial portions of the chain extension, as well as the extension and link angles, are examined for different numbers of links and applied forces. Fluctuations in these quantities are shown to be considerable until the applied force becomes large. Increasing the number of links in the chain gradually reduces fluctuations in all quantities except for the link angles, since they are independent for freely jointed chains in the isotensional ensemble. Quantities are obtained analytically whenever possible and numerically otherwise. Overall, these results provide intuitive admonitions to consider when modeling the stretching of single polymer chains or the deformation of entire polymer networks.

Recent investigations of turbulent circulation fluctuations have uncovered substantial insights into the statistical organization of flow structures and revealed unexpected geometric features of turbulent intermittency. Of particular interest here is the observation that circulation probability distribution functions admit a superstatistical representation, namely a description based on "ensembles of Boltzmann-Gibbs ensembles". A fundamental phenomenological ingredient of this approach, which serves as a natural starting point for modeling, relies on the strong correlation between the dissipation field and the spatial distribution of elementary circulation-carrying structures, i.e., small-scale vortices. Within the language of superstatistics, this corresponds to characterizing circulation statistics through an appropriate choice of conditioned (Boltzmann-like) distributions and mixing distributions. We show that the superstatistical class of q-exponentials, known to have broad applicability in a wide range of multiscale and non-equilibrium systems, provides an accurate description of the observed circulation statistics in homogeneous and isotropic turbulence. This finding opens avenues for exploring the statistical structure of the turbulent cascade in the context of non-extensive statistical mechanics, rooted in the concept of non-additive entropies.

Interfacial deformation under electric fields is a common phenomenon in many industrial processes. Particularly, we are interested in the dynamics of sessile soap bubbles in a parallel-plate electric field which exhibits a stable deformation regime followed by conical instability. Using side-view imaging, we track the equilibrium shapes, the transition to the unstable regime, and the pre-jet apex dynamics within one experimental system. In the stable regime, the meridional profile is well described by a spheroidal fit, and the aspect ratio collapses across initial bubble sizes onto a single steady-state branch when plotted against the dimensionless field $E^\ast = \sqrt{\mathrm{Bo}_e}$ for data acquired within a fixed ambient session where the electric Bond number $\mathrm{Bo}_e$ is defined as $\varepsilon_0 E_0^2 R_0/(2\gamma)$. The endpoint of this branch marks the transition to the unstable regime. Above onset of instability, the apex sharpens into a cone with half-angle $30.0^{\circ}$ $\pm$ $0.6^{\circ}$, below the classical Taylor value. To quantify the late pre-jet stage, we define the axial distance $b(t)$ from the instantaneous apex to a fixed reference vertex determined from the terminal cone geometry and measure its evolution. The corresponding rate grows as jetting is approached, and a near-tip inertia-capillary model captures the observed logarithmic trend as an approximation. Together, these measurements establish a single-system experimental benchmark in which stable electrocapillary deformation is organized by a single steady-state branch that leads into conical instability and pre-jet dynamics.

We analyze a system of bead--spring polymers interacting with Navier--Stokes turbulence to investigate chain--stretching physics and finite-time Lyapunov exponents in ultra--dilute solutions with Weissenberg number \(Wi \approx 80\). They stretch predominantly as material line elements, yet finite deviations arising from elasticity and excluded--volume forces occur with measurable probability. The chain end--to--end distance exhibits a power--law scaling regime. Polymers preferentially sample regions of axisymmetric biaxial extension, where they reach their largest extensions and stretch most rapidly. The degree of stretching is directly correlated with strain intensity, while relaxation events are concentrated in high--enstrophy regions. The chains align strongly with the second strain--rate eigenvector and tend to anti--align with the third; consequently, the second eigenvalue contributes significantly to polymer compression, despite its magnitude typically being smaller than that of the third. Along polymer trajectories, vorticity tends to align with both the first and second eigenvectors, a behavior that differs from the corresponding Eulerian statistics and from Lagrangian vortex--stretching phenomenology. After approximately ten large--eddy turnover times, the Lagrangian Lyapunov exponent histories from different chains appear to synchronise, consistent with convergence of the mean logarithmic stretch rates. All Lyapunov--exponent probability density functions exhibit departures from Gaussianity, and the intermediate Lyapunov exponent is positive in all realizations. The ratio of the mean intermediate to largest exponents is \(E[\lambda_2]/E[\lambda_1] \approx 2/7\). The largest and intermediate exponents are positively correlated, whereas the intermediate and smallest exponents are anticorrelated.

An interpretable, physics-consistent turbulence model correction framework, termed FISR-Equation Learner (EQL), is proposed by embedding equation learning directly into a Partial Differential Equations (PDE)-constrained field inversion process based on the adjoint method. Unlike conventional two-stage approaches, the correction model is optimized end-to-end in parameter space using an EQL architecture, enabling the direct identification of compact analytical expressions while maintaining consistency with the governing equations. The method is applied to the shear-stress-transport (SST) model and trained on two canonical separated flows, the curved backward-facing step and the NASA hump. The resulting explicit expression significantly reduces separation bubble overprediction and improves reattachment prediction, achieving performance comparable to neural-network-based end-to-end methods while retaining full interpretability. Generalization is demonstrated on unseen configurations, including periodic hills, a surface-mounted cube, and the high-lift NLR7301 airfoil. The model improves separated-flow predictions and stall characteristics without degrading attached boundary-layer performance. Overall, FISR-EQL provides a practical pathway toward optimal yet transparent data-driven turbulence model correction.

This study presents an efficient and accurate discrete adjoint gas-kinetic scheme (GKS) for sensitivity analysis and aerodynamic shape optimization in continuum flow regimes. Developed using the backward mode of algorithmic differentiation (AD), the adjoint solver is rigorously verified against a duality-preserving linearized GKS solver generated via forward-mode AD. The robustness and practical effectiveness of the solver are evaluated through three benchmark cases: the inverse design of turbine blades, lift-to-drag ratio enhancement, and shock-strength reduction for a NACA 0012 airfoil. To capture realistic flow physics, fully turbulent optimizations are conducted using the one-equation Spalart--Allmaras (SA) model. Numerical results demonstrate excellent agreement between the discrete adjoint and linearized solvers, exhibiting matching sensitivity convergence behaviors, identical asymptotic residual decay rates, and negligible discrepancies in final sensitivity predictions. Furthermore, the optimization studies confirm that targeted design objectives are consistently achieved within a limited number of design cycles, highlighting the solver's computational efficiency, accuracy, and suitability for complex aerodynamic geometries.

We study the navigation of a self-propelled inertial particle in two-dimensional Rayleigh--Bénard convection at Prandtl number $Pr = 0.71$ and cell aspect ratio $\Gamma = 4$ for Rayleigh numbers $Ra$ ranging from $10^{7}$ to $10^{11}$. A reinforcement-learning (RL) controller selects the propulsive acceleration, subject to an upper bound $\mathcal{A}_{\max}$, to achieve a prescribed horizontal displacement. We find that the success rate increases abruptly with $\mathcal{A}_{\max}$ at moderate $Ra$, whereas at higher $Ra$ the transition becomes more gradual and shifts to larger $\mathcal{A}_{\max}$. Moreover, although the completion time increases with $Ra$, the propulsion energy required for successful traversal decreases. Proper orthogonal decomposition (POD) reveals that these performance differences arise from reorganisation of the carrier flow. At moderate $Ra$, the dominant large-scale circulation partitions the domain through robust transport barriers, requiring a finite thrust surplus to cross them; at higher $Ra$, energy is distributed across many modes, the barriers fragment, and transient plume-assisted pathways emerge. Compared with a constant-heading baseline, the learned policy aligns with local currents and consumes significantly less energy. Lagrangian coherent structure (LCS) analysis further shows that the RL agent inherently learns to cross repelling barriers and surf along attracting pathways. Finally, by mapping these behaviours onto the local Eulerian flow topology using Voronoi tessellation and the $Q$-criterion, we distil an interpretable, physics-based heuristic strategy that achieves robust navigability. These results connect turbulent-flow organisation with autonomous navigation under bounded actuation.

Scyphozoan jellyfish exhibit the highest locomotive efficiency in the animal kingdom making them of particular interest in fluid dynamics and bioinspired robotics. Despite this prevalent analytical models of jellyfish swimming have been based on the swimming traits of hydrozoan jellyfish which utilize jet propulsion, rather than scyphozoan jellyfish which utilize paddling propulsive methods. Additionally, while stroke frequency is a driving variable in speeds achieved by undulatory swimmers, a similar dependence has not been previously explored for jellyfish. This work investigates the relationship between stroke frequency and swimming speeds in two species of scyphozoan jellyfish, Aurelia aurita and Cassiopea xamachana. An experimental study was conducted using a biohybrid technique that controls the muscle contraction frequency of freely swimming, live jellyfish with portable, implanted microelectronics. Swimming speeds were measured from video recordings in a 2.4 m tall water tank. It was found that despite differences in their natural swimming frequencies, the Aurelia and Cassiopea displayed similar speed-frequency relationships with peak swimming speeds occurring at 0.55 +/- 0.05 Hz and 0.50 +/- 0.05 Hz respectively. The difference in natural stroke frequency displayed by scyphomedusea despite the shared relationship between swimming speed and stroke frequency in these two species, suggests that natural stroke frequency may be more related to other functions such as filter feeding, rather than locomotion. A new analytical model developed for scyphozoan, paddling jellyfish was shown to have closer agreement with the experimental results than existing models based on jet propulsion. The model demonstrated the driving factors in the relationship between swimming speed and stroke frequency to be the speed of the jellyfish bell margin and changes in body kinematics with stroke frequency.

Self-propelled particles can navigate complex environments, including viscous fluid interfaces with curved geometries. In this work, we study the emergent dynamics of a suspension of self-propelled particles confined to a stationary curved viscous interface. The evolution of the particle configurations is modeled using the Fokker-Planck equation on the curved surface, formulated using Cartan's moving frame method, and coupled to the bulk and surface Stokes equations with flows driven by an interfacial nematic active stress. Specifically, for a spherical vesicle, the flow field and the distribution of the particles are analyzed theoretically and numerically within the framework of spin-weighted functions and spin-weighted spherical harmonics, which provide a natural geometric description of the probability distribution function on the sphere. A linear stability analysis about the uniform, isotropic state is performed and predicts a finite-wavelength instability, with mode selection arising from the competition between the vesicle radius and the Saffman-Delbrück length. This instability and the associated mode-selection mechanism are also confirmed in nonlinear numerical simulations using a pseudo-spectral method based on spin-weighted spherical harmonics.

Rotating detonation engines (RDEs) are a promising propulsion concept that may offer higher thermodynamic efficiency and specific impulse than conventional systems, but nonlinear phenomena, including transitions to oscillatory or chaotic propagation modes, can hinder practical operation. Deep Reinforcement Learning (DRL) has emerged as a promising method for controlling complex nonlinear dynamics such as those observed in RDEs. However, the multi-timescale nature of the RDE system makes direct application of DRL challenging. We address this challenge by reformulating the DRL problem in a moving reference frame that follows the detonation-wave pattern, making the wave structure appear quasi-steady to the agent. This reformulation enables scale separation between fast detonation propagation and slower operating-mode dynamics. We train DRL controllers to modulate spatially segmented injection pressure in a one-dimensional reduced-order RDE model and induce rapid transitions between different mode-locked states. Across a range of actuation periods, initial states, and target modes, controllers trained in the moving frame learn more reliably than those trained in a stationary frame and remain effective over a broader range of actuation periods. These results suggest that symmetry-aware moving reference frame formulations may be useful for related multiscale flow-control problems and that scale separation should be exploited whenever possible to enable DRL control of multi-timescale systems.

We present a numerical investigation of kerosene droplet mist film cooling for the thermal protection of the rotating detonation combustor (RDC) and compare its performance with conventional air film cooling and combined mist/air cooling scheme. In the study, the cooling behavior of kerosene droplets injected through wall film holes is numerically examined and compared with air film cooling and a combined mist/air cooling strategy, building on a benchmark validation against flat-plate experimental data. The results show that air film cooling exhibits an optimal operating range, beyond which excessive injection degrades film stability due to strong interaction with the rotating detonation wave. In contrast, kerosene-based mist cooling forms a more persistent near-wall cooling layer, providing enhanced heat removal through phase change and exhibiting improved resistance to film separation. In mist cooling, the droplet size primarily affects the immediate downstream cooling performance, with intermediate-sized droplets offering the improved balance between evaporation rate and film continuity. A combined mist/air cooling scheme can further improve cooling efficiency and accelerate wall temperature recovery after detonation wave passage while maintaining moderate impacts on the mainstream flow. Additionally, although kerosene droplets partially participate in combustion under film hole injection, the associated thermal load does not offset the overall cooling benefit. These findings demonstrate the feasibility and advantages of kerosene-based cooling schemes for RDC thermal management.

Unstructured meshes are among the most versatile approaches for capturing non-canonical geometries in fluid dynamics simulations. Despite this, most high-fidelity first-principles phase-change models are developed and applied on structured meshes. We present a phase-change simulation method for unstructured meshes that combines the algebraic Volume-of-Fluid (VOF) technique with geometric interface reconstruction, implemented in an in-house open-source CFD code. Phase-change rates are computed from local temperature gradients evaluated at the reconstructed interface, without empirical closure models, using a reconstruction procedure that operates on arbitrary polyhedral cells. Because the method relies on the standard finite-volume framework, it can be integrated into other cell-centred codes supporting unstructured meshes. The approach is validated against the one-dimensional Stefan and Sucking problems and the three-dimensional Scriven bubble growth on both hexahedral and polyhedral meshes, showing good agreement with analytical solutions in all three cases. A detailed analysis of the Scriven problem reveals that the interface-modified least-squares gradient stencil on Cartesian meshes overestimates the interfacial temperature gradient, producing a persistent overshoot of the analytical bubble radius and a coherent four-fold anisotropy that elongates the bubble along grid diagonals. On polyhedral meshes, the irregular face orientations eliminate both effects, yielding isotropic growth and monotonic convergence. Finally, we demonstrate the framework on turbulent upward co-current annular boiling flow, where early transient results are qualitatively consistent with a previous LES study and experimental observations of wave-modulated evaporation.

A scale-by-scale analysis of energy flux in the turbulent cascade can be performed using the spatially filtered magnetohydrodynamic (MHD) equations, while the gradient tensor invariants are widely used to characterise the structure of velocity and magnetic fields. Physical mechanisms responsible for energy flux require specific field configurations whose strength is quantified by these tensor invariants. We explore this requirement, showing that the tensor invariants act as proxies for mechanistic energy fluxes under quantifiable conditions. As a special case, the purely hydrodynamic contributions to energy flux can be expressed exactly in terms of the invariants of the velocity gradient tensor. We also show that the invariants bound the available energy flux for distinct physical mechanisms, formalising the idea that each transfer mechanism requires field configurations with gradients of sufficient strength to support a given energy flux. Results are illustrated using 3D simulations of freely decaying MHD turbulence.

Most practical engineering design problems involve nonlinear spatio-temporal dynamical systems. Multi-physics simulations are often performed to capture the fine spatio-temporal scales which govern the evolution of these systems. However, these simulations are often high-fidelity in nature, and can be computationally very expensive. Hence, generating data from these expensive simulations becomes a bottleneck in an end-to-end engineering design process. Spatio-temporal surrogate modeling of these dynamical systems has been a popular data-driven solution to tackle this computational bottleneck. This is because accurate machine learning models emulating the dynamical systems can be orders of magnitude faster than the actual simulations. However, one key limitation of purely data-driven approaches is their lack of generalizability to inputs outside the training distribution. In this paper, we propose a physics-informed spatio-temporal surrogate modeling (PISTM) framework constrained by the physics of the underlying dynamical system. The framework leverages state-of-the-art advancements in the field of Koopman autoencoders to learn the underlying spatio-temporal dynamics in a non-intrusive manner, coupled with a spatio-temporal surrogate model which predicts the behavior of the Koopman operator in a specified time window for unknown operating conditions. We evaluate our framework on a prototypical fluid flow problem of interest: two-dimensional incompressible flow around a cylinder.

Steady-state electrothermal systems involve strongly coupled heat transfer, fluid flow, and electric-potential transport, creating severe numerical challenges for standard physics-informed neural networks (PINNs) due to stark disparities in gradient scales and residual stiffnesses across the physical fields. To resolve these multiphysics bottlenecks, we introduce a Long Short-Term Memory PINN (LSTM-PINN) framework that utilizes a depth-recursive memory mechanism to preserve long-range spatial feature dependencies and maintain strict cross-field consistency. The proposed architecture is rigorously evaluated against conventional and attention-based networks across a unified five-field formulation encompassing four complex convective and drag regimes: Boussinesq electrothermal flow, drift-potential gauge-constrained transport, strong buoyancy-coupled convection, and Brinkman--Forchheimer drift. Quantitative and visual analyses demonstrate that LSTM-PINN successfully suppresses non-physical artifacts and structural distortions, yielding the highest thermodynamic fidelity and consistently outperforming state-of-the-art baselines in global error metrics. Ultimately, this memory-enhanced approach provides a highly robust and accurate computational baseline for capturing localized boundary layers and complex energy-momentum feedback in advanced electrothermal energy systems.

At the end of 2020, a new cavitation tunnel was commissioned at the Ship Hydrodynamics laboratory of TU Delft, replacing its 1960s predecessor. Since this was a new facility, a flow characterization campaign was performed to investigate the flow quality in the test section. To that end, velocity measurements were performed in the test section using Laser Doppler Anemometry. Velocities in the range of 2.13 m/s to 9 m/s were measured and a linear relation was found between the freestream velocity and the rotational frequency of the thruster. Long term measurements at the center of the test section, did not reveal any large scale fluctuations of the mean velocity. The freestream turbulence intensity was found to lie between 0.5% - 0.6% throughout the test section, after removing the measurement noise. Local measurements in various planes in the test section confirmed that the flow is uniform ($u_{local}< U_{\infty} \times 1\%$), with few outliers near the side walls, due to the turbulent boundary layer. Finally, preliminary measurements of the turbulent boundary layer (TBL) indicated that the TBL originates upstream of the test section and its growth is not strictly canonical. Smaller TBL thickness was found in the side wall compared to the top wall.

Computational fluid dynamics (CFD) has become an essential tool for predicting fire behavior, yet maintaining both efficiency and accuracy remains challenging. A major source of computational cost in fire simulations is the modeling of radiation transfer, which is usually the dominant heat transfer mechanism in fires. Solving the high-dimensional radiative transfer equation (RTE) with traditional numerical methods can be a performance bottleneck. Here, we present a machine learning framework based on Fourier-enhanced multiple-input neural operators (Fourier-MIONet) as an efficient alternative to direct numerical integration of the RTE. We first investigate the performance of neural operator architectures for a small-scale 2D pool fire and find that Fourier-MIONet provides the most accurate radiative solution predictions. The approach is then extended to 3D CFD fire simulations, where the computational mesh is locally refined across multiple levels. In these high-resolution settings, monolithic surrogate models for direct field-to-field mapping become difficult to train and computationally inefficient. To address this issue, a nested Fourier-MIONet is proposed to predict radiation solutions across multiple mesh-refinement levels. We validate the approach on 3D McCaffrey pool fires simulated with FireFOAM, including fixed fire sizes and a unified model trained over a continuous range of heat release rates (HRRs). The proposed method achieves global relative errors of 2-4% for 3D varying-HRR scenarios while providing faster inference than the estimated cost of one finite-volume radiation solve in FireFOAM for the 16-solid-angle case. With fast and accurate inference, the surrogate makes higher-fidelity radiation treatments practical and enables the incorporation of more spectrally resolved radiation models into CFD fire simulations for engineering applications.

We investigate the orientation dynamics of a settling spheroid in simple shear flow, combining a deterministic dynamical-systems analysis with a stochastic Fokker-Planck treatment. The dynamics is governed by the competition between the Jeffery torque from the background shear and the inertial torque from settling. For configurations in which gravity lies in the shear plane, the azimuthal dynamics reduces to overdamped motion in a tilted periodic potential controlled by a single effective parameter $\mathcal{R}$ that combines the particle shape anisotropy and the settling strength. A saddle-node bifurcation on an invariant circle (SNIC) at $\mathcal{R}=1$ governs the transition from sustained rotational motion to steady equilibrium, with the rotation period diverging as $(1-\mathcal{R})^{-1/2}$. When gravity is parallel to the vorticity axis, the attractor is a periodic orbit for all settling strengths. The stochastic analysis reveals that noise plays a fundamentally different role depending on whether settling-induced potential barriers are present: in the classical Jeffery problem it diffuses over the orbit constant, whereas with settling it drives Kramers-type phase slips whose rate is exponentially sensitive to the Péclet number, defined as the ratio of diffusive to convective time scales. Langevin simulations confirm the predicted intermittent dynamics, with phase slips becoming progressively rarer as the barrier height or Péclet number increases. Asymptotic results in both the small- and large-$\mathrm{Pe}$ limits, together with numerical solutions of the Fokker-Planck equation at arbitrary $\mathrm{Pe}$, quantify the orientation moments across all regimes.

This study numerically investigates two-dimensional Rayleigh-Benard convection subjected to horizontal oscillation of the bottom plate, with Prandtl number Pr=4.3, Rayleigh numbers Ra ranging from 5e6 to 1e8, and oscillation frequencies f between 0.0001 and 0.5. The imposed oscillation breaks the up-down symmetry of the classical system, inducing a strong frequency-dependent response in global heat transport, with the maximum Nusselt number enhancement exceeding 60% compared to the uncontrolled case. Central to this control efficiency is a phase-locking mechanism: at the optimal frequency, the intrinsic response time of the large-scale circulation (LSC), quantified by the sign-recovery of volume-averaged angular momentum, locks precisely to the wall oscillation period, enabling perfectly synchronized LSC reversals. Deviations from this optimal condition lead to a marked mismatch; the LSC response time becomes substantially longer when frequency exceeds the optimum and significantly shorter when frequency falls below it. In contrast, boundary layer velocities simply follow the wall oscillations and fail to distinguish control efficiency. Fourier mode analysis reveals that at the optimal frequency, a single-roll mode remains dominant throughout the cycle, facilitating efficient plume transport, whereas higher frequencies yield incomplete reversals and lower frequencies produce a double-roll structure that diminishes heat-transfer efficiency. This frequency-locking mechanism is shown to persist for optimal controls across the entire investigated Rayleigh number range, thus offering robust insight for active control strategies in thermally driven turbulent flows.

In nonlinear systems, small perturbations are conventionally attributed to negligible nonlinearity, justifying linear approximations. Here, we uncover a notable exception to this paradigm in an electrokinetic (EK) flow. Using a novel dual frequency excitation scheme with two high frequency AC electric fields ($> 10^{5}$ Hz), we efficiently excite flow perturbations at a difference frequency ($\Delta f$) four orders of magnitude lower. This approach reveals a strong nonlocal energy transfer mechanism mediated purely by the nonlinearity of the electric body force, enabling precise, clean flow control free from electrode polarization artifacts. Unexpectedly, these small, nominally linear velocity and electric conductivity fluctuations exhibit power law spectra. With increasing electric Rayleigh number, the scaling exponents agree quantitatively with predictions for fully developed EK turbulence by the Quad cascade process theory. This observation not only implies multiple flow state transitions even at low excitations, but also indicates that intrinsic nonlinearity regulates perturbations even in the linear regime, necessitating a fundamental re examination of linear approximations in electrohydrodynamics and other nonlinear systems.

Binary droplet collisions are ubiquitous in dense sprays. Traditional deterministic models cannot adequately represent transitional and stochastic behaviors of binary droplet collision. To bridge this gap, we developed a probabilistic model by using a machine learning approach, the Light Gradient-Boosting Machine (LightGBM). The model was trained on a comprehensive dataset of 33,540 experimental cases covering eight collision regimes across broad ranges of Weber number, Ohnesorge number, impact parameter, size ratio, and ambient pressure. The resulting machine learning classifier captures highly nonlinear regime boundaries with 99.2% accuracy and retains sensitivity in transitional regions. To facilitate its implementation in spray simulation, the model was translated into a probabilistic form, a multinomial logistic regression, which preserves 93.2% accuracy and maps continuous inter-regime transitions. A biased-dice sampling mechanism then converts these probabilities into definite yet stochastic outcomes. This work presents the first probabilistic, high-dimensional droplet collision model derived from experimental data, offering a physically consistent, comprehensive, and user-friendly solution for spray simulation.

The lattice Boltzmann (LB) equation with a third-order scheme can be regarded as a unified and self-consistent framework of the pseudopotential LB model for multiphase flows. In this work, we theoretically analyze pseudopotential LB simulations of two-phase Poiseuille flow at the discrete level. The finite-difference velocity equation is derived for both grid-aligned and grid-oblique cases. The terms responsible for spurious velocity oscillations near the phase interface are identified. Based on this discrete-level analysis, an improved third-order scheme is proposed to suppress spurious velocity oscillations. This scheme does not introduce any additional conceptual or computational complexity compared with the original one and reduces to the original scheme under static conditions. Numerical simulations of two-phase Poiseuille flow validate the present theoretical analysis and demonstrate the effectiveness of the improved scheme. Then, annular shear flow with a curved phase interface is considered to show that spurious velocity oscillations can also be effectively suppressed by the improved scheme in cases with such interfaces. Finally, the falling of a droplet in a vertical channel is simulated, and the results show that spurious velocity oscillations can lead to an overestimation of the drag force and distinct falling patterns. These results highlight the necessity of using the improved third-order scheme to suppress spurious oscillations and obtain reliable results.

Surrogate modeling of body-driven fluid flows where immersed moving boundaries couple structural dynamics to chaotic, unsteady fluid phenomena remains a fundamental challenge for both computational physics and machine learning. We present AeTHERON, a heterogeneous graph neural operator whose architecture directly mirrors the structure of the sharp-interface immersed boundary method (IBM): a dual-graph representation separating fluid and structural domains, coupled through sparse cross-attention that reflects the compact support of IBM interpolation stencils. This physics-informed inductive bias enables AeTHERON to learn nonlinear fluid-structure coupling in a shared high-dimensional latent space, with continuous sinusoidal time embeddings providing temporal generalization across lead times. We evaluate AeTHERON on direct numerical simulations of a flapping flexible caudal fin, a canonical FSI benchmark featuring leading-edge vortex formation, large membrane deformation, and chaotic wake shedding across a 4x5 parameter grid of membrane thickness (h* = 0.01-0.04) and Strouhal number (St = 0.30-0.50). As a proof-of-concept, we train on the first 150 timesteps of a representative case using a 70/30 train/validation split and evaluate on the fully unseen extrapolation window t=150-200. AeTHERON captures large-scale vortex topology and wake structure with qualitative fidelity, achieving a mean extrapolation MAE of 0.168 without retraining, with error peaking near flapping half-cycle transitions where flow reorganization is most rapid -- a physically interpretable pattern consistent with the nonlinear fluid-membrane coupling. Inference requires milliseconds per timestep on a single GPU versus hours for equivalent DNS computation. This is a continuously developing preprint; results and figures will be updated in subsequent versions.

In this investigation, we conduct a systematic computational search for potential singularities in 3D Navier-Stokes flows on a periodic domain $\Omega$ based on the Ladyzhenskaya-Prodi-Serrin conditions. They assert that for a solution $\mathbf{u}(t)$ of the Navier-Stokes system to be regular on an interval $[0,T]$, the integral $\int_{0}^T \|\mathbf{u}(t)\|_{L^q}^p\,dt$, where $2/p+3/q=1,\;q>3$, and the expression $\sup_{t \in [0,T]} \|\mathbf{u}(t)\|_{L^3}$ must be bounded. Flows which might become singular and violate these conditions are sought by solving a family of variational PDE optimization problems where we identify initial conditions $\mathbf{u}_{0}$ with the corresponding flows $\mathbf{u}(t)$ locally maximizing the integral $\int_{0}^T \|\mathbf{u}(t)\|_{L^q}^p\,dt$ for a range of different values of $q$ and $p$ or the norm $\|\mathbf{u}(T)\|_{L^3}$ for different time windows $T$ and increasing sizes $\| \mathbf{u}_0 \|_{L^q}$ of the initial data. We consider two formulations where these expressions are maximized over appropriate Lebesgue spaces $L^q(\Omega)$ or the largest Hilbert-Sobolev spaces $H^s(\Omega)$ embedded in them. The lack of Hilbert-space structure in the first case necessitates development of a novel computational approach to solve the problem. While no evidence of unbounded growth of the quantities of interest, and hence also for singularity formation, was detected, we were able to quantify how "close" the flows realizing such worst-case scenarios come to forming a singularity. A comparison of these results with estimates on the rate of growth of the norms $||\mathbf{u}(t)||_{L^q}$ and of the enstrophy $\mathcal{E}(t)$ indicates that the extreme flows do enter a regime where these quantities are amplified at a rate consistent with singularity formation in finite time, but this growth is not sustained long enough for singularities to form.

Overlapping fish-scale architectures are among nature's most distinctive surface adaptations, combining protection, contact regulation, hydrodynamics, optical and directional mechanical response within a thin textured integument. Here, we show that their biomimetic structural analogues can host deterministic chaos. Biomimetic scale substrates develop chaotic flexural vibrations at modest amplitudes because bending activates unilateral contact and progressive jamming, while built-in asymmetry from unequal texturing biases the restoring response and shifts the onset of chaos. From continuum mechanics, we derive a singular reduced-order model (sROM) that reduces the scale-covered beam to a nonlinear oscillator whose parameters map directly to overlap, scale inclination, damping, forcing, and substrate stiffness. Finite element (FE) simulations validate the model in quasi-static bending and long-time forced response. Stroboscopic regime maps reveal a period-doubling cascade from period-1 to period-2 and period-4, ultimately chaos. Overlap and inclination determine the strength of post-engagement nonlinearity, whereas damping bounds the chaotic operating window. Unequal top-bottom scale distributions break the antisymmetry of the restoring response, generating offset force-displacement laws. This reduced symmetry does not accelerate instability; instead, it delays the onset of chaos and fragments the response into intermittent periodic windows, whereas restoring symmetry can paradoxically widen the chaotic regime. When the texture is sufficiently sparse or steep on one side, it remains dynamically inactive, and the beam behaves as a fully asymmetric one-sided system. The results identify biomimetic scale substrates as a distinct class of contact-rich architectured metasurfaces in which chaos is programmable through geometry rather than large deflection or constitutive nonlinearity.

Recent advances in data-driven modeling have shown that diffusion models can successfully generate synthetic Lagrangian trajectories in turbulent flows. Building on this progress, we extend the method to the joint generation of pairs of Lagrangian velocity trajectories, enabling a fully data-driven representation of turbulent pair dispersion, a long-standing fundamental problem with broad relevance in fluid dynamics. We demonstrate that diffusion models accurately reproduce the evolution of particle-pair separation, including deviations from Richardson's classical scaling law, while simultaneously preserving all key single-particle statistical properties reported in previous studies. These findings underscore the potential of diffusion-based generative models to emulate high-dimensional, multi-scale turbulent dynamics, further establishing them as a powerful tool for scientific modeling and for future geophysical and astrophysical applications.

Neural operators have been increasingly used as data-driven surrogates for time-marching predictions of turbulent flows. However, long-horizon autoregressive prediction is sensitive to error accumulation and the choice of prediction interval. Excessively small time increments may increase temporal redundancy and lengthen rollouts, which can degrade the stability of neural operators in turbulence forecasting. This work pursues a unified objective: stable long-horizon autoregressive prediction at fine temporal resolution for three-dimensional turbulence. We propose a multi-stepsize mixture-of-experts (Ms-MoE) neural operator built on an implicit factorized Transformer (IFactFormer) backbone. The model conditions on a requested relative stride and uses a time-step router to activate scale-specific routed experts together with a shared expert, yielding a single architecture that represents a family of stride-parameterized time-advancement operators. We evaluate the approach on forced homogeneous isotropic turbulence (HIT) and turbulent channel flow using filtered direct numerical simulation datasets. Relative to sampling intervals used in previous studies, we construct training datasets with up to 20 times finer temporal resolution and report long-horizon autoregressive rollouts using qualitative time-slice comparisons and long-time-averaged statistics. Ms-MoE-IFactFormer yields more stable long-horizon rollouts and improved agreement with long-time-averaged statistics on both HIT and turbulent channel flow, suggesting potential for stable time-marching at fine temporal resolution in more complex turbulent flows.

We report on the shape taken by the interface of a liquid bath when hit by a smooth oblique steady jet. When the angle between the jet and the bath decreases below $50^\circ$, a cavity is formed in front of the jet. In the inertial regime we explore, the jet boundary layer detaches in the impact region, thereby delimiting a core jet region outside of which the liquid is mainly in hydrostatic equilibrium. The shape of the outer meniscus is shown to be related to the one outside a tilted fiber piercing the fluid interface. In order to unravel the flow features and separation, we perform direct numerical simulations and show that the flow detachment displays an asymmetry, which results in the acceleration of the liquid below the surface, thereby creating a depression. With this observation, we propose a model balancing the suction force of this depression with the weight of the displaced water and the surface tension force to obtain a prediction for the typical width of the cavity.

This work proposes a statistically enhanced framework to address the instability and limited predictive capability of conventional Galerkin-Proper Orthogonal Decomposition (Galerkin-POD) models. The method reformulates the correction of the Galerkin-projected ODE system as a statistical inverse problem, in which the coefficients are inferred through Bayesian inference. By accounting for model uncertainty arising from POD mode truncation and data uncertainty introduced by data noise and numerical postprocessing, the framework systematically updates the ODE system coefficients using an analytical, sampling-free solution based on Gaussian likelihood and inverse-Gamma priors. The approach is first validated using a self-sustained oscillating flow over a dimpled surface at a moderate Reynolds number (Re=3000), demonstrating stable and accurate reproduction of the temporal dynamics and phase trajectories of coherent structures when compared with direct numerical simulation (DNS). It is then applied to a centrifugal compressor featuring strong tip-leakage vortex breakdown and impeller-diffuser interactions at Re=100000, where the model successfully captures dominant unsteady structures and frequency characteristics despite limited mode retention. Overall, the results show that Bayesian inference substantially enhances the robustness, stability, and predictive fidelity of Galerkin-POD models for compressible flow systems. The proposed methodology combines the physical interpretability of Galerkin projection with the statistical rigour of Bayesian inference, offering a general, computationally efficient, and uncertainty-aware reduced-order modelling framework for complex fluid dynamic applications.

The flow of a liquid metal (LM) in a rectangular duct segment, subject to a uniform transverse magnetic field and uniform heating at the side walls is explored in an ample parameter space using Direct Numerical Simulation (DNS). We modify electrical wall conductivity, (either highly conducting or perfectly insulating) and investigate the effects of the buoyancy force, both in horizontally and vertically orientated ducts. In the latter case, it may be directed either with the flow or against the flow, creating backflow regions. In this parameter space and with the presence of vortex promoters at the inlet of the duct we identify $4$ types of flow. We calculate the Nusselt number $Nu(t)$ for each of them and study the statistical properties to compare their heat transfer capabilities in future fusion reactor blankets.

As one of the cornerstones of fluid mechanics, stability analyses provide essential physical insights into the growth of perturbations and eventual transition to turbulence. However, classical \enquote{frozen-time} stability analyses implicitly assume a time-independence of their base flow and thus fail for \enquote{rapidly} diffusing shear layers. Here, we propose a self-similar ansatz to naturally incorporate the \enquote{diffusive} base-state expansion into the stability operator. Our approach reveals two competing physical mechanisms: an \enquote{expansion wind} delays the Kelvin-Helmholtz instability whereas a diminishing effective viscosity sustains this instability far beyond classical predictions. Direct numerical simulations confirm that our framework accurately captures the instability's extended lifespan, growth rate, and spectral topology, eventually revising the timeline of shear-induced mixing fundamentally.

Dynamic soaring enables sustained flight by extracting energy from wind shear, yet it is commonly understood as a cycle-level maneuver that assumes stable flow conditions. In realistic unsteady environments, however, such assumptions are often violated, raising the question of whether explicit cycle-level planning is necessary. Here, we show that dynamic soaring can emerge from step-level, state-feedback control using only local sensing, without explicit trajectory planning. Using deep reinforcement learning as a tool, we obtain policies that achieve robust omnidirectional navigation across diverse shear-flow conditions. The learned behavior organizes into a structured control law that coordinates turning and vertical motion, giving rise to a two-phase strategy governed by a trade-off between energy extraction and directional progress. The resulting policy generalizes across varying conditions and reproduces key features observed in biological flight and optimal-control solutions. These findings identify a feedback-based control structure underlying dynamic soaring, demonstrating that efficient energy-harvesting flight can emerge from local interactions with the flow without explicit planning, and providing insights for biological flight and autonomous systems in complex, flow-coupled environments.

We study the modulational stability problem for the traveling periodic waves (called Stokes waves) in an infinitely deep fluid by using pseudo-differential operators in conformal variables. We derive the criteria and the normal forms for four bifurcations which are repeated recurrently when the steepness of the Stokes wave is increased towards the highest wave with the peaked profile. The four bifurcations are observed in the following order: (a) new figure-8 bands appearing at each extremal point of speed, (b) degeneration of figure-8 bands resulting in vertical slopes, (c) new circular bands around the origin appearing at each period-doubling bifurcation, and (d) reconnection of figure-$\infty$ bands at each extremal point of energy. Our work uses the analytic theory of Stokes waves developed previously for Babenko's equation. The novelty of our work is the analytic extension of the modulational stability problem for singular pseudo-differential operators in terms of the Floquet parameter. The derivation of the normal form uses some structural assumptions which are known to be true for the Stokes waves. For the first and second bifurcation cycles, we compute numerically with a higher-order accuracy the actual values of wave steepness for which the structural assumptions are satisfied and the numerical coefficients of the normal forms to show the excellent agreement between the normal form theory and the numerical approximations of the spectral bands.

Multiscale Proper Orthogonal Decomposition (mPOD) decomposes fluid flows into energy-optimal modes within prescribed frequency bands by combining Proper Orthogonal Decomposition with a multiresolution analysis (MRA). In its classical formulation, mPOD relies on a filter bank of finite impulse response (FIR) filters, enabling lossless reconstruction while mitigating Gibbs oscillations and temporal ringing. However, the smooth transition bands required for this purpose introduce partial spectral overlap between adjacent scales and require, for each band, the solution of an eigenvalue problem spanning the full temporal dimension. This work introduces a fast spectral formulation of the mPOD that substantially reduces the computational cost. The proposed approach replaces time-domain FIR filters with compact spectral masks enforcing strictly disjoint frequency supports, thereby exactly decoupling the problem across scales. This leads to a block-diagonal correlation operator in spectral space, so that each band can be treated independently. The resulting eigenvalue problems reduce to small systems whose size depends on the number of active frequencies per band rather than the full time dimension. The approach is validated on a synthetic dataset highlighting spectral windowing effects and on experimental particle image velocimetry (PIV) data of a cylinder wake at Reynolds number \(\mbox{Re} \approx 5000\). In both cases, the proposed formulation accurately recovers the modal structures and singular values of the classical mPOD while reducing the computational cost by orders of magnitude.

Turbulent channel flow controlled by spanwise wall oscillations is studied using direct numerical simulations to improve how spanwise forcing reduces skin-friction drag. Harmonic wall oscillations generate a periodic transverse Stokes layer whose thickness $\delta$ is determined by the forcing period $T$. Although an optimal $T$ that maximizes drag reduction is known to exist, its physical significance remains unclear. To elucidate it, we extend the spanwise Stokes layer by augmenting wall oscillation with an additional spanwise body force. In this formulation, $\delta$ and $T$ become decoupled and can be varied independently. The oscillating wall thus appears as a special and suboptimal case of spanwise forcing. Optimal performance is obtained for substantially smaller $T$ and larger $\delta$ than those of the classical Stokes layer. For the conditions examined, with Reynolds number and forcing amplitude held fixed, the maximum drag reduction increases by approximately one third, while the maximum net energy saving improves markedly from $-35\%$ to $+16\%$. These findings suggest that drag-reduction strategies based on spanwise forcing deserve renewed scrutiny: wall oscillation represents only one possible actuation method, and not necessarily the most effective one.

Recent study \cite{rajamanickam2025shear} of non-Boussinesq fluids in narrow channels identified a novel shear-induced horizontal buoyancy force that emerges upon depth-averaging the Navier--Stokes equations. This note demonstrates that this force is formally equivalent to the divergence of a Korteweg stress tensor. Unlike classical Korteweg stresses, which are typically attributed to molecular-scale cohesive potentials or implemented through assumed constitutive relations, we show that this emergent stress arises purely from self-coupled transport where the internal Ostroumov flow is "enslaved" to the local density gradient. We derive explicit expressions for the effective stress coefficients, revealing a fundamental dependence on the Prandtl number and Grashof number and identifying a transition in the effective internal pressure at $Pr=1/2$, which marks the crossover between the internal inertia of the shear flow and the hydrostatic tilting induced by the shear. This correspondence is contrasted with classical Taylor dispersion, where the absence of self-coupling yields only a uniaxial stress. Our results suggest that quadratic Korteweg-type stresses may be a universal manifestation of sub-scale transport in gradient-driven flows, providing a rigorous macro-scale origin for capillary-like stresses in miscible fluids.

Uncertainty in estimating the log-law parameters is arguably the greatest obstacle to establishing definitive conclusions regarding their numerical values and universality. This challenge is exacerbated by the limited number of studies that provide thorough uncertainty analyses of experimental data and fitting procedures, and those that do often adopt different approaches, undermining direct comparisons. The present study applies the generalised least squares (GLS) principle to the log-law velocity profile to establish a standardised, comprehensive framework for quantifying uncertainty in the log-law parameters across datasets. GLS contrasts with ordinary least squares (OLS) and weighted least squares (WLS), which do not account for correlation in errors across measured quantities, as well as with alternative heuristic methods that independently sample primitive variables. Instead, it incorporates a full covariance matrix of the residuals, propagated from the uncertainties in the primitive variables and consistent with the experimental methods employed. The study presents a systematic analysis of the response of the log-law regression model using synthetic data, emulating measurements from a hot-wire anemometer mounted on a linear traverse. This analysis serves as a predictive tool for experimental design, identifying a priori the dominant sources of uncertainty in the log-law parameters and potential mitigation strategies. The study also provides new insights into the correlation between the log-law parameters and proposes a new fitting procedure that eliminates the need to prescribe the location and extent of the log region. The open-source Python implementation of the log-law regression model is available for download on GitHub at this https URL .

A new radiation solver, RAPRAL (RAdiation Prediction based on RAy tracing and Line-by-line) implemented in C++, is developed for simulating high-temperature thermochemical nonequilibrium radiative processes. RAPRAL integrates detailed line-by-line spectral modeling with a ray-tracing solution of the radiative transfer equation, enabling accurate resolution of both spectral features and spatial radiation transport. The adopted methods and their implementation are described in detail. To assess the overall capability and accuracy of RAPRAL, we first focus on the computation of atomic and molecular bulk spectral coefficients. Through comparison with the established code in the literature, RAPRAL demonstrates its ability to accurately capture key spectral features across a wide range of conditions. Moreover, RAPRAL is applied to predict afterbody radiative heating in the Fire II flight experiment, based on a two-temperature, 11-species air flowfield. The results demonstrate that the present approach provides reliable predictions of radiative heat flux and effectively captures the dominant radiation mechanisms. Overall, the presented results demonstrate that RAPRAL is a robust tool for simulating radiative processes in hypersonic air flows, and future versions will extend its capabilities to include species relevant to planetary atmospheres.

We propose a theory based on dynamical systems to explain and predict the occurrence of extreme events, of which critical transitions form a subset. In fast-slow nonlinear systems, we identify a cascade of events preceding extreme events: (i) a slow regime, in which the fast covariant Lyapunov vectors (CLVs) are both tangent to the fast eigenvectors and remain transversal to the slow subspace; (ii) a transition regime, in which the fast eigenvalues become neutrally stable while the fast CLVs are no longer tangent to the fast eigenvectors; and (iii) a critical regime, in which a strong spectral gap in the eigenvalues causes both fast and slow CLVs to become tangent along the dominant fast direction, breaking the transversality between fast and slow subspaces. Building on this cascade, we propose two precursors to forewarn the occurrence of extreme events. We numerically test the theory and precursors on low- and higher-dimensional systems. The proposed precursors predict extreme events and critical transitions with 100% precision and recall. This work opens opportunities for time-forecasting extreme events using theoretically grounded precursors.

Context. Be stars are presently viewed as B-type stars surrounded by a disc fueled by the star itself during episodicexcretion events. The origin of these events are poorly this http URL . This article aims to determine whether or not surface equatorial Kelvin waves can be unstable and therefore canplay a role in the triggering of the Be this http URL . We first derive an analytical expression for gravito-inertial modes in the shallow-water framework. Then, weinvestigate numerically the evolution of equatorial Kelvin modes as system parameters vary. The study is extended tothick-layer configurations with a constant density fluid. We then analyze the stability of these modes under differentialrotation and viscous this http URL . We show that equatorial Kelvin waves still exist in a spherical shell of finite thickness, but that their equatorialconfinement is weaker. At low azimuthal wavenumbers, Kelvin waves are in the inertial waves frequency band and thusget specificities of inertial waves like shear layers associated with singularities of the Poincaré equation. These shearlayers are new dissipative structures for Kelvin waves. When a radial (shellular) differential rotation is imposed, we showthat equatorial Kelvin waves can be destabilised provided that differential rotation and viscosity are in an appropriaterange. The non-monotonic behaviour of the growth rate of the instability is traced back to the rise of a critical layerwhere the fluid azimuthal velocity equals the phase speed of the surface this http URL . This study provides new insights into the behavior of equatorial Kelvin waves in astrophysics, particularlyin rapidly rotating stars. The results reinforce the idea that gravito-inertial waves, and more specifically the equatorialKelvin waves, can be unstable and thus be key parts in the mechanisms leading to the Be phenomenon.

The Euler ensemble was recently supported by large-scale ($4096^3$) direct numerical simulations as the universal statistical attractor of decaying fluid turbulence. Previous mathematical derivations of this ensemble relied on measure-theoretic limits of discrete polygonal loop equations. In this Letter, we present a continuous algebraic derivation. By reformulating the Navier-Stokes equation as a covariant derivative operator flow in the Lagrangian frame, we analytically eliminate advection. Applying Feynman's operational calculus, the 3D non-commutative operator algebra maps to ordering discontinuities (finite-difference jumps) on a 1D momentum loop. This continuous formalism reduces to the discrete, number-theoretic geometric quantization of the Euler ensemble via roots of unity without requiring spatial lattice approximations, demonstrating that macroscopic fluid chaos is a deterministic projection of the Farey sequence.

Turbulent mixing remains one of the primary uncertainties in the modeling of stellar interiors. In stellar evolution simulations, regions where mixing occurs are typically identified using instability criteria. A particularly interesting situation arises when nuclear reactions produce inversions in the mean molecular weight within stellar interiors. Under these conditions, the material can become unstable to either thermohaline or a Rayleigh-Taylor instabilities. We demonstrate that the standard criterion adopted in stellar evolution calculations does not accurately distinguish between these two regimes. We derive an alternative criterion and show that chemically driven convection in stellar interiors might be viable under much smaller mean molecular weight inversions than it is normally assumed. We investigate whether inversions in the mean molecular weight can trigger chemically driven convection above the red giant branch bump (RGBB) or during the helium core flash. We find that the inversion at the base of the convective envelope above the RGBB is too weak and short-lived to sustain steady-state convection. In contrast, rapid carbon production at the base of the He-flash-driven convective zone can maintain a steady chemically driven convective region. This process could significantly alter our understanding of the He-core flash and warrants further study.

Bicuspid valves with crescent-shaped leaflets are found in lymphatic vessels and veins, where their primary function is to prevent reflux and ensure unidirectional flow toward the heart. These valves are passive, and their functionality emerges spontaneously from a complex interplay between the properties of the valve leaflets and the flow patterns developing within the vessel sinus region surrounding the valve. The main function of the valves is to limit retrograde flow, or reflux, but the optimal valve structure has not been well-characterized. Here we investigate numerically how the length of the leaflets affects the valve efficiency in preventing reflux. The valves are subjected to backward flow, akin to that imposed by gravity. We report the flux through the valve orifice as a function of key parameters: valve length, leaflet length, and leaflet rigidity. We monitor the transition in the flow regime - from reflux to complete flow blockage - by varying only the leaflet length. The transition threshold is found to depend strongly on the valve shape and stiffness. We captured these control parameters numerically to evaluate the ability of the valve to close and prevent reflux. This study allowed us to explain reflux observed experimentally in certain incompetent abnormal and immature valves, particularly those with shorter leaflets.

The electrophoretic mobility of a spherical particle is well understood, yet how particle shape modifies this mobility at arbitrary Debye length remains an open question. Here, we compute the electrophoretic mobility of a nearly spherical particle whose surface is described by $r_s(\theta) = a[1 + \varepsilon f(\theta)]$, with $\varepsilon \ll 1$, at arbitrary ratio of particle size to Debye length $\kappa a$. Using a volume-integral formulation combined with domain perturbation techniques, we derive a universal shape correction coefficient $\sigma_2(\kappa a)$ such that the mobility takes the compact form $C_\parallel = f_H(\kappa a)\,[1 + \varepsilon\,c_2\,\sigma_2(\kappa a)]$, where $f_H$ is Henry's function. We show that $\sigma_2$ interpolates between $+1/5$ in the thick-double-layer (Hückel) limit, governed solely by the Stokes drag correction, and zero in the thin-double-layer (Smoluchowski) limit, recovering the classical shape-independence theorem. The perturbation theory agrees quantitatively with exact spheroid solutions for both prolate and oblate orientations. A key finding is that only the $P_2$ (quadrupolar) component of the particle shape affects the mobility at leading order; higher harmonics are electrophoretically silent due to angular selection rules governing the coupling between the dipolar applied field and the shape perturbation. The results in this paper were generated using Claude Code (Anthropic, Opus 4.6 model) with supervision from the authors. Our thoughts on the usage of AI for theoretical research, along with representative prompts from the development process, are provided in the manuscript and Appendix.

The complex dynamics of high-dimensional oscillatory flows can be simplified using phase-reduction analysis, providing a deeper understanding of the flow response to external perturbations. Although phase-based modeling and analysis have been utilized in recent studies on oscillatory fluid flows, their usages are still limited to single-frequency flows due to difficulties in addressing chaotic characteristics induced by multiple frequencies of turbulent flows. In order to overcome this limitation, we propose a data-driven framework that models the dynamics of multi-frequency turbulent flows based on a set of oscillators. The representative oscillators are extracted from the flow field data by training specially designed autoencoders. The oscillator dynamics are modeled through a machine-learning technique using neural networks to accurately predict the multi-frequency oscillatory behavior of turbulent flows. We verify the oscillator-based model of the multi-frequency turbulent flow by applying the proposed data-driven method to the three-dimensional supersonic turbulent flow over a cavity. We show that the extracted oscillators represent the dominant large-scale flow features and reflect the physical characteristics of the turbulent cavity flow. The data-driven oscillator dynamics model accurately forecasts the oscillatory behavior of the turbulent cavity flow for a long period. The proposed data-driven method for reduced-order modeling of turbulent flows with oscillators will enable deeper investigations of perturbation dynamics and control of turbulent flows.

We present three-dimensional direct numerical simulations of turbulent Rayleigh-Bénard convection in a closed rectangular box whose width $L_y$ and length $L_x$ are 0.8 and 2.4 times the height $H$, respectively. The Rayleigh number $Ra$ varies from $10^5$ to $10^{10}$, and the Prandtl number is unity. The advantages of the present configuration are: (a) A relatively stable unidirectional large-scale circulation, consisting of two counter-rotating rolls, fills the cell and fixes the thermal plume ejection- and shear-dominated regions, in contrast to those in closed cylindrical cells. (b) The regions of plume ejection are essentially independent of the sidewalls so that their autonomous existence can be studied. This is because there is some space, or "fetch", for the velocity and thermal boundary layers to develop along the length. (c) This geometry allows one to study the influence of locally thin and thick boundary layers (which follow larger or smaller plume activity) on the scaling of convection properties. In regions of larger plume activity (defined by an incessant movement of plumes), the temperature fluctuation as well as the normalised thermal and viscous dissipation rates decay more slowly with $Ra$ than in regions of lower activity. Both viscous and thermal boundary layers thin down rapidly with increasing distance from the plume ejection region. The local thicknesses of both boundary layers decline more rapidly with $Ra$ in the ejection region than in regions of impact and shear, where they are similar to each other. Despite these details, the global heat transport laws are practically the same as those in other configurations of low to moderate aspect ratios.

Viscous resuspension, the process by which sedimented particles are re-entrained into a fluid under flow, is central to numerous natural and industrial systems, including environmental contaminant transport, riverbed erosion, and biogeochemical cycling. Despite its ubiquity and importance, predicting when and how resuspension occurs remains challenging, particularly under oscillatory shear, where particle interactions are nonlinear, collective, and time-dependent. Here, we examine the resuspension dynamics of dense, non-Brownian suspensions under both steady and oscillatory shear using bulk rheometry and in situ rheo-microscopy over a broad range of particle volume fractions ({\phi}= 0.30 to 0.55). We demonstrate that strain is the key control parameter governing the transition from a sedimented bed to a fully suspended state. This strain-driven onset is mediated by effective interparticle collisions and collective particle motion. We develop a predictive model that captures the observed strain thresholds as a function of volume fraction, allowing for the construction of a new state diagram delineating sedimentation, resuspension, and full suspension regimes. These findings reveal a robust, strain-controlled resuspension mechanism and establish a unified framework for predicting suspension behavior across steady and oscillatory flows, offering new tools for managing particle-laden transport in geophysical, biological, and industrial environments.

We report high-resolution measurements of three-dimensional (3D) turbulence in a rapidly rotating fluid. By decomposing the velocity field into a vertically averaged component and a three-dimensional residual, we show that each dominates distinct frequency ranges: the quasi-2D component at low frequencies and the 3D component at higher ones. This separation is not intrinsic to the flow but strongly depends on the finite vertical span of the measurements. As the vertical scan range increases, the apparent crossover between 2D and 3D-dominated regimes shifts systematically, revealing that the commonly assumed partition is strongly shaped by measurement limits. These findings call into question the usage of the concept of pure 2D manifold, in the theoretical description of rotating turbulence and highlight the need for frameworks that account for resolution-dependent parts of the flow and the coupling between wave-like and vortex-like motions.

Direct numerical simulations are performed to investigate the combined effects of surface roughness and wall heat transfer on spatially developing compressible turbulent boundary layers at $Ma=2.5$. The roughness consists of transverse square bars with $\lambda_x/k=8$ and $k^+ \approx 35$, under adiabatic and wall-cooling ($T_w/T_r = 0.5$) conditions. Dynamically, the conventional zero-moment method fails to yield a consistent zero-plane displacement for the present cavity-type roughness. Instead, a fitting-based optimization procedure is proposed to determine the kinematic virtual origin, which successfully restores the logarithmic behavior. Based on this displacement, Griffin--Fu--Moin (GFM) transformation outperforms the classical van Driest transformation in recovering outer-layer similarity for the velocity defect. Thermodynamically, the physical disparity between momentum form drag and the absence of a corresponding heat transfer mechanism disrupts the classical Reynolds analogy. The effective turbulent Prandtl number ($Pr_e$) deviates severely from unity within the roughness sublayer, leading to the breakdown of the classical Generalized Reynolds Analogy (GRA). To address this, a modified rough-wall GRA (rGRA) is formulated by introducing an equivalent slip-plane or reference-point boundary conditions, which accurately reconstructs the temperature-velocity relationship by bypassing the near-wall thermal heterogeneity. Finally, the refined strong Reynolds analogy (RSRA) is shown to maintain predictive accuracy for fluctuation intensities in the outer layer despite near-wall modulation by roughness and cooling.

We demonstrate that the Ising all-to-all (ATA) model exhibits a range of dynamics, from integrable to chaotic, including mixed behaviour across symmetry blocks within a single system. While other works have explored the dynamics of all-to-all systems by varying parameters, we analyse a fixed set of parameters and examine the dynamics within different blocks. In addition to investigating the dynamical properties, we show that the system remains resilient to noise when the norm of the Hamiltonian representing the noise is close to 1. Our results are presented by mapping each symmetry sector of the system to a kicked top (KT) and observing that KT parameters for each sector depend on its dimension. This system, similar to the Bunimovich billiard for classical chaos, provides a new platform for studying dynamics determined by the symmetry sector, advancing quantum chaos research.

Convolutional neural networks (CNNs) often exhibit poor generalisation in limited training data scenarios due to overfitting and insufficient feature diversity. In this work, a simple and effective chaos-based feature transformation is proposed to enhance CNN performance without increasing model complexity. The method applies nonlinear transformations using logistic, skew tent, and sine maps to normalised feature vectors before the classification layer, thereby reshaping the feature space and improving class separability. The approach is evaluated on greyscale datasets (MNIST and Fashion-MNIST) and an RGB dataset (CIFAR-10) using CNN architectures of varying depth under limited data conditions. The results show consistent improvement over the standalone (SA) CNN across all datasets. Notably, a maximum performance gain of 5.43% is achieved on MNIST using the skew tent map with a 3-layer CNN at 40 samples per class. A higher gain of 9.11% is observed on Fashion-MNIST using the sine map with a 3-layer CNN at 50 samples per class. Additionally, a strong gain of 7.47% is obtained on CIFAR-10 using the skew tent map at 200 samples per class. The consistent improvements across different chaotic maps indicate that the performance gain is driven by the shared nonlinear and dynamical properties of chaotic systems. The proposed method is computationally efficient, requires no additional trainable parameters, and can be easily integrated into existing CNN architectures, making it a practical solution for data-scarce image classification tasks.

The quantum kicked top (QKT) is one of the most widely studied models in quantum chaos, providing a minimal yet powerful framework for exploring the relationship between classical nonlinear dynamics and quantum behavior. Unlike many chaotic systems with infinite-dimensional Hilbert spaces, the QKT possesses a finite-dimensional Hilbert space, making it analytically and numerically controllable while still showing a rich dynamical phenomena. In this chapter, we present a comprehensive introduction to the QKT as a paradigmatic model of quantum chaos. Starting from the classical kicked top, we derive the discrete nonlinear map governing the dynamics on the unit sphere and analyze its phase space structure through fixed points, stability analysis, bifurcations and Lyapunov exponents. We then discuss the role of symmetries, including rotational and time-reversal symmetry, and how their breaking modifies the dynamics. The quantum description is developed using Floquet theory, where the periodically driven spin system is represented by a unitary Floquet operator acting on a $(2j+1)$-dimensional Hilbert space. Within this framework, signatures of quantum chaos such as spectral statistics, entanglement generation and recurrences are discussed. The model also admits an interpretation as a system of interacting qubits, enabling explicit few-qubit realizations and direct connections with quantum information measures through reduced density matrices and entanglement entropy. By linking classical phase space structures with quantum dynamical indicators, the QKT provides a clear setting to investigate the emergence of chaotic behavior in the semiclassical limit. The chapter, therefore, highlights the quantum kicked top as a bridge between nonlinear classical dynamics, quantum chaos and modern quantum information science.

The Melnikov-Arnold integrals (MA-integrals) is a well-known instrument used to measure the splitting of separatrices in Hamiltonian systems. In this article, we explore how calculation of MA-integrals can be used as well to estimate sizes of secondary resonances. Within the standard map model, we show how the newly developed MA-based procedure allows one to estimate the sizes of secondary resonances of any order (up to the order of the optimal normal form), without relying on the cumbersome traditional normalization procedure.

Semiclassical methods have been applied very successfully to describe the nontrivial transition from the quantum to the classical regime in $\textit{single}$-particle or at least $\textit{few}$-particle systems. Challenges on the way to an extension to $\textit{many}$-body systems result from the exponential proliferation of the number of classical orbits in chaotic systems and the exponential growth of the quantum Hilbert-space dimension with the particle number. To circumvent these problems, we apply here our recently developed duality relation. Considering the kicked spin chain as example for a many-body system, we show how the duality relation can be used to extract the classical orbits from the quantum spectrum. For coupled cat maps, we analyze the spectral statistics of chaotic many-body systems and discuss the double limit of large semiclassical parameter and large particle number.

We investigate a many-body interacting system of quantum kicked rotors, where each rotor resides in its respective quantum resonance. Rich many-body dynamics are found to emerge from the interplay between the principal and secondary resonances. In particular, for both the wavepacket and bipartite entanglement entropy, we analytically demonstrate three distinct dynamical regimes -- quadratic spreading (growth), period-2 oscillation, and their hybrid -- governed by the respective symmetries of the relevant potentials. Based on these symmetries, the connection between the wavepacket and the entanglement dynamics is illustrated. Other related issues are also discussed, including higher-order resonance effects, the robustness of the predicted dynamical behaviors, extension to many-body kicked tops, and relevance to experimental studies.

We discuss the semiclassical approximation to transport problems in quantum chaotic systems. The figures of merit are moments of the transmission matrix and of the time delay matrix. After reviewing a few results obtained by treating these matrices are random matrices, we show how expressions for their elements in terms of sums over trajectories lead to diagrammatic formulations that correspond to perturbative calculations. This semiclassical approach agrees with random matrix theory when it should, and allows further elements to be incorporated, like tunnel barriers, superconductors, absorption effects. We also discuss how this approach can be encoded in matrix integrals, resulting in a powerful and versatile theory that is amenable to algebraic solutions.

We investigate iterated function systems (IFS) that randomly alternate between two non-identical one-dimensional maps. Our primary focus is on finite invariant sets exhibiting ``toss-and-catch'' dynamics, in which trajectories alternate between fixed points and periodic orbits of the constituent maps. We derive exact parameter conditions for several toss-and-catch structures in a pair of logistic maps (logistic IFS) and a combination of logistic and tent maps (logistic-tent IFS). Notably, we identify cases in which the invariant set contains bridging points that belong to neither of the invariant sets of the individual maps.

Neutrino billiards serve as a model system for the study of aspects of relativistic quantum chaos. These are relativistic quantum billiards consisting of a spin-1/2 particle which is confined to a planar domain by imposing boundary conditions on the spinor components which were proposed in [Berry and Mondragon 1987, {\it Proc. R. Soc.} A {\bf 412} 53) . We review their general features and the properties of neutrino billiards with shapes of billiards with integrable dynamics. Furthermore, we review the features of two neutrino billiards with the shapes of billiards generating a chaotic dynamics, whose nonrelativistic counterpart exhibits particular properties. Finally we briefly discuss possible experimental realizations of relativistic quantium billiards based on graphene billiards, that is, finite size sheets of graphene.

In generic Hamiltonian systems that are neither completely integrable nor fully chaotic, phase space consists of a mixture of regular and chaotic components. In classical dynamics, transitions between different invariant sets in phase space are strictly forbidden, and these sets act as dynamical barriers to one another. In quantum mechanics, in contrast, wave effects allow transitions through such dynamical barriers. This process, known as dynamical tunneling, refers to penetration through dynamical barriers in phase space and was first recognized in the early 1980s. Since then, various aspects of dynamical tunneling have been elucidated, significantly advancing our understanding of such a novel quantum phenomenon. In this article, we provide an overview of several phenomenological perspectives of dynamical tunneling, including chaos-assisted and resonance-assisted tunneling, and also introduce approaches based on classical mechanics extended into the complex domain. In particular, we seek to clarify what is meant by the common claim that "chaos leads to an enhancement of the tunneling probability", which is often made when dynamical tunneling is dressed. We discuss what regime this refers to and, if such an enhancement occurs, what its likely origin is.

Spatiotemporal chaotic systems are difficult to characterize in a model-free manner because of their high dimensionality, strong nonlinearity, and sensitivity to initial conditions. Coupled map lattices, as a representative class of extended nonlinear systems, exhibit diverse regimes such as frozen random pattern, defect chaotic diffusion, and fully developed turbulence. In this work, we propose an ensemble version of multiplexing local reservoir computing for the data-driven characterization of spatiotemporal chaos. By constructing multiple base learners with randomized hyperparameters and combining their outputs, the method improves prediction robustness and quantifies predictive uncertainty through ensemble spread. More importantly, we show that this uncertainty contains direct dynamical information. It identifies frozen positions in frozen random pattern, supports the estimation of defect diffusion coefficients in defect chaotic diffusion, and provides an effective indicator of chaotic intensity in fully developed turbulence. Analyses of the spatial power spectrum and Lyapunov exponent spectrum further support the consistency between the uncertainty field and the intrinsic dynamical properties of the system. These results show that ensemble reservoir computing can serve not only as a prediction tool but also as a data-driven framework for the dynamical characterization of high-dimensional nonlinear systems.

This chapter gives an overview of transport problems where chaotic dynamics of the system plays a crucial role. We begin with single-particle transport problems and then come to conservative and then dissipative systems of identical particles, which follows the historical way of developing the theory of Quantum Chaos over the past 40 years. We also include brief descriptions of key laboratory experiments on the discussed transport problems.

Through semiclassical methods the subject of quantum chaos motivates and depends on Hamiltonian chaos research. Presented here is a selection of Hamiltonian chaos topics that in this way get directly related to any of a variety of quantum chaos research problems. The chapter begins with a description of various useful theoretical and computational tools of chaos research, e.g.~surfaces of section, paradigms of chaos, stability analysis, and symbolic dynamics... This is followed by discussions regarding the geometry of chaos, how chaotic systems respond to perturbations, and the complexification of Hamiltonian dynamics. The emphasis is on intuitive explanations and illustrations of various ideas with the references containing more mathematically rigorous expositions.

In quantum systems with a classical limit, advanced semiclassical methods provide the crucial link between phase-space structures, reflecting the distinction between chaotic, mixed or integrable classical dynamics, and the corresponding quantum properties. Well established techniques dealing with ergodic wave interference in the usual semiclassical limit $\hbar \to 0$, where the classical limit is given by Hamiltonian mechanics of particles, constitute a now standard part of the toolkit of theoretical physics. During the last years, these ideas have been extended into the field theoretical domain of systems composed of $N$ indistinguishable particles, aka quantum fields, displaying a different type of semiclassical limit $\hbar_{\rm eff}=1/N \to 0$ and accounting for genuine many-body quantum interference. The foundational concept behind this idea of many-body interference, the many-body version of the van Vleck-Gutzwillers semiclassical propagator, is explained in detail. Based on this the corresponding semiclassical many-body theory is reviewed. It provides a unified framework for understanding a variety of quantum chaotic phenomena addressed, including random-matrix spectral correlations in many-body systems, the universal morphology of many-body eigenstates, interference effects kin to mesoscopic weak localization, and the key to the scrambling of many-body correlations characterized by out-of-time-order correlators.

Mesoscopic devices, with system sizes in the range of several to several dozens wavelengths, represent paradigmatic model systems for the observation of quantum chaotic behaviour based on semiclassical concepts. Those electronic and photonic billiard cavities are small enough for interference effects not to be ignored. Nonetheless, the classical ray or particle tracing picture can often provide a substantial understanding of the dynamics of the system along the lines of classical-quantum, or ray-wave correspondence. This well-established principle turns out to be particularly useful when applied not only in real space, but by extending it to phase space such that both location and momentum information can contribute to a deeper and more comprehensive understanding of the dynamical behaviour.

One of the fundamental manifestations of classical chaos is exponential sensitivity to initial conditions that is, two trajectories starting from nearly identical initial states diverge exponentially over time. This behavior is quantified by the Lyapunov exponents. Due to the unitary nature of quantum mechanics, such exponential divergence is elusive in quantum systems. As a result, several alternative quantities have been proposed and studied in recent years to capture analogous behavior. In this article, we present a pedagogical overview of three such quantities that have been the focus of intense research in recent years: the Loschmidt echo, out-of-time-order correlators (OTOCs), and Krylov complexity.

Out-of-Time-Order Correlators (OTOCs) quantify quantum information scrambling, but their connection to localized phase-space structures, such as chemical transition states, requires formal development. We derive a leading-order semiclassical expansion for the local microcanonical OTOC in systems with an index-1 saddle point, expressing the scrambling rate as a coherent sum over unstable periodic orbits on the Normally Hyperbolic Invariant Manifold (NHIM). Valid in the semiclassical limit and the intermediate-time regime before the Ehrenfest time, our derivation utilizes the Normal Form theory of the transition state, which transforms the Hamiltonian near the saddle into an integrable (though generally non-separable) form dependent on conserved actions. We outline the derivation of the microcanonical trace, the semiclassical propagator for integrable systems, the factorization of the stability matrix, and the Schur complement reduction of the stationary phase approximation. Our result extends periodic-orbit trace methods to scrambling observables, yielding a local instability exponent {\Lambda}(J) governing the leading semiclassical growth window. As a special case, when the observation time coincides with the intrinsic periods of the contributing orbits, the trace sum reduces to an effective 1.5{\Lambda} scaling, resulting from the competition between local hyperbolic growth and wavepacket dilution. This simplified form is conditional; the full expansion retains a coherent sum over orbit periods. Finally, we discuss how the dependence of the instability on transverse actions establishes a theoretical mechanism for mode-selective control of scrambling, and outline a numerical evaluation strategy to test these predictions.

The kicked rotor provides a simple yet powerful model for introducing many of the central concepts of classical and quantum chaos. Despite its apparent simplicity, it exhibits rich dynamical behavior and has found applications across a wide range of fields, including atomic and optical physics, condensed matter physics, and emerging quantum technologies. This chapter begins by exploring foundational ideas using the kicked rotor as a unifying framework. We first discuss the transition from regular to chaotic motion in the classical system, and then introduce key quantum phenomena such as dynamical localization and quantum resonances. Special attention is devoted to the emergence of characteristic time scales and their role in the quantum-classical correspondence. To make these ideas more concrete, we also provide a brief overview of experimental realizations of the kicked rotor and its variants, illustrating how theoretical concepts are implemented in practice. In the second part of the chapter, we guide the reader toward more recent and advanced developments. Topics include near-resonant dynamics, topological features of kicked systems, the emergence of quantum dynamical phases inferred from classical transport properties, and extensions to non-Hermitian physics. We conclude with a discussion of open problems and future perspectives, outlining directions in which the kicked rotor continues to offer valuable insights.

The notion of Shannon entropy is crucial for the theory of classical information. In quantum information theory, an analogous key role is played by the von Neumann entropy: quantum information processing is closely related to entropy dynamics. This reveals a direct link with the theory of quantum chaotic systems, which can be characterized by a positive entropy production. Furthermore, noise, which inevitably affects any quantum system, can be modeled by a random quantum operation or by coupling to an environment in a generic chaotic state. In this contribution, we emphasize the universality of quantum chaotic dynamics and discuss its implications for quantum information processing.

Factor models characterize the joint behavior of large sets of financial assets through a smaller number of underlying drivers. We develop a network-based framework in which factors emerge naturally from the structure of interactions among assets rather than being imposed statistically. The market is modeled as a system of coupled iterated maps, where assets' return depends on its own past returns and those of related assets. Effectively modeling the influence of irrational traders whose decisions are based on the past movements of a collection of stocks. The interaction structure between stock returns is defined by a coupling matrix derived from an orthogonal transformation of a Laplacian matrix that gradually links initially isolated clusters into a fully connected network. Within this structure, stable patterns of co-movement arise and can be interpreted as financial factors. The relationship between the initial clustering and the number of observed factors is consistent with a center manifold reduction. We identify an optimal regime in which assets' variance is effectively explained by the set of factors produced by the network. Our framework offers a structural perspective based on interaction-based factor formation and dimension reduction in financial markets.

The 100,000-year problem concerns the dominant period of glacial-interglacial cycles over the past 800,000 years and their correlation with Earth's orbital eccentricity, despite eccentricity's weak influence on solar radiation. Two theories compete: the astronomical theory, in which orbital forcing drives the cycles with amplification from Earth system feedbacks, and the geochemical theory, in which internal dynamics dominate with orbital forcing synchronising oscillations. We investigate these theories using conceptual models. Augmentations to the Budyko energy balance model fail to reproduce the 100,000-year period, revealing formulation limitations. Linearised versions of existing non-linear ice volume models perform comparably to their full counterparts, indicating the data does not necessitate non-linear dynamics. We develop two simple linear models: a feedforward model aligned with the astronomical theory and a feedback model aligned with the geochemical theory. The feedforward model reproduces the ice volume record well and offers a novel explanation for the absence of eccentricity's 400,000-year period, arising from oceanic heat storage and tropospheric energy responding with differing phase lags. Conservative estimates show bulk ocean temperature variation can be explained by eccentricity alone, challenging the geochemical theory's core assumption. We also show that widespread use of Q65 may bias models towards geochemical explanations by underrepresenting eccentricity. The feedback model's improvement is concentrated around Marine Isotope Stage 11, suggesting this anomalous interglacial reflects Earth-based events rather than a general requirement for feedback mechanisms. We conclude that 800,000 years of glacial cycles can be largely reproduced by a linear astronomical model, emphasising the importance of parsimony when interpreting palaeoclimate data.

Self-gravitating systems of $N$ particles are chaotic. We wonder how chaotic the Galaxy is, and what the consequences are. We therefore simulate the dynamical evolution of a galaxy-scale distribution of point masses in order to measure the degree of chaos in such a system. These calculations were performed using the softened gravitational $N$-body tree-code Bonsai, with up to 40 million equal-mass particles. Smaller simulations were performed to establish the scaling of the Lyapunov time $t_L$ with $N$. We establish the relations between the degree of chaos, the number of particles, and the softening length in the gravitational force calculation of large-scale $N$-body simulations. The moment the bar forms appears insensitive to infinitesimal perturbations to the initial realisation. In contrast, the bar strength and its further evolution sensitively depend on such perturbations. Interestingly enough, the run-to-run variation in the bar strength has its maximum around the maximum bar strength, and drops to the moment the bar buckles. The galaxies we simulated are highly chaotic, but the softening in the simulations suppresses chaos. Still, our models show considerable variations in the macroscopic behaviour due to infinitesimal perturbations to the initial conditions. Real galaxies, however, should be orders of magnitude more chaotic than our simulations, and we are unable to quantify their consequences. Smooth galactic potentials to study individual stellar orbits should be handled with caution on timescales longer than the Lyapunov time. Extrapolating to the number of stars in the Galaxy, ignoring planets and other minor bodies, we conclude that the Milky Way-size galaxies are chaotic on a timescale $\lesssim 0.1$ Myr.

This chapter offers a principled approach to the prediction of chaotic systems from data. First, we introduce some concepts from dynamical systems' theory and chaos theory. Second, we introduce machine learning approaches for time-forecasting chaotic dynamics, such as echo state networks and long-short-term memory networks, whilst keeping a dynamical systems' perspective. Third, the lecture contains informal interpretations and pedagogical examples with prototypical chaotic systems (e.g., the Lorenz system), which elucidate the theory. The chapter is complemented by coding tutorials (online) at this https URL .

The Gaussian radial function-based Regression (RfR) method is a data-driven modeling approach that utilizes physically understandable variables from scalar time series, constructed using delay coordinates and Gaussian radial basis functions. Even when a model successfully describes an approximate trajectory of the original system, data-driven models rarely reconstruct negative Lyapunov exponents of chaotic dynamics. An ''ideal model'' should reconstruct the dynamical structure, including the negative (physically dominant) Lyapunov exponents. Comparing the ideal model and the non-ideal model, we investigate the geometric structure of the attractor of such models using the Lyapunov exponents and the corresponding Lyapunov vectors. Our investigation suggests that the ideal model reconstructs the original system's attractor as a time-delay embedding. By applying the results, we search for a method to construct an ideal model, which persists against the change in hyperparameters.

Targeted energy transfer (TET) from a Van der Pol oscillator coupled to a nonlinear energy sink (NES) is investigated under the action of a high-frequency external drive, which tunes the effective natural stiffness and promotes resonance capture, facilitating energy transfer. Using \textit{direct partition of motion} with \textit{complexification averaging}, the mechanism of energy flow and instability control through \textit{hopf bifurcation} is characterized. A spectrally evaluated Q-factor, based on FFT at the effective slow frequency, captures the resonance peaks indicating the efficient energy transfer. Finally, the energy-dissipation metric is consistent with these Q-maps and identifies the regions where transient energy pumping is most effective.

We investigate whether ideas from symplectic topology, in particular Gromov's non-squeezing theorem and symplectic capacity, can provide useful geometric insight into classical reaction dynamics near an index-1 saddle. Using Poincaré-Birkhoff normal form theory, we describe the phase-space structures that organize transport through the transition-state region, including dividing surfaces, normally hyperbolic invariant manifolds (NHIMs), and the associated bath-action geometry. For quadratic saddle-center and saddle-center-center models, the normal-form geometry identifies natural bath-action area scales associated with the reactive bottleneck. For anharmonic systems (Eckart-Morse and Eckart-Morse-Morse), we formulate corresponding candidate symplectic width scales -- based on transverse bath actions -- using high-order normal forms for bounded local neighborhoods associated with the reaction bottleneck near the saddle. We then present two numerical illustrations: the backward propagation of a locally coupled phase-space ball to examine linear non-squeezing behavior, and a bath-localized ensemble calculation in an anharmonic normal-form model. These computations are consistent with the idea that heavily biasing the initial phase-space distribution of an ensemble toward the high-action boundaries of the bath modes can induce a severe finite-time dynamical delay, influencing reactivity in ways not captured by total phase-space volume or flux alone. The results suggest a new geometric perspective on mode selectivity and reaction bottlenecks, while highlighting open mathematical questions concerning the precise relation between these candidate width scales and genuine symplectic capacities of suitably defined reactive neighborhoods.

Solute mixing plays a pivotal role in a broad spectrum of chemical and biological processes across natural and engineered porous media. However, current understanding of mixing dynamics remains largely constrained to steady flows in fully or partially water-saturated environments. Multiphase flow systems are generally unsteady, with moving fluid interfaces and flow paths that change in time. Despite the widespread occurrence of dynamic multiphase flows, their impacts on solute mixing are largely unknown. Here, we use experiments and numerical simulations to investigate the effect of dynamic two-phase flow on the stretching and folding of fluid elements, a fundamental mechanism driving solute mixing and reactions in porous media. We find that dynamic two-phase flows induce chaotic mixing, characterized by exponential stretching of fluid elements, leading to strongly enhanced mixing compared to steady single phase flows. By extensive numerical multiphase flow simulations, we establish dynamic steady states where we reliably measure the mean fluid stretching rate as a function of flow rate. We show that stretching is maximized at an optimum flow rate which balances fluid shear deformation against the frequency of flow reorientation by the intermittent motion of the fluid interface. The findings are rationalized by a mechanistic model linking basic multiphase flow characteristics to the stretching rate, opening new perspectives to understand and control mixing and reactions in a wide range of multiphase flow systems.

Reservoir computing (RC) is a computational framework known for its training efficiency, making it ideal for physical hardware implementations. However, realizing the complex interconnectivity of traditional reservoirs in physical systems remains a significant challenge. This paper proposes a physical RC scheme inspired by the biological vestibular system. To overcome hardware complexity, we introduce a designed uncoupled topology and demonstrate that it achieves performance comparable to fully coupled networks. We theoretically analyze the difference between these topologies by deriving a memory capacity formula for linear reservoirs, identifying specific conditions where both configurations yield equivalent memory. These analytical results are demonstrated to approximately hold for nonlinear reservoir systems. Furthermore, we systematically examine the impact of reservoir size on predictive statistics and memory capacity. Our findings suggest that uncoupled reservoir architectures offer a mathematically sound and practically feasible pathway for efficient physical reservoir computing.

This paper presents an improved Matlab routine, FO_LE, for the numerical computation of Lyapunov exponents of fractional-order systems modeled by Caputo's derivative. It is conceived as an enhanced version of the former FO_Lyapunov and FO_NC_Lyapunov codes for commensurate and non-commensurate orders, respectively. The proposed approach replaces the Gram-Schmidt orthogonalization procedure with QR-based reorthonormalization and uses the new quadratic LIL predictor-corrector scheme for the integration of the extended variational system. Compared with the former implementations, the present routine benefits from the higher order of the fractional integrator LIL and applies to both commensurate and non-commensurate models. Like the previous code, FO_LE retains the full memory structure of the underlying Caputo model. The Matlab code for the LIL solver and for the computation of Lyapunov exponents with FO_LE are provided, while a fast implementation of LIL for commensurate and non-commensurate orders, LIL_nc, is available on MathWorks File Exchange. A benchmark problem with exact solution is used to compare the LIL-based solver with ABM-type methods, whereas the Rabinovich-Fabrikant system illustrates the computation of Lyapunov exponents in different dynamical regimes. The results indicate that the proposed implementation is a compact, robust, and efficient tool for the numerical study of stability and chaos in fractional-order systems.

We study the nature of chaos in finite and infinite dimensional systems through a comparison between the Kuramoto Sivashinsky (KS) equation, the Lorenz system, and a Lorenz type reduction of the KS equation proposed by Wilczak. Numerical simulations of the KS equation reveal intrinsic spatio temporal chaos, with disorder evolving simultaneously in space and time. In contrast, the Lorenz system and the Wilczak reduction exhibit low dimensional temporal chaos lacking spatial complexity. Lyapunov exponent analysis highlights the finite-dimensional convergence properties of the reduced systems and underscores the fundamentally different dynamical nature of chaos in the KS equation. In particular, we demonstrate that low-dimensional reductions may reproduce transient chaotic signatures but do not necessarily retain the structural properties of infinite-dimensional dissipative systems.

Irreversible transport in time-periodic flows is commonly attributed to vorticity, nonlinear forcing, or symmetry breaking. We show that finite-memory reconstruction of the velocity gradient generates a purely geometric mechanism for transport even when the instantaneous flow remains locally irrotational at all times. Memory promotes the velocity gradient to a history-dependent connection along particle trajectories whose noncommutativity produces a finite curvature over one forcing cycle. The associated holonomy generates a measurable loop displacement controlled solely by the dimensionless parameter {\omega}{\tau}_m, which quantifies the phase mismatch between forcing and reconstruction. The predicted scaling is consistent with independently reported measurements across distinct oscillatory flow configurations, supporting the interpretation of memory-induced curvature as a minimal geometric origin of irreversible transport in periodically driven continua.

In this paper, the Ensemble Kalman Filter is compared with a 4DVAR Data Assimilation System in chaotic dynamics. The Lorenz model is chosen for its simplicity in structure and its dynamical similarities with primitive equation models, such as modern numerical weather forecasting. It was examined whether the Ensemble Kalman Filter and 4DVAR are effective in tracking the control for 10%, 20%, and 40% of error in the initial conditions. With 10% of noise, the trajectories of both methods are almost perfect. With 20% of noise, the differences between the simulated trajectories and the observations, as well as the true trajectories, are rather small for the Ensemble Kalman Filter but almost perfect for 4DVAR. However, the differences become increasingly significant at the later part of the integration period for the Ensemble Kalman Filter, due to the chaotic behavior of the system. For the case with 40% error in the initial conditions, neither the Ensemble Kalman Filter nor 4DVAR could track the control with only three observations ingested. To evaluate a more realistic assimilation application, an experiment was created in which the Ensemble Kalman Filter ingested a single observation at the 180th time step in the X, Y, and Z Lorenz variables, and only in the X variable. The results show a perfect fit of 4DVAR and the control during a complete integration period, but the Ensemble Kalman Filter shows disagreement after the 80th time step. On the other hand, a considerable disagreement between the Ensemble Kalman Filter trajectories and the control is observed, as well as a total failure of 4DVAR. Better results were obtained for the case in which observations cover all the components of the model vector.

The inverse energy cascade in turbulent Taylor-Couette flow is studied in line with the results of the large eddy simulation. The simulation results show that the inverse energy cascade first occurs within the core region of the flow channel of the Taylor-Couette flow at higher Reynolds number. It is uncovered that this phenomenon is induced by the pulsed zero shear stress resulting from the singularities of the Navier-Stokes equation. In the core area between the two cylinders, the shear stress is nearly zero at higher Reynolds number. The turbulence generated there has high turbulent energy due to discontinuity of the tangential velocity. Since the energy transfer between the fluid layers is inhibited due to the low shear stress, the turbulent energy cannot be transferred along the radial direction, and small-scale vortices with high turbulent energy are produced. These small-scale vortices are located with the large-scale vortices and cannot be dissipated owing to low shear stress. A peak in the energy spectrum at middle frequency (or wave number) is formed due to the concentration of the small-scale vortices. As the number of the singular points of the Navier-Stokes equation increases with the increasing Reynolds number, the region with zero shear stress expands along the radial direction, intensifying nonlinear instability and energy accumulation. This, in turn, leads to more prominent peaks in the energy spectrum, resulting in a more pronounced inverse energy cascade.

Reservoir observers provide a data-driven approach to the inference of unmeasured variables from observed ones for nonlinear dynamical systems. While previous studies have demonstrated wide applicability, their performance may vary considerably with different input variables, even compromising reliability in the worst cases. To enhance the performance of inference, we integrate residual calibration and attention mechanism into the reservoir observer design. The residual calibration module leverages information from the estimation residuals to refine the observer output, and the attention mechanism exploits the temporal dependencies of the data to enrich the representation of reservoir internal dynamics. Experiments on typical chaotic systems demonstrate that our method substantially improves inference accuracy, especially for the worst cases resulting from the traditional reservoir observers. We also invoke the notion of transfer entropy to explain the reason for the input-dependent observation discrepancy and the effectiveness of the proposed method.