We carry out a numerical investigation of the Oberbeck--Boussinesq equations in a fluid layer inclined against gravity. Equilibria containing different numbers of co-rotating rolls are computed. Mixed-mode branches connect branches containing states with four and six identical co-rotating rolls. These branches display two contrasting routes to reducing (or increasing) the number of rolls, one in which rolls disappear (or appear) and another route in which rolls merge (or split). These results are interpreted in light of the $(2,3)$ mode interaction scenario.

Fluid--fluid interfaces are seldom clean due to the presence of surfactants, which can strongly modify their dynamics. Interfacial flow redistributes surfactant, creating concentration gradients whose Marangoni stresses can immobilise the interface. By contrast, surface diffusion or exchange with the bulk can reduce these gradients and restore interfacial motion. We study this competition using a two-dimensional model of a surfactant-covered leaky-dielectric drop in a uniform electric field. Electric stresses drive the classical Taylor circulation, in which the drop remains non-rotating. At stronger fields, convection of interfacial charge can destabilise this state and produce the Quincke regime, characterised by spontaneous mean rotation. Using a fully nonlinear model on a fixed circular interface, we show that weak surfactant diffusion allows Marangoni stresses to suppress the Taylor circulation almost completely. Quincke rotation remobilises this nearly arrested interface and restores a substantial straining circulation, whose orientation varies with the applied field. Surfactant also shifts the critical field for rotation and can change the onset from subcritical to supercritical. Surface diffusion and exchange with a well-mixed bulk reservoir can produce similar flow responses and rotation thresholds despite different surfactant distributions. The spatial variation of surfactant concentration therefore provides additional information for distinguishing the two transport mechanisms.

We present a predictive fluid mechanics model to calculate pressure drops (0.25 atm) and fluid velocities (2.50 m/s) governed by localized phase change and choking phenomena in a capillary-constrained, coaxial microfluidic actuator. Driven by near-infrared thermal absorption, the analytical framework describes how energy deposition drives vapor cavity growth and subsequent cavitation bubble collapse, inducing a transient suction force across a curved, two-radii Young-Laplace capillary boundary. Velocity drops are derived from closed-form analytical equations that explicitly couple vapor volume dynamics with non-linear flow area restriction and fluid drag. The model predicts a maximum boundary layer wall shear stress of 30.06 Pa at the target interface. Crucially, this shear magnitude matches the physical threshold required to mechanically strip surface contaminant boundary layers while remaining below the damage threshold of underlying target substrates. Finally, we formulate a closed-form expression for the maximum allowable liquid inlet temperature required to prevent thermal saturation and sustain stable, continuous microfluidic suction cycles. These equations establish direct engineering design rules for optimizing phase-change microfluidic actuators and next-generation coaxial fluidic systems.

Driven-dissipative oscillator networks have been proposed to simulate spin models on physical hardware, mostly focusing on systems of binary (Ising) spins, or systems of spin vectors in low dimensions. The equalized hyperspin machine was recently introduced to provide a single platform to simulate general models of $N$ coupled spin vectors with tunable dimension $D$, realizing dynamical annealing protocols to vary the spin dimensionality in time. These schemes are limited to real spins coupled via real coupling matrices. We propose a generalization of the hyperspin machine that works with complex fields and deals with complex Hermitian coupling matrices, implementing an amplitude equalization scheme. This system, which we name complex hyperspin machine, can work on optimization problems with complex valued hyperspins that can be cast on complex $D$-vector Hamiltonians. We benchmark the machine against a differential evolution (DE) algorithm on complex $D=2$ hyperspins up to $N=80$, showing that the fraction of instances where a lower-energy solution is found grows with system size and coupling density, reaching $92.5\%$ at the largest considered sizes. When the DE finds a lower-energy solution, the machine still reaches a median relative energy deviation that lies between $10^{-15}$ and $10^{-12}$ while running at substantially lower computational cost. Using the complex nature of the field, we introduce a new dimensional reduction protocol that we name symmetry quenching, which collapses complex variables that map to XY spins onto real Ising spins by switching on the parametric pump. We show on Max-Cut instances with known ground states that symmetry quenching outperforms a fixed-pump Ising machine, reaching exact ground states in the presence of equalization. We scale the system to $N=10^6$ hyperspins, or $8\times10^6$ dynamical variables, on a Hermitian sparse two-dimensional lattice.

The modulus plateau is widely regarded as a hallmark of topological entanglement in homopolymer melts and has been used to identify entanglement in semiflexible conjugated polymers. Using regiorandom poly(3-alkylthiophenes) as a model system, we show that their plateau elasticity relaxes through an Arrhenius process decoupled from segmental and terminal dynamics, reorganizes persistently under mechanical perturbation, and varies systematically with side-chain length. These behaviors are hard to reconcile with a purely topological-entanglement picture and instead support a transient network dominated by reversible interchain associations, consistent with {\pi}-{\pi} interactions between conjugated backbone segments. The results thus demonstrate that plateau elasticity alone does not uniquely identify topological entanglement in conjugated polymers. More broadly, they identify the strength and lifetime of interchain association as molecular design parameters linking backbone packing to stress relaxation, viscoelastic properties, and processability in conjugated polymers, complementing their established role in electronic structure and charge transport.

In this contribution, we review existing multivalent models of Influenza A Virus (IAV) systems to study virion dynamics and design of multivalent entry blockers. We review existing biochemical estimations of the dissociation constants and catalytic activities of the two virion ligands [hemagglutinin (HA) and neuraminidase (NA)], which can be used to develop quantitative theories and experiments. Multivalent models are statistical mechanics frameworks for studying the simultaneous interaction of multiple reversible ligand-receptor bonds. They quantify the effects of both combinatorial entropy terms and single-molecule ligand-receptor affinities. Multivalent frameworks led to the rationale of superselectivity, the ability of probes to sense specific concentrations of conjugated receptors. Multivalent models guided the design of antiviral nanomedicines constituted by polymeric scaffolds conjugated with small molecules such as sialic acid receptors targeting the ligands on the surface of the virion. Importantly, neuraminidase is an enzyme that limits the number of host-guest bonds through receptor desialylation. Like active particles, neuraminidase activity enhances virion motility in the extracellular medium. Modeling the dynamics of Influenza A virions requires developing out-of-equilibrium multivalent models.

Non-volatile solutes accumulate near a receding drying front, generating concentration gradients that can drive directional colloidal transport by diffusiophoresis. This dynamic spatial arrangement of colloidal particles could affect the microstructure and macroscopic properties of the dried film. Here, we combine experiments and theory to investigate polystyrene particles suspended in electrolyte solutions drying within a capillary tube. By varying the electrolyte composition and ambient relative humidity, we show that evaporation-induced ion gradients drive particles toward the liquid-gas interface and enhance interfacial accumulation, whereas slower drying at higher humidity weakens the gradient and particle migration. We use the heat balance integral method to predict the transient solute field for a receding interface and couple it to particle transport to capture the observed particle trajectories and accumulation trends. These results identify background electrolytes and drying rate as coupled controls on particle distribution and provide a predictive framework to optimize formulation and processing parameters for manufacturing slurry-based materials, such as battery electrodes and turbine coatings.

If a liquid is cooled rapidly, it may fall out of equilibrium before it can crystallize. It may, however, crystallize later from the nonequilibrium glassy state. Using the Random First-Order Transition (RFOT) theory of glasses, we discuss a variety of mechanisms of crystallization as a route to devitrification. Ordinary nucleation is sped up by the frozen in energy of the glass relative to the liquid. At sufficiently low temperatures, a mechanism of nanonucleation appears, producing nanometer scale crystal inclusions in the glass. Nanocrystallization depends strongly on the local fluctuations in stability, and the transition from classical nucleation and growth to nanocrystallization occurs dominantly through rare, less stable glassy regions that percolate through space, producing an additional dramatic speedup in the crystal nucleation and growth rates. Similar fluctuations in local stability also explain anomalies of crystal growth in deeply supercooled systems.

Within classical nucleation theory, crystal nucleation requires sufficient supersaturation, but is suppressed at low temperatures due to reduced molecular mobility, leading to a maximum nucleation rate typically above the glass transition temperature $T_g$. Here, we experimentally show that this conventional picture breaks down in a biocompatible polymer poly(2-methoxyethyl acrylate)(PMEA)/water mixture. We find that the number of nuclei increases dramatically below $T_g$, with the effective nucleation rate exhibiting an unusual maximum at approximately $T_g-10$ K. Calorimetric experiments reveal a strong temperature-history dependence of cold crystallization of water in hydrated PMEA, which is explained by the observed nucleation behavior. We propose that the unusual enhancement of nucleation below $T_g$ provides a key mechanism linking high glass-forming ability and cold crystallization upon heating, thereby explaining the striking asymmetry in crystallization behavior between cooling and heating. Our findings suggest that a hidden nucleation-rate maximum below $T_g$ may also underlie cold crystallization in other glass-forming liquids.

Precise control of molecular heteroepitaxy offers a route to multilayer architectures with well-defined interfaces. However, the role of intramolecular flexibility in epitaxial matching remains insufficiently understood. Here, we investigate the heteroepitaxy of intact 1,3,5-tris(4-carboxyphenyl)benzene (BTB) on a molecular $\delta$-layer composed of fully deprotonated BTB molecules on Ag(111). Combining scanning tunneling microscopy, low-energy electron microscopy and diffraction, X-ray photoelectron spectroscopy, and density functional theory, we identify the key interactions controlling molecular packing and epitaxial growth. We show that intermolecular bonding motifs are preserved on the molecular template, but their lattice parameters and molecular conformations change as compared to a silver surface. Individual molecules exhibit distinct appearances in scanning tunneling microscopy, consistent with site-dependent conformational variations identified by theory. Our calculations reveal that the competition between molecule-substrate interactions and conformational energy produces different compromise geometries, resulting in conformational frustration at the epitaxial interface. Crucially, constraining BTB into a planar geometry changes the preferred lateral adsorption positions, demonstrating that molecular flexibility directly modifies the energetic preferences for epitaxial registry. Comparison with more rigid molecular overlayers further supports this interpretation. Our findings reveal that molecular flexibility contributes to epitaxial matching by allowing unfavorable molecule-substrate interactions to be compensated by energetically favorable conformations while preserving the intermolecular network.

Weakly conducting spheres suspended in a leaky dielectric fluid can undergo spontaneous Quincke rotation when the applied electric field exceeds a critical value. We investigate how electric and hydrodynamic interactions modify this instability and the subsequent rotation of two spheres at fixed separation and orientation. Starting from electric dipole and hydrodynamic rotlet interactions, we develop a systematic far-field asymptotic theory. Away from onset, slow drift of the rotation axes makes a regular expansion fail at long times. A multiple-scale expansion gives slow phase equations that select the axes according to pair orientation and field strength. Near onset, weak interactions produce corrections comparable to the isolated rotation magnitude. A detuned multiple-scale expansion gives coupled equations for the transverse dipole amplitudes. Their linearization identifies four collective rotation modes, whose critical fields and steady branches with one active mode are determined together with their stability. At leading order near onset, electric interaction shifts all four modal thresholds equally, whereas hydrodynamic interaction makes counter-rotation appear first for pair angles below $\cos^{-1}(1/\sqrt3)\simeq54.7^\circ$ and co-rotation above it. Away from onset, the angle separating stable counter-rotation from stable co-rotation increases with field strength. Boundary element method (BEM) simulations place onset within a field interval for each configuration and resolve the growth and relaxation of rotation. Steady-speed comparisons show how pair orientation changes the balance between electric and hydrodynamic effects. We compare the unexpanded dipole-rotlet model of Das and Saintillan [Phys. Rev. E 87, 043014 (2013)] with our asymptotic theory and BEM simulations.

The natural environments habitable to life are inseparable from dissipative and entropic forces, which mandate active matter to operate on constant fluxes of energy and momentum to survive and propagate through spacetime. In contrast to fundamental particles which are characterized by energy and momentum, we postulate that energy expenditure rate and momentum generation rate are the fundamental dynamical quantities driving this evolution of swimming active matter and accordingly construct the corresponding Lagrangian and Hamiltonian of motion of the active matter. Furthermore, living systems broadly employ periodic, non-repeating motion for both locomotion and various biological functions, with meaningful information stored in the periods of these functions. Consequently, analyzing these dynamics in the Fourier space lands us at the familiar tools of the operator based, quantum mechanics. This is accomplished by introducing a complex field to describe the evolving probability distribution of a single unit, as well as the population density of mutually non-interacting active particles under the constraint of scarce resources. The resulting single-unit wavefunction evolves analogously to the Dirac equation with minimal coupling, wherein gauge symmetry reflects the generality of the governing equations across arbitrary resource landscapes. Additionally, we present a Schrödinger-like equation where the effective potential term represents the environmentally mandated, non-motile base metabolic rate. Finally, we formalize the bidirectional coupling between active swimmers and the surrounding fluid via a multipole expansion of the active force with an emphasis on force monopoles and dipoles, where each pole corresponds to a distinct mode of active motility.

High-fidelity simulation of supercritical flows requires accurate values of thermodynamic properties including the density (rho), specific heat cp, enthalpy h, and entropy s as well as transport properties such as the viscosity (eta) and thermal conductivity (lambda) as functions of the temperature T and pressure P. In simulations of mixtures, such as supercritical carbon dioxide (sCO2) with contaminants, a generalized equation of state (EoS) is often used, leading to errors in rho(T,P) when compared to results from correlations developed specifically for individual species. Similarly, generalized correlations for eta and lambda are often used, with a corresponding decrease in accuracy. However, a second source of error is introduced in calculations of transport properties. These correlations are created and computed as functions of T and rho instead of as functions of T and P. Because of this, when eta(T,rho )and lambda(T,rho) are calculated, errors in rho(T,P) propagate through the calculation. This work creates a procedure for tracking both errors caused by using a generalized correlation for eta(T,rho) and lambda(T,rho), and for tracking the errors caused by using a generalized correlation for rho(T,P) in these calculations. The viscosity and thermal conductivity of supercritical CO2, N2, andCH4 are used as examples to demonstrate how to separate the errors due to the generalized property correlations and the errors due to the generalized EoS. Both sources of error are largest near the critical temperature Tc. These errors are large enough to impact both the numeric stability and the accuracy of simulations.

We consider a recently derived mathematical model for the mechanism by which a wind driven flow entrains particles into a fluid from an otherwise static particle bed, a process that is fundamental in initiating and driving the phenomenon of particle cloud formation. This model was previously applied to the "helicopter brownout" problem, in which, as a helicopter descends towards a bed of sand, the downwash and swirling flow from the rotors entrain particles into the air, forming a high-velocity particle-laden cloud around the helicopter. Here, we define a new measure of particle cloud formation potential, outline how the model can be incorporated into existing Computational Fluid Dynamics software, and extend the model to scenarios including: formation of particle clouds in the absence of swirl, such as those caused by a bathysphere descending to the ocean bed, or a rocket landing on the lunar surface, in which case we can precisely predict the critical height above the surface at which particle cloud formation is initiated; generation of dust clouds by less powerful downwash and swirling flows caused by drones or other smaller rotorcraft, such as NASA's Ingenuity Mars helicopter, in which case gravitational effects are included in the model; formation of dust devils (dust clouds formed within and around an upwardly circulating columnar air flow), in which case downwash is replaced by updraft. In each case, predictive models are derived through minor adaptations to key modelling assumptions.

The ablation area of an ice sheet can undergo melting both directly at the surface and in the metre or so below the surface, due to the penetration and absorption of shortwave radiation. The fate of the meltwater has important implications for the mass balance of the ice sheet; some of it runs off into surface streams and eventually to the ocean, while some is stored in the porous `weathering crust', and can refreeze. We present a fluid-mechanical model to analyse the downward percolation and lateral drainage of the meltwater in the crust, and its influence on porosity, saturation, temperature and melting rate. Previous models have either ignored the possibility for lateral drainage, in which case the crust is always saturated with water, or have made ad-hoc assumptions about where and how the meltwater runs off. Through a series of analytical and numerical solutions to the model, we find that lateral drainage has the effect of controlling the water table within the weathering crust, which separates an unsaturated region near the surface from a saturated aquifer beneath. Under fluctuating weather conditions that induce melting and refreezing, the lateral drainage can result in the near-surface ice being more porous and also colder than is the case without lateral drainage. The model is able to predict the partitioning of the meltwater between surface and subsurface runoff, and refreezing, and has potential to be incorporated within larger-scale models of the ice-sheet mass balance.

We present a cross-validated dataset of turbulent wakes behind nine bluff bodies at Reynolds number Re = 10,000: a circular cylinder, a 2:1 elliptical cylinder at 0° and 90°, short and long isosceles triangles with the apex upstream or downstream, and a square cylinder at 0° and 45°. Each body was studied by wall-resolved direct numerical simulation (DNS) with a spectral-element solver and by time-resolved planar particle image velocimetry (PIV) in the MIT Intelligent Towing Tank. The DNS records contain time- and spanwise-averaged velocity, pressure and Reynolds stresses, 24-bin phase-averaged fields keyed to the lift signal, drag and lift histories, and one three-dimensional instantaneous snapshot per body; the PIV records contain the matching time-mean and phase-averaged fields in the same coordinate frame. The DNS set-up is verified against reference cylinder data at Re = 3900, and DNS and PIV at Re = 10,000 are compared field by field. The dataset supports the development and testing of data-driven turbulence closures, reduced-order models, and wake-stability analyses across geometries with distinct separation behavior.

Machine-learning surrogates are increasingly used to accelerate computational fluid dynamics, yet progress is limited by the lack of benchmarks capturing realistic, time-dependent turbulent flows. We introduce TurtLES, a 14 TB dataset of 3D turbulent cylinder wakes in the shear-layer transition regime, computed via high-fidelity implicit large-eddy simulations. The dataset contains 400 trajectories of 400 time steps each, with 3-11 million points per frame, spanning variations in geometry, Reynolds number, and angle of attack. Unlike existing datasets, TurtLES combines (i) physically realistic turbulence with an active energy cascade driven by vortex stretching, (ii) dense irregular meshes, and (iii) long-horizon temporal dynamics. We benchmark state-of-the-art neural operators on autoregressive rollouts and identify key failure modes, including temporal instability, loss of small-scale energy, and challenges in learning on large irregular domains. TurtLES provides a new benchmark for evaluating surrogate models on 3D turbulent wakes at industrially relevant mesh resolution.

Neural solvers offer structural flexibility for the Dubreil-Jacotin--Long (DJL) equation of internal solitary waves, which also admits the trivial state, oscillatory wavetrains and broadened near-solutions. A solver must select the physical wave before resolving it. Turkington's variational principle selects the wave through the nonlinearity of the available potential energy (APE). An exact virial partition shows that every localized wave carries more kinetic energy than APE, so a quadratic APE would favour a broadened field. The nonlinear APE enhancement, $1.27$--$2.06\times$ for the computed waves, reverses this ordering, although the preferred width remains weakly selected. From a shared KdV-derived start, a constrained Deep Ritz objective recovers the mode-1 wave, whereas strong- and weak-form residual objectives, which vanish at every exact solution and therefore do not favour the physical wave over other roots, lose the prescribed APE within one descent round. The recovered wave is under-resolved because its residual is dominated by high-wavenumber error that the energy barely penalizes, and a residual refinement at exact APE then meets every acceptance criterion. Structurally excluding mode 1 from the trial space, we compute mode-2 waves on four stratifications. A computed wave core qualitatively reproduces the two-lobe structure observed on the South China Sea shelf. In the deep basin, the selected core misses the residual criterion, and residual refinement widens it with little change in the energy objective. The two resolved linear estimates suggest weaker relative mode-1 radiation at larger ratios of wave half-width to resonant wavelength.

Time-resolved velocimetry inside cloud cavitation remains a fundamental measurement problem. Particle image velocimetry (PIV) requires uniform tracer seeding and undistorted particle images, and cavitating flow violates both, because tracers do not penetrate vapor structures and refractive index mismatch across deforming interfaces produces spurious vectors. We present a domain-adapted deep optical flow framework for two-phase velocimetry, built on a Recurrent All-Pairs Field Transforms (RAFT) architecture fine-tuned on synthetic image pairs rendered from multiphase OpenFOAM simulations (RAFT-CloudCav). It is evaluated against a pre-trained generalist RAFT model, Farnebäck and OpenPIV on 130,000 frames/s recordings of a Venturi test section at 30 and 48 L/min. As no experimental ground truth exists, validation uses three quantities that require none, namely the integrated flow rate against a turbine meter, the liquid-phase velocity divergence, which mass conservation requires to vanish, and the station-to-station spread of the flow rate. RAFT-CloudCav recovers 47.75 L/min against a metered 48.0 $\pm$ 0.5 L/min, the closest of the four methods, and its flow rate varies by 2.0% across four streamwise stations, versus 6-7% for the classical methods. It returns a coherent near-wall reverse flow of -0.71 m/s, the time-averaged signature of the upstream-propagating re-entrant jet, where OpenPIV returns none. In the non-cavitating control, at 51 $\mu$m/pixel only three grid points fall inside a 0.68 mm boundary layer and the peak wall-normal gradient is under-predicted more than thirtyfold, while 13 and 19 $\mu$m/pixel agree with each other. The mean field is recovered without tracer particles at roughly three times the per-frame uncertainty. Uncertainties are estimated a posteriori from the image residual and propagated conservatively.

A comparative study of sub-filter-scale (SFS) quantities in hypersonic Couette flow and flat-plate boundary layer turbulence under strongly cooled-wall conditions is carried out using filtered direct numerical simulation (DNS) data to characterize the differences in SFS dynamics between internal and external wall-bounded turbulence. The two flows exhibit similar near-wall behaviour in the mean velocity profiles and SFS stress components; however, marked differences emerge in the outer layer and thermal structure. The two configurations also exhibit different thermal fields, leading to different temperature-velocity relations. The SFS behaviour shows strong sensitivity to the filtering operation: the top-hat filter yields larger SFS magnitudes, whereas the sharp spectral filter preserves a distinct spectral separation near the cutoff, leading to characteristic SFS features. Decomposition of the SFS terms shows that the residual component provides the dominant contribution to the mean SFS shear stress and heat flux. Differences between the two flows are primarily associated with the interaction terms between the resolved and residual components, which contribute with opposite signs in the two configurations, consistent with their different thermal structures. The different thermal structures also lead to distinct SFS heat-flux behaviour, including a sign change in the flat-plate boundary layer. Instantaneous SFS fields further reveal that local extrema arise from the combined contributions of multiple decomposed terms. Although these terms exhibit large local fluctuations, their net contributions to the averaged SFS quantities are relatively small. The trace of the SFS stress exhibits local negative values, reflecting local energy redistribution across the filter scale rather than a loss of physical energy.

We experimentally investigate fundamental unstable breather wave groups propagating across the transition from focusing to defocusing regimes. In hydrodynamics, this transition is realized through a rapid reduction in water depth over a short spatial interval. We demonstrate that the time-periodic Akhmediev breather develops a Talbot-like recurrence pattern in the defocusing regime, although only its initial stages are experimentally accessible. In contrast, the Peregrine breather exhibits qualitatively different behavior, characterized by oscillatory envelope dynamics. These oscillations can be understood as a purely linear phenomenon arising within the nonlinear Schrödinger framework when dispersion dominates over nonlinearity, as further confirmed by numerical simulations over extended propagation distances. The experimental observations agree closely with finite-depth nonlinear Schrödinger predictions across regimes with substantially different relative strengths of dispersion and nonlinearity. Our findings reveal a temporal analogue of diffraction and provide a foundation for exploring focusing-to-defocusing transitions in other nonlinear dispersive media.

The Kuramoto model is a paradigmatic system for emergent synchronization phenomena, and significant efforts have been made to investigate its transition from incoherent to coherent dynamics. However, previous studies have almost exclusively assumed global coupling between the oscillators, even though many real-world systems are organized in specific network structures. Here, we fill this gap by examining finite-size effects in Kuramoto oscillator ensembles on networks with mixed-order interactions. Using numerical simulations, we show how parameters such as the size of the system, the average degree of the nodes and the strength of the interactions alter the behaviour of the transition to synchronization with respect to the known theoretical results that are derived for globally coupled infinite systems.

Collisionless self-gravitating systems, such as merging galaxies, have long seemed an exception to the statistical-mechanical principle that chaotic many-body systems relax to maximum-entropy states: Lynden-Bell's statistical mechanics of their "violent relaxation," constrained by exact conservation of phase-space volume -- equivalently, of infinitely many collisionless "Casimir" invariants -- has appeared not to be a good description. We propose that violent relaxation does give rise to Lynden-Bell's maximum-entropy equilibria, but that both are underpinned by gravitational turbulence, in which large-scale gravitational fluctuations drive chaotic phase-space mixing of the particles' distribution function. We derive the universal small-scale (sub-Jeans) spectra of this turbulence and show that it leads to phase-space-volume conservation being broken on a timescale only logarithmically longer, in the particle number N, than the dynamical (violent-relaxation) time. This timescale separation lets the system relax "adiabatically" through a sequence of Lynden-Bell equilibria, each corresponding to instantaneous values of the Casimirs. At long times, it approaches an equilibrium close to its "ground state": a distribution whose Casimirs have adjusted so that the system's energy is now its minimum possible energy. Thus, the system's universal tendency is toward a minimum-energy, maximum-entropy state. We corroborate this picture with 1D N-body simulations and hypothesize that it can explain the universal equilibria of galaxies and dark-matter halos.

We investigate the spatiotemporal dynamics of a three-state active Potts model with a cyclic transition bias. Starting from microscopic Glauber-type dynamics, we derive macroscopic continuum field equations through a spatial mean-field approximation. Linear stability and weakly nonlinear analyses reveal that increasing the coupling strength induces a Hopf bifurcation, near which the critical amplitude dynamics is described by the complex Ginzburg--Landau equation. In the spatially homogeneous limit, the system exhibits limit-cycle oscillations and ordered states, with an intermediate regime of bistability bounded by a $\mathbb{Z}_3$-symmetric heteroclinic bifurcation. In two dimensions, the system sustains stable rotating spiral waves. Using perturbation theory based on one-dimensional traveling fronts, we semianalytically predict the curvature-dependent propagation velocity of circular fronts, as well as the rotational angular velocity and pitch of spiral waves. Finally, we compare the continuum model with discrete Monte Carlo simulations to clarify the role of thermal fluctuations and evaluate the validity of the mean-field approximation.

Accurate approximation of soliton solutions of the Korteweg--de Vries (KdV) equation remains challenging for physics-informed neural networks (PINNs) due to localized wave structures, high-order spatial derivatives, nonlinear interactions between solitons, and difficulties in long-time prediction. In this work, we address these challenges using a scaling PINN framework to approximate KdV soliton solutions. The framework transforms the governing equation into a normalized form, approximates its solution using a PINN solver, and reconstructs the solution in the original variables through inverse scaling. We introduce scaling transformations and PINN solvers tailored to one- and two-soliton problems. For the one-soliton case, we employ a PINN solver that incorporates a traveling-wave coordinate to capture soliton propagation. For the two-soliton case, we employ a two-step training procedure for the PINN solver. The first step learns the individual soliton profiles and estimates their propagation speeds, while the second step uses the estimated speeds to construct traveling-wave coordinates in the PINN solver and approximate the full two-soliton solution, including nonlinear interactions. We also introduce soliton-informed sampling (SIS), which places additional collocation points around the soliton trajectories. Numerical results show that the scaling PINN framework accurately captures one-soliton propagation, resolves two-soliton interactions, and preserves soliton profiles during long-time extrapolation in both cases. An additional three-soliton experiment suggests the applicability of the proposed two-step training procedure to multi-soliton solutions.

We numerically investigate dissipative dark-soliton (DDS) microcombs under the action of pure high even-order normal (HEON) dispersion in a microresonator with the self-injection locking (SIL). Pure 4th, 6th, 10th, and 14th-order normal dispersion can support DDSs formed by interlocked switching waves, directly excited through a SIL-based turnkey scheme without detuning sweeps. Compared to the pure 4th-order case, the switching-wave tail oscillation period increases and its decay rate decreases with the increase of the dispersion order. Although the overall comb bandwidth narrows, the number of non-pump comb lines above a common absolute power threshold increases. Furthermore, the feedback phase controls the DDS duty cycle and intracavity comb-line power distribution, while the increase of the pump power improves the estimated pump-to-comb output conversion efficiency.

We present a numerical and conceptual overview of classical scattering under a Lennard-Jones potential. All results were obtained by direct integration of particle trajectories in the two-dimensional plane for varying impact parameters and energies. From these trajectories, we compute deflection functions, identify critical values associated with unstable circular orbits, and visualize non-monotonic behavior in the angular deflection. We construct color maps representing the deflection angle and interaction delay time as functions of energy and impact parameter, and determine the differential cross section from the deflection function, accounting for multi-valued contributions. These results are displayed both as individual plots and as a full color map in the energy-angle plane, providing a detailed picture of the scattering behavior in this central potential.

The classification of the motion of a heavy symmetric top when conserved angular momenta are different is studied by considering modern method and Routh's geometrical method. It is shown that Routh's method provides correct classification for four cases; however, it fails in two cases.

Active model B+ (AMB+) explains how motility-induced phase separation can be arrested by reverse Ostwald ripening, but its coefficients have not been derived from a microscopic lattice model that shows it. We provide an exact hydrodynamic description of a six-polarity lattice gas on a hexagonal geometry and employ a full gradient expansion with angular-harmonic elimination to rigorously derive AMB+ with every coefficient fixed by the Péclet number Pe. Near the critical point (3/4, 4), coarsening is ordinary; further away, field theory predicts reverse Ostwald ripening of vapor bubbles above Pe $> 4 \sqrt{3}$, and simulations show long-lived bubbly states.

We study first-order condensation in finite open wedges using classical density functional theory (DFT) and compare the resulting microscopic phase behaviour with recent macroscopic predictions. Two geometries are considered: a symmetric wedge formed by two identical inclined walls and an asymmetric wedge formed by a vertical and an inclined wall. The DFT calculations confirm the two condensed morphologies predicted for the symmetric wedge and the three morphologies predicted for the asymmetric wedge and their emergence depending on the wedge size, opening angle, and wall contact angle. Under partial-wetting conditions, the microscopic phase boundaries are in nearly perfect quantitative agreement with the macroscopic predictions, including reentrant changes between pinned and depinned meniscus configurations and the appearance of the semi-double-pinned state in the asymmetric wedge. Under complete-wetting conditions, the DFT phase diagrams retain the topology predicted by the macroscopic theory, but the single-pinned region is systematically enlarged. This shift is attributed to adsorbed liquid films, which reduce the effective width available to the gas and thereby increase the effective aspect ratio of the confinement.

Rayleigh-Taylor instability (RTI) is of fundamental importance in fields such as inertial confinement fusion and supernova explosions, and its evolution is commonly described by potential--flow theory and buoyancy--drag models. However, both types of models struggle to accurately capture the overshoot behavior of bubble and spike velocities, as well as the subsequent reacceleration stage. To address these limitations, we develop a physics-constrained, data-driven framework based on the integral formulation of Sparse Identification of Nonlinear Dynamics (SINDy), which extracts low-dimensional dynamical equations for bubble and spike evolution directly from data. By introducing the nondimensional initial amplitude $A_0 = k\eta_0$ as an explicit parameter, we identify distinct dynamical equations for the bubble and the spike based on data spanning multiple Atwood numbers and initial amplitudes. The resulting low-dimensional dynamical equations not only reproduce the overshoot behavior of the velocity with good accuracy, but also capture the reacceleration stage well, while maintaining high predictive accuracy at unseen values of the wavenumber, acceleration, and Atwood number. This work provides a physics-constrained, data-driven framework complementary to conventional potential-flow and buoyancy--drag models, accurately describing the dynamical evolution of the bubble and spike at high Atwood numbers, and provides a new perspective for directly extracting the dynamical equations of interfacial instabilities from data.

This study presents a systematic investigation of the second-shock induced micro jetting from sinusoidally perturbed tin surfaces using a combined smoothed particle hydrodynamics (SPH) and molecular dynamics (MD) approach. The key contributions of this work are: 1) identification of three distinct bubble morphologies after the first shock, controlled by k 0 h 0 ; 2) revealing that two dimensional unloading and weak Richtmyer-Meshkov instability at the bubble base drive the morphological transition; 3) development of a novel predictive model for second-shock ejecta mass by treating the post shock interface as a multi mode perturbation and incorporating explicit mode coupling effects.

We numerically investigate the collision and fracture processes of ball milling based on a minimal model of a three-sphere geometry using discrete element method (DEM) simulations combined with Christensen-type and Weibull-type normalized fracture criteria. The outcome of the brittle target particle (ejected versus trapped, fractured versus intact) depends on the impact geometry and velocity. We develop a reduced three-sphere collision description in which trapping is governed by impact geometry and friction, while fracture inside the trapping regime is evaluated from DEM output using stress-based and contact-force-based normalized criteria. The trapping regime follows a closed-form geometric condition, while the critical conditions for fracture vary with impact angle, obliquity angle, impact velocity, and particle size ratio. Head-on collisions with larger size ratios require lower critical impact velocities for fracture.

We extend the BGK-type kinetic model for polymer dumbbells and its lattice Boltzmann implementation by incorporating hydrodynamic interaction (HI) effects to accurately recover the slow-variable dynamics governed by the Smoluchowski equation. Unlike Brownian dynamics approaches, which demand the computationally expensive evaluation of the square root of the configuration-dependent diffusion tensor at every time step, this kinetic method is straightforward to implement and avoids such overhead entirely. Consequently, it achieves a significant reduction in computational cost. We validate the model in steady and transient shear flows, demonstrating its ability to capture the distinct signatures of hydrodynamic interactions on bulk rheological properties.

Rigid-origami folding has versatile applications in the fields of architecture, engineering, medicine and aerospace. Given the design parameters of a single waterbomb cell, the global geometry of the origami tessellated shell at an intermediate state of folding is directly determined. Even though existing numerical methods of rigid-origami can be used to describe geometric forms, algebraic solutions of the waterbomb folding kinematics and tessellations reduce the algorithmic complexity and determine the range of admissible configurations exactly. The existing analytical solution for a symmetrically folded waterbomb cell and tessellation is extended to the case of a cell folded semi-symmetrically, i.e. a cell with a 180° rotation symmetry. The algebraic derivation provides the solution for the entire folding process. The resulting functional relationship between the design parameters and the 3D cell geometry of the folded waterbomb cell enables efficient studies of achievable shell geometries. This development facilitates a deeper understanding of the correspondence between the geometric parameters of a single waterbomb cell and the statically relevant geometric properties, i.e. the shell curvature and the effective cross-sectional height. The systematic description of this correspondence provides the basis for innovative design concepts using modern cementitious composites, e.g. textile-reinforced concrete, to produce thin-walled, high-performance, lightweight shells.

Ostracism was the practice in use in Athens and other ancient Greek cities to send into exile citizens whose influence was deemed to be dangerous. Quite similarly, splay ostracism is here the approximation that bans splay distortion from thin films of ferroelectric nematic liquid crystals on a curved shell in space. This reduces to a mere geometric problem the quest for equilibria of director vortexes and the walls isolating them, as splay ostracism requires the director field lines to be everywhere orthogonal to systems of geodesics on the shell. Consequences of this theorem are explored for shells with Gaussian curvature of either sign. The resulting quasi static dynamics reveals both cases where walls escape from the shell and cases where they are trapped on it, with possibly different reflections on the vortex dynamics.

The molecular dynamics and glass-forming behavior of 4-cyano-3-fluorophenyl 4-butylbenzoate (4CFPB) liquid crystal was investigated by broadband dielectric spectroscopy in anodic aluminum oxide cylindrical nanopores of 35 and 73 nm diameter. The primary $\alpha$-relaxation was analyzed using the Vogel-Fulcher-Tammann (VFT) and Mauro-Yue-Ellison-Gupta-Allan (MYEGA) models. Confinement reduces the glass transition temperature from 217 K in bulk to 208-210 K, while preserving the super-Arrhenius character of the $\alpha$-relaxation and a fragility index of approximately 60. Unlike in previously studied 6 and 8 nm pores, the secondary $\beta$-relaxation remains detectable, with possible intramolecular contributions examined by density functional theory calculations. Next to the pore-size-dependent changes in molecular dynamics and glass transition temperature, cold crystallization is not observed. These findings highlight the distinct effects of geometrical confinement on molecular relaxation, glass formation, and crystallization kinetics.

Externally driven systems are non-equilibrium but accessible to stationary states. By combining theoretical calculations and particle-based simulations, we investigate the orientational configuration of a transversely-magnetized slender particle in a rotating magnetic field. Our results reveal nonequilibrium orientational bistability in both regimes that the particle rotates synchronously and asynchronously with the field. The relative populations of standing and lying orientations depend strongly on the driving frequency in the synchronous regime, whereas they are primarily controlled by the magnetic field strength in the asynchronous regime. Effective free-energy approximations further capture the principal features of the steady-state orientational distributions in both regimes. Our work aims to give a statistical-thermodynamic description of orientational bistability in magnetically-driven slender particles, paving the way for relevant experimental designs and advanced applications.

We present a high-dimensional coarse-grained model of alanine dipeptide that explicitly incorporates global translation and rotation alongside internal conformational dynamics. Using atomistic molecular dynamics trajectories, we construct a 10-bead Markovian Langevin model with a 24-dimensional internal potential of mean force and a full matrix of site-specific friction coefficients. The equilibrium landscape is represented by a Gaussian mixture model, while a rotational-entropy correction accounts for the coupling between internal conformation and global molecular motion. Friction coefficients are obtained using a generalized Einstein relation based on time-correlation functions. We show that the rotational-entropy correction is essential for obtaining a physically admissible friction matrix and significantly affects the inferred dynamics. Without fitting to coarse-grained dynamical observables, the resulting model reproduces a broad range of atomistic auto- and cross-correlation functions. The result is a compact and interpretable dynamical representation of the entire peptide at the chosen CG resolution, which explicitly preserves distinctions between energetic and dissipative coupling over a wide range of motions, including those between conformational fluctuations and global translational and rotational diffusion.

Topological defects in nematic liquid crystals are high-energy sites of reduced order. We show that a point defect can be stabilized in pillbox-shaped pores. The pore shape promotes lock-and-key docking similar to that observed for colloidal particles. The defect docks in one lobe or the other, displaying bistability. Furthermore, the defect moves like a charged object in an external electric field. An in-plane field drives the defect from one lobe to the opposite lobe, where it remains once the field is removed. The velocity is linear in field strength and reverses with polarity, consistent with flexoelectric coupling. Within the pore, the nematic around the defect carries a positive bulk bound charge density, compensated by negative space charge in the rest of the fluid and on the bounding surfaces. The external field breaks the mirror symmetry of the pore and drives the defect motion. Defect displacement increases the component of the net dipole in the domain along the field. Antagonistic curvature in peanut-shaped pores repels the defect, allowing pore geometry to set distinct switching thresholds. The defects, while not topologically required, are long lived, so information can be stored in their position, allowing them to serve as topological bits. Arrays of topological bits store and rewrite binary information in defect positions, offering a route to reconfigurable, field-addressable soft materials.

Understanding how per- and polyfluoroalkyl substances (PFAS) partition into biological membranes and alter their properties is central for elucidating PFAS toxicity. Here, we experimentally investigate how the partitioning of anionic PFAS affects the surface charge of phospholipid vesicles and consequently, their electrokinetically driven vesicle motion, in particular diffusiophoresis. We find that PFAS partitioning enhances vesicle diffusiophoresis, consistent with a model combining the Nernst-Planck and Langmuir adsorption equations. Desorption experiments, together with quartz crystal microbalance with dissipation monitoring (QCM-D), further reveal that substantial lipid loss occurs during PFAS partitioning. We attribute this loss to lipophobic interactions between the fluorocarbon chains of PFAS and the alkyl chains of lipids. Our findings provide new mechanistic insights into how PFAS may disrupt biological systems.

In two dimensions, the ordered phase of constant-density flocks is described by a single angle field, which makes them arguably the simplest systems with a scale-free ordered phase of collective motion. We show that the equation governing the corresponding Nambu-Goldstone mode, completed with terms previously discarded, possesses on large scales an invariance combining a shear and a Galilean boost. Broken at the bare level, this symmetry is restored at the unique attractive fixed point, and the associated Ward identities fix the scaling exponents exactly, as confirmed numerically.

Physical learning studies how physical systems themselves can be trained to perform learning tasks using physical laws. For instance, disordered spring networks can be trained by local rules to route a mechanical signal from one site in the network to another. Disordered spring networks play key roles in many facets of cell biology, not just in terms of mechanics, but also in terms of motility. How then can training on the substrate itself impact the action of an organism, such as a bacterium? Here, we train a spring-network model of the bacterial cell wall and embed it in a motile agent. The stimulus is the load the cell generates by colliding with a surface. The trained wall routes that load across the body to distant flagellar motors, where it drives stator release, and the resulting turn biases the cell toward escape and delays subsequent surface contacts. On the first near-wall tumble after entrapment, the trained cell recovers 89% of the advantage an ideal side-resolved controller provides. We call this arrangement embodied physical learning: the stimulus, the actuator, and the consequences all belong to the agent, and the training force scale is inherited from the agent's own sensing rather than imposed. An actuator with its own kinetics imposes a second, tighter constraint: the routed signal must switch the actuator within the stimulus window. We also find that behavior converges within a few hundred wall encounters, comparable to what a cell in sustained contact with structure experiences in a single generation, and that the routing survives continuous crosslink remodeling provided crucial, tension-bearing bonds are protected. Experimental tests of embodied physical learning are discussed.

Reconstructing turbulent flow fields from sparse and irregular measurements remains challenging because the underlying inverse problem is severely underdetermined. Here we present MANTRA, a manifold-based tensor framework that represents each velocity component in a continuous tensor-product space while constraining its coefficient tensor to a low-rank Tucker manifold. This structure provides a compact, data-adaptive representation without requiring gridded observations or governing equations. Riemannian optimization and adaptive selection of rank and basis complexity enable the model to exploit coordinate-wise spatiotemporal correlations. In simulations of forced isotropic turbulence and flow over a cylinder, MANTRA recovers multiscale structures at sampling densities orders of magnitude below the underlying grids and remains accurate under Gaussian noise up to 20% of the peak velocity. It also recovers leading coordinate-wise correlation structures from sparse observations. Applied to experimental particle-tracking velocimetry of an oscillating impinging jet, MANTRA reveals time-evolving structures that are not apparent from the scattered measurements alone.

We assess the non-linear version of the Entropy Stable Extension to the Navier-Stokes-Fourier equations which were originally derived in arXiv:2407.17334 . Using an identity for the derivative of the inverse of linearized collision operator, we show that the Entropy Stable Extension takes the form of a fourth-order quasi-cubic system of equations when written in entropy variables. Furthermore, we find that the quasi-linear contributions to the extension retain the highest order derivative contributions and the entropy stability of the full extension. This quasi-linear approximation is applied to the stationary heat transfer between parallel plates where we find that a specification of the boundary conditions that interpolates between the continuum and collisions limits can yield temperature profiles that better agree with DSMC predictions than Navier-Stokes-Fourier equations with Smoluchowski boundary conditions, while also giving a heat flux prediction that better agrees with the Sherman-Lees heat flux than the Navier-Stokes-Fourier prediction. We conclude with a brief study of dispersion of plane waves according to the linearized equations in one dimension where we show that all frequency modes are stable and relate this to entropy stability.

Small spheroids settling through turbulence are turned broadside-on by fluid inertia and tilted away by velocity gradients. We describe their orientation and slip statistics through the crossover from random orientation to alignment, in the overdamped limit. With quasi-static Stokes drag the leading inertial torque is an exact gradient flow on the orientation sphere, its potential quadratic in the cosine of the tilt and only rescaled by mobility anisotropy. The orientation performs an overdamped random walk in a quadratic well, and isotropic Gaussian white noise gives exactly a Boltzmann distribution. For forcing of finite correlation time, a closure keeps this form with its width set by linear response; it recovers the uniform density as settling vanishes and, for fixed-orientation forcing statistics, the aligned coefficient of rapid-settling theory, and errs most in the crossover. The root-mean-square lateral slip peaks where the alignment rate approaches the Kolmogorov rate, as faster settling strengthens the sideways drift at a given tilt but suppresses the tilt; the nearly shape-independent ratio, which tensor-forced simulations reproduce, lets a measured peak constrain the torque coefficient or dissipation rate for given forcing statistics. Dissipation intermittency enters as a lognormal superposition of Boltzmann distributions, which fattens the tails but leaves the leading aligned mean-square tilt unchanged. The superposition reproduces the shape of plate orientation distributions from direct numerical simulations, where a single Boltzmann distribution fails; published moments confirm the predicted spread beyond the weakest torques, and at strong alignment the measured fourth-order tilt moment lies between the two predictions.

When a liquid drop impacts a liquid surface, it deforms the surface, trapping a thin layer of air between drop and bath. The drop then either bounces off the bath or, if the gas film ruptures, merges with it. We present a model for drop-bath impacts that can accurately predict whether a drop will bounce or merge, and compare it to theory-driven experiments. The model incorporates a lubrication description of the deforming trapped gas film, which accounts for its significant curvature, within a finite-element framework. Capturing this outcome requires micro- and nano-scale physics: van der Waals-driven disjoining pressure and gas-kinetic effects that depend on the mean free path of the gas. Using only independently measured material parameters, we obtain the first quantitative agreement with experiment for the critical impact speed separating bounce from merge. We explore the behaviour of drop-bath impacts at low ambient air pressure, and then investigate the bounce-merge threshold for impacts onto shallow baths and thin films, finding a bounce-merge-bounce-merge transition as the bath depth decreases.

A model is proposed for the wall-normal Reynolds stress and its one-dimensional spectrum in channel flows. The model is tested for friction Reynolds numbers from 550 to 5200. The formulation for the stress is a simple modification of the one devised for boundary layers by Kunkel & Marusic (J. Fluid Mech. 548, 2006), and holds for $y/\delta < 0.75$. The model for the spectrum holds for all wall distances. It is constructed in wavenumber space, and comprises two principal contributions to the spectrum: energy-containing motions and viscous-dominated motions. It is in accord with the attached eddy model where that applies, and the viscous contribution scales on the Kolmogorov length and velocity. Its extension to boundary layers, with no change to the constants, appears promising, including at Reynolds numbers well above those of the channel data.

The interaction between the hypersonic flow over a cone and a side jet creates complex multiple recirculation regions as well as separation, reattachment and bow shocks known as Edney-Type IV shock-shock interactions. The interactions between these multi-scale structures are shown to be well captured with the direct simulation Monte Carlo (DSMC) method, a particle-kinetic approach. This computational technique was used because even though the free stream conditions were continuum-like, sufficiently strong gradients in the shock and jet expansion were observed to cause continuum breakdown. The time-accurate DSMC approach has been shown in previous work to capture the multi-scale structures and unsteadiness in the shock structure that occurs in such flows, as was also observed in this work. These sources of unsteadiness in the shock system are shown to locally affect surface parameters such as heat transfer and skin friction as well as predict a low frequency unsteadiness consistent with earlier values in the literature.

Small unmanned aerial vehicles commonly regulate propeller thrust through rapid changes in rotational speed, yet it remains unclear how the inflow, the wake, and the near-surface velocity respond to these changes at low Reynolds numbers. A commercial two-bladed propeller was tested in hover with custom blade holders at three additional pitch offsets relative to the original blade geometry, $\Theta =\,$0, 5, and $10^\circ$, and accelerated and decelerated between 3000 and 5000 RPM with open-loop step responses. The resulting nondimensional acceleration and deceleration numbers, below 0.011 and 0.007, suggest negligible acceleration effects. Phase-locked particle image velocimetry (PIV) at 40, 60, and $80\,\%$ rotor radius and in the meridian plane was combined with load measurements. The thrust coefficient responds quasi-steadily at $\Theta = 10^\circ$, but shows hysteresis at the higher pitch offsets, with lower values during acceleration and higher values during deceleration than under steady conditions. This trend opposes expectations from dynamic inflow theory. The effect is largest at $\Theta = 5^\circ$, with deviations from the steady values of up to 8\,% during acceleration and $5\,\%$ during deceleration, compared with $4\,\%$ and $3\,\%$ at $\Theta = 10^\circ$. PIV reveals that the rotor-disk inflow, blade deformation, and sectional circulation remain largely quasi-steady, whereas velocity fluctuations, blade-wake vorticity, and tip-vortex circulation vary strongly, with the largest deviations at low rotational speeds rather than at peak acceleration or deceleration.

Direct numerical simulation (DNS) of blood flow through the whole human arterial tree is limited by the number of lattice sites that must be advanced on a high-performance computer. We address this limit by combining the lattice Boltzmann solver HemeLB with Smagorinsky large-eddy simulation (LES). HemeLB runs with the same scaling behaviour on AMD, Intel and NVIDIA graphics processing units (GPUs) and sustains about 10 trillion lattice-site updates per second (TLUPS) on both the Frontier and Aurora exascale supercomputers. In stenotic aortic flow, LES on lattices five and ten times coarser than a 20~$\mu$m DNS reproduces the wall pressure and the cross-sectional pressure and velocity, and its plane-averaged pressure differs from that of the DNS by at most 0.75~mmHg, below 1\% of the local pressure. At 100~$\mu$m, LES reduces the estimated cost of a full-human simulation by a factor of about 625 relative to DNS. We use this resolution to compute blood flow from the head to the feet in a full-human arterial model with 295 million fluid sites, one inlet at the aortic root and 432 Windkessel outlets, at about 15--18 node-hours per cardiac cycle on two Frontier nodes. A single simulation resolves every region simultaneously, from the cerebral arteries to the arteries of the feet. The pressure pulse grows as it travels from the aorta to the feet, the shear stress concentrates in the branches rather than in the aorta, the pulse reaches the outlets later with increasing distance from the heart, and the flow in the legs and feet is triphasic, as in Doppler measurements of the human leg. These results bring patient-specific whole-body lattice Boltzmann simulations within reach of current supercomputers and pave the way for ensemble simulations towards a standard human model.

We present an axisymmetric continuous simplex space-time finite element method for incompressible fluid flow. Compared to conventional time-stepping methods, the space-time approach has several advantages. First, the motion of the domain is incorporated into the space-time geometry, allowing for large boundary motion without remeshing or projection of the solution. Second, the method allows for time-periodic solutions to be computed directly, without the need to simulate multiple cycles. Third, the space-time mesh can be partitioned in time as well as in space, which enables parallelism in time. The method is demonstrated on an intra-aortic balloon pump (IABP) in a rigid tube. The balloon inflation is modelled based on measured data, and includes a travelling wave along the balloon. The method is able to resolve complex flow features such as jets and recirculation zones. A refinement study shows convergence under temporal, spatial and combined space-time refinement. In weak scaling tests up to 960 ranks, the cost per solver iteration remains approximately constant, and partitioning the mesh into time slabs improves the convergence of the linear solver compared to partitions that cut through both space and time.

Using kinetic theory of gases, we derive the diffusive compressible Euler (dcE) model for ideal gases. The derivation covers all steps from the particle description of a gas, to macroscopic averages, to a discrete system of conservative balance equations in finite volumes, to the system of partial dif- ferential equations. Along the way, we discuss the modelling assumptions, and derive approximations of the diffusion coefficient. In the next part, we discuss the modifications needed to model real gases. In particular, we propose a tentative model for intermolecular friction forces.

The hulusi is a free-reed instrument from Yunnan, Western China, known for its unique sound. Its reed and frame are cut from a single brass sheet in a symmetric shape, the free end narrower than the clamped end. Its free reeds are coupled to tubes that determine the instrument's pitch during normal playing. With reduced playing pressure, the reed frequency takes over the instrument sound. We report point-by-point laser Doppler vibrometry on the reeds of six handmade hulusi, two each in the keys of F, B$\flat$ and C, measured at 29 points on every reed or tongue over nine fingerings and two supply pressures. Steady-state spectra carry two components: a tube-dominant frequency $f_\mathrm{tube}$, locked to the air-column resonance and carrying a complete harmonic series, and a reed-dominant frequency $f_\mathrm{reed}$, which is not an integer multiple of it. Their difference $\Delta = f_\mathrm{tube} - f_\mathrm{reed}$ runs from 38 to 523~Hz across the dataset, from about three semitones to more than an octave. The reed-dominant frequency rises with the pressure at the reed, by $28.0 \pm 10.3$ Hz/kPa once $f_\mathrm{tube}$ is controlled for. At low pressure supply the oscillation loses its lock to the air column, falls silent for about 100~ms, and returns at the reed frequency within 0.1 Hz. The spatial patterns are forced oscillation shapes of one limit cycle at its fundamental and harmonics rather than eigenmodes: the measured frequencies stand in strict 1:2:3 ratios, far from the bending ratios of a cantilever. The reed-dominant pattern is pure bending and holds across fingerings and supply pressures, whereas the tube-dominant pattern breaks up near the oscillation threshold.

Data-driven turbulence closures can improve Reynolds-averaged Navier-Stokes (RANS) predictions, but their use is limited by two issues: learned constitutive relations are often difficult to inspect, and predictions typically lack reliable uncertainty estimates. We develop a Bayesian tensor-basis Kolmogorov-Arnold network (BKAN) for Reynolds-stress anisotropy that addresses both within a single closure. Learnable univariate spline functions on network edges provide an inspectable representation that can, where sufficiently simple, be approximated symbolically. Variational posteriors over spline coefficients yield a predictive distribution separating epistemic uncertainty, due to limited training data, from aleatoric uncertainty, the irreducible scatter of high-fidelity targets at given inputs. Galilean and rotational invariance, symmetry, and tracelessness are enforced through the tensor basis, while physical realisability is treated separately through soft regularisation. A controlled regression benchmark assesses predictive accuracy, calibration, and Bayesian parameterisation. Placing the posterior on spline coefficients gives the best overall balance of accuracy, calibration, parameter cost, and interpretability. Applied to Reynolds-stress anisotropy, the BKAN is accurate in distribution, with calibrated, informative uncertainty that tends to identify larger prediction errors. Under geometric extrapolation, however, the model becomes overconfident: epistemic uncertainty increases but does not fully account for growing prediction errors. Finally, the framework is extended to three-dimensional wind-farm wakes, where the learned correction transfers to unseen layouts and posterior samples are propagated through the RANS solver, with the aleatoric component injected as a spatially correlated field, to obtain uncertainty bounds on the predicted wake flow.

Physics-informed neural networks(PINNs) offer a mesh-free and continuously differentiable approach to fluid simulation. However, standard monolithic PINNs for incompressible Navier-Stokes (NS) equations often suffer from severe constraint coupling and spectral biases, limiting both convergence and accuracy. To address this challenge, we propose a segregated, iterative, and multi-stage PINN (SIM-PINN) inspired by the classical projection method in computational fluid dynamics. In SIM-PINN, the nonlinear NS equations are decoupled into the linearized momentum and pressure Poisson equations. Each is addressed separately using dedicated multi-stage neural networks and coupled through projection-based inner iterations. Each stage of the multi-stage neural networks for the momentum equations corresponds to one iteration of the projection method, in which the velocity fields are progressively refined at targeted frequencies. Upon iteration convergence, solutions to the fully coupled and nonlinear NS equations are recovered. By integrating the segregated and iterative framework with the multi-stage training, SIM-PINN alleviates the optimization difficulties of the incompressible NS equations arising from nonlinearity, constraint coupling, and spectral biases. The improved convergence and accuracy are demonstrated by simulations of steady lid-driven cavity and unsteady Kolmogorov flows.

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

In the lattice Boltzmann method (LBM), the momentum-exchange method (MEM) is widely used to evaluate hydrodynamic forces at fluid-solid interfaces due to its computational efficiency and geometric flexibility. However, when mapping complex geometries onto structured Cartesian grids, the physical boundary rarely intersects the lattice links exactly at their midpoints. This discrepancy violates an implicit assumption inherent to the conventional momentum-exchange (CME) formulation. In this study, we systematically analyze this geometric deficiency and demonstrate that it induces significant force inaccuracies, even in elementary flows where the solid boundary deviates from the midway position. To resolve this, we propose a modified momentum-exchange (MME) method that explicitly accounts for the exact boundary location along the lattice links, demonstrating enhanced accuracy for both flat and curved geometries. Furthermore, we address another critical issue with the interpolation-supplemented bounce-back (ISBB) schemes, and that is their inherent violation of local mass conservation. This mass leakage induces unphysical pressure buildup in the system, which compromises the accuracy and stability of the LBM. We propose a mass-conservative remedy for ISBB schemes that eliminates this leakage. Through a series of benchmark simulations of increasing complexity, we demonstrate that combining the proposed MME with the mass-corrected ISBB scheme drastically improves the fidelity of hydrodynamic force evaluations, establishing a robust framework essential for moving boundary problems and fluid-structure interactions.

We construct a divergence-free velocity field $\mathbf{u}(\mathbf{x},t)$ on $\mathbb{T}^{n}$ that is a genuine function of position and carries both defining properties of turbulent transport: Richardson pair dispersion and a dissipative anomaly. No synthetic field has carried both, because the frame that gives the first destroys the field the second requires. The key is a dichotomy: deforming a spectrally localised pattern smears it across scales, whereas pushing its generating centres forward and re-convolving leaves the spectral envelope exactly invariant --- so transporting the eddy centres preserves both cascade and frame. In the field the finite-size Lyapunov exponent obeys $\zeta(R)=h(R)-1$ threshold by threshold within the scaling range, with a sweeping deficit $\Delta_{\rm sw}=+0.038\pm0.019$, consistent with zero, against $+0.091\pm0.019$ for the frozen field on the same data, a gap that doubles at Navier--Stokes intermittency. Companion papers prove that this family shows Richardson dispersion and a dissipative anomaly (Fefferman and Mayboroda 2026), and that a scalar advected by this flow obeys Yaglom's relation (De Lellis 2026), at small Kubo number. Trajectories forget their starting point as the smallest eddy is removed: the median separation of pairs released from one point with independent Brownian kicks varies as $\kappa_{p}^{0.0333\pm0.0038}$ over 22 decades of particle diffusivity, against $\kappa_{p}^{1/2}$ for a smooth control. A scalar in the same field closes the exact scale-by-scale variance budget, four independently measured terms balancing the dissipation to 15\% over 1.2 decades with no adjustable constant, and reaches its inertial--convective asymptote $S_{L}=-\chi r$ to $0.9995\pm0.0018$ once the measured diffusive transfer is restored, while under an imposed mean gradient $\chi$ changes by 14\% over a factor 5.8 in $\kappa$.

We investigate an extension of perfect spin hydrodynamics that includes dissipation in the spin sector. The presence of dissipation implies that antisymmetric parts of the energy-momentum tensor should be taken into account. Their form follows from the Navier-Stokes or Israel-Stewart theory, which introduces a priori unknown kinetic coefficients and relaxation times. We find that the inclusion of the antisymmetric parts of the energy-momentum tensor has twofold effects: i) they form source terms for the spin tensor allowing for the transfer between the spin and orbital parts of the total angular momentum (spin-orbit interaction) and ii) they appear in the conservation laws for the energy and linear momentum, indirectly affecting the spin dynamics. Numerical results are obtained for two boost-invariant expansion geometries: one-dimensional longitudinal motion (Bjorken model) and two-dimensional boost-invariant and cylindrically symmetric expansion. They indicate (for various choices of the spin kinetic coefficients and the relaxation times) that the spin polarization tensor approaches thermal vorticity. We also observe that Israel-Stewart dynamics on the way to local equilibrium approaches first the Navier-Stokes regime. In general, we find that the Israel-Stewart formalism naturally helps to consistently combine the conservation laws for linear and angular momentum, while the Navier-Stokes framework itself can lead to a disruption in the structure of the equations through the inclusion of terms involving derivatives of an order higher than one.

The Characteristic Mapping (CM) method is a transport scheme which discretizes the Lagrangian flow map as a composition of spatial interpolants. This adaptive approximation technique has demonstrated novel resolution properties and the ability to efficiently simulate the fine scales of inviscid turbulent flows. In this work, we construct an extension of this approach to the solution of dissipative problems, including the Navier-Stokes equations. The extension lifts a general scalar evolution equation to a path in a group of diffeomorphisms, where the semigroup approach of the CM method can be exploited. We give an interpretation of this lift through the geometric framework of optimal transport. We then introduce a semidirect product evolution technique to perform the time stepping of the map components. The map is evolved based on the semi-Lagrangian CM approach, and its log-Jacobian is evolved explicitly by an exponential integrator. The numerical scheme is demonstrated to be high-order accurate and is tested on a range of canonical nonlinear dissipative equations. By retaining the resolution properties of the CM method, the approach shows a promising ability to simulate turbulent fluid flows across all Reynolds numbers.

The present paper establishes the Richardson dispersion law, predicting the particle separation with time according to $\E R_t^2 \sim t^3$, as well as anomalous dissipation for the associated tracer, for a random Hölder continuous velocity vectorfield with controlled sweeping.

We present a computational framework that combines machine-learning-based discovery with rigorous computer-assisted numerical certification and formal verification for strongly nonlinear partial differential equations. We demonstrate the approach for periodic gravity-capillary traveling water waves. Physics-informed neural networks are used as a search mechanism, with the wave profile, wave speed and, in continuation experiments, surface tension learned directly from the governing equations without training data. Through a staged training and refinement procedure, the neural networks achieve near-machine-precision residuals of the governing equations, even in strongly nonlinear regimes. A single formulation recovers high-amplitude Stokes waves, Crapper waves and Wilton ripples. Continuation from a high-amplitude Wilton ripple in surface tension reveals new high-amplitude candidate solutions. We freeze one candidate as an explicit finite representation and rigorously certify a uniform bound on its governing-equation residual using interval arithmetic, accounting for floating-point roundoff, Fourier truncation, aliasing and grid-to-continuum errors. This independently validates the neural-network accuracy. We formalize the certification argument in Lean, which machine-checks the deductions from certified numerical bounds to the residual theorem. Both the interval certification and formalization were developed with substantial assistance from a large language model, while the validity of the result remains independent of the language model: the numerical bounds are rigorously enclosed by interval arithmetic and the subsequent mathematical deductions are checked by the Lean kernel. Together, these steps provide a pipeline from neural discovery to rigorous numerical certification and machine-checked verification with auditable mathematical guarantees.

At finite magnetic Reynolds number, the field induced by a moving conducting fluid or solid extends into open space, so a finite mesh needs an outer boundary condition that represents the decaying exterior field. Magnetohydrodynamic (MHD) codes widely use pseudo-vacuum or truncation at a finite radius. Neither condition is physically correct for a vacuum exterior, but the exact alternatives are costly or limited to simple geometries. We present a Dirichlet-to-Neumann (DtN) closure on a fixed enclosing sphere and release it as part of the open-source multi-region finite-volume solver FreeMHD. The closure matches each Cartesian component of the vector potential to its decaying exterior solution, which retains all three decaying vector-Laplace families. A meshed vacuum buffer connects non-spherical conductors to the sphere. We verify the closure with manufactured modes, sphere free decay, sphere and oblate dynamos, and a freely braking rotor. Under refinement, oblate dynamo thresholds and sphere growth rates converge toward independent spectral references, and the rotor torque matches an exact transient reference. On the same sphere, pseudo-vacuum and truncation give the larger errors predicted by their exterior models.

A reduced-order model is developed for the nonlinear dynamics of electrostatically actuated microbeams, including the full squeeze film effect. The model uses Petrov-Galerkin projection on damped complex modes of the fully coupled fluid-structure problem. The Euler-Bernoulli theory for calmped-clamped and clamped-free microbeams, with mid-plane stretching and electrostatic nonlinearities, and the nonlinear compressible Reynolds equation are discretized by the differential quadrature method for the static solution and eigenvalue problem. The calculated eigenmodes are either complex conjugates describing the coupled behavior of the device or real depicting the fluid relaxation. The natural frequencies and quality factors are compared to experimental and numerical results found in the literature. Depending on the ambient pressure, the geometry of the microbeam, and the fluid boundary conditions, squeeze-film effect can impact not only the effective damping of the device but also its dynamics. It is shown that in some cases dropping fluid relaxation modes cannot be compensated by any set of purely structural modes. The non-classical damping introduced by the fluid modes is a spatially distributed phase difference between pressure and deflection. The convergence analysis of the dynamic response resulting from the reduced-order model showed that a basis with one set of coupled modes and one fluid mode can reproduce the results of a fully discretized model within 1.5% error and at much faster computational time.

The lattice Boltzmann (LB) method is widely regarded as a very flexible and efficient solver for a broad class of transport phenomena in fluids, soft matter and related fields. In this paper, we posit that such flexibility is a direct result of its generative nature as a rule-driven information-processing machine. Its update, a relaxation toward a local target followed by a shift along the lattice, belongs to the same class of iterated relaxation dynamics as residual networks and transformers, with the difference that in LB the operators are fixed by conservation and symmetry rather than learned from data. We show that three properties of this update are sufficient to promote the emergence of closed macroscopic laws from the underlying iteration process, the physical content of the target deciding the specific law in question. A machine whose target is drawn at random generates the transport law predicted from its moments. A network given the same three properties on a graph, where there is no lattice, is trained on a traffic process and generates a conservation law of its own. The mechanism has a precise limit, where the damping of the non-conserved modes fails, and on the lattice the macroscopic law gives no warning of it. In this reading, LB is a lattice Boltzmann machine whose informing rules are supplied by physics rather than by training. Its three properties then state what a new ingredient should preserve when it enters an LB model, whether it comes from physics or from data.

Two-stage contagion, in which adoption requires two successive contacts with adopters, combined with population turnover produces bistability and relaxation oscillations in Katriel's differential-equation model, but no chaos. We derive from the elementary reactions of the process, without reference to the differential equations, a discrete-time model in which the population is updated in rounds of length $\tau$, as in elections, meetings or turns of a game: each individual makes at most one transition per round, events compete as exponential risks, and adoptions take effect from the next round. The model is a Markov chain whose large-population limit is a map $F_\tau$; Katriel's equations are recovered as $\tau\to0$. Taking the probability $p$ of adoption after a single contact as bifurcation parameter, with rates and round length fixed, $F_\tau$ goes from extinction through a window of chaos to a stable equilibrium; for $\beta/\gamma=46$, $\mu/\gamma=0.002$, $\gamma\tau=5.5$ the window is $0.023\le p\le0.056$, bounded by the invasion threshold and by a boundary crisis beyond a subcritical Neimark--Sacker point. One-stage contagion ($p=1$), $p=0$ and permanent adoption showed no chaos. The chaotic attractor is essentially unique, with one positive Lyapunov exponent and an outbreak--recharge geometry. In the same window Katriel's equations have a periodic relaxation cycle with troughs of $10^{-44}$--$10^{-164}$: the round structure does not create the oscillation but turns it into chaos and shrinks the oscillatory range in $p$ from $(0.022,0.41)$ to $(0.022,0.056)$. The chaos is therefore not an artefact of discretising a stable state, but a property of two-stage contagion with synchronous updating.

We study a single-species vegetation model in which a strong Allee effect acts locally and competition acts through a nonlocal kernel, and we describe the kernel with the one-parameter family of q-Gaussians, which goes from compact support to power-law tails. The local activation introduced by the Allee effect allows a finite-wavelength instability even when the Fourier transform of the kernel is positive, so Gaussian and heavy-tailed kernels can produce patterns. We derive in closed form the coefficients of the hexagonal amplitude equations and verify them against independent numerical steady states. The quadratic coefficient $Q$ results from the balance between the curvature of the local growth and the competitive inhibition at the pattern scale, and at onset its sign depends only on the fraction of the local activation that diffusion removes at the critical wavenumber. The same coefficient controls the morphology, since spots, labyrinths and gaps appear with pairwise competition only as $Q$ changes sign, and the amplitude equations predict the choice between hexagons and stripes in every simulated state in which the cubic truncation holds. It also controls the total biomass, which increases for spots and decreases for gaps.

Rational solutions of partial differential equations (PDEs) are notoriously difficult to approximate via spectral Fourier methods due to their algebraically slow decay rate. In this work we discuss approximating rational PDE solutions in a basis of orthogonal functions known as the Christov functions, allowing for the computation of its spectrum via the fast Fourier transform. An explicit fourth-order integrating factor method is derived. The effectiveness of the method is tested on several nonlinear PDEs. Relative to a straightforward pseudo-spectral approximation, the integrating factor method supports larger regions of stability resulting in a more efficient scheme.

The formation and dynamics of dissipative solitons are governed by the interplay of dispersion and nonlinearity, alongside the gain-loss balance. While it is known that dispersion orders beyond the conventional second order support stable solitons, the possibility of the creation of dissipative topological solitons in this setting was not explored. Here, we reveal a class of stable dissipative solitons enabled by the pure-high-even-order dispersion (PHEOD), with dispersion orders m=4, 6, 8, and 10. The resulting dissipative topological solitons (DTSs) and moving topological solitons (MTSs) are dark-type structures featuring a zero-amplitude point that separates two CW backgrounds with opposite signs. In particular, the PHEOD solitons feature oscillatory tails, which are not present in the conventional dark states. The linear-stability analysis confirms full robustness of the PHEOD-supported DTSs and MTSs. We also explore collision dynamics of MTSs, whose repulsive interactions are inelastic, leading either to rebound, accompanied by emission of dispersive radiation, or complete fusion. These findings establish PHEOD as a means for the generation of new species of dissipative solitons, and broaden the variety of nonlinear modes available to experimental studies in nonlinear optics.

A metasurface is an electrically thin interface that controls the phase, amplitude and polarization of a wave, upon reflection or transmission. Printed on a grounded dielectric substrate and spatially modulated across the aperture, it converts a guided surface wave into a radiated leaky wave, a mechanism used in holographic metasurface antennas. Controlling this conversion requires synthesizing a prescribed distribution of admittance tensors, each derived from the homogenization of a subwavelength unit cell. Many numerical and semi-analytical methods have been proposed to relate the geometry of a meta-atom to the tensor it produces. This paper presents, to the author's knowledge, the first analytical model, restricted to elliptical meta-atoms on a uniform lattice. The Galerkin method is applied directly to the geometry of the patches, without spatial meshing. An affine transformation maps any rotated ellipse onto the unit disk, so that a single formulation covers every configuration. A wideband response takes from minutes to tens of minutes with a periodic full-wave solver, while the proposed model evaluates it in a few tens of milliseconds on the same workstation, roughly three orders of magnitude faster. The predicted admittance agrees with a method-of-moments reference up to the fundamental resonance and captures the guided-mode anomaly of the substrate. Beyond the physical insight it brings, the model is a differentiable function of the geometry, which makes the quasi-real-time design of optimized metasurfaces possible.

Rheoscopic flow visualization is widely used to study turbulent decay in wall-bounded flows, although the physical interpretation of the measured decay times has received less attention. By comparing rheoscopic visualization with particle image velocimetry in plane Couette–Poiseuille flow, we show that the measured decay times are closely associated with the slower decay of streamwise streaks rather than the faster decay of vortical rolls. These findings improve our understanding of rheoscopic measurements in transition to turbulence in plane shear flows.

Capillarity governs interfacial relaxation and hydrodynamic motion in binary fluids through parity-even mechanical stresses. Here, we introduce \emph{odd capillarity}, a parity-breaking interfacial mechanical response, by incorporating a symmetric, nonvariational, parity-odd capillary stress into the Cahn--Hilliard--Navier--Stokes (CHNS) equations. This stress generates forces along interfaces, transverse to ordinary capillary forces, and performs mechanical work that is not balanced by changes in the composition free energy. Direct numerical simulations reveal that odd capillarity arrests domain coarsening while sustaining turbulent fluid motion without a conventional inertial energy cascade, as energy injection is predominantly balanced by viscous dissipation. In asymmetric mixtures, odd capillarity driven deformation and breakup interrupt droplet growth, producing dynamically arrested emulsions with composition hyperuniformity and suppressed large-scale vorticity fluctuations. These findings establish odd capillarity as a distinct interfacial mechanism for controlling phase separation and sustaining nonequilibrium fluid motion.

Quantitative full-field measurements of vapor concentration remain challenging near receding liquid-gas interfaces. We develop and quantitatively assess an infrared absorption imaging method for measuring vapor mole-fraction fields during evaporation. Broadband mid-infrared attenuation is converted into mole fraction using a spectrally weighted absorption coefficient. A vertical Hele-Shaw cell provides a controlled, nearly one-dimensional evaporation benchmark, with calibrated object-plane sampling of $30.5\,\mu\mathrm{m/pixel}$. Small transverse concentration variations in the central measurement region justify reducing the two-dimensional fields to axial profiles. Five profiles spanning different retained gas-phase interval lengths and three hydrocarbon liquids are compared with Stefan predictions using only measured interval lengths and endpoint concentrations, without fitting interior concentration data. At the higher vapor loading of n-pentane, the measurements resolve the nonlinear Stefan concentration profile and distinguish it from the linear diffusion limit. At the lower vapor loadings of n-hexane and n-heptane, the profiles progressively approach that dilute limit. The profiles agree with Stefan predictions, with normalized root-mean-square deviations of 0.0055-0.0185, and collapse onto the predicted identity relation after the logarithmic Stefan transformation. These results demonstrate quantitative recovery of both the magnitude and spatial structure of vapor concentration fields under the tested conditions. The method provides a full-field, tracer-free diagnostic for investigating evaporating flows in geometries and regimes where analytical concentration fields are unavailable.

Microfluidic droplet generation is critical for many applications, yet efficient device design in high-dimensional parameter spaces remains computationally prohibitive due to complex multiphase flow dynamics. This work presents a unified methodology that couples adaptive surrogate enhancement with simulation-driven inverse design. High-fidelity Volume-of-Fluid simulations provide ground-truth data, while neural network ensembles predict flow regimes and droplet diameters. Ensemble-based uncertainty quantification identifies epistemic uncertainty using consensus levels for regime classification and the coefficient of variation for diameter prediction, revealing that uncertainty concentrates near regime transition boundaries where physics is highly sensitive to parameter perturbations. A physics-informed enrichment strategy targets these critical zones and addresses class imbalances by deploying additional targeted simulations and retraining the surrogates forming the ensembles. A framework that integrates Particle Swarm Optimization for constrained inverse design, balancing accuracy with predictive confidence and physical consistency is therefore proposed. Validation on independent test datasets demonstrates that the enriched ensembles achieve higher accuracy, with the fraction of predictions within the 0-3% error range on droplet diameter nearly doubling, and high-error cases (above 10%) dropping substantially. The inverse design procedure reliably identifies physically realizable configurations meeting target droplet sizes. This approach significantly reduces computational costs while ensuring reliable predictions, offering a framework with potential applicability to the optimization of a broad range of microfluidic systems.

Mafic microgranular enclaves in granitic plutons record magma mingling, and their shapes are often interpreted as a record of the flow that deformed them. We investigate how a dense, low-viscosity droplet deforms in a lighter, much more viscous host under shear and gravity, using 96 two-dimensional Level-Set simulations. The viscosity ratio ($\mu_r$) spans $10^{-6}$ - $10^{-3}$, the capillary number ($\mathrm{Ca}$) ranges from $10^{6}$ to $8\times10^{9}$, the Bond number ($\mathrm{Bo}$) takes values of $3.5\times10^{6}$ and $9.8\times10^{6}$, and the Reynolds number ($\mathrm{Re}$) remains below $10^{-2}$, with a fixed density contrast ($\Delta\rho$) of $400~\mathrm{kg\,m^{-3}}$. Two broad regimes identified- sinking and non-sinking which spread over six outcomes like sinking, edge, mid and multiple break-up, rotation, and retraction. The ratio $\mathrm{Ca/Bo}$ separates sinking from shear-dominated behaviour near unity, although the transition spans a range of $\mathrm{Ca/Bo}$ values that shifts with confinement. In the shear-dominated regime, a lower viscosity ratio promotes stretching. Multiple pinch-off occurs mainly at viscosity ratios of $10^{-6}$ - $10^{-5}$, rotation occurs only at the higher vertical confinement, and retraction occurs only at the lower vertical confinement. The strain at maximum stretch averages 1.1 - 1.4 and increases with $\mathrm{Ca/Bo}$, with a stronger increase at higher confinement. The orientation of the major axis decreases by approximately $10^\circ$ per unit strain and is lowest for rotating droplets. Because the capillary number exceeds conventional critical values for breakup for droplets, breakup is interpreted in terms of accumulated deformation rather than capillary stability alone. Enclave shape therefore reflects the flow regime and is not a direct measure of finite strain.

Cavitation bubbles generated by focused ultrasound can mechanically destroy tissues, as in histotripsy, where tissue damage scales with maximum bubble size. We extend an energy budget analysis to include viscoelastic and compressibility effects and derive an analytical expression for the maximum radius of a spherical bubble. The maximum radius decreases with increasing shear modulus but increases with pulse amplitude and wavelength. Our model accurately predicts the maximum radius under explosive growth conditions, established from pulse amplitude and frequency. These findings clarify the physics governing bubble growth and may inform the design of ultrasound-based therapies.

Experimental observations and computer simulation of formation and structural properties of so far experimentally never seen electrically charged propagating 3D solitons are reported. The propagating solitons appear spontaneously without an external field in a ferroelectric nematic (NF) liquid crystal under rapid cooling from the antiferroelectric (SmZA) phase. The observed solitons propagate either parallel or antiparallel to the ferroelectric polarization and annihilate when they collide with each other. They are attributed to either positively or negatively charged propagating local polarization splay formed to screen excess negative or positive mobile charge lumps in the NF phase. The presence of mobile charge is attributed to a spatially periodic charge distribution present in the antiferroelectric phase that temporarily remains after the temperature is quenched through the antiferroelectric- ferroelectric phase transition.

Frank elastic constants of associating rigid rodlike systems are investigated using a mean field theory combined with the Straley elastic free energy formalism. The aggregation equilibrium and orientational ordering are treated self-consistently to analyze the concentration and temperature dependences of the elastic constants. Both a monomer--dimer model and a fully polydisperse rodlike aggregate model are considered. We find that aggregation selectively enhances the bend elastic constant through the long-tail structure of the aggregate-size distribution. As a result, a pronounced elastic anisotropy, $K_{33}\gg K_{11}>K_{22}$, emerges in the nematic phase. Decreasing temperature or increasing concentration promotes the formation of long rodlike aggregates and induces a rapid increase in the bend elastic constant, while the relation $K_{11}=3K_{22}$ remains unchanged. The exceptionally large bend elastic constants predicted here should be regarded as upper-bound estimates for the rigid-aggregate limit.

Materials constructed from interlocking and tangled fibers are challenging to model and understand due in part to the complex interplay between fiber shape and contact mechanics. Much of our intuition about contact mechanics comes from the Hertzian description, which is based on interactions between convex bodies. However, fibers often form clasp shapes, which involve saddle-shaped contact surfaces; the ability for two interacting bodies to conform to each other along a saddle surface confounds many existing mechanical contact models. Following an observation that contact surfaces between fibers tend to look like minimal, constant mean-curvature surfaces, we seek to test this hypothesis and provide a direct link to geometric modeling methods. To do this, we leverage the medial axis transformation, which generalizes the notion of a Voronoi tessellation to generating curves and surfaces. Through computational studies on an orthogonal clasp and a simple knit structure, we find that the medial axis transformation provides a reasonable model for contact surfaces between identical curves. We also show that a generalization of the medial axis transformation based on radical Voronoi tessellations can be used to well-approximate contact surfaces between non-identical curves. We apply this ``radical axis transform'' to curves of different radii and demonstrate a trend for surfaces to adopt finite mean curvature. Our results may point the way towards more sophisticated geometric methods for modeling tangles.

We experimentally investigate the applicability of Kolmogorov's first similarity hypothesis to shear-dependent viscosity fluids. We assess whether dissipative range statistics exhibit a self-similar behavior in nearly homogeneous and isotropic turbulence, using stereo particle image velocimetry in aqueous Carbopol solutions across two concentrations and a range of forcing conditions. We observe that, when normalized by the mean viscosity and mean dissipation rate, second- and third-order structure functions collapse across the different experimental conditions and exhibit functional forms compatible with classical Newtonian results. These observations are in general agreement with the recent numerical results of Rosti [J. Fluid Mech. 1012, R5 (2025)], who proposed that Kolmogorov's similarity hypotheses can be extended to shear-thinning fluids by considering dissipation scales based on the mean viscosity, the mean dissipation rate, and the flow index.

Coarse-grained models of protein conformational dynamics use $\mathrm{C}_\alpha$ geometry to describe the probabilities of regular helices, ordered turns and disordered conformations. To test how much of this order arises from local chain elasticity, we connect discrete Hasimoto frame transport to neighboring bending mismatch, deriving a curvature-product torsion interaction and a six-parameter generalized von Mises density. Fitted on 194 chains from the ATLAS molecular dynamics database and tested on 1744 sequence-nonredundant proteins, this baseline reduces negative log-density loss from 1.490 to 1.160 nats, torsion-sign error from 12.26 to 2.15 percentage points, and helix-fraction error from 21.84 to 10.41 points. Ablations and circular-moment projections against reference generative models motivate extensions to anisotropic stiffness and two partition-function-weighted elastic states, further lowering test loss to 0.790 nats and helix error to 1.65 points. The fixed hierarchy also improves predictions across 72 trajectories of peptides $\mathrm{Fs}$ and $(\mathrm{AAQAA})_3$ and miniprotein $\mathrm{HP35}$ spanning varied starting conformations and force fields. Remaining angular errors in these trajectories are associated with atomic context at shared bends, as bend-matched peptide frames adopt opposite torsion signs with distinct hydrogen-bond patterns and a proline-containing $\mathrm{HP35}$ turn remains at negative torsion. Introducing a bilinearly coupled $\mathrm{C}_\alpha$--$\mathrm{N}$ orientation angle largely reparameterizes the existing bend-dependent harmonics, with an empirical $L^2$ Gram projection placing 96.7\% to 99.6\% of its added coefficient-function squared norm within the original six-function span. These results link discrete Hasimoto elasticity to statistical backbone potentials and clarify the scope and limits of local $\mathrm{C}_\alpha$ geometry.

Reconstructing full flow fields from sparse sensors requires prior assumptions about unmeasured regions and physical variables. Yet it remains unclear when learned models outperform classical estimators and which aspects of their predictions can be trusted. FlowReconBench evaluates ten learned and five classical methods on three regimes: a laminar cylinder wake across Reynolds numbers, two-dimensional Kolmogorov turbulence and a large-scale three-dimensional (3D) isotropic turbulence. Methods share leakage-controlled splits and sensor draws and are scored on per-channel error, ensemble spread, calibration, spectra and cost. The leading method changes for each regime. Classical methods perform strongly in low-order and dense-sensing regimes. On the cylinder wake, linear stochastic estimation and gappy proper orthogonal decomposition lead, including for unobserved pressure. In 3D, inverse-distance weighting matches the best learned methods on observed channels. Data-driven methods become superior at decreasing sensor density or poor sensor observability. On Kolmogorov flow, continuous ranked probability score and error yield different method rankings: generative models offer broader but underdispersed ensembles, while deterministic models prioritize pointwise error. Generative models balance this tradeoff through their sampler budget, with a larger budget improving ensemble quality at higher computational cost. In 3D, scaling tests demonstrate that queryable methods are flat in memory, while full-grid construction methods run out of memory. Observing only 2 of 4 fields leaves the problem kinematically underconstrained, yet a latent model can reproduce structural similarities to the ground truth.

We investigate the interscale energy dynamics of nearly homogeneous isotropic turbulence (HIT) generated in a spherically forced, propeller-driven device. From a spatial perspective, by employing the Kármán-Howarth-Monin (KHM) framework, we analyze the scale-by-scale energy transfer without isotropy assumptions. In contrast to other forcing strategies, where regions with inverse and forward cascades often coexist in scale space, we show that spherical forcing produces a purely forward energy cascade across the entire scale space. While the energy distribution remains highly isotropic and orientation-averaged structure functions align with Kolmogorov's two-thirds law, the energy flux exhibits a directional dependence, suggesting a higher sensitivity to residual forcing asymmetries. Regarding the temporal dynamics, the reduced mean flow generated by this device allows us to investigate the temporal variability in conditions where Taylor's frozen turbulence hypothesis does not apply. Our results provide experimental validation of Tennekes' Eulerian frequency spectrum, where intermediate scales evidence an inertial-convective range with statistics determined by the integral velocity scale and the dissipation rate. Finally, we adopt a global approach to investigate whether the main turbulent scales can be linked to external experimental parameters. We propose a framework that captures the propeller frequency dependence of the main turbulent variables obtained in our measurements and those of previously reported HIT chambers. These findings contribute to the understanding of how external forcing influences the complex interscale energy dynamics of turbulent flows from a spatial, temporal, and global perspective.

Non-Gaussian stationary fluctuations with heavy tails and finite-order moment cutoffs are ubiquitous in non-equilibrium systems. Here, we derive the Pearson type IV distribution as the stationary solution of a standardized Fokker-Planck equation with linear drift and quadratic diffusion. We establish necessary and sufficient conditions for its emergence and show that the linear-quadratic structure, although sufficient, is not necessary. We also give explicit closed expressions for the cumulative distribution function, a moment recurrence relation, skewness, kurtosis, and mode. From a physical perspective, our results reveal that heavy tails and asymmetry originate from distinct features of state-dependent diffusion: its local nonlinear curvature and gradient, respectively. In particular, asymmetric stationary fluctuations can emerge even in the presence of a symmetric linear restoring drift. This framework provides a general stochastic description of asymmetric heavy-tailed fluctuations in non-equilibrium systems, including space plasma turbulence.

This paper extends our prior work on interface conditions between two poroelastic domains to the case when a poroelastic domain interacts with a pure fluid. The porous medium is assumed to be deformable and modeled following mixture theory. When not in a mixture, each constituent of the porous domain is assumed to be incompressible. An arbitrary Lagrangian--Eulerian formulation is developed for both the fluid and porous domains. The fluid velocity and pressure fields are allowed to be discontinuous across the pure fluid/porous domain interface. A globally continuous displacement field is defined to represent both the deformation of the solid skeleton of the poroelastic medium and the mesh motion in the pure fluid domain. As an interface condition, the continuity of the normal component of the filtration velocity is enforced via a Lagrange multiplier. The mixture momentum jump condition is implemented so as to transfer the traction from the fluid side to the porous domain. A dissipative behavior is attributed to the interface, and the jump condition for the fluid momentum, derived from Hamilton's principle, incorporates this prescribed behavior. The model implementation is verified using the method of manufactured solutions, and a sample problem is solved to compare an inert interface with a fully dissipative one. The results show satisfactory convergence rates, while the proposed model successfully reproduces the analytical solution of a benchmark problem using conventional jump conditions. Furthermore, the findings highlight the significant influence of the selected interface model on the behavior of the system.

A pore-scale lattice Boltzmann model is developed for reactive transport in phase-changing porous media, coupling solute transport in the liquid with conjugate heat transfer across the solid and liquid phases. Two methodological developments are introduced: a novel link-based Volume-of-Pixel formulation for direction-dependent interface motion, and a generalized Robin boundary treatment for solute redistribution at moving interfaces. The phase-change formulation is validated against thermal benchmarks, while the Robin treatment is assessed through literature test cases, exhibiting convergence rates between first and second order. The coupled model is then applied to a local pore-scale segment of a sea ice brine channel in a purely diffusive regime. The simulations recover the expected ideal mushy-layer behaviour under appropriate scale separation. At sea-ice-relevant concentration ratios, thermal perturbations produce relatively large variations in brine salinity, causing freezing rather than melting to reshape the pore geometry in a non-uniform way. The resulting framework provides a pore-scale numerical tool for resolving coupled temperature, solute redistribution, and phase-boundary dynamics in mushy layers.

The Johnson-Koplik-Dashen viscous characteristic length $\Lambda$ and its thermal analogue $\Lambda'$ introduced by Champoux and Allard govern the leading $O(\omega^{-1/2})$ boundary-layer behaviour of fluid-saturated porous media, but omit higher microgeometric effects associated with interface curvature and field gradients. We develop the asymptotic high-frequency expansions of dynamic tortuosity and dynamic compressibility beyond the leading boundary-layer terms. By resolving the oscillatory Stokes and heat conduction problems in the thin boundary-layer limit, we establish a recursive hierarchy, which can be continued to any order, defining successive microgeometric parameters, given by wall integrals. Each order requires transport equations of WKB type across the boundary layer, closed by a non-secularity condition, together with one Neumann problem for the potential displacement flow that the boundary layer induces. Applied to the values fitted on highly absorbing foams, these expressions show that the negative surface parameter is consistent with strong in-parallel disorder of the pore sizes, whereas the large positive third-order term points to strong constrictions or enlargements along part of the flow paths. The thermal parameters reduce to geometrical quantities: the integral mean curvature of the pore walls, a Willmore-type measure of their departure from umbilicity and, at the next order, this measure weighted by the mean curvature. Using the Avellaneda-Torquato relaxation-mode representation, we show that all these parameters are spectral data of the distribution of relaxation times. For isolated sharp edges across which the fluid flows, the singular terms of the formal expansion cancel, and the description persists with apparent, logarithmically varying values of the parameters.

Although the phenomenon of wave growth under the effect of wind still holds many open questions, the approach initiated by Miles [1] is a cornerstone of the current comprehension. This theory is based on physical arguments, keeping phenomenological input to a minimum, but it can be perceived as intimidating, especially in view of concrete applications. Here we argue that Miles' results can be summarised in terms of a simple functional form, which provides an easy-to-use expression to work with. We furthermore show that Miles' predictions do not, as is often stated, underestimate growth rates, once the presence of a whole wave spectrum is accounted for. Finally, we illustrate that the generalisation of Miles' original result to complex hydrodynamic situations can be quite straightforward. Our hands-on summary should make it heretofore very easy to exploit Miles' approach in practice.

We investigate mixing dynamics in porous media at finite times, using pore-scale lattice-Boltzmann simulations combined with Lagrangian particle tracking. We compute fluid deformation in randomly packed beds based on the moving Protean frame approach introduced by Lester 2018. From the extracted Lagrangian kinematics, we construct a mixing model based on lamellar aggregation that well predicts the Eulerian scalar fields obtained from simulations. Our results reveal an early time mixing regime dominated by shear-driven fluid deformation, where solute mixing arises from the random overlap of diffusive concentration elements. In this regime, mixing proceeds slowly and follows a temporal decay of concentration variance, $\sigma_c^2 \sim Pe^{-\alpha/(2\alpha+1)} t^{-1/2}$, where Pe is the Peclet number and $\alpha$ the exponent characterizing shear deformation. This dynamic arises when the Peclet number is small relative to the ratio between the exponential-mixing and shear-deformation timescales. This analysis also demonstrates that shear-induced mixing govern the homogenization of early-stage reactions at the fluid-solid interface in finite-size random packed beds, typically operating at moderate Peclet numbers $Pe =O(10^2)$.

We investigate two-dimensional Couette flow between parallel plates as a model of protoplasmic streaming in plant cells using a combined Langevin and Navier?Stokes simulation. The interaction between the fluid and biological materials is implemented using a Finsler geometry (FG) modeling technique, in which the interaction strength, represented by quantities such as relative viscosity, effectively varies with an internal degree of freedom (IDOF) associated with the biological materials. The simulations demonstrate that the Couette flow exhibits a linear velocity profile along the vertical direction perpendicular to the plates, as well as a peak structure in the velocity distribution consistent with reported experimental observations obtained by laser light scattering. The simulations also demonstrate that the model exhibits shear-thinning behavior typical of non-Newtonian fluids, with the viscosity minimized in the boundary region. Additionally, we find that the rheological properties are connected to the conformal transformation of the interaction between the fluid and the IDOF. Within the FG modeling framework, the conformally flat configuration of the IDOF, which is neither anisotropic nor randomly isotropic, is introduced as a minimum-energy state that characterizes the shear-thinning rheological properties of two-dimensional Couette flow.

We develop a physics-informed method for aerodynamic shape optimisation of turbine blades, treating the flow field and blade geometry as coupled unknowns. The method translates prescribed surface-pressure distributions into geometric modifications through pressure-target continuation and alternating flow-geometry updates. A differentiable representation of the blade surfaces allows their positions and orientations to be optimised within the current flow field, followed by flow re-adaptation to the modified boundaries. The inverse formulation uses the two-dimensional steady compressible Euler equations as physics constraints and is evaluated on the LS89 turbine cascade using 28 pressure-target points derived from experimental data. Starting from a modified profile and a warm-started flow network, the final pressure-side and suction-side root-mean-square fitting errors are 1.13% and 2.21% of inlet total pressure, respectively. Independent forward verification with SharC reproduces the principal surface-pressure trends of the experimental measurements, with remaining differences near the trailing edge. These results demonstrate the translation of experimental-origin loading data into geometric blade modifications through coordinated optimisation of the flow field and moving boundaries.

The role of small atmospheric particulates in the initiation of the laminar-turbulent transition is investigated for the HIFLIER vehicle during Mach 6 ascent condition. High-fidelity simulations are used to examine the disturbance wavepackets generated by particles following either grazing trajectories through the boundary layer or trajectories that lead to impact and rebound at the cone surface. Grazing particles that penetrate less than halfway through the boundary layer are found to generate wavepackets with amplitudes comparable to those produced by wall-impinging particles. To identify the receptivity mechanisms responsible for this behaviour, a multiple-scales asymptotic formulation is developed that accounts for the extended streamwise region over which a particle interacts with the boundary layer. The analysis shows that a grazing particle can generate a strong disturbance response when crossing the critical layer, where the streamwise-momentum component of the adjoint mode is largest and the boundary layer is most receptive. Thus, direct surface impact is not required for atmospheric particulates to excite dynamically significant instability waves. Root-mean-square disturbance estimates for submicron grazing particles predict transition-onset locations close to those measured in flight, suggesting they may have contributed significantly to the onset of transition on HIFLIER at the trajectory condition considered.

Biofilm growth in hydrogen-generating fractures modifies fluid flow and hydrogen transport, while microbial activity consumes hydrogen. These coupled processes influence hydrogen recovery in stimulated geologic hydrogen systems. We use high-fidelity simulations to investigate flow, biofilm dynamics, and hydrogen transport in a rough fracture with reactive walls. Flow rate and biofilm permeability were varied to quantify changes in fracture permeability, biomass accumulation, and outlet hydrogen concentration. Biofilm growth reduced apparent fracture permeability by up to 65\% as biomass occupied the aperture. Two hydrogen concentration regimes are identified. For highly permeable biofilms (Type I), outlet concentration evolved non-monotonically as roughness-induced vortices initially restricted hydrogen transport before biofilm growth suppressed them. Low-permeability biofilms (Type II) result in an approximately monotonic outlet concentration decrease dominated by transport resistance and microbial consumption. The regimes were distinguished by a Darcy-scale Reynolds number ($Re_D=u\sqrt{K_0}/\nu$). Temporal hydrogen concentration variations in field studies may help determine intrinsic biofilm permeability.

The method of regularized Stokeslets (MRS) is widely used to model fluid-structure interactions of microscopic bodies in viscous environments. Specifically, MRS computes the fluid velocity generated by regularized forces distributed on an immersed body, which in turn defines a system of ordinary differential equations with which to evolve the body so that the no-slip condition is enforced. To accurately model material properties such as elasticity and bending rigidity, the resulting ODE system is often stiff and, therefore, computationally expensive to solve with explicit time-integration methods. Here we demonstrate the potential of linearly implicit Rosenbrock (ROS) time integration methods to greatly reduce the computational time required to solve such ODE systems. We focus on the classic model problem of the swimming of a flexible filament driven by preferred curvature forcing. Our findings indicate that, compared to previous MRS simulations, the increased stability of ROS methods allows for speed-ups between twenty and two thousand times over explicit Runge-Kutta (ERK) methods. Moreover, we present approximate scaling laws for this speedup as a function of the key model parameters (bending rigidity and slenderness) at the root of numerical stiffness. Lastly, beyond the basic ROS approach, we discuss several additional strategies that further improve performance.

Binary neutron star (BNS) mergers excite a Kelvin--Helmholtz instability (KHI) in the shear layer between them. It is parasitized upon by the magnetic field to form a powerful magnetic dynamo. Using a large ensemble of high-resolution visco-resistive KHI-driven dynamo simulations we construct analytical, asymptotic in Reynolds number ($\rm{Re}$) models for the magnetic field growth rates and mean vertical field dynamo onset times. Our models suggest that in the $\rm{Re} \gg 1$ limit, the mean vertical field is seeded immediately, kinematic growth rates become asymptotic in $\rm{Re}$, and the dynamo moves out of the kinematic stage on $\mathcal{O}(0.1\,\rm{ms})$ timescales, readily attaining magnetar-strength fields during this transition. This suggests that most global BNS merger simulations are not time-resolving the correct KHI-driven dynamo regime.

Data-driven methods can recover compact equations, yet the physical dependence of their coefficients across operating conditions often remains unresolved. Dimensionless groups can explain this variation, but selecting relevant groups from the many dimensionally admissible combinations remains challenging. Here, we introduce a knowledge-guided framework for dimensionless learning, called {\pi}-former. It learns patterns of variable association and exponent assignment from a corpus of 1,288 established dimensionless groups. Under exact dimensional constraints, the model proposes interpretable basic groups whose combinations are optimized against observations. Across seven physical problems, the framework identifies predictive dimensionless coordinates within seconds. Integration with equation discovery further expresses condition-dependent coefficients through these coordinates, recovering established physical scalings in multi-condition simulations. Applied to experimental measurements of evaporation-driven wetting, the framework discovers dimensionless coordinates and uses them to construct a unified trajectory equation. The resulting model generalizes to held-out conditions across liquids and initial volumes, outperforming existing empirical models. These results establish dimensionless learning as a transferable bridge between accumulated scientific knowledge and data-driven equation discovery, enabling artificial intelligence to uncover physically meaningful laws from observations.

Self-supervised world models are often said to organize their latents around physical quantities. We test this on 2D decaying Navier-Stokes flow in three pre-registered studies, each tested once on held-out data. In Study 1, a joint-embedding predictive architecture (JEPA) trained to predict the flow fails the pre-registered criteria for organizing its latent around fluid quantities better than an untrained network of the same architecture (not supported); a JEPA trained on non-physical linear dynamics and a static invariance model that never sees time do as well or better. In Study 2, plain autoencoders that render the field make enstrophy prominent in their slowest unsupervised latent directions (best r 0.80-0.86 vs 0.38 untrained; fresh seeds, sealed data). Adding VICReg lowers this prominence in every comparison, though not by the pre-registered margin for vorticity, while raising the autoencoders' linear decodability (partially supported). In Study 3, we build steerable directions ("dials") by routing: the decoder gets overall scale only through a small conditioning code, while its other pathway carries a degraded copy of spectral shape. Label-free rules find a loudness dial in all 8 trained models and a shape dial in 3 of 5 fresh seeds on sealed data, against a pre-registered bar of 4; neither control shows a shape dial (partially supported). Across the studies, what a latent contains and what can be controlled through it come apart. In exploration, a supervised direction reading spectral shape almost perfectly moved nothing when steered. During the build, the loudness dial had to be found by its effect on the output (closest to a pure rescaling), not by data variance; for shape, a variance rule and an effect-constrained rule each worked in 3 of 5 seeds. The program used about 70 logged hours on one consumer GPU; all pre-registrations, deviations, code and outputs are public.

The Stroh sextic formalism, developed by Stroh, offers a compelling framework for representing the equilibrium equations in anisotropic elasticity. This approach has proven particularly effective for studying multilayered structures and time-harmonic problems, owing to its ability to seamlessly integrate physical constraints into the analysis. By recognizing that the Stroh formalism aligns with the canonical Hamiltonian structure, this work extends its application to Biot's poroelasticity, focusing on scenarios where the solid material is incompressible and there is no fluid pressure gradient. The study introduces a novel Hamiltonian-based approach to analyze such systems, offering deeper insights into the interplay between solid incompressibility and fluid-solid coupling. A key novelty lies in the derivation of canonical equations under these constraints, enabling clearer interpretations of reversible poroelastic behavior. However, the framework assumes perfectly drained conditions and neglects dissipative effects, which limits its applicability to fully realistic scenarios involving energy loss or complex fluid dynamics. Despite this limitation, the work provides a foundational step toward understanding constrained poroelastic systems and paves the way for future extensions to more general cases, including dissipative and nonlinear regimes.

Single precision (FP32) halves the memory and data movement of double precision (FP64), and on accelerators is often several times faster. Its rounding errors are harmless except in the stored state. A modified equation for Runge-Kutta methods in Shu-Osher form and linear multistep methods separates the rounding of the stored state, a forcing proportional to $1/\Delta t$, from truncation and from right-hand-side rounding, which sets a $\Delta t$-independent floor. We bound this forcing for strong-stability-preserving schemes and identify two mechanisms that keep its sign fixed, so it accumulates as a bias: past a turnaround step, refining the step increases the error, in FP64 as in FP32. For a model oscillator the analysis predicts the floor and the FP32-to-FP64 ratios of turnaround step and minimum error within 30%. Our remedy needs no FP64 arithmetic: each state variable is stored as the unevaluated sum of two FP32 numbers, updated with error-free transformations, while every right-hand-side evaluation stays in FP32. Unlike compensated summation, it needs no rewriting of the scheme. In model problems from geophysical flow, mechanical dynamics and celestial mechanics, with five Runge-Kutta and multistep schemes, it restores design-order convergence to the floor. In large-eddy simulations of a high-lift airplane wing on three refined grids, up to 544 million cells, with time steps $\Delta t$, $\Delta t/2$ and $\Delta t/4$, FP32 overpredicts the lift by 2.1, 4.5 and 7.7%, while the two-float lift agrees with FP64 within 0.3% on every grid, and on graphics processing units the production solver runs 1.6 to 2.7 times faster than FP64.

A stretched wire driven near its fundamental frequency can leave the plane of the driving force and whirl. At larger amplitudes the whirl becomes modulated, reverses its direction, and becomes chaotic. Three models of this motion are in common use: the geometrically exact string equations; a two-mode model -- the Kirchhoff-Carrier equation with one transverse mode in each plane; and the averaged equations for the slow amplitudes of those two modes. We integrate all three under similar conditions and compare them along the route to chaos, which starts with a Hopf bifurcation of the steady whirl and passes through period doublings to chaotic attractors organized by a Shil'nikov homoclinic orbit. The small parameter of the averaging, the ratio $\varepsilon = c/\omega_1$ of the modulation rate to the fundamental frequency, runs from 0.005 to 0.02. Qualitatively the three models agree in the sequence of bifurcations, the coexisting attractors, the return maps and the Lyapunov exponents. Quantitatively, averaging places each local bifurcation $0.7\varepsilon$ to $1.2\varepsilon$ higher in the scaled detuning. The geometrically exact and two-mode models agree with each other to within 0.002 at the local bifurcations for $\varepsilon \le 0.01$. The Shil'nikov ratio, which decides whether chaos accompanies the homoclinic orbit, agrees among the three models to within 1.5% for $\varepsilon \le 0.01$, yet the homoclinic bifurcation itself moves by about $\varepsilon$ at the lower damping and by 6 to 9 times $\varepsilon$ at the higher; the difference is set by how quickly the return of the homoclinic loop changes with detuning.

Chemical reaction networks can evolve from stable oscillations to chaos through successive period doublings. We investigate general properties of entropy-production fluctuations near the onset of chaos and within the chaotic regime in reversible, well-mixed reaction networks. Near an isolated supercritical period-doubling bifurcation, we find a one-sided divergence of the diffusion constant with exponent one. For chaotic attractors satisfying the stated conditions, the entropy variance per unit volume grows exponentially when the macroscopic limit is taken first. Its exponential growth rate is $2\lambda_{\max}$, where $\lambda_{\max}$ is the largest Lyapunov exponent, implying a divergent diffusion constant. We also discuss the volume dependence of the fluctuations and the underlying physical mechanisms.

Non-Hermitian skin lattices can directionally amplify propagating signals. Here we show that this amplification and nonlinear feedback together drive a bypass transition to self-sustained motion, familiar from shear flows. A finite local excitation can trigger sustained periodic or chaotic motion while the resting state remains linearly stable. We develop a return-map theory that predicts the triggering threshold, its scaling with directional gain, and the instability governing near-critical dynamics. The threshold decreases exponentially with chain length. Weak noise triggers sustained motion as well, with a characteristic ignition length that grows logarithmically as noise weakens at fixed observation time. Our work establishes a skin-effect route to bypass transitions, opening a new avenue for predicting and controlling nonlinear wave dynamics.

Higher-order interactions are ubiquitous in biological systems and can be used to better describe the ensemble dynamics of self-propelled particles. To this end, this article investigates a Vicsek-Kuramoto model with distance-dependent higher-order interactions and obtains analytical results, albeit under certain assumptions, that characterize its collective dynamics. Subsequently, these are validated through simulations of the system equations, demonstrating both continuous and explosive transitions between the asynchronous and synchronous collective states. Further numerical results also reveal that short-range interactions and tightly clustered initial states can lead to deviations from the theoretical predictions, whereas the latter can be offset by increasing the common self-propulsion velocity. These results offer insights into a broad class of active matter systems with higher-order interactions, and provide a framework for designing and utilizing them for specific applications.

A discrete chain of one-dimensional elements with concentrated elastic stiffness is analyzed to investigate the effect of self-equilibrated dead loads acting at the microscale. Three homogenization models are formulated for a finite chain whose total length is much larger than the unit-cell length. Model (i) homogenizes the elastic properties and the microscopic loading simultaneously, yielding an equivalent rod with homogeneous axial and flexural stiffnesses, an effective prestress state, and a distribution of nonlinear rotational springs. In Models (ii) and (iii), the microforces remain periodically distributed as external loads. Model (ii) has homogeneous axial and flexural stiffnesses, whereas Model (iii) retains piecewise-constant axial stiffness. Model (i) is shown to recover the continuum limit of the fully loaded discrete system and to provide the most accurate, fully homogenized description. Incorporating the microforces into the nonlinear homogenization procedure produces an unconventional prestress and a distributed rotational constraint, including rotational springs with negative tangent stiffness. The nonlinear equilibrium equation of Model (i) admits a closed-form solution in terms of elliptic functions, enabling analysis of large deflections and initial post-buckling behavior of a cantilever. The model predicts tensile and compressive buckling, as well as restabilization of the straight configuration. Finally, combined control of the end load and microforces is explored for soft-robotic actuation. Suitable loading paths allow switching between straight and bent configurations and changing the bifurcation character from supercritical to subcritical.

Competition between tension and bending waves in a pre-stretched soft beam Pre-stretched one-dimensional soft beams serve as an important and simplified model in mechanics, biomechanics, and soft material characterization. The propagation characteristics of transverse waves excited on such beams are commonly used to characterize elastic stiffness and tensile state. However, conventional pure beam or string models cannot fully explain the phase velocity dispersion of transverse waves in pre-stretched beams, particularly when the dispersion coexists with an increase in wave speed as tension increases. This frequency-dependent transition between tension-dominated and bending-dominated behavior has not yet been directly validated using measured dispersion curves in one-dimensional soft beams. Here, we use optical elastography, a high spatiotemporal resolution technique, to track transverse wave propagation in a soft incompressible cylinder under different tension levels and obtain the corresponding phase velocity dispersion curves. Through modelbased inversion of the experimental dispersion curves, we demonstrate that a coupled Timoshenko-beam/string model successfully captures both the string-dominated and bending-dominated regimes observed experimentally. This result indicates that transverse wave propagation in pre-tensioned beams should be understood as a frequencydependent competition between tension and bending effects.

Classical shock-wave theory relies on ideal-gas assumptions that fail in dense and supercritical fluid regimes. By coupling the Navier–Stokes equations with a real-fluid thermophysical model for supercritical CO 2 , this study resolves the internal spatial structure and non-ideal jump relations across shocks. Surprisingly, while non-ideal thermodynamics strongly alters pressure–density jumps, the physical shock thickness remains primarily governed by the upstream Mach number. These results reveal how dense- fluid thermodynamics reshapes compressive discontinuities, defining the limits of classical shock theory.

Understanding how nonequilibrium systems evolve between distinct statistical regimes remains a fundamental challenge in statistical physics. Here we show that particle deposition at an evaporating contact line provides an experimental realization of cooperative one-dimensional deposition, in which post-deposition capillary attraction drives particles to migrate, cluster, and coarsen. As deposition proceeds, the cluster-width distribution undergoes a striking re-entrant transition, evolving from an initial exponential form to a peaked Gamma distribution and subsequently returning to an exponential form. This dynamic transition is accompanied by a non-monotonic crossover in fluctuation scaling, $\sigma_w\sim\langle w\rangle^\kappa$, with $\kappa$ changing successively from $1$ to $1/2$ and back to $1$. Monte Carlo simulations reproduce these statistical transitions. Our results establish evaporative contact-line deposition as a simple model of correlated one-dimensional assembly and reveal how local interactions can produce re-entrant statistical behaviour in a nonequilibrium system.

Twilight clouds are small, optically faint warm clouds whose droplets fluctuate between haze and activated growth. We develop a nonequilibrium statistical field theory linking this regime to cloud-field organization through Köhler microphysics, supersaturation transport, and turbulent mixing. At parcel level, supersaturation rapidly tracks slow droplet growth with a finite lag. Mixing-induced supersaturation removal drives a saddle-node bifurcation, shifting the activation threshold and supporting intermittent hovering under turbulent fluctuations. Starting from turbulent transport of supersaturation coupled to droplet growth, we derive a droplet-supersaturation field system and formulate it within the Martin-Siggia-Rose framework. A Gurari-type variational reduction inspired by polaron theory eliminates the fast bath. Turbulence dresses the slow droplet field, shrinks the forbidden zone below the equilibrium curve, and raises the mixing threshold required to suppress activation. Each droplet population induces a screened supersaturation halo that couples neighboring cloud elements; its delayed adjustment generates dynamic inertia and temporally correlated noise. The resulting nonlinear, non-Markovian pseudoparabolic stochastic equation has a bounded frozen-background response at short wavelengths. Its long-wave coupling amplifies contrasts where the dressed slow manifold turns downward. Comparisons with the parent two-field system show that a spatially correlated Markovian closure preserves droplet-radius distributions and cloudlet organization. Near the activation fold, restoring residual-bath fluctuation memory improves recurrent-hovering frequency and patch extent without recalibrating the drift or fitting a correlation time. More broadly, the framework identifies how slow fields acquire interactions and inertia through the relaxing, diffusive environments they modify.

The gas dynamics of high speed flows over several compression-expansion ramp geometries with large separation regions were investigated using a particle kinetic approach and data driven methods. These large separation regions allow study of the role of scaled angle predicted by triple deck theory on recirculation strength, separation size, and appearance of secondary recirculation regions, all of which lead to flow unsteadiness. Examining four different free stream conditions for the same geometry using the direct simulation Monte Carlo (DSMC) approach, we show that the stability of single recirculation in the separation region is more sensitive to wall temperature and free stream velocity than physical ramp angle. Stability in this context refers to appearance of secondary separation regions. In addition, configurations with similar types of recirculation regions from literature considered, we find that general trends regarding unsteadiness, such as appearance of secondary recirculation regions, mostly hold; however, the flows are too complex to be characterized by only scaled angle. Thus, stochastic flowfields generated by DSMC were investigated using data driven methods, namely spectral proper orthogonal decomposition and dynamic mode decomposition. We found that both methods yield similar frequency components and mode shapes for spatio-temporal coherent structures of unsteady DSMC flows. With the help of these structures, the main mechanisms of unsteadiness were identified as oscillations of the reattachment shock, Kelvin-Helmholtz like instability of the shear layer, and c-shaped mode of the separation bubble. This is the first time SPOD has been applied to a DSMC generated flowfield and compared with DMD.

Self-assembly enables complex structures to emerge from simple building blocks through local interaction rules. Are some structures intrinsically easier to design, that is, do they admit more sets of assembly rules than others? And, can this be predicted from their geometry? We address these questions using a three-dimensional polycube model with programmable face-to-face binding, defining a structure's assembly rule probability as the chance that a randomly chosen rule set produces it. For polycubes, this probability decreases exponentially with assembly complexity, the minimum information required to specify a structure's assembly rules. Intuitively, this follows because structures with low assembly complexity are generated not only by minimal rule sets but also by numerous more elaborate ones, and so arise disproportionately often. Symmetry can reduce assembly complexity by allowing the same building blocks and local interactions to be reused across different parts of a structure. Indeed, we find that the highest probability structures come from a tiny subset of highly symmetric structures. However, symmetry alone does not determine assembly complexity. Structures with the same symmetry can differ substantially in the amount of assembly information they require, depending on how effectively their global symmetry can be exploited by local growth rules. Overall, our results link information, symmetry, and assembly rule probability and suggest that identifying which geometric features permit rule reuse is central to designing minimal programmable self-assembling systems.

Hyperuniform fluids suppress density fluctuations at large length scales, but microscopic protocols for designing their asymptotic scaling remain limited. Here we show how effective driving noise generated by particle dynamics can select the hyperuniform exponent while preserving ordinary diffusion and pairwise center-of-mass conservation of the organized particles. We establish this connection through two protocols based on biased random organization (BRO). First, a two-dimensional BRO layer is nonreciprocally coupled to a three-dimensional Brownian gas through density-dependent kick amplitudes. Bulk density fluctuations generate spatially nonlocal noise with a $q^3$ power spectrum in the adiabatic limit, producing $S(q\to0)\sim q^1$. Second, we introduce reciprocal kicks whose lengths follow a Pareto-like distribution, $P(\ell)\sim\ell^{-1-b}$. For $2

Particle-resolved colloid simulations are often limited by the fastest microscopic time scale retained in the model, which can be many orders of magnitude shorter than the collective process of interest. This is especially restrictive for aggregating colloids, where explicit near-contact potentials force the time integration to resolve the rapid positional relaxation of bonded pairs within narrow attractive wells. Here we introduce an overdamped constraint-based Brownian dynamics method that replaces the time-resolved integration of stiff near-contact forces by a geometric projection step. After each free Brownian update, hard-sphere exclusion, sticky bonds, and hard-wall interactions are enforced by projecting the particle positions onto the constrained configuration set. The method preserves hard-sphere structure and diffusion, recovers the aggregation kinetics of sticky hard spheres, and extends the physical time reached at fixed computational cost by one to two orders of magnitude relative to the explicit-potential simulations tested here. This acceleration makes Brownian-dominated, low-Péclet electrophoretic deposition accessible to particle-scale simulations, revealing a pathway in which the suspension first densifies and only subsequently develops a bonded network. Implemented as a LAMMPS fix, the framework provides a modular route to long-time Brownian simulations of dense constrained colloidal systems.

This paper addresses the packing fraction of polydisperse similar hyperspheres with a discrete binomial and continuous lognormal particle size distribution. First, a closed form expression is derived of a mix consisting of multiple discrete particles in D-dimensional Euclidean space R^D with small size differences. A recently developed analytical model for binary packings with small size ratio u is used, here applying it to the statistically probable particle pairs in the multi-sized mix. The new model is subsequently applied to discretely sized particles with a binomial number distribution and a constant size ratio u between each subsequent particle size. By taking the limit of u -> 1 and an infinite number of particles sizes, the binomial particle distribution is transformed into a continuous lognormal distribution. The resulting expression for the packing fraction can be solved in closed form, resulting in an original expression for the packing fraction of mixtures of hyperparticles with a lognormal distribution. This explicit expression is governed by the standard deviation, the Euclidean dimension D, and the monosized packing fraction of the considered particle shape. For a number of particle shapes and their packing modes (from looser to denser) the scaled expression is thoroughly compared with data reported in the literature. They concern packed particles with small standard deviations and in Euclidean dimensions D = 2 and 3, and good agreement is found. For large standard deviations the scaled packing fraction approaches a limiting value, which appears not to depend on the Euclidean dimension. Based on the insight, a closed form expression is put forward for the packing fraction that matches the small standard deviation solution, and the large standard deviation asymptote, so covering arbitrary standard deviations, Euclidean dimensions, particle types, and their mode of packing.

Boundary conditions strongly influence bacterial turbulence, motivating the question of how hydrated porous substrates affect near-interface collective motion. We characterize the spatiotemporal dynamics of dilute and dense Escherichia coli suspensions above agar substrates of varying concentrations, with glass serving as a nonporous reference. In dense suspensions shortly after loading, collective in-plane kinetic energy varies nonmonotonically with agar concentration, while individual swimming energy and characteristic spatial scales show comparatively little variation. Over five minutes above agar, the collective flow attenuates strongly, accompanied by shorter spatial correlations, longer temporal correlations, and a greater relative spectral weight at higher wavenumbers. To explore how the porous boundary may contribute to these changes, we extend mean-field kinetic theory (MFKT) to incorporate normal seepage and tangential slip at the interface. Linear stability analysis distinguishes near-interface collective modes from those in the bulk and identifies how fluid-layer thickness and permeability-dependent slip length modify the instability cutoff. The predicted reduction in the associated length scale provides a qualitative interpretation of the smaller flow structures observed over time and at higher agar concentrations. These findings reveal distinct substrate-dependent changes in the intensity, persistence, and spatial organization of near-interface bacterial turbulence.

Mechanical disturbances such as seismic shaking can set a granular slope in motion. Understanding the resulting transport before arrest is important for predicting topographic change, assessing landslide hazards and controlling powder flows in industrial processes. Experiments show that smaller disturbances can trigger avalanches and larger areas are mobilized as slopes approach their stability limit. Yet how much transport varies between events under the same macroscopic conditions and forcing remains unclear. Here we use numerical simulations to show that transport variability is amplified near the critical angle. We apply identical basal pulses to static granular layers with the same macroscopic conditions but different initial particle configurations. Although the mean transport increases approximately in inverse proportion to the angular distance from the critical angle, the standard deviation increases even faster and can exceed the mean. Thus, identical forcing can produce widely different transport amounts. Deterministic constitutive laws that assign a unique response to given macroscopic conditions cannot capture this variability. We introduce fluctuations into the energy balance to develop a stochastic model that captures the main features of the broadening transport distribution. These results show that assessing transport near the critical angle requires considering its distribution, not just its mean, and motivate constitutive descriptions that incorporate fluctuations.

Topological defects are commonly characterized by their charge, although defects with the same charge can have different internal morphologies. We study the annihilation of isolated $\pm1$ defect pairs in a two-dimensional compressible Toner--Tu model, varying the morphology of the $+1$ defect while keeping the initial charges and separation fixed. Activity produces a morphology-dependent mobility asymmetry: reversing the radial orientation of an aster reverses which defect travels farther, and asters show the strongest response. An early-time analysis reveals that the initial morphology selects distinct density modes whose gradients subsequently feed back on the polarization. Consistently, removing the density-gradient coupling strongly suppresses the asymmetry. These results establish defect morphology, in addition to topological charge, as a dynamical variable governing defect-pair motion in active polar matter.

Wormlike micellar solutions exhibit formulation-dependent nonlinear startup responses, including stress overshoot, undershoot, and strain hardening, making prediction across compositions and shear rates challenging. We developed a multi-fidelity machine-learning framework to predict stress-growth curves in cetylpyridinium chloride (CPyCl)-based wormlike micelles from sparse experimental measurements. The framework combines a low-fidelity analytical model describing the overall startup response with high-fidelity experimental data capturing formulation-specific nonlinear features. This approach addresses the limited and uneven coverage of salt chemistry, concentration, and shear rate without relying solely on data-intensive neural-network training. The trained model predicts complete stress-growth responses at untested shear rates and enables extraction of strain-hardening characteristics from interpolated curves. By augmenting sparse rheological measurements, the framework provides a basis for exploring relationships among formulation variables, linear viscoelastic properties, and nonlinear startup behavior, while supporting more efficient characterization of wormlike micellar solutions.

The long-wavelength dynamics of two-dimensional (2D) nematic liquid crystals (LCs) is dominated by the motion of topological defects, which behave like interacting particles endowed with both topological charge and orientation. In experimentally relevant regimes, the translational dynamics of the defect positions can be accurately described by effective nematoelastic particle-particle interaction forces. By contrast, analogous quasistatic torque descriptions for the orientational dynamics typically fail due to a breakdown of time-scale separation, severely hindering the inverse design of texture response dynamics in nematic LCs. To overcome this obstruction, we introduce a linear phase-diffusion formulation that accurately predicts the orientational relaxation dynamics of pinned topological defects in the nonlinear 2D Landau-de Gennes theory. The broad practical potential of this approach is demonstrated by showing how it enables the inverse design of transient nematic patterns as well as the inference of hidden defect configurations from sparse measurements.

Structural thixotropic viscoelastic models describe the rheology of human blood accurately, but their structural kinetics are postulated, so their compatibility with the second law of thermodynamics is not guaranteed. We present ROUGE (ROUleaux model Guided by free Energy), a tensorial model of blood that describes the deformation of individual red blood cells and of rouleaux with two conformation tensors, and the degree of aggregation with a scalar variable. A single postulated Helmholtz free energy determines the stress, the relaxation of all three variables, and the entropy generation, so the model satisfies the second law in any flow. To build it, we extend a simplified formulation of nonequilibrium thermodynamics, which accounts for conformational energy and entropy, to microstructures described by several structural variables of different kinds. The coupling between aggregation and rouleaux deformation is motivated by the Langmuir adsorption of fibrinogen and is restricted so that the quiescent, fully aggregated state is the stable minimum of the free energy. Fits to published data for step-ups and step-downs in shear rate show that the fibrinogen binding sites remain far from saturation, so that the free energy has no adjustable parameters. They also show that rouleaux breakdown requires no empirical shear-activation term: the structure is destroyed in proportion to the work done by the flow on the aggregates, and a single structural time produces both breakdown within seconds and an algebraic recovery over tens of seconds. The resulting model has five well-determined parameters, and its fitted solvent viscosity coincides with that of plasma.

A central challenge in colloidal self-assembly is understanding how interaction strength influences the competition between structural optimization and kinetic arrest during the formation of hierarchical structures. Here, we investigate the assembly process of a binary mixture of differently sized silica colloids dispersed in a near-critical water/2,6-lutidine solvent, where critical Casimir forces provide reversible and temperature tunable attractions. By systematically tuning the effective interactions between large-large (L-L), large-small (L-S), and small-small (S-S) particle pairs, we directly observe how the nucleation and growth of the binary colloid assemblies evolve in a wall-confined quasi-two-dimensional geometry when multiple pair-interactions are present. Confocal laser scanning microscopy imaging shows that combined L-L interactions and L-S interactions lead to compact L-S core-shell clusters with high shell occupancy, while the additional presence of S-S interactions suppress the shell formation and lead to extended, branched binary networks. Particle-resolved analyses of cluster growth and bond dynamics reveal that these structural transitions are governed by the motion of the small particles in the clusters changing from highly dynamic leading to structural reorganization to frozen dynamics resulting kinetic trapping. Our findings demonstrate how the interaction-governed mobility and kinetic arrest of small particles influence the growth of finite binary clusters and offers microscopic insight into the formation of binary crystals and kinetically trapped space-spanning binary colloidal networks and gels.

Self-propelled particles such as swimming micro-organisms often accumulate at boundaries. Active Brownian particles (ABPs), that is, particles moving at constant speed with an orientation undergoing rotational diffusion, provide a simple model. ABPs have a finite probability to be on the boundary. Their probability density therefore includes both regular bulk and singular boundary components. Exchanges between these represent capture at the boundary and re-entry into the bulk. We examine the distribution of ABPs in the stationary regime. We first obtain a similarity solution that describes the probability density near the turning points, where orientation is tangential to the boundary and particles re-enter the bulk. This shows that the bulk density is singular and the boundary density is non-differentiable. We then add spatial diffusion to the ABP model and investigate the limit $\eps \to 0$ of small spatial diffusivity. We use matched asymptotics to describe the regularising effect of a finite $\eps$, focusing on the vicinity of the turning points. We assess our predictions against numerical simulations using both lattice Markov chain and finite-element discretisations.

The ubiquitous power-law relaxation emerges from complex mechanical systems with a vast number of interacting exponential responses. Here we demonstrate that power-law responses satisfy a maximum entropy criterion, regulating the individual contributions under partial knowledge. This leads to a prediction that frequency range of validity decreases with power-law exponent, a property which is confirmed for some biological materials. The close relation with the fractional standard linear solid also leads to an incorporation of the equally ubiquitous stretched exponential behavior.

Accurate prediction of phase equilibria is essential for chemical process design, particularly in systems characterized by complex intermolecular interactions. This work investigates the influence of conformer selection and sigma-profile characteristics on COSMO-RS predictions of liquid-liquid equilibria (LLE), using the tetrahydrofurfuryl alcohol (THFA)-methyl isobutyl ketone (MIBK)-water system as a case study. Calculations were performed at the TZVP and TZVPD-FINE levels of theory. While TZVP failed to capture the experimentally observed phase behavior, TZVPD-FINE provided substantially improved predictions. The differences are attributed to the relative importance assigned to less-polar conformers and more-polar conformers capable of hydrogen bonding. Although the TZVPD-FINE calculations reproduced the main experimental trends, the predicted organic-phase composition showed a mean percentage deviation of 5.27%, slightly exceeding the adopted 5% agreement threshold. Investigations using individual conformers demonstrated that predictions can be strongly influenced by conformer selection and that representative conformer ensembles are necessary for reliable results. Further analysis showed that diversity in sigma profiles is more important for predictive accuracy than the total number of conformers. These findings emphasize the importance of carefully selecting conformers when applying COSMO-RS to liquid-liquid equilibria involving phases of contrasting polarity.

Stable stratification reorganizes turbulence, suppressing vertical motion and altering the balance between vortical and strain-dominated flow structures. How these changes affect the temporal asymmetry of kinetic-energy exchange along fluid-particle trajectories remains incompletely understood. Using direct numerical simulations of homogeneous Boussinesq turbulence, we investigate Lagrangian power statistics across four local velocity-gradient topology classes and three nonzero stratification strengths, with an unstratified reference case. With increasing stratification, the global power variance decreases while the standardized skewness becomes more negative, indicating enhanced asymmetry despite weaker fluctuations. Conditioning on local topology reveals distinct responses: axial-strain-dominated regions exhibit the most negative total-power skewness at all stratification strengths, whereas biaxial-strain-dominated regions change sign from positive to negative under stratification. Horizontal and vertical component powers also respond differently, revealing directional dependence. Among the dynamical contributions to power, the pressure contribution, nearly symmetric in the unstratified case, becomes more negatively skewed with increasing stratification. Energy-conditioned pressure statistics further indicate altered pressure-mediated energy redistribution. Finally, tracer persistence-time distributions exhibit exponential tails, with time scales that differ across topology classes and respond differently to stratification. Increasing stratification is thus accompanied by three concurrent changes: enhanced asymmetry of Lagrangian power, modified energy redistribution by pressure, and altered temporal sampling of local flow structures by tracers. These co-occurring signatures characterize the response to stratification, though their causal relations remain to be established.

Reconstructing the full state of a multiscale chaotic system from observations of only a subset of its degrees of freedom is a central problem in data assimilation. Turbulent Rayleigh--Bénard convection offers a paradigmatic example, for which Charney conjectured that temperature measurements alone should suffice to determine the velocity field. Synchronization-based methods such as nudging and direct replacement nonetheless fail in chaotic regimes, because they require the measurement of the determining modes of the system, a set to which the velocity belongs but the temperature does not. Here we show that the Ensemble Kalman Filter (EnKF), equipped with a proper inflation scheme, removes this asymmetry by exploiting the flow-dependent cross-covariances between temperature and vorticity, and recovers the velocity from noisy and spatio-temporally sparse temperature data alone. We assess the filter in two chaotic regimes of two-dimensional bulk convection by means of a scale-by-scale spectral analysis. When the whole temperature field is observed, both fields synchronize with the true state at all resolved scales, with the temperature estimate becoming even more accurate than the measurements themselves for sufficiently frequent observations. Equispaced observation networks preserve this full-spectrum synchronization down to a threshold density, below which only the largest scales remain synchronized, as also happens when observations are confined to a subdomain. We conclude that Charney's conjecture is numerically verified in two-dimensional turbulent convection when the assimilation is performed using a properly calibrated EnKF.

Turbulence is defined by a set of emergent and singular phenomena: a constant-flux energy cascade, intermittency, a dissipation rate that survives the vanishing of viscosity, and the spontaneous loss of determinism of the inviscid limit. Which physical ingredients produce them remains unclear, because in fluids they always come together with incompressibility, spatial structure and vortex dynamics. Here we show that a hierarchy of inertia, coupled by the purely geometric nonlinearity of rigid constraints, is enough. A planar chain of rigid pendula whose lengths and masses decrease geometrically, coupled only through nearest-neighbor constraints, develops a far-from-equilibrium cascade that replaces thermal equipartition, with statistically local and time-irreversible energy transfer despite intrinsically nonlocal coupling. Its fluctuations are intermittent, yet self-similarity is restored by a hidden scale symmetry. As the viscosity vanishes, the dissipation rate saturates at a finite value, and thermal noise consistent with fluctuation-dissipation balance is amplified from the smallest to the largest scales within a fraction of a large-scale period. Because the hierarchy can be tuned and the same dynamics can be realized mechanically or electrically, turbulence becomes a property that can be designed and measured in the laboratory.

Rarefied gas--solid interactions determine mechanical loads, heat transfer, and material exchange in microscale devices and low-pressure processings. Modeling these interactions becomes challenging when gas non-equilibrium effect and complex moving boundaries must be resolved together. We develop a diffuse-interface kinetic model (DIKM) that describes rarefied gas transport and gas--solid interactions in one kinetic formulation on a single fixed Eulerian mesh. A smooth order parameter represents solid geometry, while a localized molecular flux operator incorporates boundary interactions directly into the kinetic equation by distinguishing incident and reflected distributions in the interface region and specifying their mass, momentum, and energy exchange, including prescribed surface absorption. Matched asymptotic analysis shows that the diffuse formulation recovers the corresponding partially absorbing diffuse-reflection boundary condition for smooth stationary or moving surfaces in the sharp-interface limit. Discretization uses Strang splitting, combining an order-parameter-weighted discrete unified gas kinetic scheme for the transport substep with a positivity-preserving update of the interfacial source. Benchmarks over planar and curved, stationary and moving boundaries reproduce rarefaction-dependent velocity slip and wall heat transfer, absorption-driven flow, and feedback between gas forces and solid translation and rotation. In final simulations, the order parameter evolves by a Cahn--Hilliard equation with degenerate mobility, and thin-film growth exhibits distinct surface profiles at different vapor incidence angles. By connecting implicit geometry to molecular surface exchange, DIKM provides a basis for coupling rarefied gas dynamics to solid motion and material evolution.

Predicting the history force on a sphere beyond the creeping-flow limit remains challenging. Existing formulations have been derived or calibrated for selected flow histories, with limited evidence of their predictive accuracy under more general conditions. We develop a systematic approach to extract the history kernel of a fixed sphere in spatially uniform, unsteady flow from axisymmetric Navier-Stokes simulations of finite-duration acceleration and deceleration ramps at initial Reynolds numbers from 0.2 to 200. The resulting kernel surface recovers the Basset limit at short lags and in the creeping-flow limit and is continued beyond the resolved lags using far-wake asymptotics. At higher Reynolds numbers, the kernel develops non-monotonic behaviour at intermediate lags, associated with delayed adjustment of the boundary layer and wake. For the cases tested, the present kernel substantially improves history-force predictions for finite ramps, oscillatory forcing and non-periodic composite velocity histories relative to the literature formulations considered, without case-specific adjustment. These findings indicate that lag and Reynolds number capture the dominant memory response.

Direct numerical simulations (DNS) are performed for a Mach 8 flow over a 15 degree compression ramp undergoing ablation to analyze fluid-ablation interaction (FAI) effects on instability growth and transition of the high-speed boundary layer. Wind-tunnel experiments at these conditions show characteristic heating streaks which are first replicated for laminar flow over an inert ramp. Perturbations superimposed on the laminar baseflow are informed by stability calculations. The ramp is then replaced by a low-temperature ablator in our DNS and the interaction of the streaks with the ablating surface is examined. Ablation models implemented in two independently-developed fluid dynamics solvers are used to study this problem. Overall, both solvers have shown an excellent agreement regarding heat fluxes, mass blowing rates, and recession patterns. Numerical experiments are performed to assess the impact of accelerating recession and of higher amplitude perturbations. We demonstrate accurate predictions of ablative recession and present novel findings regarding its influence on the perturbation evolution for this configuration.

Gas transport driven by thermal transpiration under temperature gradients, known as a Knudsen pump, has shown strong potential in gas separation and delivery applications. However, its performance and operational stability are strongly affected by structural design, system integration, and manufacturing complexity, highlighting the need for efficient and manufacturable multi-stage configurations. In this study, a novel spiral-structured Knudsen pump is proposed. Within the microchannels, a temperature gradient drives gas from the low- to high-temperature region, inducing pressure rise and thermal transpiration. In the main channel, a pressure gradient drives gas from the high- to low-temperature region, forming Poiseuille flow. Numerical methods are employed to investigate the flow mechanisms, and the effects of varying the numbers of series and parallel microchannels on gas transmission behavior are evaluated. The results indicate that bends of the main channel lead to nonlinear variations in pressure and temperature, as well as flow deceleration in the curved regions. Increasing the number of serial channels reduces the pressure load across the microchannel, thereby enhancing the overall transport performance. For instance, a ten-stage serial configuration improves performance by 3.35% compared with the four-stage case, reaching 3.10E10-7 kg/(m*s). In contrast, increasing the number of parallel microchannels reduces pressure loading while enhancing gas rarefaction, thereby strengthening thermal transpiration. A five-stage parallel configuration yields an 70.80% improvement over the two-stage case, reaching 3.07E10-7 kg/(m*s). These results provide valuable guidance for the design and fabrication of high-performance Knudsen pumps.

In this paper, a compact high-order gas-kinetic scheme (HGKS) is developed for compressible arbitrary Lagrangian-Eulerian (ALE) computations on three-dimensional unstructured meshes. To achieve high-order spatial accuracy, a large number of matrix inversions are required for spatial reconstruction. In ALE computations, the mesh moves and the geometric information must be recalculated at each time step, which reduces computational efficiency. To improve efficiency, a memory-reduction reconstruction strategy is employed to construct a quadratic polynomial on unstructured meshes. By differentiating the candidate polynomial, the quadratic terms are obtained by the least-squares method using the average gradient values of the cell itself and its neighboring cells. The linear terms of the polynomial are also determined by the least-squares method. On three-dimensional unstructured meshes, a $3\times3$ coefficient matrix must be stored, and four least-squares procedures are required to construct a quadratic polynomial. To suppress numerical oscillations in flows with discontinuities, generalized essentially non-oscillatory (GENO) reconstruction and a gradient compression factor are adopted. To accelerate the computation, a multi-GPU accelerated code is implemented using Compute Unified Device Architecture (CUDA) and Message Passing Interface (MPI). The current scheme is fully explicit, and the acceleration framework can be developed based on cell-level parallelism. Numerical examples are presented to evaluate the accuracy and robustness of the scheme, including flows with strong discontinuities, pitching wings, and helicopter rotors. Numerical results confirm the excellent performance of the compact ALE scheme on unstructured meshes.

Inferring upper-ocean velocity from altimetric sea surface height (SSH) remains challenging below 50~km, scales now resolved by the Surface Water and Ocean Topography (SWOT) mission. Conventional methods rely on geostrophic or cyclogeostrophic balance. Here, we demonstrate that deep learning can predict the full velocity vector from SSH and environmental data and recover derivative-based diagnostics, including spectral energy flux. We trained a U-Net encoder--decoder on hourly fields from the pre-SWOT Cape Basin extraction of the LLC4320 ocean simulation, with 1.5-km grid spacing ($11.8$--$15.8^\circ$E, $41$--$45^\circ$S). Inputs were SSH, sea surface temperature (SST), and wind stress; targets were horizontal velocities at the surface and 50~m, where wind influence is weaker. At 50~m, the best model achieves a speed RMSE of $0.049\,\mathrm{m\,s^{-1}}$, 29% lower than the geostrophic approximation. Predicted relative vorticity has a correlation of 0.93, compared with 0.75 for the geostrophic approximation. The model also recovers divergence with a correlation of 0.66, whereas geostrophic velocity is nondivergent by definition. Tests of training strategies yield four findings: SSH gradients outperform raw SSH as inputs; wind stress is the most useful covariate for total velocity prediction; SST benefits vary seasonally; and including vorticity and divergence in the loss improves accuracy. These results offer a path for transferring high-fidelity simulation physics to SWOT applications, where kilometer-scale SSH snapshots contain superposed balanced and unbalanced signals.

Prestress governs the stability, stiffness, and dynamic behavior of tensegrity structures, but it is not directly observable from sparse structural measurements, and it may decrease during service life. Under strong excitation, the cables may slacken and the dynamics become nonsmooth. Existing identification methods are limited to the taut regime, and physics-informed networks for tensegrities solve only the forward problem of predicting the response from known member parameters. This study formulates the inverse problem. Neural networks are trained on the equation-of-motion residual in constrained Cartesian coordinates, where the mass matrix is constant and the force densities enter linearly. The force densities, damping, and axial stiffness are trainable parameters, and the tension-only cable law is kept. A Fisher-information analysis shows, before inversion, which member parameters a record can determine. The method is tested on simulated planar tensegrity frames with up to five modules and a three-dimensional prism, and on measured records of a biomimetic leg and a full-scale tensegrity simplex. On the one-module frame, the identifiable force densities are recovered within 1.5% from noisy accelerations at half the free coordinates, on records with and without taut-slack transitions. Records with transitions determine members that taut records leave undetermined. On the five-module frame, a 16-cable two-span bridge, the median force-density error rises moderately, to 4.2%. On measured records, an identified spring stiffness is within 0.1% of its independently measured value on average, and the identified simplex prestress at 13 levels agrees with its cable force transducers to 2.9% root-mean-square.

The transmission of shock waves generated by underwater electrical foil explosions across solid materials with varying acoustic impedances and thicknesses is investigated. Copper foils with thicknesses of 10 and 18 $\mu$m are exploded on planar substrates of aluminum, copper, and 3D-printed PLA with thicknesses up to 5 mm using a multi-gigawatt pulsed-power electrical discharge. The resulting shocks are visualized in water using high-speed shadowgraphy at 5 million frames per second, while high-resolution fiber optic hydrophone measurements provide direct quantitative measurements of shock strength after transmission through the impedance-mismatched materials. One-dimensional magnetohydrodynamic simulations are used to reproduce the foil explosion dynamics and provide insight into the thermodynamic, acoustic, and electrical properties of the foil during the explosion. The results show that shock transmission is governed not only by the impedance mismatch at the solid--water interface but also by the finite thickness and dynamic response of the supporting material. These findings provide a quantitative framework for understanding and controlling shock transmission in underwater electrical foil explosions and establish the feasibility and limitations of using solid substrates as structural supports in complex shock-generating geometries.

Linear and nonlinear mechanical structures with closely spaced modes and non-classical (nonproportional) damping distribution are susceptible to modal interactions with energy exchanges between modes. In this work we analyze these interactions in a two-degree-of-freedom (2 DoF) coupled oscillator subject to impulse excitation, utilizing action-angle variables and the method of multiple scales. To show the basic steps of the methodology we start from the linear system, then proceed to analyze modal interactions in the system with strongly nonlinear cubic stiffness nonlinearity. In contrast to the linear case, once the dynamics of the nonlinear system is captured in 1:1 resonance, strongly nonlinear modal interactions occur depending on energy. These regimes as well as attraction to capture, 1:1 capture and escape from capture are analyzed in detail. Our analytical study determines the ranges of parameter values for which nonlinear modal interactions due to resonance capture occur. The analytical predictions are fully verified by direct numerical simulations of the governing equations of motion. Possible extensions of the present work to systems of oscillators with more DoF and other types of dissipative elements, e.g., friction or hysteresis are discussed.

In this paper we establish a new theorem for nonintegrability of a perturbed, autonomous, two-degree-of-freedom Hamiltonian dynamical system with two independent resonances, based on a criterion which utilizes the well-known theorem of Poincaré and a Lie-series symplectic transformation. We also make certain assumptions and suggestions as to when the theorem holds and when it does not.

We investigate the interaction of dissipative Kerr solitons in two nearly identical coherently driven, coupled microresonators in the presence of third-order dispersion (TOD). Using an asymptotic reduction of the coupled Lugiato--Lefever equations, we derive effective interaction equations governing the soliton separation and collective drift for weak intercavity coupling. TOD breaks the parity symmetry of the soliton profile and qualitatively modifies the effective interaction, leading to asymmetric interaction forces and multiple stable and unstable soliton clusters. The existence and stability of these clusters are controlled by the relative phase of the driving fields and the group-velocity mismatch between the resonators. In particular, an appropriate value of the group-velocity mismatch can give rise to multiple stable bound states, whereas deviations from this value trigger successive saddle-node bifurcations, ultimately leading to periodic soliton collisions. The analytical predictions are confirmed by numerical simulations of the full coupled system.

Topological insulators can host chiral, disorder-robust edge states that dissipate energy when coupled to an external bath. We show that nonlinear interactions enable all-optical control over edge-state dissipation in a laser-written Floquet topological insulator periodically coupled to a photonic bath. Although moderate nonlinearity enhances dissipation due to mode mixing, increasing the nonlinear strength to an optimal value dramatically suppresses dissipation by forming highly localized traveling edge solitons. These results establish engineered system-bath coupling and nonlinear interactions as a route to suppress dissipation of chiral topological edge transport.

A magic square exemplifies balance in inequality: its $n^2$ entries $\{1,\dots,n^2\}$ are distinct, yet every row, column, and main diagonal sums to $\mu_n=n(n^2+1)/2$. Lifting centred grid cells into $\mathbb{R}^3$ as radial vectors $\mathbf{p}_{ij}(\lambda)=(x_j,y_i,\lambda z_{ij})$ and taking their convex hull---the Magic Gem $\mathcal{G}_\lambda(S)$---asks: when does line-sum equality suffice for equilibrium in 3D, and when a nonlinear realization breaks balance, how can an opposing inequality restore it? We test this across all $880$ order-$4$ magic squares in four regimes. For radial spokes from $O$, natural lengths balance identically, while unit spokes break equilibrium on all $832$ non-associative squares in 3D and on all squares in 2D, where the ring-radius ratio $r_2/r_1=\sqrt{5}$ bounds the resultant below by the Pell convergent $9/4\approx\sqrt{5}$. By length--weight duality, balance is restored via tip weights $\mathbf{w}^*>\mathbf{0}$ on $S^2$ or power-law spoke scaling ($r^{\alpha^*}$ in 2D and $(\mathbf{V}_3)_z=0$ in 3D). In 3D rotation, equal point masses make every semi-magic square an axisymmetric top with spherical-top transition $\lambda_{\mathrm{iso}}=(n^2+1)^{-1/2}$, whereas entry masses $m_{ij}=s_{ij}$ expose the quadrupole $Q_{xy}=\sum z_{ij}x_jy_i$, triggering $180^\circ$ Dzhanibekov flips on $824$ squares. Passing to the uniform solid hull $\mathcal{G}_0(S)$ shifts the centroid off $O$ on $829$ squares; re-engaging the opposing core $\mathcal{G}_1(S)$ restores balance via two-density inclusions, nested wireframes, or the $K_{n^2}$ strut network, while all $880$ hulls unfold into non-overlapping nets with $f_0-1$ glue tabs. Finally, $\lambda=1/5$ stabilizes $74.5\%$ of facets on a table, and alternating $\mathcal{G}_\lambda(S)$ with its mirror twin $\mathcal{G}_\lambda(r^2\overline{S})=-\mathcal{G}_\lambda(S)$ locks chiral blocks into a vertical tower.

Piezoelectric bending actuators provide deflections of several hundred micrometers and are used in electrical and mechanical engineering, acoustics, automation, automotive technology and healthcare. Highly efficient, low-cost piezoceramics offer a wide range of technical solutions. Their highpiezoelectric coefficients enable large strains at low electric field strengths. However, hysteresis, drift and creep impair positioning accuracy. Precise switching and positioning require compensation for these material-related effects, as well as varying mechanical loads and vibrations. A non-contact inductive proximity sensor is therefore combined with high-precision electronic circuit. Within a closed-loop control system, this sensor-actuator arrangement detects disturbances and enables their compensation, allowing highly efficient piezoceramics to be used for high-accuracy positioning. This paper investigates the electrodynamics of a specially developed eddy-current-based proximity sensor suitable for integration into confined spaces. A theoretical description explains its physical operating principle and enables analytical determination of the relative change in inductance as a function of actuator tip deflection. Experimental measurements validate the electrodynamic approach. The paper also considers energy harvesting applications. Measuring tip deflection allows the power dissipated in the piezoelectric transducer to be determined. The sensor system thus provides a basis for investigating and evaluating the performance of piezoelectric energy harvesters.

Macromolecular crowding has long been known to alter biochemical equilibria and enzyme kinetics, with reported catalytic activities that may increase, decrease, or vary non-monotonically with crowder concentration. Classical Michaelis--Menten kinetics does not by itself identify which of these responses should occur for a conformationally active enzyme. Here, we develop a minimal non-equilibrium mechano-chemical theory for a fueled enzyme embedded in a bath of passive crowders and uncover a fluctuation-induced effective force dipole acting on the enzyme subunits, akin to a generalized form of dispersion or depletion interaction. Since the preferred conformation of the model enzyme varies through the catalytic cycle, the fluctuation-induced mechanical load affects the relevant kinetic activation barriers and is sufficient to produce both monotonic inhibition and non-monotonic modification of turnover. The framework provides a thermodynamically consistent route for linking crowded environments to catalytic currents, suggesting how mechanical design principles could be leveraged to control enzymatic pathways.

We study an inherently nonequilibrium system consisting of self-propelled particles using molecular dynamics simulation in $d=2$. The system self-organizes through quorum-sensing interactions characterized by an interaction range $\lambda$ and a parameter $c_{\mathrm{th}}$. When the local concentration sensed by a particle, represented by an auxiliary variable $c_i(t)$ exceeds $c_{\mathrm{th}}$, its self-propulsion velocity abruptly drops to zero, leading to the emergence of particle rich domains. For small $\lambda$, we observe a droplet-like morphology of clusters, which crosses over to a bicontinuous structure as $\lambda$ increases. We confirm this transition by computing the eccentricity of the domains. Next, we characterize the evolving domain morphologies using equal-time correlation function $C(r,t)$ and structure factor $S(k,t)$ of the density field. For a fixed $\lambda$, the scaled $C(r,t)$'s at different times are indistinguishable from each other, indicating dynamical scaling. However, at a fixed time $t$, the scaling functions differ for different values of $\lambda$, confirming a $\lambda$-dependent morphological transition. In the large-wavevector limit ($k\rightarrow\infty$), the tail of $S(k,t)$ consistently follows the Porod's law: $S(k,t)\sim k^{-3}$. Furthermore, the average domain size $L(t)$ exhibits a power-law growth, $L(t)\sim t^{1/3}$, independent of $\lambda$.

Predictive COSMO-RS-based electrolyte models such as COSMO-RS-ES describe electrolyte solutions from quantum-chemical information, but treat the liquid as incompressible and give no access to densities or pressure effects. This work presents openCOSMO-RS-ES-Phi, to our knowledge the first open-source implementation of a predictive electrolyte equation of state based on openCOSMO-RS. It combines the COSMO-RS-based equation of state openCOSMO-RS-Phi with the ion interaction energies and the long-range term of COSMO-RS-ES, which is first refitted on the same simplified short range. With this refit, a dielectric decrement improves the mean ionic activity coefficients (MIAC), whereas a Born term counts the solvation of the ions a second time and is therefore left out. The equation of state then adds only volume, dispersion and temperature parameters of the ions, fitted to aqueous MIAC and densities. openCOSMO-RS-ES-Phi reproduces COSMO-RS-ES in dilute aqueous solutions, improves on it in concentrated ones and also yields solution densities. Extrapolating from aqueous systems, it predicts the MIAC in water + cosolvent mixtures as accurately as the fitted COSMO-RS-ES, as well as the MIAC and bubble points of a benchmark database of water-alcohol-salt systems. Salting-out of organic components is not described as accurately, and salts come out too soluble in organic solvents. Overall, the interaction model developed for COSMO-RS-ES carries over to a large extent to an equation of state, which makes openCOSMO-RS-ES-Phi a sound base model for further development, with ion transfer between solvents as a clear target for fitting to non-aqueous data.

The dynamics of the nonlinear Dirac equation (NLDE) under the influence of dissipation and parametric forcing exhibit complex phenomenologies, including soliton destruction and chaotic transitions, which have been extensively observed in numerical simulations. However, a rigorous analytical understanding of the underlying instability mechanisms in the subcritical regime has remained open. In this work, we provide a theoretical answer to these numerical findings by establishing the spectral instability of the fundamental soliton solution. Our methodology relies on a three-step approach linking local asymptotic analyses with global topological arguments. First, we characterize the generalized null space at the critical parameter ($\lambda_c$), revealing the onset of instability through the splitting of the zero eigenvalue within a parity-dependent subspace. Second, in the non-relativistic limit ($\lambda \to 0$), we use a Lyapunov--Schmidt reduction to reduce the linearized Dirac's operators into a Pöschl--Teller Schrödinger operator, thereby identifying the instability source as a unique real pair of discrete eigenvalues in the restricted problem. Third, we extend these local results to the entire subcritical domain using a topological continuation argument, which tracks the invariance of the spectral parity in a subset of the complex plane. These analytical results rigorously confirm the instability of the soliton, providing the mathematical mechanism for the wave collapse observed in the driven-damped system.

Population-balance models offer a route to connect dispersed vapor bubbles with macroscopic cavitation, but their closures require experimental constraints. Here, point-by-point optical probe measurements reveal self-similar void-fraction and bubble-velocity profiles, yielding an effective Schmidt number for the bubbly/non-bubbly transition. The measurements further show that bubble-size distributions and bubble velocities depend strongly on the local flow region, providing new guidance for region-dependent population-balance closures in cavitating flows.

Spatially patterned tangential activity provides a route to program polymer topology through both geometry and propulsion direction. We use Langevin-dynamics simulations of a flexible, self-avoiding linear polymer to determine how active-domain placement and independently assigned propulsion polarities control nonequilibrium knotting. Reversing the polarities of two terminal active blocks switches the steady state from a nearly always-knotted regime to effective knot suppression, changing the knotting probability by more than three orders of magnitude despite identical active-block positions and activity magnitude. Across symmetric terminal two-block architectures, we further identify an approximate zero-one-two free-end-alignment rule: zero, one, and two free-end-aligned active blocks correspond, respectively, to suppressed, intermediate, and high-knotting states. A two-state kinetic decomposition shows that the conditional knot-formation rate changes only by about threefold under polarity reversal, whereas the mean knot lifetime changes by several orders of magnitude, demonstrating that knot survival and passive-region storage dominate the polarity-controlled switch. Block placement provides an additional geometrical gate: moving an active domain from the chain interior to a terminal region strongly enhances both knot formation and survival. Knot-center residence, knotted-arc distributions, and episode-resolved kymographs reveal formation near free-end-aligned active blocks, directed contour migration, tightening, and long-lived retention in passive regions. Together, these results support a source-conveyor-reservoir-sink mechanism in which signed polarity and spatial activity patterning control whether knots are generated, transported, stored, or rapidly lost, providing a route to programmable topological states in nonequilibrium active polymers.

Understanding the passive wrapping of adhesive particles by lipid membranes is a crucial step in untangling more complex endocytotic processes. However, despite the variety of computational approaches used to study passive endocytosis, a direct comparison of results across different modeling methods has never been performed. In this work, we present a comparative analysis of three distinct frameworks: numerical solutions of the axisymmetric membrane shape equation, a particle-based molecular dynamics model (MesoMem), and an energy-based triangulated surface model (FreeDTS). First, we validated our numerical solver for spherical particles against established literature and extended the implementation to include closed vesicle membranes and non-spherical particles. Next, we studied the same system with our two simulation methods, and found that the phase plots obtained from our numerical solution agree with those from our simulations. We then extended our study to anisotropic particles. By tracking engulfment pathways in MesoMem and FreeDTS, we observed a dynamic rotational transition where non-spherical particles initially bind in a horizontal ('submarine') orientation and subsequently rotate to a vertical ('rocket') orientation to complete wrapping - a behavior impossible to capture with standard axisymmetric models. Lastly, we considered the wrapping of soft vesicles with FreeDTS. Our simulations of a deformable, fixed-connectivity particle show that stronger adhesion promotes wrapping, whereas increasing membrane tension suppresses it. Complete engulfment is accompanied by a substantial reduction in particle volume, suggesting that particle compressibility provides an additional pathway for wrapping.

Predicting the highest packing fraction that disordered packing of bidisperse discs can achieve, $\phi_{max}$, is an important unresolved problem. Such a predictive theory is hindered by the density dependence on the packing protocol and by ensuring disorder. In bidisperse packings, this is more complicated because $\phi_{max}$ is not a number but a function of the disc species size ratio, $D$, and one of the disc species concentration, $p$. These difficulties have been overcome in monodisperse disc packings by using the cell order distribution (COD)~\cite{Bl21}. Focusing on size ratios that prohibit rattlers, a COD-based theory is constructed here. It introduces bidisperse statistical closure equations, which combine an explicit disorder criterion with consistent cell and edge statistics, and yields $\phi_{max}(p,D)$ and structural predictions. The a-priori disorder-guaranteeing criterion proposed here ensures fast exponential a decay of the occurrence probability of ordered clusters with size. Using a constrained maximum-entropy analysis to ensure maximum disorder, the occurrence probabilities of all the possible cell and edge configurations are derived in terms of $p$ and $D$ and they are found to be binomial. All the results are assembled to yield an exact prediction of $\phi_{max}(p,D)$.

Soft colloidal particles, such as microgels, made of cross-linked polymer gels that can swell by absorbing a good solvent, have internal degrees of freedom that allow them to respond to external stimuli by changing size. Sensitive responses to variations in temperature and concentration have inspired many practical applications, e.g., to drug delivery, biosensing, filtration, and photonic crystals. At sufficiently high concentrations, mutual crowding can drive microgels to interpenetrate or deform by faceting. To explore the influence of particle softness and compressibility on thermodynamic phase stability, we develop a coarse-grained model in which spherical microgels interact via the Hertz elastic pair potential and can respond to crowding by deswelling and faceting or interpenetrating, as governed by the Flory-Rehner theory of polymer networks. In our model, faceting reduces the volume available for swelling, while interpenetration affects polymer solvent mixing entropy. By performing Monte Carlo simulations that incorporate novel trial changes in particle size and shape, we compute equilibrium swelling ratios and Lindemann ratios to determine the fluid-solid phase stability boundary over a range of particle softness, tuned by varying cross-link fraction. Predictions from our facet model are in qualitative agreement with experiments and molecular-scale simulations. In contrast to the phase behavior of incompressible Hertzian spheres, we find that suspensions of compressible microgels crystallize at significantly lower volume fractions when accounting for the free energy costs of faceting and interpenetration. Our results extend previous studies of microgel phase behavior and can help to interpret experiments.

Applying insights acquired when studying idealized particle systems to real-world amorphous materials remains a significant challenge, primarily due to the complex interplay between particles' shape and interaction mechanisms. It is known that regular pentagons do not tessellate the two dimensional plane, making them the simplest regular polygons unable to form periodic tiling. This geometric constraint, combined with the complexity of interactions among non-spherical particles, may give rise to rich emergent behaviors, especially when dealing with self-propelled pentagons. Thus, geometry, interactions, and self-propulsion collectively lead to novel dynamical emerging phases. In this context, we investigate how activity and excluded-volume interactions affect the collective behavior of a two-dimensional suspension of active pentagon-shaped particles. Our results reveal that active pentagons not only undergo an arrested motility-induced phase separation (MIPS) but, under given conditions, they form traveling/rotating clusters exhibiting translational/chiral motion. Interestingly, both phases present an enhanced stability due to particles' activity, shape and excluded-volume interactions, forming an ice-ray lattice whose internal structure represents the densest packing fraction a two-dimensional pentagon suspension may achieve.

Understanding how confinement alters the transport of charged molecules is central to the advancement of separation, energy, and sensing technologies. Polyamines are small, linear molecules with ionizable groups, making them an ideal model for investigating charge transport in confinement beyond monatomic ions. Using all-atom molecular dynamics (MD) simulations, we investigate how molecular length, net charge, and charge placement affect the electrophoretic transport of polyamines through single-walled carbon nanotubes (CNTs). We find that nanometer-scale confinement reverses the mobility ordering observed in free solution -- in a CNT of radius 0.68 nm, spermine (q = +4) travels more slowly than ethylamine (q = +1), contrasting with the expected scaling of mobility with valence in bulk. Further, we find that mobility decreases faster than the inverse of valence, though molecular size and length vary alongside this trend. Comparisons of doubly protonated spermidine microspecies reveal the additional influence of charge placement at fixed net valence. Upon moving one proton of dicationic spermidine from the central to a terminal nitrogen, the mobility is increased by 42%. We analyze hydration structure and solute-solvent association, identifying local-solvation differences between protonation topologies that accompany these distinct transport responses under confinement. These results suggest that neutral CNTs could support valence-selective nanofluidic transport, with additional sensitivity to molecular structure and protonation topology.

Shells and grains separately exhibit complex nonlinear behavior when confined - shells buckle and snap, while grains transition from fluid-like to solid-like. When coupled, elastogranular structures have the ability to display a remarkable variety of mechanical behaviors. Gere we created an elastogranular shell where spherical grains are sandwiched between two thin, elastic shells. By evacuating the air enclosed by the two layers, we can tune the stiffness of the elastogranular shell and alter its critical buckling load. Introducing controlled vacancy defects in the arrangement of the grains allows us to more finely tune critical buckling parameters, as the shell must balance the combined effects of defect size and resultant granular packing density. Defects in the jammed granular layer have a counterintuitive effect on the shell's buckling load, as they can stiffen the shell away from the defect. With an empirically determined scaling model, we established how the shell and grains distribute load and create a compliance-shifting structure with a tunable buckling load.

Independent Brownian noise can rapidly separate trajectories launched from the same microscopic configuration, but configuration-space distance need not reveal their later assembly outcomes. We studied this distinction in 480 two-dimensional Brownian-dynamics trajectories generated as three independent-noise replicas of 40 parent configurations under four finite-duration quenches. Ninety-two of 160 replica sets sharing one parent and one protocol reached both ordered and non-ordered terminal outcomes. A relative-diffusion calculation relates the free-particle mean-squared replica separation to the time-integrated diffusivity. The measured mean-squared separation remained about one-sixth of the free-particle reference, while its scaling was indistinguishable for replica pairs with the same and different outcomes. In contrast, outcome-resolved global sixfold order, ordered-particle population and coherence, and reciprocal-space translational order separated progressively after quench completion. With quench durations weighted equally, global order, the state score combining global and population order, coherence, and translational order remained informative 0.50 reduced time units before terminal assessment. This result persisted after either changing the terminal window or reducing the integration timestep. Transient threshold crossings were common, and 94.5\% of non-ordered crossings subsequently lost the required ordered-particle population. An independent $N=128$ ensemble showed state-score discrimination at temperatures for which both terminal classes occurred. The assembly dynamics therefore separate generic microscopic decorrelation from the later emergence and finite-window persistence of collective order associated with terminal structure.

An experimentally accessible measure of structural restraint in supercooled liquids is defined based on the variance of the intensity of speckle pattern arising from elastic scattering of coherent radiation. Using simulation data, the resulting measure of structural restraint is shown to correlate with the temperature dependence of the shear modulus and the Debye-Waller factor. The paper includes consideration of the influence of the choice of the scattering wavevector and the degree of coarse graining used in intensity measurements on the measured restraint.

Predicting how nanoparticles interact in concentrated electrolytes remains a central challenge in nanoscience, with implications spanning energy storage, catalysis, and soft materials design. While Derjaguin-Landau-Verwey-Overbeek (DLVO) theory provides a widely used framework for modeling colloidal interactions, its electrostatic component relies on electric double-layer (EDL) theories whose validity in ionic liquids and concentrated electrolytes is consistently debated. Experiments have revealed significant deviations from classical screening behavior, including underscreening and oscillatory charge ordering, yet the consequences of these nonclassical effects for collective nanoparticle behavior remain unresolved. Here, we demonstrate that the extended range and oscillatory nature of electrostatic screening in concentrated electrolytes predicts different phase behavior and morphology of colloidal ionogels, yielding distinct thermodynamic signatures, percolation thresholds, and amorphous network structures. Using molecular dynamics simulations with DLVO-type pair interactions parameterized by competing EDL models, we systematically compare the consequences of different screening theories on gel formation and configurations.

The description of macroscopic properties in out-of-equilibrium amorphous solids such as gels and glasses, typically processed under finite cooling rates, remains a fundamental challenge for modern statistical physics. In this work, we employ the Non-Equilibrium Self-Consistent Generalized Langevin Equation (NESCGLE) theory to construct a microscopic description of the structural and calorimetric glass transition under continuous cooling. Building upon the microscopic Onsager-Machlup interpretation of Narayanaswamy's material time (the inner clock $u(t)$) [ this http URL . 156, 244506 (2022)], we recover Tool's fictive temperature $T_f$ directly from the evolving spatial pair correlations and show that wavenumber dispersion naturally generalizes the classical scalar $T_f$ into a continuous mode spectrum governed by de Gennes narrowing at the primary cage peak. Across wide variations in cooling rate down to the quasi-static limit, the theory yields first-principles non-equilibrium Kauzmann diagrams for the two-body excess entropy that dynamically avert the Kauzmann crisis above the ideal dynamic arrest temperature $T_c$, while predicting sigmoidal relaxational heat-capacity steps consistent with computer simulations and calorimetry. Finally, we extract the cooling-rate-dependent glass transition temperature $T_g(q)$ from both equal-area integrals and differential heat-capacity landmarks, demonstrating that its asymptotic approach toward $T_c$ obeys a critical power-law scaling governed directly by the equilibrium dynamic arrest exponent.

We study adsorption kinetics of low-molecular-weight adsorbate particles on a polymer via the Langevin dynamics. The impact of the polymer molecular weight and of the strength of the polymer-particle attraction are examined. We consider mixtures of $n_p$ chains of the length $N$ with adsorbate, where $n_pN=600$ holds. Analysis includes examination of visualizations and evaluation of adsorption capacity, binding energy, average gyration radius, and asphericity of the polymer-adsorbate complexes. Both adsorption capacity and total binding energy show monotonic, logistic-like behavior; the former reaches a plateau sooner than the latter does, indicating further optimization of the maximum-capacity complex. Binding energy per particle and asphericity of complexes both demonstrate non-trivial behaviors, with distinct extrema at the intermediate stages of adsorption. The analysis reveals three stages of adsorption: (i) formation of small polymer-particle complexes, (ii) gradual merge of these into a single complex, (iii) stationary state. The stage (i) completes faster for short chains, as in this case fewer conformational rearrangements are required. The stage (ii) completes faster for long chains because of the necklace-like arrangement of small complexes along a long chain, which promotes their merge vs. diffusion-driven merge of the complexes of short chains. Our results indicate that for the rapid removal of pollutants in the high interaction regime, it is more effective to use the set of short polymer chains. On the other hand, long linear chains are optimal for adsorbing pollutants in a weak interaction regime.

Non-volatile reconfiguration of optical devices, in which a configuration persists without continuous energy input, remains a challenge. We introduce multistable elastic pixels (MEPs), lithographically defined pores filled with a nematic liquid crystal, whose curved ends capture a scattering inclusion in one of two mechanically stable sites. Simulations and experiments show that pore geometry and homeotropic surface anchoring define the energy minima and the height of the barrier between them. This barrier far exceeds thermal energies, stabilizing a scatterer location absent an external field. Colloidal inclusions switch reversibly between sites under transient electric fields. Using arrays of static scatterers, we show that the two positional states produce distinct responses at visible wavelengths, demonstrating the potential of MEPs for reconfigurable devices and metasurfaces. Unlike phase-change and liquid-crystal-tuned approaches, which switch a material surrounding fixed scatterers, MEPs use the nematoelastic energy landscape to move the optical element itself.

Platinum-coated polystyrene (PS) Janus particles (JPs) propelled by the catalytic decomposition of hydrogen peroxide (H2O2) are a widely used model system for active matter, yet reported speeds for similar particles and fuel concentrations differ by more than an order of magnitude. Broad adoption of these materials requires increasing consistency in the preparation and achieving improved repeatability in their behavior. Herein, we focused on two routine, but rarely reported, preparation steps that we found to alter the particle speed. First, we found that pre-exposing the platinum cap to H2O2 before cell assembly increased the mean speed by a factor of 2.4. The size of this effect depended on batch history, where an aged batch responded strongly, while a freshly prepared batch sped up by only 16%. Second, we found that plasma cleaning of the glass substrate decreased the speed 2.7 times. In a 120 $\mu$m cell the suppression was the same at both walls even when only one wall was treated. The suppression grew with the treated glass area per unit fluid volume, which pointed to species released into the bulk solution rather than to a change at the wall. Plasma-cleaned glass released more ions into water than untreated glass, and XPS detected an ionic metal fluoride on the plasma-cleaned surface. A model in which the released ions lower the speed through the solution conductivity reproduced the measured speeds in all four cell geometries. Of the 17 published studies compared here, pre-activation is reported in only four studies and substrate cleaning in only six studies. We propose a minimum reporting standard for the preparation and associated speed measurements of catalytic Janus particles.

Physical vapor deposition can produce organic glasses with enhanced stability and pronounced structural anisotropy (layering) even when the constituent molecules are nearly spherical. However, the microscopic origin of the layering in spherical molecular glass formers remains unclear. We investigated vapor-deposited films of 9-(3,5-di(naphthalen-1-yl)phenyl)anthracene ({\alpha},{\alpha}-A) by grazing-incidence wide-angle X-ray scattering, atomistic molecular dynamics, and coarse-grained simulations. Experimentally, the layering signal varies nonmonotonically with deposition temperature and is strongest near 0.8T_g. Simulated scattering calculations reproduce the principal experimental features and show that the layering peak does not originate from shifts in single molecule degrees of freedom. In fact, the simulated deposited and bulk glasses show largely the same single-molecule conformations. Interestingly, a one-site coarse-grained liquid with isotropic interactions develops a comparable interfacial layering signature. These results indicate that layering in {\alpha},{\alpha}-A arises primarily from collective density correlations generated at the free surface during deposition rather than from conformational bias or orientational ordering. The findings connect structural anisotropy in vapor-deposited molecular glasses to the generic interfacial organization of simple liquids.

We present a variational functional neural network (vfNN) algorithm that optimizes physically motivated continuum functionals in integral form (e.g., Lagrangian, Hamiltonian, or free energy) to find the states of a system. That way, vfNN bypasses solving the equations of motion (a.k.a. the Euler-Lagrange equations), which are in the form of differential equations. To this end, our approach is fundamentally different from conventional physics-informed neural networks (PINN) that solve differential equations by minimizing a phenomenological loss function involving higher order derivatives and ad hoc weight factors. In contrast, vfNN merely evaluates lower order derivatives of the generating functional and replaces the weight factors with rigorous physical scales. This also fundamentally changes the loss landscape, and the desired solutions may become unstable. For this emergent nonconvex optimization problem, we develop a quasi-Newton optimization algorithm with simulated annealing that converges to the solutions of the corresponding Euler-Lagrange equations of the functional regardless of their stability properties. Our simulations using vfNN give accurate results for benchmark systems governed by linear or nonlinear ordinary differential equations.

Microswimmers near walls and interfaces can switch between qualitatively different modes of motion depending on the slip properties of the neighbouring boundaries. To study this theoretically, a two-dimensional point-singularity model of a microswimmer, which does not self-propel in unbounded fluid, is placed near a flat viscosity discontinuity between two fluids with viscosity ratio $\sigma$, and also near a partial-slip wall with Navier-slip length $\lambda$. Using complex-variable methods, the dynamical systems governing the swimmer motion are derived explicitly in both scenarios. Near the viscosity discontinuity, below a universal critical viscosity ratio $\sigma_c=1/2$, the swimmer is trapped at a fixed height with its stresslet axis normal to the boundary. When $\sigma=\sigma_c$ it glides parallel to the boundary at a speed selected by its orientation, with a terminal speed determined by its initial state. For $\sigma>\sigma_c$ it oscillates periodically in height and orientation while drifting along the boundary. The dynamics near a partial-slip wall depend on the ratio of the slip length to the length scale of the singularity and are similar in exhibiting an analogous transition at a critical slip length. It is found, however, that the dynamics near a viscosity discontinuity for $\sigma$ above $\sigma_c$ are richer than those near the partial-slip boundary, including the existence of a hydrodynamic bound state with zero net displacement over one period. Although the study is limited to two dimensions, these results show how a single boundary parameter organises qualitatively distinct modes of locomotion, in close analogy with slip-induced transitions reported for three-dimensional swimmers.

We study density and current fluctuations in a one-dimensional gas of run-and-tumble particles (RTPs), whose intrinsic velocities switch between two opposite values at a constant rate. We consider particles with and without pair interactions, including regularized Riesz gases, and also obtain corresponding results for Brownian particles. By linearizing the Dean-Kawasaki (DK) equations around a homogeneous stationary state, we compute density correlations and the variance of the integrated current through the origin. For repulsive Riesz interactions decaying as $1/|x|^s$ with $s>0$, this variance grows at long times as $t^{1/2}$ for $s>1$, but as $t^{s/(1+s)}$ for $0

Temporal memory can stabilise collective motion by filtering noisy local observations, but persistent information can also impede adaptation when the collective state changes. We investigate this competition in Vicsek-type systems using two distinct alignment rules: a finite buffer of past observations and a recursive update of an internal directional state. In both models, increasing effective memory shifts the loss of polar order to stronger noise and can restore ordered motion under conditions for which the corresponding memoryless Vicsek model is disordered. The stationary responses of the two models show an approximate correspondence when parameterised by a kernel-based effective memory, consistent with temporal averaging playing a common role in their ordering behaviour rather than from the details of the memory implementation. Their transient dynamics, however, are not determined by effective memory alone. Following a collective perturbation, recovery is fastest at an intermediate memory depth and becomes slower when outdated observations are retained too strongly. Temporal integration therefore produces a trade-off: deeper memory improves noise resilience, whereas excessive persistence reduces responsiveness. These results identify memory depth as a control parameter that separates the optimisation of stationary order from that of dynamical recovery in noisy active systems.

We develop a computational framework to investigate the flow kinematics of viscoplastic materials, described by the Herschel-Bulkley model, in vane-in-cup rheometers. Numerical simulations are performed using augmented Lagrangian finite element and regularised finite volume methods for two- and three-dimensional configurations, respectively, to characterise the hydrodynamics and yielding behaviour over a broad range of effective parameters. Three types of vanes are investigated: conventional 4- and 6-arm bespoke vanes and a 24-arm fractal vane (Owens et al., J. Rheol., vol. 64(3), 2020, 643-662). Our previous two-dimensional study (Chaparian et al., J. Non-Newtonian Fluid Mech., vol. 307, 2022, 104857) demonstrated the superiority of the fractal vane over conventional N-arm designs. The bespoke vanes produce highly non-uniform yielding, leading to significant deviations from the circular Couette analogy, whereas the 24-arm fractal vane generates nearly axisymmetric yield surfaces that effectively "cloak" the vane geometry. Consequently, the resulting flow closely resembles the azimuthal shear in a conventional "bob & cup" rheometer, providing substantially more accurate rheological measurements. Building on these findings, the present study revisits the torque-to-stress and rotation-to-strain rate conversions used in vane-in-cup rheometry. In particular, we re-examine the circular Couette analogy that underpins both the physical interpretation of the flow and the extraction of flow curves from raw rheometric data. Based on our extensive two- and three-dimensional simulations, we identify limitations of the existing conversion relations and propose improved closure expressions that enable more accurate determination of material's rheological properties. Furthermore, the three-dimensional flow structures and yielding patterns within the vane-in-cup fixtures are characterised.

When a small solid island slides across a crystalline surface, the outcome (smooth flow or stick-slip, free rotation or angular locking) is controlled almost entirely by the geometric relationship between the island and the surface: their relative orientation, size and lattice symmetry. These phenomena are central to nanoscale friction, to the interpretation of colloidal monolayer experiments and to structural superlubricity. FLAKE (Friction and Lattice Analysis of Kinetics and Energetics) is a Python package for simulating the statics and Langevin dynamics of a rigid 2D cluster sliding over a periodic or quasiperiodic substrate potential. It enables fast, systematic exploration of how geometry and substrate symmetry control the energy landscape and friction, studies that are prohibitively expensive with fully atomistic simulations. FLAKE has been the primary simulation tool for three published studies on structural superlubricity and colloidal friction.

In a crowded extracellular environment, viruses and nanoparticles must reach the cell membrane within a few nanometers before the first ligand-receptor bond can form. Crowders generate an entropic depletion attraction, yet continuum models usually assume contact is already established or treat the approach deterministically. We formulate a thermodynamically consistent stochastic theory for this pre-contact stage. The sphere-plane depletion geometry uses the exact Asakur-Oosawa spherical-cap overlap, rather than a fitted cap, with either ideal van 't Hoff or pressure-only Carnahan-Starling osmotic pressure. A spatially varying near-wall mobility introduces a noise-induced drift that is essential for thermodynamic consistency and is often omitted. The first specific reaction is modeled by a Robin radiation boundary; the outer boundary is reflecting or absorbing. Three first-passage problems are solved analytically by quadrature: the mean reaction time, the reaction-before-escape probability, and the conditional success time, the last encoded by a Doob transform that exposes the selection bias of conditioning on capture. The theory separates thermodynamic inputs from conditional parameters and reveals a reaction-limited to diffusion-limited crossover controlled by the local Damköhler number. For typical virus and nanoparticle parameters, the depletion well reaches $2$-$6\,k_{\rm B}T$, capture times are $0.1$-$1\,{\rm ms}$, and the conditional success time is measurably shorter than the unconditional mean. Finite-volume and Chebyshev schemes reproduce the analytic results within their discretization errors and satisfy the radiation-boundary mass balance. This provides a quantitative theoretical framework for crowding-assisted capture prior to membrane wrapping and a reference for comparing crowding, near-wall mobility, and surface reactivity in endocytosis.

After a particle forms its first receptor--ligand bond near a cell membrane, stable attachment often requires a threshold number of additional bonds. This paper develops a biophysical kinetic theory of this post-capture stage. The bond-number dynamics are modeled as a finite birth--death chain on $n=0,1,\dots,m$, where $0$ is loss of the initial bond and $m$ is the stabilization threshold. The mesoscopic rates $\lambda_n$ and $\mu_n$ encode the local energy landscape, accessible receptor--ligand pairs, steric and orientational constraints, and cooperative interactions within the growing cluster. The probability of reaching the threshold before losing the first bond is derived in closed form for general rates and, in the constant-ratio case, reduces to a geometric series controlled by the free-energy bias $\rho_n=\mu_n/\lambda_n$. The mean time to failure or stabilization follows from a tridiagonal backward equation. Conditioning on successful attachment is treated as a trajectory-selection effect: the conditioned chain is a Doob $h$-transform whose dissociation rate at $n=1$ vanishes, because successful trajectories cannot lose the first bond early. A minimal interface between the spatial first-capture probability and the bond-number chain is formulated, together with the conditions under which the stable capture probability factorizes into their product. The analysis shows that hitting probabilities constrain only the rate ratios, whereas the absolute rate scale requires time-resolved or dwell-time data. The threshold $m$ is a model-defined stabilization criterion, not a directly measured ligand count. The rates and threshold are effective parameters specified independently or inferred from kinetic data. The theory provides a quantitative framework for interpreting attachment probabilities, lifetimes, and the transition from first bond formation to stable multivalent adhesion.

Onsager's variational principle (OVP) constructs dissipative dynamics from free energy, dissipation, and input power, but deterministic rate laws alone do not identify fluctuations or chemical fuel consumption. We examine these distinctions for nonlinear reaction kinetics in active matter. Comparing Gaussian diffusion and Poisson reaction events clarifies when statistical fluctuations match a physical Rayleighian: the reaction dissipation potential must be consistent with counting statistics, local detailed balance links rate bias to chemical affinity, and kinetic scales remain constitutive inputs. Under these conditions, the normalized Rayleighian excess gives the leading rate-fluctuation cost in the frozen-state, many-event regime. Three models illustrate the consequences. Spatially uniform reactions exhibit protocol-dependent nonreciprocal response compatible with fixed-state OVP; different Rayleighian representations can select the same rate without specifying the same fluctuations. In an active emulsion, a finite fuel pool accounts for free-energy transfer and dissolution of a chemically maintained domain after replenishment stops. In a membrane-cytosol model, distinct reaction-channel realizations yield identical protein-density trajectories but different chemical input power. Under a separate kinetic assumption, an exact total-density equation still requires an initial rate and does not determine chemical work or fluctuations. These results clarify the physical and statistical inputs required for constructing reaction-transport models and interpreting their fluctuations.

Hemoglobin-oxygen equilibrium is normally studied within the grand canonical ensemble, which assumes that each hemoglobin is immersed in a reservoir of unbound oxygen molecules of the plasma. We show that this assumption is incorrect inside the RBC (red blood cell or erythrocyte), where the hemoglobin concentration is larger than the concentration of unbound oxygen in plasma. We suggest a better model, where a single hemoglobin and a few oxygen molecules around it reach a canonical equilibrium at a fixed volume (determined from the RBC structure) and a fixed temperature. The basic models of hemoglobin-oxygen equilibrium -- Pauling's model and Monod-Wyman-Changeux model -- can be reformulated for this canonical situation. They predict cooperative interaction energies, which are significantly lower than predictions of the same models in the grand canonical ensemble. Larger cooperative energies, in particular those predicted by the grand canonical ensemble, lead to instabilities (cascade processes) in oxygen release within the canonical approach. Oxygen-binding fluctuations within this approach are sizably smaller than those in the grand canonical situation. These results suggest that the hopping diffusion of oxygen from one hemoglobin to another may play a role in oxygen diffusion within the RBC.

Machine learning for chemical vapor deposition (CVD) of carbon nanotubes (CNTs) has largely mapped static synthesis conditions to final properties, implicitly treating these conditions as a complete description of growth. Here, we test this assumption by integrating gas-flow conditions with in-situ time-resolve growth profiles (growth curves) of vertically aligned CNT forests. We introduce an observation-window analysis, in which prediction is evaluated as a function of observation time by providing models with the growth curve only up to progressively later times, to determine not only whether a property can be predicted, but when the necessary information becomes available during synthesis. Clustering of normalized growth curves revealed distinct growth patterns independent of final forest height. The gas conditions alone could predict the initial growth rate but not the growth lifetime and failed to capture the variation in yield (R^2<0). Adding the growth curve improved yield prediction (R^2~0.4-0.5), with the relevant information emerging during the intermediate and later stages of growth rather than at its onset. In contrast, density and G/D ratio, which forest height does not record, showed no consistent improvement. The maximum height and lifetime could be estimated with moderate accuracy midway through the 10-min growth. Permutation feature importance identified water vapor and H_2, both linked to catalyst activity, as the most informative gas variables. These results indicate that variation unexplained by synthesis conditions is not merely noise but reflects an evolving catalyst state, and they establish mid-growth decision points for autonomous synthesis, enabling early termination of unpromising batches and, ultimately, in-batch adjustment of growth conditions.

In spite of the qualitative differences between Stokes flows in 2 and 3 dimensions, most particle-resolved computational studies of microswimmers and other colloidal systems dominated by low-Re hydrodynamic interactions are carried out in triply periodic geometries, while the corresponding continuum descriptions are frequently solved in 2-dimensional doubly periodic domains. Furthermore, most experimental examples of biological and synthetic microswimmers are realised in confined, quasi-2-dimensional geometries with a finite thickness in one of the three dimensions. To enable studying the non-trivial differences between these system geometries, in this paper we systematically derive Ewald representations for periodic Stokes force multipoles in geometries with two periodic directions, treating both three-dimensional Stokes flow with one unbounded coordinate and intrinsically two-dimensional singularities. Starting from the periodic Stokeslet, we obtain explicit expressions for force dipoles and quadrupoles and analyse the non-trivial zero-wavevector contribution arising under partial periodicity. The analytical expressions are independently validated by comparing with results from an explicit lattice Boltzmann solver in each geometry.

This paper studies the phase transition from an isotropic to a nematic liquid crystal driven by controlled cooling, motivated by the manufacturing of next-generation pharmaceutical drugs. Using the non-isothermal Ericksen model for liquid crystals with a variable degree of orientation, we formulate the problem as a stiff, quasilinear system of parabolic partial differential equations. We establish a consistent thermodynamic framework, prove the well-posedness of the system, and conduct a rigorous asymptotic and numerical scaling analysis of the moving phase boundary in a cylindrical cell subjected to bottom-wall convective cooling. Our analysis identifies a critical sample thickness that separates two distinct physical regimes. Below this threshold, the transition follows the cooling dynamics and the material remains quasi-isothermal. Above the thickness threshold, bulk thermal diffusion governs the dynamics, imposing a dominant thermal delay characterized by a concave quadratic propagation front. These results demonstrate that scaling from laboratory characterization to industrial production fundamentally alters the spatial thermal history of the material, providing a predictive mathematical framework to optimize cooling protocols for kinetic arrest.

A dual-band mid-infrared absorption imaging method is demonstrated for spatially resolved measurement of ethylene concentration and temperature in a Mach-2 cavity flow. The method used narrowband filters selected to exploit the differing in-band temperature sensitivities of ethylene absorption, together with a broadband infrared source and high-frame-rate mid-wave infrared camera. Temperature-dependent, filter-weighted absorption cross-sections were used to measure two-dimensional ethylene number density and temperature fields. Measurements were obtained for cavity, curtain, and discrete fuel-injection configurations, including cases with the leading edge of a quasi-steady shock near the cavity. Cavity equivalence ratio measurements agreed well with independent extractive measurements and reproduced trends previously observed using hyperspectral imaging. A complementary single-band implementation using a temperature-independent filter provided instantaneous ethylene concentration fields at 100 Hz and revealed intermittent reductions in cavity equivalence ratio associated with plume deflection by the shock train leading edge. The dual-band approach provides quantitative full-field measurements with substantially simpler spectral instrumentation than hyperspectral imaging while retaining flexibility for time-resolved flow measurements.

Laminar-turbulent transition governs skin friction, heat transfer and losses in turbomachinery, yet Reynolds-averaged Navier-Stokes (RANS) transition models rely on empirical correlations and hand-calibrated activation functions whose structural deficiencies cannot be resolved by recalibration. We propose a CFD-driven sparse symbolic regression framework to learn interpretable, closed-form corrections to the production and destruction activation functions in the intermittency equation of the local, Galilean-invariant $k$-$\omega$-$\gamma$ model of Ge et al. Each correction combines a polynomial of a local pressure-gradient parameter, controlling amplitude and sign, with a bounded exponential of local flow features, controlling spatial support. This construction bounds the corrections without ad hoc limiters. Coefficients are identified by gradient-free optimization with the RANS solver in the loop, accelerated by POD-Kriging field surrogates, using mean-velocity data from wall-resolved large-eddy simulations (LES) of the ERCOFTAC T3 flat-plate cases. Elastic-net hyperparameters are selected automatically through bi-level optimization with leave-one-case-out cross-validation. The resulting model retains 11 of 21 candidate terms, compared with 20 under conventional grid-search tuning, while achieving comparable or slightly better accuracy on training and unseen cases. Both approaches recover the same leading-order correction. Applied without retraining to the transonic LS89 turbine cascade, far beyond the training envelope, the augmented model remains numerically robust and improves heat-transfer predictions at all four operating points, reducing errors by up to 70% where the baseline predicts premature transition under high freestream turbulence. Residual errors in transition onset and length highlight the limits of training on flat-plate data alone.

The dissipation of turbulent kinetic energy is conventionally attributed to a scale-invariant spatial multiplicative cascade, with Lagrangian statistics inferred through bridge relations. Direct numerical simulations with tracers reveal instead that Eulerian coarse-grained dissipation has a squared-logarithmic cascade depth and scale-dependent multipliers, whereas time-averaged dissipation along trajectories displays multifractal scaling and an approximately scale-invariant temporal cascade. The classical bridge fails at the level of individual trajectories. Eulerian multipliers nevertheless possess a multifractal organization whose accumulation accounts for the squared-logarithmic spatial statistics. This contrast motivates a material-inheritance picture in which Eulerian dissipation statistics reflect the spatial assembly, deformation, and mixing of distinct Lagrangian histories. The results therefore distinguish the temporal cascade organization revealed along fluid trajectories from the non-stationary spatial refinement observed in the Eulerian frame.

The presence of extreme ocean waves poses substantial threats to the safety of marine engineering applications and navigational activities. Accurate prediction of the nonlinear wave loads on offshore structures in large-diameter cylindrical configuration, such as monopile wind turbines and platform columns, requires a robust solution to the high-order wave diffraction problem. This paper introduces a novel, highly nonlinear time-domain numerical pseudo-spectrum model based on potential flow theory. By leveraging the Fredholm integral equation of the second kind and Legendre polynomials, a distinct efficient solver for computing the velocity potential on the cylinder surface and vertical velocity at free surface is developed. The present method is verified by comparing with a direct approach based on Fourier transform and established theoretical models for simulating the scattering of small steepness uniform waves. The convergence and computational efficiency of the present method is also demonstrated. The validation of the new model for simulating highly nonlinear transient water waves will be reported in Part II. The proposed model provides a powerful and efficient new framework for analyzing high-order nonlinear wave diffraction and hydrodynamic loads, with significant implications for both scientific research and the engineering design of coastal and offshore structures.

The aerodynamic performance of a thick, cambered FFA-W3-301 airfoil section near and beyond stall was examined under elevated freestream turbulence using time-resolved surface pressure measurements for chord-based Reynolds numbers from 125,000 to 275,000. Three passive turbulence grids were used to isolate the effects of turbulence intensity and integral length scale, and the results were compared with a clean inflow. The elevated turbulence largely had a positive effect on the mean performance of the airfoil section, eliminating premature flow separation and recovering lift and drag polars more representative of a higher effective Reynolds number; however, resolving the lift in time showed that the time-averaged polars concealed bistable switching. The time-averaged lift was an occupancy-weighted average of two states, and conventional mean and standard-deviation statistics misrepresented the true post-stall unsteady loads. Beyond the maximum-lift angle of attack, the lift alternated repeatedly between two distinct levels with no characteristic frequency. At the highest tested Reynolds number, the switching persisted over an angle-of-attack range of up to nine degrees, more than an order of magnitude wider than that reported for a thin, symmetric section in a low turbulence inflow. The lift levels of the two states were also found to be nearly independent of the inflow turbulence level, whereas the fraction of time spent in each differed between turbulence conditions. conditionally averaged surface pressure distributions and proper orthogonal decomposition of the surface pressure consistently showed that neither state is fully attached; the states correspond to two positions of a single separation front on the suction side, a switching accurately captured by a single pressure mode from the decomposition.

Moisture transport in cement-based materials involves transient multiphase flow through highly irregular pore networks, where evolving air--water interfaces strongly influence liquid invasion and gas displacement. Here, pore-resolved, image-based direct numerical simulations (DNS) are used to investigate spontaneous imbibition in a FIB--SEM-reconstructed cementitious microstructure, resolving air--water interface dynamics at nanometre-to-micrometre spatial scales and nanosecond-to-microsecond timescales. As these dynamics remain inaccessible to direct experimental observation at such scales, the simulations provide, to the best of our knowledge, the first direct view of transient imbibition within the capillary porosity of a realistic cementitious microstructure. The three-dimensional simulations reveal highly heterogeneous wetting-front propagation, continuous interface reconfiguration, and progressive air entrapment, showing that local dynamics depend on evolving interface curvature and capillary-pressure fields rather than on characteristic pore size alone. Significant air entrapment develops even within the capillary pores and under perfectly water-wetting conditions, progressively reducing the saturation rate, while the capillary pressure of trapped-air clusters depends strongly on local interface geometry rather than gas volume alone. Controlled two-dimensional analyses show that the balance between capillary, viscous, inertial, and gravitational effects is strongly scale-dependent. Comparison with the three-dimensional simulations highlights the importance of out-of-plane interface curvature and pore-network connectivity. The framework also resolves moisture conditions at the steel--concrete interface, illustrating its potential for corrosion-relevant pore-scale analysis.

This study utilizes reinforcement learning algorithms to develop advanced control strategies for manipulating synthetic jets positioned on a cylinder, aiming to achieve effective flow control. It addresses critical challenges in achieving robust performance across moderate to high Reynolds numbers (Re) and varying jet placement configurations. The results demonstrate that placing synthetic jets near flow separation regions yields optimal control performance. At Re = 500, the multi-objective flow control strategy achieves up to 37.4% drag reduction and 99% suppression of lift oscillations, while completely suppressing vortex shedding. At Re = 1,000, drag reduction improves to 49.1%, with equally effective lift suppression and complete vortex shedding suppression. At Re = 2,000, the strategy achieves a maximum drag reduction of 58.8% and suppresses 90% of lift oscillations, although some residual wake instabilities persist. Additionally, synthetic jets effectively disrupted detached vortices and stabilized the wake, resulting in streamlined flow and suppressed vortex shedding. These findings underscore the pivotal influence of jet placement in optimizing flow control efficacy, while affirming the advanced capability of control strategies to tackle intricate challenges.

A sharp interface can retain material and structural information about an unresolved fluid transition zone. We formulate a local thermodynamic framework for isotropic surfaces carrying constituent surface mass densities and a thickness descriptor. The distinction between densities of additive contents and internal descriptors determines the area conjugate, reversible surface stress, and Gibbs-Duhem relation. A volume-per-area thickness has a pressure-like conjugate, a mechanical work contribution, and a separate evolution equation. Independent, constrained, and rapidly equilibrating thicknesses require different kinematics and reductions. Material storage can be retained without retaining surface inertia. The balances and entropy production specify admissible exchange and structural relaxation. For a moving surface patch, an available-free-energy identity accounts for mechanical power and for the contributions of material and structural fluxes across its boundary. Equilibrium reduction retains the production and transport needed to follow the reduced state. An explicit mass-thickness free energy has a positive-definite material Hessian and gives coupled adsorption, expansion, compression, and dissipative relaxation. Pressure response yields conditional restrictions on reduced states and demonstrates that distinct independent and constrained states can share an entire pressure-tension curve. Geometric thickness realizations and finite-rate transfer are treated with their associated mechanical and balance requirements. The framework separates state selection, constitutive closure, reduction, and identification from observations.

Premixed flames exhibit a progressive enhancement in burning rates with turbulence, with the ultimate limits governed by the onset of local extinctions. Piloted premixed burners have enabled access to turbulence far exceeding the theoretically predicted extinction limits, with the measured flame speeds still improving. This study explores the role of small scale turbulence on the burning rates of premixed flames using a piloted high Karlovitz number burner. Premixed CH$_4$-air mixtures with equivalence ratios ($\phi$) from 0.7--1.0, stabilized using a $\phi$-matched pilot flame, were subjected to increasing rms fluctuating velocities, $u'$, up to 36.0 m/s. The experimental setup enables a progressive increase in turbulent kinetic energy (TKE) at smaller scales, with the Kolmogorov scales reaching approximately 4 $\mu$m under the highest turbulence condition. Global consumption flame speeds, $S_\mathrm{T,GC}$, derived from the binarized Planar Laser-Induced Fluorescence (PLIF) imaging of OH radicals, scale with turbulent diffusivity, $\mathcal{D}_\mathrm{T}$. Further increases in $u'$, however, lead to a maximum and an eventual decline in flame speeds. The measured flame speeds exhibit a common scaling with the measured upstream $u'$. Assessments of the flame structure using CH-PLIF images further reveal progressive straining and extinction events with increasing $u'$ despite flames maintaining their flamelet-like appearance, suggesting that the observed limits derive from the increasing extinction propensity across the flame front. Finally, these findings are incorporated into a scaling relation accounting for the role of straining and extinctions in the observed flame-speed trends.

We investigate the instability of streaks induced by free-stream vortical disturbances in cooled-wall high-supersonic boundary layers. Distinct types of instability modes are identified: modified Mack second modes, a newly discovered varicose secondary-instability mode and sinuous or varicose secondary-instability modes akin to those in incompressible boundary layers. Unique characteristics of the new secondary-instability mode are that its eigenfunctions concentrate in high-speed valley regions near the wall and feature intense temperature fluctuations at the wall. The streaks in high-supersonic boundary layers destabilise the three-dimensional secondary-instability modes, but suppress the growth of the modified Mack second modes, both radiating and non-radiating. The suppression of radiating modes amounts to a reduction of the two-dimensional noise they emit. Numerical results indicate that, unlike streaks in adiabatic-wall boundary layers, whose instability concentrates in low-speed peak regions away from the wall, the secondary instability of streaks in cooled-wall high-supersonic boundary layers occurs both in low-speed peak regions and in high-speed valley regions.

Geophysical flows are routinely decomposed into mean flow and waves, and the procedure used determines how the motion is divided between the two. Ideally, the wave and mean motions of interest evolve on distinct timescales, in which case they can be separated by taking an infinite-time average over all wave periods. Individual waves average away, while exactly resonant interactions contribute to the averaged dynamics because they are steady on the fast timescale. We generalize this averaging to finite windows, yielding a family of decompositions that additionally retain near-resonant interactions whose phases do not fully cancel over the time window. Such averaging necessarily invokes a choice of reference frame; the same flow averaged in two frames may yield mean flows differing by a drift. The averaging formulation developed here enables us to express Stokes drift through resonant and near-resonant interactions, confirming the intuition that it is a slow quantity generated by fast waves and revealing a coherent near-resonant contribution generally present in Stokes drift calculated over finite time from broadband wave fields. We use the fast-wave evolution underlying the exact average to define both the wave reference frame, in which the fast phase is steady, and a wave-frame average. We cast familiar Eulerian and Lagrangian averages and this wave-frame average in a common form to further illustrate how the chosen frame determines which motions enter the mean. This view of averaging provides a common basis for comparing decompositions and choosing among them according to the physical processes one seeks to isolate.

We investigate the dynamics of self-propelled spheroidal particles in electroosmotic channel flows generated by uniform, patterned, and combined zeta-potential distributions. The coupling between self-propulsion, particle shape, and electroosmotic advection gives rise to distinct regimes of confinement and transport. For a uniform zeta potential, the dynamics reduce to a two-dimensional system in cross-stream position and orientation. We show that this system possesses a non-canonical Hamiltonian structure, allowing its phase-space organization to be characterized analytically. For spherical particles, the dynamics admit a nonlinear-pendulum description, yielding the characteristic oscillation frequency and extent of the confined region. The oscillation frequency depends non-monotonically on electrostatic screening and reaches a maximum at an intermediate Debye parameter. Spatially patterned zeta potentials reorganize the dynamics by generating counter-rotating vortices and coupling streamwise position, cross-stream position, and particle orientation. Numerical simulations and dynamical-systems analysis reveal regimes of single-cell confinement and cross-cell migration, controlled by particle shape and electrostatic screening. When uniform and patterned components coexist, mean electroosmotic advection competes with vortex-induced recirculation, producing transport sensitive to particle shape and initial conditions. Together, these results connect Hamiltonian phase-space dynamics in uniform electroosmotic flow to vortex-mediated trapping and transport in patterned flows, highlighting the potential of surface electrostatic patterning to control particle motion without altering channel geometry.

Proper orthogonal decomposition (POD) represents physical fields with orthogonal modes ordered by variance, so that one decomposition gives reduced coordinates in every dimension, but it needs many modes when the data lie near a curved manifold. Nonlinear autoencoders are more compact, but their information loss happens inside a nonlinear encoder, and a model trained with one latent dimension gives no model with a smaller one. We introduce Orthogonal Projection in Invertible Nonlinear Embeddings (OPINE), which learns an invertible nonlinear change of coordinates and performs POD in the transformed coordinates. Because the map is invertible, all information loss occurs in the POD projection, and ordering its basis after training gives reduced coordinates of every smaller dimension from a single model. Training alternates gradient updates of the map with a damped update that tracks the evolving POD subspace, and we prove that this update converges locally to the exact POD subspace. We evaluate OPINE on synthetic manifolds, chaotic Kuramoto-Sivashinsky dynamics, forced Burgers turbulence, two-dimensional Kolmogorov flow, and three-dimensional minimal channel flow. OPINE is more accurate than POD at every tested retained dimension above one, and on the Kuramoto-Sivashinsky and Burgers dynamics, it is more accurate than convolutional and fully connected autoencoders by more than two orders of magnitude at the largest retained dimension.

Accurate computation of the acoustic terms in weakly-compressible SPH, including the equation of state, its inverse, and the evaluation of the local speed of sound, is essential to ensure energy conservation, robust solid boundary conditions, and correct open boundary behavior. In the classic Cole's equation of state, using values of the polytropic constant $\gamma \ne 1$ can lead to significant precision loss, particularly when computations are performed in single precision, as is common in GPU implementations. We extend here our previous results on the optimal choice of state variable by introducing a new higher-precision form for all three acoustic terms, denoted \texttt{explog}, and assess its numerical accuracy and computational performance across a variety of devices and test cases. We find that the new form evaluates the acoustic terms with a maximum ULP of~2 for arguments less than $0.125$, and has higher errors in less than 1\% of the arguments larger than the threshold. Combined with a rewritten expression of the pressure at solid boundary particles in the ``dummy'' model, it provides consistently more accurate results, maintaining deviations from the reference pressure profile to below 2\%, even in presence of a rough bottom terrain. Computationally, the new formulation is also faster than the naive one on GPU, and only marginally slower on CPU.

The ability to emulate complicated and computationally-expensive physical systems in an efficient and stable manner is a popular motivation for scientific machine learning (SciML). Stable numerical solvers tend to be computationally expensive, as they attempt to resolve small (spatial and temporal) scales that receive and dissipate spectral energy. Learned coarse-grid forecasters remove the dissipative channel, allowing unresolved frequencies to re-emerge as grid-scale noise (aliasing). In this paper, we use the Neural Discrete Equilibrium (NeurDE) method to explore stable emulation at extremely coarse grids, demonstrating physically-principled control over entropy dynamics that reinforces the physical system's dissipative mechanism. Entropically-stabilized NeurDE produces stable long-time rollouts for thousands of forecasting steps on large Reynolds number turbulent flows ($\mathrm{Re}=100{,}000$) with very coarse grids (down to $\mathbb{R}^{16\times16}$). At these very coarse grid scales, entropically-stabilized NeurDE can be more stable than even our stabilized data-generation numerical method.

The mechanisms governing the formation and maintenance of polar vortices on Saturn and Jupiter represent a significant challenge in current planetary atmospheric dynamics. In the presence of internal heat sources, the existence of condensable components leads to widespread moist convection in the polar regions of these gas giants. However, the role of moist convective organization in the formation and maintenance of such polar vortices remains poorly understood. To investigate the interaction between convection and polar vortices, this study develops a polar $\gamma$-plane shallow-water model coupled with a quasi-stochastic convective parameterization. In this quasi-stochastic scheme, convection is prescribed as localized impulsive mass sinks, with the inception probability depending on local vorticity, thereby assigning a higher convective likelihood to cyclonic regions. Numerical experiments successfully reproduce shielded cyclones and persistent vortex crystals reminiscent of Jupiter's polar configuration. Increasing mesoscale feedback promotes vortex growth, shield formation, and spectral organization, while the characteristic vortex scale depends on both the deformation radius and the convective parameterization. The resulting patterns exhibit both clockwise and counterclockwise structural drift, whose direction and rate are not adequately captured by a conventional Rossby wave phase-speed estimate. A Biot--Savart diagnostic reveals competing contributions to structural drift, with predominantly counterclockwise advection induced by the other vortices and clockwise advection induced by the background vorticity outside the identified vortices. These results provide a possible formation pathway for shielded vortex crystals and highlight the role of convective feedback in vortex formation.

Free-surface water waves provide a macroscopic platform in which topological localization can be measured through surface-elevation fields. Higher-order topological phases offer a route to localizing wave modes at structural corners, yet their experimental realization in water-wave systems remains largely unexplored. Here, we experimentally demonstrate a water-wave higher-order topological crystal, where surface waves are confined to structural corners and spectrally identified through measured free-surface responses. Bulk band analysis and finite-system simulations predict topological edge and corner states in the designed structure, while frequency-resolved surface-elevation measurements confirm the corresponding localized modes. The measured spectra and field distributions reveal pronounced in-gap corner localization consistent with the predicted higher-order topological modes. These results establish surface water waves as a directly measurable platform for higher-order topological physics, enabling spatial localization and spectral characterization of hydrodynamic wave modes.

We present a generalized variational approach for constructing energy-stable macroscopic partial differential equations (PDEs) directly from microscopic physical laws. Rather than fitting the PDE evolution for prescribed variables from macroscopic trajectories, we construct an extendable variational structure by adjoining auxiliary variables to seek autonomous reduced dynamics in an enlarged state space. By defining these variables as micro--macro encoders with explicit microscopic counterparts, we cast the learning problem as the sample-wise joint identification of the reduced state representation and the variational ingredients from time-discrete data, enabling systematic law-level transfer across scales. The resulting PDEs preserve frame indifference, physical constraints, and energy stability by construction, and admit a fluctuation--dissipation-consistent stochastic extension. Numerical results for the non-Newtonian hydrodynamics of polymeric fluids show that the learned models capture the viscoelastic responses induced by nonlinear and heterogeneous molecular interactions beyond empirical closures.

Three-dimensional magnetohydrodynamic (MHD) turbulence, the flow of astrophysical and fusion plasmas, is costly to simulate. We present, to our knowledge, the first learned surrogates of three-dimensional resistive MHD turbulence, and compare three standard backbones in that role: a convolutional UNet, a shifted-window transformer and a Fourier neural operator. They are trained as autoregressive emulators of decaying MHD turbulence at a resolution of $128^3$ and Reynolds numbers of 1000, 3000 and 6000, on 500 simulations per Reynolds number, each with one two-stage procedure, single steps and then short rollouts, and stopped by one rule. Over a window of about one large-eddy turnover time, the UNet and the transformer reach relative velocity errors of 0.018 to 0.053 and keep the current sheets, the enstrophy, the current density and the energy spectra of the simulation; which of the two is the more accurate depends on the Reynolds number, the UNet leading at 3000 and 6000 and the transformer at 1000. Applied with the same backbones and training procedure to two public benchmarks, the models reach the lowest error reported to date on the isotropic turbulence set of FactFormer, 39% below the best published model. On the compressible MHD set of The Well, their rollout errors are a third to a half below those of the best of The Well's baselines. They also match a 1.3 B-parameter pretrained foundation model in its rollout windows, with 20-62 times fewer parameters. The code, the configuration of every model, the evaluation scripts and the data generator with the seed of every simulation will be released upon publication.

Neural surrogates can accelerate many-query aerodynamic analyses, but their standalone predictions may be insufficiently accurate or robust to support reliable design evaluations. We develop a learned warm-start formulation that predicts mean-flow and turbulence fields directly on native CFD meshes for subsequent correction by the RANS solver. A common architecture and objective structure are used across subcritical and transonic flows, including challenging conditions with shock-induced separation. A condition-modulated Transolver combines Fourier and wall features with target-gated regularization, a Sobolev-type loss, adaptive loss weighting and sampled training. Prediction requires no preliminary flow solution, and training requires no solver-residual evaluation. Extensive 3D CFD evaluations on SuperWing, the NASA Common Research Model (CRM) and DLR-F6 assess geometric and operating-condition generalization, including interpolation, extrapolation and cross-mesh deployment, using Spalart-Allmaras and $k$-$\omega$ SST closures on million-cell meshes. Unseen nominal cases achieve geometric-mean iteration speed-ups of approximately $2$-$4\times$ under a common convergence criterion based on cold-run aerodynamic coefficients. On CRM, learned initialization provides greater aggregate acceleration than nearest-condition restarts using the same solution library. Resolution invariance enables direct deployment of coarse-mesh models on finer meshes without retraining, solution interpolation or target-condition coarse solves. Including data generation and training, estimated campaign speed-ups reach $2.1$-$2.3\times$. No warm run diverges; fewer than $2\%$ fail to satisfy the cold-reference convergence criterion. These results support learned initialization for repeated aerodynamic analyses, while highlighting initialization sensitivity near separation as a remaining limitation.

This study develops and implements a Harrow-Hassidim-Lloyd (HHL) quantum algorithm for solving a one-dimensional linear advection equation with periodic boundary conditions. The governing equation is first discretized using a classical finite difference (FD) scheme to obtain a linear system suitable for quantum solution. We present a newly designed, circuit-level implementation of HHL assembled from Qiskit circuit components and exploit the circulant structure of the periodic discretization matrices through Fourier-based matrix evolution. The HHL algorithm is benchmarked with three explicit schemes and one implicit scheme. The implicit scheme requires a nontrivial linear solve arising from the discretized PDE on progressively finer grids, whereas the explicit schemes provide different input fields for testing state preparation and reconstruction with identity coefficient matrices. HHL solution states are validated against direct classical solves in noiseless simulation. For hardware execution, the periodic matrix structure permits a Fourier implementation that applies reciprocal eigenvalues without phase estimation. Results on the IBM Rensselaer Nighthawk processor are compared at a shared final time. Noiseless reconstructed fields approach the transported profile on resolved grids, while substantial hardware errors remain for both explicit and implicit schemes. Crank-Nicolson remains exceptionally well-conditioned and utilizes similar circuit re sources to the explicit controls, proving that hardware degradation in our tests was not driven by poor matrix conditioning. Ultimately, this study shows new means for HHL algorithms to study quantum CFD problems involving advection equations with implicit time integrations, while demonstrating how state preparation and measurement affect the practical performance of quantum solvers on current devices.

Background. The pyriform aperture is a critical anterior bony constriction governing nasal airflow and is clinically relevant to both functional and aesthetic nasal surgery, yet the degree of pyriform aperture enlargement (PAE) needed to capture its aerodynamic benefit is undefined. This study employs high-fidelity computational fluid dynamics (CFD) to quantify the aerodynamic effects of progressive PAE and identify a threshold beyond which further enlargement yields minimal benefit. Methods. A CT-derived three-dimensional nasal airway model was digitally modified to produce baseline, 5%, 10%, 15%, and 20% increases in pyriform aperture cross-sectional area. Pressure-driven large-eddy simulations (LES) were performed at a fixed transnasal pressure difference of 11.25 Pa to quantify changes in inspiratory flow rate, total airway resistance, and local airflow characteristics. Results. Progressive PAE monotonically increased inspiratory flow from 15.063 to 15.252 L/min (approximately 1.25%) and reduced airway resistance from 0.6138 to 0.6028 this http URL (approximately 1.80%). The aerodynamic response was strongly nonlinear, with the greatest improvement occurring between 10% and 15% enlargement. Increasing the aperture from 15% to 20% produced negligible additional improvement. Conclusions. PAE improves nasal airflow by reducing the resistance imposed by the anterior bony constriction. In the anatomical model investigated, approximately 15% area enlargement represented an efficient aerodynamic threshold, after which the dominant resistance shifted toward downstream nasal structures and further enlargement produced little additional benefit. These findings support a conservative, anatomy-dependent approach to PAE and warrant validation across a broader range of patient-specific geometries.

This study investigates inhalation-exhalation asymmetry in population-derived median unilateral human nasal cavity under pressure-driven breathing using time-resolved computational fluid dynamics (CFD). A standardized geometry reconstructed from averaged CT data of 30 adults was subjected to a sinusoidal nasopharyngeal pressure waveform over a complete breathing cycle. Low, intermediate, and high pressure amplitudes were considered to quantify breathing-phase-dependent changes in flow rate, Reynolds number, wall shear stress, nasal resistance, and olfactory-region airflow. For identical imposed pressure magnitudes, inhalation produced a consistently larger flow rate and lower aerodynamic resistance than exhalation, demonstrating a direction-dependent pressure-flow response. Increasing breathing intensity increased Reynolds number and nasal resistance while largely preserving the spatial pattern of the flow. During inhalation, stronger airflow penetrated further into the superior nasal cavity and produced higher and more localized wall shear stress, whereas exhalation exhibited smoother airflow redistribution. The breathing-phase asymmetry also affected regional ventilation: the fraction of total airflow reaching the olfactory region increased with inspiratory intensity and reached approximately 6% under the high-pressure condition, while the expiratory fraction remained comparatively insensitive to breathing intensity. These results demonstrate that pressure-driven transient simulations naturally capture geometry-dependent inhalation-exhalation differences that are suppressed when identical flow rates are prescribed for the two breathing phases, with consequences for both global nasal resistance and regional airflow delivery.

Quantifying thermal transport across micro- and nanoscale heterostructures is critical for solid-state devices and relies on fitting heat-transfer models to thermal-wave spectra. When probing scales approach optical absorption depths, electron-phonon equilibration lengths, or phonon mean free paths, classical surface-heating Fourier models can match measured phase spectra while returning biased, measurement-dependent parameters. Here we introduce PRISM (Physics-Resolved Inference and Screening Meta-framework), an agentic framework coupling multilayer optical transfer-matrix electrodynamics, two-temperature electron-phonon relaxation, and nonlocal Guyer-Krumhansl phonon hydrodynamics within a unified admittance formalism, paired with singular-value-decomposition identifiability screening and knowledge-guided routing. Demonstrated with frequency-domain thermoreflectance across stacks relevant to microelectronic contacts and dielectric barriers, PRISM corrects a 24-28% interfacial conductance underestimation in Au/Si, recovers intrinsic silica conductivity in Au/Ti/SiO$_2$, and eliminates a 40% cross-plane conductivity underestimation in Au/MoS$_2$. In bimetallic Au/Ti/Si stacks, where all three non-classical mechanisms act simultaneously, nonlocal modeling reconciles the $116$-$137$ W m$^{-1}$ K$^{-1}$ local-fit scatter across spot sizes and frequency windows into a configuration-independent intrinsic silicon conductivity of $141$ W m$^{-1}$ K$^{-1}$. For ion-irradiated and graded media with continuous conductivity profiles, PRISM can autonomously construct and verify a deep operator network solver to reconstruct steep damage gradients. By uniting non-equilibrium transport physics and identifiability screening with autonomous model synthesis, PRISM establishes a generalizable paradigm readily extensible to broader optothermal and thermal-wave metrology modalities.

Many dynamical systems operate in disordered environments. In this Letter, we investigate how quenched randomness modifies particle diffusion. We show that, in finite-strength potential landscapes, low disorder densities can induce logarithmically ultraslow diffusion. The underlying mechanism originates from local symmetry breaking in particular potential configurations: Barrier-well structures form directional channels, causing particles to undergo hierarchical capture, escape, and recapture processes. A coarse-grained channel theory yields an approximate scaling prediction for the mean-square displacement. Counterintuitively, when the disorder density reaches the fully disordered limit, the system returns to normal diffusion, revealing a nontrivial, nonmonotonic relationship between disorder density and transport type. This mechanism is observed in both nonlinear maps and stochastic systems.

Iterated nonlinear quantum protocols provide a straightforward way of realizing nonlinear dynamics in quantum systems through measurement and postselection. We investigate a family of protocols in which the order of the induced nonlinearity is controlled by the number of qubits involved in a single step. By examining the resulting rational maps and applying a set of numerical diagnostics, we identify extended parameter regions that exhibit ergodic-like dynamics for protocol orders $n=3,4,$ and $5$. We further characterize the associated chaotic behavior through the distribution of Lyapunov exponents. Our results show that ergodic-like dynamics persists beyond the quadratic case, while the geometry of the corresponding parameter regions and the typical degree of chaoticity depend strongly on the order of the nonlinear transformation.

Repeatedly combining entangling gates on an ensemble of qubits with measurement and postselection on a part of them induces a nonlinear evolution of the unmeasured qubits' state, whose fractal convergence boundaries make the outcome sensitive to the initial state. We study a family of iterated protocols in which $n$ identical qubits are coupled by CNOT gates, $n-1$ of them are postselected, and a parametrized single-qubit unitary acts on the survivor. For orders $n=2$ to $5$, we map the box-counting dimension of the pure-state Julia sets over the complex parameter plane and identify the symmetries that constrain it. Allowing mixed initial states, we find that moderate preparation noise preserves the main parameter-dependent trends of the boundary dimension over much of the studied range, and that the three-dimensional quasi-Julia boundary in the Bloch ball has a dimension that is approximately equal to the dimension of the pure-state Julia set plus one. We further model gate imperfections by an effective depolarizing channel and by fixed coherent interactions. Weak errors leave the estimated dimensions consistent with their ideal values even where the convergence regions visibly deform, and $ZZ$ errors are shown to be exactly conjugate to the ideal protocol at a rotated parameter. Finally, we analyze the postselection and storage cost of an implementation and propose a diagnostic test combining conditional fidelity with acceptance statistics, which we demonstrate on IQM Emerald and Rigetti Cepheus-1-108Q.

The definition of self-organized criticality (SOC) is ambiguous and controversial. Here we discuss the nonlinear physics of six basic SOC definitions, such as: phase transitions, fractal structures, power laws, SOC contingency, exponential growth, and diffusive decay. Statistics of SOC events or avalanche processes can be inferred from their size distributions, or from their spatio-temporal evolution.

Analog computers solve problems through physical representations of mathematical variables and relations, often using the dynamics of electronic circuits and their associated signals. Many analog computers directly represent nonlinear dynamical systems; they encode their solutions in the signals that they generate. Although most modern scientific computing relies on digital architectures with inherently discrete-valued representations and algorithmic approaches, the design constraints of such architectures increasingly limit both performance and energy efficiency. Analog systems can circumvent some of these constraints; they execute specific computations very efficiently by mapping them directly onto physical processes using smaller and simpler computing elements than the ones in digital architectures. In this article, we provide an interdisciplinary perspective on modern analog and hybrid (i.e., analog-digital) computing. We discuss how modern scientific computing workflows can leverage analog approaches in various applications, such as in simulating dynamical systems, performing optimization, and enabling more energy-efficient implementations of artificial intelligence.

Action variables are adiabatic invariants: their values are preserved during adiabatic time evolutions in completely integrable classical Hamiltonian systems. Nevertheless, an adiabatic cycle can alter how an action variable depends on phase-space variables that are independent of adiabatic parameters. Such a change, which we call action variable holonomy, induces adiabatic torus pumping in phase space. For a family of completely integrable kicked-top systems, a homotopy classification of adiabatic cycles identifies which adiabatic cycles induce action variable holonomy and adiabatic torus pumping. A physical example is also provided.

We investigate three-dimensional light bullets (LBs) in an optically injected, vertically emitting Kerr-Gires-Tournois interferometer operating in the normal dispersion regime. In the uniform field limit, the dynamics is governed by a generalized Lugiato-Lefever equation with third-order dispersion, paraxial diffraction, and fourth-order diffraction, stemming from lens and mirror aberrations close to the self-imaging condition. Using direct numerical simulations, we show that without aberration only transversely drifting, tilted multi-peak localized states (LSs) are stable in two dimensions, whereas no stable LBs exist in three dimensions. However, a small negative spherical aberration stabilizes a rich multistable family of two-dimensional LSs, including straight and tilted multi-peak LSs, oscillating states, and complex bound states, which persist even for negative paraxial diffraction. We identify an Andronov-Hopf bifurcation followed by a homoclinic transition toward tilted states, accompanied by hysteresis. Finally, we demonstrate that stable straight and tilted LBs exist in three dimensions in the presence of aberration, the latter forming a continuous family parametrized by the transverse tilt direction.

Switching networks arise across physics, biology, and engineering, where interactions turn on and off due to communication limits, control protocols, failures, or scheduling. Most synchronization theory for switching networks of continuous-time oscillators relies on the fast-switching approximation, yet many systems operate outside this regime, where switching can produce unexpected and counterintuitive collective dynamics. We develop the first analytical framework for synchronization in non-fast-switching networks of saddle-focus continuous-time oscillators. Using Rössler and piecewise-smooth systems as canonical examples, we leverage a structural property of saddle-focus oscillators to reduce the variational dynamics to a linear system with constant coefficients, enabling a Floquet-theoretic stability characterization under periodic switching. The analysis identifies explicit switching intervals that stabilize synchronization even when neither switching mode nor the corresponding average system supports synchronization in isolation, thereby revealing the mechanism underlying the emergence of "windows of opportunity" at intermediate switching rates. We further derive a switching-dependent master stability function linking the network Laplacian spectrum to the switching rate. The master stability function provides two complementary routes to inducing or preserving synchronization: adjusting the switching schedule for a fixed network or adapting the network spectrum to a prescribed schedule through our constructive edge-pruning or edge-augmentation algorithms. These results provide a rigorous basis for understanding and leveraging intermediate-rate switching in the design and control of evolving networks.

Frequency-comb spectra can arise from distinct time-domain waveforms. We develop a Fourier-based framework that relates waveform symmetry, regularity, and modulation to the structure of overtone- and sideband frequency combs. Analytical derivations show that symmetry determines the allowed harmonic orders, while waveform regularity governs spectral decay: discontinuities produce $n^{-1}$ scaling, derivative discontinuities yield $n^{-2}$ scaling, and smooth nonlinear mappings can produce rapidly decaying harmonics. For modulated carriers, we distinguish consecutive sidebands, symmetry-induced missing orders, and nonuniformly spaced frequency components. In particular, spectral sparsity does not necessarily imply a nonuniform frequency lattice. Comparisons of analytical coefficients with calculated time-domain signals and Fourier spectra establish the correspondence between waveform properties and spectral signatures. The results provide a mathematical basis for interpreting frequency-comb structures while identifying the limitations of magnitude-only spectra in determining their underlying physical mechanisms.

A binary Bose--Einstein condensate in an elongated trap supports unpolarized excited states, in which both components share the same spatial profile. Within mean-field theory we show that the interspecies repulsion at which these states demix rises with the excitation level. Since each component keeps its atom number, the components separate by moving in opposite directions in the trap, and demixing sets in when the interaction energy released by the separation balances its cost in kinetic and trap energy. We show that the threshold also marks the onset of an exponential, non-oscillating growth of the separation, which divides the cloud into domains of opposite polarization, with walls at the density nodes and further walls interlaced with them. In the Thomas--Fermi regime of a quasi-one-dimensional condensate the rise of the threshold follows power laws in the ratio of the trap oscillator energy to the chemical potential. The trap raises the ground-state threshold, in units of the intraspecies repulsion, by 1.82 times the square of this ratio. Each density node of an excited state near the trap center raises the threshold further by 1.24 times the cube of this ratio. Because the steps between successive levels scale as the cube of this ratio, they fall as the inverse square of the atom number, and the dependence on the excitation level is a mesoscopic effect, appreciable only when the chemical potential is no more than a few times the oscillator energy. In a hyperfine mixture of $^{87}$Rb a Feshbach resonance tunes the interspecies repulsion across the thresholds of the lowest states.

We investigate effects of longitudinally varying nonlinearity on periodically distributed amplification systems in optical fibres. Emphasis is made on configurations in which the nonlinear coefficient exponentially grows or decays along the propagation distance, while the group-velocity-dispersion (GVD) coefficient is held constant. Such systems are of practical relevance to the design of highly efficient nonlinear devices, including broadband light sources and advanced amplification schemes, where precise management of the interplay between the GVD, nonlinearity, and gain is essential. Adopting the known generic integrability condition, we derive exact analytical expressions for the evolution of the optical field in the presence of the tailored nonlinearity profiles and periodically distributed gain. The resulting periodic wavetrain solutions and their long-wave limit in the form of bright and dark solitons provide insight into the controlled enhancement or suppression of nonlinear effects under realistic amplification conditions. The robustness of these solutions is examined by introducing finite perturbations and directly evaluating their effects on the corresponding intensity profiles. The structural stability of solutions against deviations from the integrability condition is demonstrated too. Outcomes of this study contribute to a deeper understanding of the nonlinear pulse dynamics in engineered gain-managed fibres and offer guidance for the development of novel optical systems, where the spatial distribution of the nonlinearity is exploited to optimise the performance.

We study rogue wave formation in the dam-break problem for the Kundu--Eckhaus equation with deterministic and randomly perturbed box initial data. For the unperturbed real box, the gauge transformation and Galilean invariance relate the intensity evolution to that of the focusing nonlinear Schrödinger equation. The Kundu--Eckhaus parameter determines the phase, the real shift of the discrete spectrum and the drift velocity. We compare uniform, Gaussian and Laplace perturbations with equal variance and the same correlation scale in the underlying Gaussian field. At the larger perturbation strengths considered, the Laplace perturbations yield larger mean maximum intensities and higher exceedance probabilities for the normalized intensity at the final simulation time, but smaller amplification relative to the initial maximum intensity.

Magnetic hopfions are three-dimensional topological solitons: ``knots'' in the vector field of magnetization of magnetically ordered materials, which are a key element of the three-dimensional spintronics emerging today. In this work, a simple analytical model for a new type of magnetic hopfions --- ``concentric'' ones --- is constructed and solved. Their size and equilibrium energy are estimated, their stability region on the magnetic phase diagram of a helimagnet is mapped out, and the requirements for materials admitting equilibrium concentric hopfions with high Hopf index on a uniformly magnetized background are determined.

We study the spectral stability of soliton solutions of the parametrically driven and damped nonlinear Schrödinger (PDDNLS) equation with power-law nonlinearity $|\Psi|^{2\kappa}\Psi$ in $N$ dimensions. We identify two families of stationary solutions, $\Psi_\pm$, whose existence is determined by two conditions: one involving the nonlinearity exponent~$\kappa$ and the spatial dimension~$N$, and another involving the forcing amplitude~$r$ and the damping coefficient~$\rho$. By linearising around these solutions and introducing a convenient parametrisation through~$\varepsilon$, we reduce the stability problem to a dissipationless eigenvalue problem for two Schrödinger-type operators, $L_0$ and $L_1$. We prove that $\Psi_-$ is always unstable, while for $\Psi_+$, we carry out a complete spectral analysis by decomposing the problem into angular momentum sectors $\mathcal{S}_l$. We show that modes with $l \geq 2$ generate no instabilities and that no complex quadruplets arise on~$\mathcal{S}_1$. We also derive an analytical instability criterion on $\mathcal{S}_l$ by combining a Vakhitov--Kolokolov-type argument with a local analysis that determines the direction of the eigenvalue splitting near the origin. In addition, we uncover new phenomena at both small and large values of $\kappa$ that were not investigated in earlier one-dimensional studies. Numerical stability diagrams for $N = 1, 2, 3$ are presented.

Individual bicycle configurations can be assessed in situ using power and speed measurements without a velodrome or wind tunnel. We apply an integrated energy-balance workflow to five configurations tested by one rider on a road section. Five nominal power levels, each ridden in both directions, yield 25 paired observations. Kinetic-energy changes are corrected explicitly; gravitational work cancels between spatially matched outward and return sections. A shared effective rolling-resistance coefficient Crr and a separate aerodynamic drag area CdA for each setup are estimated jointly. The fitted drag areas range from 0.2288 to 0.3601m^2, with a common Crr=0.00551 +/- 0.00047. At 40km/h, the estimated differences are 17.4 +/- 5.5W favouring the EZ-covered over the uncovered 80mm rear-wheel configuration and 64.3 +/- 4.0W favouring the aerobar position over the drops on the tested road bike. The helmet swap yields a difference of 3.5 +/- 2.8W. Reported uncertainties combine statistical variability and assumed input uncertainties and represent one standard deviation. The study demonstrates a practical workflow for quantifying individual setup differences and connecting resistance estimates to power-speed predictions under specified reference conditions.

Acoustic spin enables intriguing chiral sound-matter interactions, yet its mechanical consequences remain much less explored. Here, we demonstrate spin-induced lateral acoustic forces on chiral and achiral particles coupled to a substrate. Under plane-wave incidence, left- and right-handed chiral particles scatter fields with opposite acoustic spin that selectively couple to counterpropagating guided waves, generating lateral forces of opposite signs on the enantiomers. The lateral forces can also be realized for achiral particles by employing acoustic vortex-beam illumination. We experimentally validate the spin-dependent excitation of guided waves and lateral forces. Our results provide a route to spin-controlled acoustic manipulation and chirality-selective particle transport.

Directivity is a defining feature of musical-instrument radiation and is known to vary strongly with frequency. With the growing availability of measured directivity datasets and their use in sound-field simulation and spatial audio, there is a practical need for representations that are both compact and comparable across sources. This work addresses that need by proposing a statistically grounded description of frequency-dependent directivity that reduces complex radiation patterns to a small set of meaningful descriptors. The approach enables directivity patterns to be summarized in an interpretable way and compared consistently across frequency bands, even when the radiation is not well described by a single dominant direction. The resulting representation supports tasks such as analysis, categorization, and model building, providing a bridge between detailed measurements and higher-level descriptors useful for musical acoustics and audio rendering. Experiments on a corpus of 41 orchestral instruments show that the proposed method preserves the distance geometry well while reducing the full order-4, 30-band corpus from about 492~kB to about 100~kB in double-precision storage.

When two glass disks are rubbed together by hand with an abrasive between them, their surfaces spontaneously converge to perfectly matching spherical curves, accurate to tens of nanometers. How does such optical precision emerge from an essentially random manual process? Starting from Preston's law of material removal, we derive a first-principles explanation. Symmetries of the grinding stroke imply that planes and spheres are the generic equilibria of the process. Their stability is governed by a hierarchy of timescales: small-scale irregularities decay exponentially on the grinding timescale $T_\text{grind}$, while large-scale deviations from a sphere diffuse away on the longer spherizing timescale $T_\text{sphere} \propto (R_\text{mirror}/R_\text{stroke})^2\, T_\text{grind}$. Gravity and finite disk size destabilize planar surfaces, but for sufficiently short strokes spheres remain stable ($T_\text{deform} \gg T_\text{sphere}$), with only their radius of curvature varying adiabatically. The same framework unifies telescope mirror grinding with everyday phenomena: rock tumbling (explaining why rotary tumbling rounds edges more than vibratory, and why neither produce spheres) and sanding (explaining why small flat surfaces inevitably round). These examples offer an accessible classroom context for stable and unstable equilibria, exponential relaxation, diffusion, multi-timescale analysis, and the emergence of the Laplacian operator from averaging over a local area.

Enstrophy dynamics is investigated in homogeneous isotropic turbulence, revealing the interplay between vortex stretching, diffusion, and interscale transport. Using direct numerical simulations and a two-point statistical framework, the interscale enstrophy transfer is shown to simultaneously transfer longitudinal vorticity increments towards larger scales and transverse vorticity increments towards smaller scales, resulting in a net transfer towards smaller scales. Conditional correlation coefficients are used to provide further insights into the role of pressure in energy and enstrophy interscale transport events.

We report on a suite of direct numerical simulations of rotating plumes interacting with a pre-existing density interface. For an experimentally realizable range of rotation rates and buoyancy source sizes we find evidence of long-lived plumes that bifurcate from the source region and twist around each other as they descend. These plumes are a novel example of coherent structure formation at intermediate Reynolds number.

Data-driven closure modeling of transport systems is limited by the difficulty of generating diverse training data. We develop the Generalized Forcing Method, which uses prescribed forcings to excite the dynamics in the reduced space while preserving the target closure relation. Applications to linear transport problems, from shear dispersion to passive-scalar transport in homogeneous isotropic turbulence, demonstrate that the framework can identify accurate and stable reduced models.

In this paper, we report the impacts of isothermal compound drops for various combinations of viscous fluids. We extend an existing parameter-free model based on kinematic closure of drop impact to predict the maximum spreading diameter of both the core and the shell of compound drops. Then, we report impacts of compound drops on a cold surface. By using two liquids with different melting/freezing temperatures, it is possible to freeze either one of the two liquids or both and doing so, different patterns of frozen drops are obtained.

Approximate Deconvolution (AD) frameworks for Large-Eddy Simulation (LES) offer a promising approach for modeling multiscale interactions in turbulent multiphase flows. However, some conventional formulations exhibit structural inconsistencies, identified in our previous work [Amani E., Molaei M.B., Ghorbani M. 2024 Novel mixed approximate deconvolution subgrid-scale models for large-eddy simulation. Physics of Fluids 36] which can impact the accuracy and robustness of AD-LES. To address this issue, the present study extends a family of structurally consistent AD closures to turbulent two-phase flows. Specifically, we introduce the Alternative Local Dynamic Model with Kinetic energy equation (A-LDMK), an improved non-equilibrium one-equation mixed eddy-viscosity AD framework. These closures are evaluated through a posteriori analyses of a single-phase turbulent channel flow and a turbulent two-phase gas-liquid mixing layer. The results indicate that the consistent frameworks enhance numerical stability and can sustain energy backscatter under less restrictive stability constraints compared to standard dynamic procedures. Specifically, the proposed A-LDMK provides the most accurate prediction of the multiscale primary atomization cascade in terms of droplet size distribution, compared to the other assessed closures.

The acoustic mechanism of flue instruments originates in the interaction of an air jet with a sharp edge, the labium. Previous studies have examined isolated edge-tones or full instruments in which acoustic resonance obscures the underlying hydrodynamics, and a systematic understanding of how geometric parameters govern jet stability is lacking. We present a large-scale parametric study of the jet-labium interaction in a simplified recorder mouthpiece without a resonator, using more than 200 two-dimensional direct numerical simulations with an immersed boundary method. We vary the mouth distance, the labium angle, the vertical offset of the labium, and the Reynolds number (Re), and characterize the dynamics through spectra of the transverse force on the labium. The baseline configuration oscillates as a predominantly periodic Stage I edge-tone with Strouhal number St ~ 0.07, nearly constant for Re >= 330 and for all labium angles at the baseline mouth distance, so the frequency is set by the geometry rather than by viscosity. The mouth distance has the strongest influence: it is the only parameter that introduces a second oscillation stage, and the Stage I frequency is inversely proportional to it. The second stage is weakly present at five and six windway heights, established from six and a half, and dominant from eight, where it strongly modulates the amplitude. The vertical offset mainly affects the strength of the oscillation, and the labium angle does not change the instability mechanism. A baseline configuration is identified for future aeroacoustic coupling studies.

Solvent extraction and drying of substrate-supported viscoelastic films and gels produce quasiperiodic networks of three-armed surface folds. In this Letter, we examine the physical mechanisms governing their formation, length scales, and geometric organization. We observed that swelling-induced compression in the pinned film drives localized folding of a stiffening, diffusively thickening surface skin over a drained underlayer. Combining experiments and theory, we reveal that both the pattern wavelength and fold-arm length scale with the dried-film thickness following a power-law with an exponent 5/8, with remarkably weak dependence on elastic modulus. The folds form 120-degree junctions on a triangular lattice, defining an open honeycomb network whose pitch satisfies p = sqrt(3)(aL + g), where g is the junction gap. Notably, the folds accommodate less than 0.1% of the stored compressive strain, implicating elastocapillary arrest, rather than strain relaxation, in limiting their amplitude. These findings establish distinct geometric, kinetic, and interfacial constraints governing pattern selection in drying soft solids.

At low Reynolds number, microswimmers are coupled by the flows they create, even when they are apart. The best way for each swimmer to push itself forward then depends on its neighbors, turning swimming together into a game. To study this, we optimize the shape changes of soft swimmers, alone and in pairs, with a differentiable Stokes solver. From random initial membrane motions, a lone swimmer converges to a traveling membrane wave. In a pair, the stroke of a swimmer affects its neighbor far more than the neighbor affects its own best stroke. For swimmers in line, this influence decays as $1/\ell$ with their separation $\ell$, whereas the incentive to respond decays as $1/\ell^2$. Selfish swimmers, which maximize their own payoff, respond only to the weak incentive. The cooperative gain they miss decays only as $1/\ell^2$, and their selfish adaptations leave the pair worse off than if both had kept their solitary strokes. Related swimmers, which also value the payoff of their neighbor, recover this gain, whereas competitors pay to hinder each other, both following a law that we derive analytically. Hydrodynamics alone thus makes swimming in company a social dilemma, whose outcome depends on how much the swimmers value each other.

Transverse propulsion changes topological ordering in dense ellipsoidal Quincke rollers. Under an alternating-current electric field, a polar velocity field coexists with perpendicular nematic particle alignment. The system supports integer +1 velocity vortices with radial particle axes and -1 saddle defects. Oppositely charged defects migrate along domain walls and annihilate as polar domains merge. These results identify propulsion direction relative to particle shape as a control parameter for defect textures and collective ordering.

Chiral symmetry breaking is a defining feature of life, visible at all scales from molecules to organisms. Yet how microscopic chirality propagates to shape the macroscopic properties of living matter remains poorly understood. Here, using a new experimental system of spinning microalgae, we show that a living chiral fluid behaves fundamentally differently from an externally driven one. As their density increases, cells self-assemble hydrodynamically into small rotating clusters which merge into a percolating chiral fluid. Strikingly, microscopic and macroscopic vorticity have opposite signs: individual cells all spin clockwise, yet clusters orbit counterclockwise. Combining experiments, theory and simulations, we show that both chirality inversion and percolation are direct consequences of the cells' internally driven nature. We then show how percolation reshapes transport, with even and odd diffusivities responding differently to the emerging network topology.

We develop a nonlinear visco-elasto-plastic (VEP) model for the stress-strain response of metallic glasses by connecting the deformation dynamics with the material relaxation time obtained from independent stress-relaxation measurements. The material is modeled as a Maxwell-type element, with a nonlinear elastic spring and a stretched-exponential dashpot whose behavior is determined from the separate stress-relaxation data. The model captures the effects of temperature and strain rate on the initial elastic response, stress overshoot, post-yield softening, and steady flow. We independently determine the reference material-time function $X_0(\varepsilon)$ from the stress-relaxation response and the nonlinear material-time variable $X(\varepsilon)$ from the elastic-viscoplastic strain decomposition based on the stress-strain response. We introduce an Eyring-type function or material-time ratio $\phi(\varepsilon)=X(\varepsilon)/X_0(\varepsilon)$ which quantifies the change of relaxation dynamics during nonlinear deformation. Our model provides a simple connection between structural relaxation and yielding in metallic glasses.

This paper formulates a kinematically and variationally consistent phase-field theory for cohesive fracture at finite deformation. The theory introduces an independent compliance-damage field, which accommodates both diffuse distributions and singular concentrations. The phase-field is thereby freed from the dual burden of describing crack geometry and material degradation. A rank-one additive split of the deformation gradient makes separation explicit through independent crack-strain and reference-normal fields. All fields are governed by a single principle of minimum potential energy, which consistently couples nonlinear bulk deformation, crack separation, and crack-plane rotation. One-dimensional energy comparisons show that minimization favors Dirac-type concentration of compliance damage and crack strain. Strong displacement discontinuities thus emerge naturally at a finite phase-field length without being prescribed a priori, while the phase-field remains continuous. The concentrated energy recovers the exact bulk--interface structure of a sharp-crack cohesive zone model. General objective hyperelastic bulk potentials and admissible mixed-mode cohesive laws can therefore be prescribed independently, with the nominal traction--separation law unaffected by the bulk law or phase-field length. Diffuse damage can coexist with concentrated cracks, retaining deformation modes for bulk-energy relaxation during nucleation. Two- and three-dimensional examples validate the theory across large stretches, finite rotations, and complex crack paths. Notably, the computed near-tip Cauchy stress closely matches the analytical 1/r crack-tip asymptotic solution of Long et al. (2011) outside the cohesive zone.

We develop a stochastic Dean--Kawasaki field theory to predict the static structure factor and collective intermediate scattering function of interacting active Brownian particles. Starting from the microscopic overdamped dynamics, we derive coupled stochastic equations for the density and polarization fields using an angular-moment closure. Gaussian linearization then yields closed analytical expressions for static and dynamic density correlations in terms of propulsion speed, mean number density, interaction potential, translational and rotational diffusivities. The coupling between density and polarization predicts a crossover from exponential relaxation to damped oscillations despite the absence of inertia. For Gaussian-core potential, the predictions contain no fitting parameters. Brownian dynamics simulations show quantitative agreement at low activity and long wavelengths, and reproduce the crossover behaviour. For Weeks--Chandler--Andersen potential, the nonintegrable core makes both the Fourier transform of the potential and the self-interaction correction term in the Dean--Kawasaki field theory ill-defined. We therefore introduce an approximation that replaces the interaction potential with a passive direct-correlation function fitted separately at each density and temperature. This approximation requires no additional activity-dependent fitting parameters.

Physics informed machine learning provides a framework to study and simulate fluid dynamics, potentially at a fraction of the computational cost of traditional numerical methods, with the goal of improving the explainability, accuracy and robustness of purely data driven machine learning methods. In this work, we extend the hard constraint projection (HCP) method developed by Chen et al. [Journal of Computational Physics, 445, 110624, 2021] from a linear partial differential equation (PDE) to a nonlinear PDE: the 1D Burgers' equation. To strictly impose a discrete approximation of the governing equation, the Burgers' equation is first locally discretised (using a finite difference stencil) then decomposed into a constraint matrix and a prediction matrix. Using tools from linear algebra, the constraint matrix is used to construct a projection matrix. A physics informed neural network (PINN) [Raissi et al. Journal of Computational Physics, 378, 686, 2019] is used to predict the velocity, and a final unlearnable layer projects the velocity prediction to the hyperplane of exact solutions to a discretised form of the Burgers' equation. Our initial results indicate that the HCP-PINN initially trains similarly to an equivalent PINN, and as the PINN loss plateaus, the HCP-PINN loss continues to decline. When tested on a previously unseen uniform grid of points covering the domain, the HCP-PINN exhibits higher accuracy, converging to a data error approximately an order of magnitude lower than the comparable PINN. We also observe that the inclusion of the HCP layer results in better observance of the governing PDE. Our findings suggest that the HCP-PINN can be more robust to the selection of physics collocation points, and less dependent on collocation point quantity.

This work investigates the formation and growth of Rayleigh-Taylor instabilities (RTIs) during the onset of radiatively driven convection (RDC) in seasonally ice-covered freshwater lakes. Two-dimensional direct numerical simulations (DNS) and linear analysis allow for the investigation of how environmental factors, including thermal stratification, water clarity, and solar forcing influence RTI formation. It is found that for strongly stratified lakes, there is a period of dormancy before the water column forms a gravitationally unstable layer that allows RTI growth. Conversely, for weakly stratified lakes the water column can become unstable almost immediately, allowing for rapid RTI growth. A linear analysis is performed to investigate the early RTI growth dynamics, and its results compare well with DNS. Notably, the wavelengths and depths of RTIs, and their associated time-dependent growth rates, are all captured by the linearised dynamics. Predictions of RDC onset obtained using the linear model show good agreement with DNS results. When the analysis is applied to field measurements of ice-covered lakes, it is found that weakly stratified lakes may take a few hours before RDC onset whereas strongly stratified lakes may not see RDC onset after a full day of clear-sky spring conditions.

Detailed chemical kinetic mechanisms are computationally expensive in reacting-flow simulations because of their high dimensionality and numerical stiffness. We develop an end-to-end physics-informed autoencoder neural ordinary differential equation (PI-AE-NODE) framework in which an encoder compresses the thermochemical state into a low-dimensional latent space, a Neural ODE advances it continuously in time, and a decoder reconstructs the temperature and all species mass fractions. Elemental conservation, mass conservation, and enthalpy consistency are embedded in the training objective. The framework is applied to H$_2$/air, NH$_3$/air, and CH$_4$/air autoignition using detailed mechanisms of increasing size and complexity, which are represented accurately with only a few latent variables. Compared with an otherwise identical data-driven model, the physical constraints improve ignition delay prediction and conservation behaviour. The models reproduce major and intermediate species evolution at both training and unseen conditions, and their latent dynamics permit efficient explicit integration, with the computational advantage over the detailed mechanisms increasing with mechanism size.

Turbulent cascades in high Reynolds number regimes span many decades in scale, which can be challenging for numerical simulations. Cascade models that use logarithmic discretization can help, but these have limited capabilities to describe spatial structures or real space details. Hybrid Lattices (HLs) are proposed in order to provide a novel framework to investigate turbulent cascades in Fourier space, combining regular grids and cascade models based on logarithmic discretisations. The approach consists of a regular spectral region, capable of resolving large scale coherent structures, that is extended in a recurrent, asymptotically self similar fashion, spanning many decades in scale. The idea comes from shell models and their extensions, namely the logarithmic lattices, the nested polyhedra models or the spiral chain models. The logarithmic spacing factor of those models, such as the golden ratio, typically prevents interactions between a regular grid and a self similar model. HLs are constructed by expanding a regular region in Fourier space through recurrence relations (e.g. the Fibonacci recurrence relation), generating an asymptotically logarithmic lattice where Cartesian components remain integer multiples of the regular Fourier space grid spacing. This way, the resulting grid preserves triadic interactions linking regular and recurrent regions, allowing energy transfer across these different regions. However, the sharp reduction in triads connecting the two regions creates a bottleneck effect, and in order to address this issue, a region of ghost points at the boundary had to be introduced, efficiently allowing the flux to leak into the recurrent part. The HL framework is then tested for the one dimensional Burgers equation, and for two dimensional incompressible Navier Stokes turbulence.

The water entry of solid bodies, in particular spheres, has been the subject of numerous studies due to its relevance in multiple applications, especially focusing on cavity dynamics and the resulting forces and subsequent trajectories. The role of wettability in cavity formation and sustainability has been experimentally and theoretically addressed in the past; however, typically only up to the occurrence of a primary air cavity pinch-off. What is less explored is how wettability can influence higher-order pinch-offs. In the following study, especially secondary pinch-offs are shown to determine whether a sphere trajectory is terminally ascending, i.e., the sphere returns to the surface, or terminally descending: wettability is shown to be a strong influencing factor. This study begins with a series of systematic experiments, comparing the entry and trajectory of spheres over a range of impact Reynolds and Froude numbers, but also with varying surface wettability. From time resolved trajectories, a force balance is computed, illustrating the role of buoyancy, arising from the volume of any sustained air cavity in the wake of the sphere. Secondary pinch-offs alter this volume; hence, the terminal trajectory. A force-scale comparison and local radial balance at the cavity neck are then presented, suggesting how wettability influences the secondary pinch-off.

This paper presents a study of the viscoelastic behavior of suspensions of carbonyl iron particles coated with a superplastifier molecule and dispersed in ethylene glycol. The experiments were done in plate-plate configuration with the rheometer MCR502 of Anton Paar. The discontinuous shear thickening (DST) transition manifests by a large jump of the storage and loss modulus. For low magnetic fields ( H <___50___kA/m) the increase of moduli is at least of two orders of magnitude compared to the one induced by the magnetic field in the absence of DST. The behavior of the critical strain and the critical stress where the transition happens are presented for different frequencies and fields and a qualitative interpretation of the observed behavior is presented.

Particle image velocimetry (PIV) measures fluid motion from images of tracer particles, but its accuracy depends on choices throughout the estimation pipeline, including image preprocessing, flow estimation, and postprocessing. These choices are typically left to expert tuning, and a fixed configuration can become less accurate as conditions change. This matters especially when PIV supplies feedback for real-time control, where measurements must be both accurate and fast, and flow conditions vary. We introduce ART of PIV -- short for Agentic Real-Time and also a nod to the art of tuning a PIV pipeline -- which automates pipeline choice for each image pair. A learned agent selects a configuration according to a chosen measurement objective from a library assembled for a specified speed budget. Across cross-correlation, classical optical-flow, and learning-based estimators, ART of PIV reduces average end-point error (AEPE) by 12.2-22.4 % relative to the best single estimator at matched speed, with gains extending to 1000-4000 image pair/s. In a simulated local velocity regulation task, it reduces mean normalized closed-loop cost by 13.24-13.59 percentage points relative to a tuned fixed estimator, with the same classical controller in both cases. In a tabletop water channel, we illustrate two ways to tune ART of PIV for a fluidic pinball of three rotating cylinders: selecting between complementary optical-flow tunings for accuracy, and selecting regions of interest with coherent rotation or shear using a common flow estimator. For the first variant, we train a DreamerV3 reinforcement learning controller directly in the physical world and demonstrate tracking of a prescribed flow field in the wake of a fluidic pinball.

Interactions between floating wind turbines and the marine atmospheric boundary layer affect turbine wakes and power output. This study examines the impact of turbine representations and platform pitching motion on power predictions for aligned floating wind turbine arrays. Large-eddy simulations (LES) are performed for a fully developed wind turbine array boundary layer with periodic streamwise and spanwise boundary conditions and moving surface drag (MOSD) at the bottom surface. A proposed power-curve-aware extension of the conventional actuator disk model (PCADM) is compared with the traditional constant coefficient actuator disk model (CCADM), which is valid in principle only during Region 2 operation. Harmonic pitching motion matched to a representative ocean wave frequency is prescribed for IEA 15MW turbines mounted on the UMaine VolturnUS-S platform. Results demonstrate that the CCADM produces unphysical power overshoot when relative velocities induced by harmonic pitching periodically exceed rated speed, while the PCADM eliminates these unrealistic excursions from the actual turbine operating range. Various wind-wave conditions and relative pitching motions for an aligned farm with PCADM turbines are analyzed, including in-phase, opposite-phase, and incommensurate-phase row-to-row relative turbine motion. Results reveal that, depending on operational regions, turbine pitching motion can either increase or decrease mean turbine power output. Among the relative phases considered, in-phase motions produce larger fluctuations at the farm scale due to stronger turbine-turbine correlations. These findings highlight the importance of accounting for turbine motion and associated changes in operational regions when modeling turbine and wind farm power production in LES of offshore floating wind farms using actuator disk representations.

Classical theories attribute wind-wave momentum transfer to a critical layer, where the mean wind speed equals the wave phase speed. For waves that travel faster than the near-surface wind, this layer may lie outside the wave boundary layer or be absent altogether. We develop an analytical description of the wave-coherent airflow in this regime for a prescribed mean wind, using a Wentzel--Kramers--Brillouin--Jeffreys (WKBJ) approximation to the viscous Orr--Sommerfeld equation in wave-following coordinates. The solution combines an outer Rayleigh mode, which carries the dominant wave-coherent motion, with a thin viscous Stokes layer that supplies the phase shift producing the pressure form stress. At leading order, the form stress scales with the inverse square root of the wave Reynolds number, with a coefficient set by an integral of the outer response, and transfers momentum from the waves to the air. For an exponential mean profile, the WKBJ approximation gives closed-form expressions for the wave-coherent response. To accommodate the rapid near-surface variation of realistic wall-bounded profiles, we develop a long-wave expansion near the surface and match it to the outer WKBJ mode (LW--WKBJ). For wall-modelled simulations, whose first resolved level lies above the viscous sublayer, we replace the molecular viscosity in the Stokes layer with a constant-stress effective viscosity. Using mean profiles from direct numerical simulations and wave-phase-resolved large-eddy simulations, the LW--WKBJ framework closely reproduces the dominant wave-coherent velocity and pressure obtained from numerical solutions and available simulation data. The predicted form-stress coefficients also agree well with the available LES estimates.

The magnetic Prandtl number ($\mathrm{Pm}$), the ratio of viscosity to magnetic diffusivity, spans many orders of magnitude in astrophysical plasmas. It shapes how turbulence amplifies and structures magnetic fields. In direct numerical simulations (DNS) the viscosity and magnetic diffusivity can be controlled explicitly and independently, whereas in implicit large eddy simulations (ILES) they are set by the numerical scheme. We test whether, in a finite-volume code, $\mathrm{Pm}$ can be varied through the reconstruction scheme by applying different methods to the hydro and magnetic variables. As a proof of concept, we simulate driven, subsonic, homogeneous magnetohydrodynamic turbulence using five pairs of hydrodynamic and magnetic reconstruction schemes at varying resolutions. We measure the effective viscosity and resistivity from the energy transfer between scales. Reconstructing the magnetic field at higher order than the fluid raises the effective magnetic Prandtl number and vice versa. We demonstrate that a mix of second- and third-order reconstruction alone results in a $\gtrsim20\times$ change in $\mathrm{Pm}$. A comparison of DNS with matched explicit dissipation at these values agrees with the ILES. Mixed reconstruction thus offers a simple and efficient way to explore $\mathrm{Pm} \not\simeq 1$ in ILES without adding explicit dissipation.

We present a geometric interface reconstruction method for Volume-of-Fluid (VOF) simulations that captures both curved interfaces and sharp features using only volume fraction data. We represent interfaces with linear facets, circular arcs, and corner facets formed by two lines or arcs joined within a single cell. We first propagate local orientation constraints through a graph and merge cells to resolve ambiguities, treating topological consistency as a first-class constraint. An optional conservative refinement improves $C^0$ continuity while preserving local volume constraints. Users can independently enable circular facets, corner facets, cell merging, and continuity refinement to balance accuracy and computational cost. In its simplest configuration, our method provides a fast local line-fitting scheme competitive with state-of-the-art PLIC methods. On standard static benchmarks, the full configuration reconstructs identifiable lines, circles, and sufficiently resolved corners to numerical precision on coarse, perturbed Cartesian meshes. On varying-curvature interfaces, it achieves third-order convergence in facet-gap error and approximately first-order convergence in curvature error. These results demonstrate global volume conservation and accurate reconstruction of curved and corner features.

Scientific foundation models (SciFMs) have achieved remarkable performance on a wide range of PDEs, including the ability to efficiently adapt to unseen data distributions with additional finetuning. As with all neural architectures, finetuning such models comes with the risk of catastrophic forgetting, whereby adapting to new tasks degrades prior knowledge of the model. We study catastrophic forgetting in Walrus-1.3B, a SciFM for continuum dynamics, over the course of a two-stage sim-to-real adaptation: first finetuning on simulated flow around a cylinder and then adapting to experimental data of the same system. We find that finetuning on the simulations rapidly degrades rollout performance on the original pretraining datasets, with one-step errors increasing up to 35x after just 20 epochs. Subsequent adaptation to real data further erodes performance on the simulated task. We characterize the potential drivers of forgetting, such as dataset dependence and task representation similarity. We then show that replaying as little as 1% simulated data during real-data finetuning recovers most of the lost simulation performance while retaining effective adaptation to the experimental dynamics. Our results identify catastrophic forgetting as a practical obstacle to sim-to-real adaptation of SciFMs and show that lightweight replay strategies significantly improve retention.

Classical computational fluid dynamics (CFD) methods encounter significant computational bottlenecks in large systems and at high Reynolds number flows due to the rapid increase in degrees of freedom, even on flagship supercomputers. As quantum computers emerge, the Quantum Lattice Boltzmann Method (QLBM) has been proposed as a quantum-native alternative for solving fluid dynamics problems. However, until recently, nearly all studies have relied on classical quantum simulators rather than real quantum hardware. This study presents a benchmark of a one-dimensional QLBM implementation executed on three different IBM Quantum hardware. We design and test a quantum circuit for the advection-diffusion equation using amplitude encoding, a Bhatnagar-Gross-Krook (BGK)-type collision operator, and a streaming step with periodic boundary conditions. Our numerical experiments evaluate transpiled two-qubit gate count, total circuit depth, runtime, and accuracy metrics including maximum absolute error ($L_\infty$ norm) and root-mean-square error (RMSE). We find that the present collision and streaming operators dominate the overall cost and become the primary scalability bottleneck on current hardware. To mitigate the prohibitive cost of full quantum state tomography on hardware-based benchmarking exercises, we introduce a sampler-based measurement strategy that reconstructs macroscopic density fields directly from computational-basis measurements. This approach substantially reduces measurement overhead while preserving the expected advection-diffusion dynamics on hardware. These results provide a quantitative assessment of QLBM performance in the noisy intermediate-scale quantum (NISQ) regime and identify the principal algorithmic and experimental limitations that must be addressed for QLBM to become viable for fluid dynamics.

We present FLUCS, an open-source framework for solving systems of partial differential equations efficiently on graphics processing units (GPUs), targeting models of fluid and plasma turbulence. It comprises a set of numerical solvers specialised for a well-defined class of problems and independently developed systems that supply specific systems of equations. This allows different models to share numerical infrastructure while retaining control over their individual implementation and optimisation. The present release provides a Fourier pseudospectral solver for one-, two-, and three-dimensional periodic domains solved on a single NVIDIA GPU, with integrating-factor time integration and several time-stepping and dealiasing methods. We verify its convergence, quantify its computational costs, and demonstrate its application to three reduced models of fusion and astrophysical plasma turbulence.

We propose a model, based on a spectral energy balance argument, that provides an estimate of the dimension of the inertial manifold of the one-dimensional Kuramoto-Sivashinsky equation (KSE). By identifying the wavenumber at which energy injection and dissipation balance out, we obtain a cutoff scale $k_d=\sqrt{5/(3\nu)}$ that we use to calculate the number of dynamically active Fourier modes. This leads to an explicit expression $d_M(L,\nu)$ for the dimension of an effective manifold spanned by these modes, which we take as our estimate of the inertial manifold dimension and which scales extensively with domain size. Direct numerical simulations are consistent with the estimated spectral cutoff and its scaling with viscosity. Using convolutional autoencoders as well as Lyapunov-based estimates, we show that the minimal latent dimension required for accurate reconstruction coincides with $d_M$ across a range of $(L,\nu)$.

We consider a topographic extension to the well known Klausmeier model describing vegetation on sloped undulating terrain with a primary uphill direction and perpendicular small amplitude undulation forming ridges and valleys. Previous studies of this system have shown that, like 1-dimensional sloped terrain, as rainfall levels decrease through a threshold, vegetation forms into patterned states consisting of bands or stripes which are transverse to the primary upslope direction and move slowly uphill. In this paper we investigate the links between undulation amplitude and pattern dynamics, with the goal of understanding how the terrain impacts the resilience of the vegetation. To do this we take advantage of features of the domain, the ridge and valley, to reduce the analysis to two related 1-dimensional problems. Using a combination of analysis and numerical simulations, we argue that a combination of the ridge and valley equations provide insight to the full 2-dimensional dynamics. In particular, we find that at small undulation, the ridge plays a critical role in determining the existence and stability of patterns. For undulation amplitudes smaller than a well-defined threshold, the added sensitivity of vegetation on the ridge to aridity stress causes vegetation to be less resilient than indicated by uniformly sloped models. For undulation amplitudes above this threshold, vegetation is able to survive longer by becoming localized in the valleys, but the amplitude must be increased further to mitigate the original detrimental effects.

We obtain exact solutions of the nonlinear Dirac (NLD) equation in $1+1$ dimensions of the form $\psi(x,t) = e^{-i\omega t} \psi(x)$ for all possible combinations of scalar-scalar (SS), vector-vector (VV) and pseudoscalar-pseudoscalar (PP) interactions at nonlinearity parameter $\kappa = 1$, which corresponds to the most general 4-Fermion interactions. We look for solutions where $0 < \omega < m$ where $\omega, m$ are frequency and mass respectively. Remarkably, we show that at $\kappa = 1$, all the NLD models with SS, VV and PP interactions can be reduced to suitable combinations of SS and VV interactions and hence all solitary waves in these models must also be bound states. We show that two of the ten possible combinations are equivalent to $SS -(1/p) VV$ interactions while two other combinations are equivalent to $VV -(1/q) SS$ interactions for which we already know the results. For the remaining six combinations of SS, VV and PP, we show that depending on the parameters, whereas in some cases entire range of $0 < \omega < m$ is allowed, in some other cases $\omega$ is restricted to a smaller range $\omega_{min} < \omega < m$. Further, depending on the parameters, while the solitary waves in some cases have only one hump, in other cases the solitary waves have both single and double hump depending on the value of $\omega$. We compute the charge $Q$ and the energy $E$ for each of the solitary wave solutions and show that while $E$ and $Q$ depend on coupling constant $g$, their ratio $E/Q$ is independent of $g$. When $\kappa = 1$, all the NLD models with SS, VV and PP interactions can be reduced to suitable combinations of SS and VV interactions. As a result all solitary waves in these models are bound states with $E/Q

Although nonconservative forces and extended phase space are individually common topics in Hamiltonian dynamics, their combination is seldom developed explicitly. This note derives the full Hamiltonian equations of motion for nonconservative and nonautonomous dynamical systems formulated on extended phase space. Particular attention is given to the momentum coordinate and generalized force associated with time. The classic analytical dynamics framework is used throughout, with all developments formulated in terms of arbitrary symplectic coordinates (i.e., canonical coordinates) or functions thereof.

We present for the first time an approach for identifying the geometric and material characteristics of layered composite structures through an inverse wave and finite element approach. More specifically, this Non-Destructive Evaluation (NDE) approach is able to recover the thickness, density, as well as all independent mechanical characteristics such as the tensile and shear moduli for each layer of the composite structure under investigation. This is achieved through multi-frequency single shot measurements. It is emphasized that the success of the approach is independent of the employed excitation frequency regime, meaning that both structural dynamics and ultrasound frequency spectra can be employed. It is demonstrated that more efficient convergence of the identification process is attained closer to the bending-to-shear transition range of the layered structure. Since a full FE description is employed for the periodic composite, the presented approach is able to account for structures of arbitrary complexity. The procedure is applied to a sandwich panel with composite facesheets and results are compared with two wave-based characterization techniques: the Inhomogeneous Wave Correlation method and the Transition Frequency Characterization method. Numerical simulations and experimental results are presented to verify the robustness of the proposed method.

The free surface of thin film of a yield stress fluid has been shown to develop undulations when subject to uniaxial compression. In this paper, using a novel experimental setup, we characterize this surface instability for the first time. We show that the amplitude of the undulations depends linearly on the Bingham number, the non-dimensional yield stress, whereas the wavelength scales with the initial thickness of the compressed layer. These experiments enhance our understanding of surface instabilities in related systems, such as recent experimental work scraping a thin layer of a viscoplastic fluid.

In the late 1970s, J.S. and S.E. Tsakadze carefully monitored the long-term spin down of a vessel containing superfluid helium initially set into rotation. They occasionally observed short spontaneous spin-up events followed by relaxation. These strange events are still a mystery, but it is thought that they are due to the quantum nature of the rotating superfluid (the presence of quantized vortex lines). If so, Tsakadzes’ experiments shed light onto another mystery: the observed glitches of the rotation of neutron stars. We revisit Tsakadzes’ experiments and discuss them in view of the current understanding of quantized vortex lines and quantum turbulence.

Can a floating ring protect offshore structures from impactful ocean waves? This study presents how a floating annular viscoelastic plate can significantly reduce wave-induced forces and wave run up on a vertical cylinder by combining elastic deformation with viscous energy dissipation. The results reveal that tuning the plate’s flexibility and damping can provide appreciable protection to the central structure. These findings provide a promising passive strategy for enhancing the resilience of offshore structures.

The inertial layer is a cornerstone of wall-turbulence theory and is characterized by a balance dominated by Reynolds shear stress. Using direct numerical simulation of turbulent channel flow at Re τ ≈ 16000 , we identify a wall-normal region where the Reynolds shear stress approaches its expected constant value and where additional inertial-layer predictions for velocity fluctuations and dissipation are simultaneously satisfied. These observations provide strong evidence for the emergence of inertial-layer dynamics at this Reynolds number.

Motivated by experiments on rotating Bose-Einstein condensates, we investigate the statistical mechanics and the non-equilibrium dynamics of an imbalanced gas of oppositely signed Onsager point vortices confined in a disk. To model external forcing and dissipation, we supplement their Hamiltonian dynamics with an annihilation-reinjection (AR) mechanism that preserves the imbalance: oppositely signed vortices are annihilated when they approach closer than a distance representing the healing length, and are subsequently reintroduced into the domain at random locations. At positive energies, the system self-organizes into a large-scale coherent dipole at low imbalance and into a zonal flow at higher imbalance. While AR breaks energy and angular momentum conservation, we argue that the vortex gas evolves quasi-adiabatically through the equilibrium phase space. We capture the topological transition between dipolar and zonal flows both from a statistical and a hydrodynamical perspective. In particular, the bifurcation reflects a non-trivial equilibrium diagram in terms of energy $e$, angular momentum $\mu$, and vortex imbalance $\eta$. We characterize this phase diagram in the "strong mixing'' regime studied by linearizing the Joyce-Montgomery mean-field theory about the weakly non-uniform state. We show that the linear theory is surprisingly relevant for the numerical simulations with AR and suggest that the selection between the dipolar and the zonal configurations in the $(e,\mu,\eta)$ phase space is driven by a hydrodynamical shear instability.

Food proteins play a critical role as emulsifiers, where adsorption at the oil and water interface governs emulsion formation and stability. However, quantitative characterization of interfacial protein load remains challenging due to polydispersity in conventional emulsification methods. We combine microfluidic generation of monodisperse emulsions with colorimetric protein quantification to measure the post-collection initial interfacial load ($\Gamma_0$) and subsequently monitored over 48 h to obtain the saturation load ($\Gamma_\infty$). Interfacial load exhibited a strong bulk concentration-dependent trend and was well described by a pseudo-first-order model. Both $\Gamma_0$ and $\Gamma_\infty$ followed sublinear scaling with concentration ($\Gamma_0$ ~ C^{0.21}$, $\Gamma_\infty$ ~ C^{0.12}$). Interfacial loads were largely independent of droplet diameter, with modest reductions in initial loading for the smallest droplets at low protein concentration. Measured loads exceeded idealized monolayer predictions and fell between bilayer and trilayer bounds, consistent with accumulation beyond a simplified monolayer model. Additionally, high-throughput mapping was performed across three proteins, seven concentrations, three pH values, and two ionic strengths, revealing that $\alpha$-Casein exhibited higher interfacial loads than $\beta$-Casein and Whey protein Isolate, with maximum adsorption near the isoelectric point and at elevated ionic strength. In summary, this study establishes a quantitative experimental framework for linking protein properties, formulation conditions, and interfacial behavior using monodisperse microfluidic emulsions, while requiring only milligram-scale protein quantities.

Soft composites, materials consisting of inclusions within a polymeric matrix, offer a broad design space with diverse mechanical properties. Composite stiffness is normally set by the volume fraction of filler, and classical theory predicts at most ~25% stiffening when inclusions occupy 10% of the volume. Here we introduce a composite of phase-separated DNA droplets that occupy <10% of an entangled actin network, yet stiffen it 25-fold, reversibly. Microscopy reveals that actin penetrates the DNA droplets, leading network elasticity to determine their size; thus the system exhibits reciprocal control between matrix and droplet properties. We attribute the extraordinary stiffening to entrainment of actin by the droplets, which enlarges the effective inclusions until their contact network dominates the mechanics. This shows that liquid-liquid phase separation can control not only local compositions, but also mechanics, achieving exceptional stiffening at modest filler fractions through local geometries that constrain the matrix beyond the inclusions themselves.

In a liquid-filled vertical tube, a Taylor drop typically rises far more slowly than a Taylor bubble owing to the much larger density and dynamic viscosity of the former. In this work, we demonstrate experimentally and numerically that instead of being slowed down by the attached drop, a Taylor bubble-drop assembly rises at the same velocity as an isolated Taylor bubble, leading to a significantly faster rise of the Taylor drop. We discuss the underlying mechanism and use an analytical model to predict the drop radius within the assembly. This phenomenon offers a means for bubble-assisted rapid transport of an immiscible liquid phase in vertical tubes, with potential applicability in gas-lifting systems in confined environments.

Full-order surrogates for high-dimensional nonlinear flows are often unnecessary when applications require only selected degrees of freedom. We propose reduced-order models that bypass full-state reconstruction by deploying graph neural networks (GNNs) directly on coarse meshes. Applied to parameterized 2D/3D confined cylinder flows and an unevenly heated cavity over Reynolds/Rayleigh-number ranges, the models generalize to unseen conditions and accurately predict sparse probe locations and integrated quantities. Coarse-mesh GNNs match or outperform finer-mesh surrogates while reducing training time and memory, even for 3D chaotic dynamics. A dynamics-informed adaptive sampling strategy guided by frequency-spectrum variations reduces maximum errors by an order of magnitude versus uniform sampling at negligible cost. Coarse-mesh training also makes noise-augmented multi-step unrolling practical, improving long-horizon autoregressive predictions. The approach outperforms parametric DMD, sparse MLPs, U-Nets, and Fourier neural operators at lower cost, and enables system identification and state estimation from sparse observations. These results show that coarse-mesh representations, adaptive sampling, and noise-augmented unrolled training form an efficient framework for reduced-order modeling of parameterized unsteady flows without solver-resolution reconstruction.

Lipid bilayer membranes can be solubilized in the form of disks of approximately 10 nm in diameter by several types of hydrophobic polyelectrolytes (HPE). The disks are stabilized by wrapped HPE along the rims of the disks. We compare the solubilization behavior of anionic HPE with chain lengths in between 20 - 100 monomers, and with varying molecular composition. We find that (1) HPE as short as 20 monomers can readily solubilize lipid bilayer membranes; (2) spatial intermolecular arrangement of ionic and hydrophobic groups in HPE determine if solubilization occurs; (3) anionic HPEs may exhibit two distinct pH-dependent solubilization transitions: the first is encountered in the lower-pH regime upon increasing the pH, whereas the second emerges at higher pH when the pH is decreased; (4) a binomial composition distribution of hydrophobic and ionizable groups over the chains, compared to a fixed composition, does not lead to a measurably wider pH range where solubilization occurs for the transition at low pH. We link the solubilization behavior of one of the HPE's to pH-dependent partitioning between macroscopic oil and water phases. Finally, (5) we find that linear composition superposition of the hydrophobic groups in HPE quantitatively accounts for the composition dependence of the pH's where solubilization occurs. This result holds within a range of compositions and breaks down below a critical fraction of hydrophobic residues in a HPE chain. Throughout, we compare the observations to a recently developed model for ligand-mediated cooperative transitions. Our findings have potential impact on anti-cancer medicine and drug delivery applications.

How much does a feedback controller need to know about the fluctuations it exploits? We address this question using a macroscopic information engine driven by self-propelled bristle-robots. Experimentally measured occupancy time series show that temporal correlations strongly affect vacancy detection. At short measurement intervals, mean first-passage times exceed independent-measurement predictions by more than an order of magnitude. A first-order Markov approximation captures much of this effect. It does not reproduce the full first-passage distribution, revealing higher-order temporal memory. Nevertheless, Markov-selected protocols come within 0.15\% of the maximum experimental power. Neglecting correlations causes power losses of several percent and favors larger compression distances. Introducing a sensing cost shifts the optimal strategy toward sparse sensing. The independent model cannot predict this shift, whereas the Markov model captures it. Cross-validation on separate time segments confirms the near-optimal performance of Markov-selected protocols. These findings demonstrate that near-optimal feedback control in correlated nonequilibrium systems can require a simpler statistical description than predicting their full temporal dynamics.

Using machine learning, we identify a second transition in polymer chain stretching driven by planar elongational flow, beyond the well-known coil-stretch transition. We achieve this by developing a conditional extension of Universal and Identifiable Dissipative Dynamics (UIDD) that jointly learns reduced stochastic dynamics from microscopic trajectories across flow strengths and yields the corresponding stationary nonequilibrium free energy landscapes. As the flow strength increases, the evolving landscape exhibits the expected coil-stretch transition, and then a previously unrecognized dynamical transition. In the latter, the stretched states persist, but the distribution along a folding coordinate becomes bimodal when conditioned on small end-to-end separation. Large-deviation analysis of a simplified analytical chain model reproduces both transitions and shows that they are phase transitions in the long-chain limit. Single-molecule DNA experiments provide qualitative support for the dynamical transition through the predicted reversal of the folding response.

Clay films that dry on a rigid substrate crack, peel or stay intact, and which of these happens matters for coatings, barrier layers and ceramic processing. Composites of clay with polymers have been studied widely. Clay composites, whose components differ in size and charge, are much less explored. We show that mixing the nano scale clay Laponite with the micron scale clay Bentonite reduces desiccation damage on both a hydrophobic and a hydrophilic substrate, Laponite films stay essentially intact, Bentonite films fracture extensively, and on glass most intermediate compositions are less damaged than a simple average of the two would suggest. Rheology of the gelled suspensions reveals a two step yielding in every composition, and the cohesive energy derived from it depends by orders of magnitude on which step is used, a point that any rheology cracking correlation must specify. A dimensionless cohesion adhesion index, whose sign we derive from an energy balance, is consistent with compositions that peel on polypropylene and crack on glass. Replicate experiments were performed for robustness of results. The results identify composition as a simple handle on the crack resistance of clay films and open the search for the critical crack-free thickness as a function of clay composition.

In this study, we investigate the waiting time dependence and the protocol dependence of thermally activated events in structural glasses using molecular simulations and potential energy landscape analysis. We find a qualitative crossover in the nature of activation events; from avalanche-like events to local events. We also use the isoconfigurational ensemble analysis and reveal that the events become less diverse and more reversible. We discuss these crossovers from the perspective of the stability and the potential energy landscape of glasses. To investigate the protocol dependence, we compare the two types of glasses whose stability is controlled by waiting time and parent temperature, respectively. Surprisingly, at the same inherent structure energy level, the parent-temperature-controlled glasses are more unstable and maintain their avalanche-like nature. These results demonstrate that the activation properties of structural glasses are not determined solely by their energy levels, highlighting the essential role of state connectivity and the dynamical sampling in the complex energy landscape.

The ideal glass transition has often been associated with the extrapolated vanishing of configurational entropy $S_c$, yet how this thermodynamic criterion is reflected in microscopic dynamics remains unclear. Here, we show that the vanishing of deterministic chaos quantified by the maximum Lyapunov exponent $\lambda_{\mathrm{max}}$ provides such a dynamical signature. Using molecular dynamics simulations across diverse model glass-forming liquids in two and three dimensions, we show that $\lambda_{\mathrm{max}}$ follows an approximate scaling $\lambda_{\mathrm{max}} \propto (T-T_{\lambda})^{1/2}$ and extrapolates to zero at a temperature $T_{\lambda}$ consistent with the Kauzmann temperature $T_{\mathrm{K}}$. Furthermore, we establish the quantitative relation $\lambda_{\mathrm{max}}^2 \propto T S_c$, directly linking chaotic dynamics to configurational entropy. By demonstrating that $\lambda_{\mathrm{max}}^2 \propto \sigma_K^2$, where $\sigma_K^2$ is the variance of local potential energy landscape curvature fluctuations, we connect the suppression of chaos directly to landscape geometry. These results provide a unified thermodynamic, dynamical, and geometric framework for glass formation, identifying the ideal glass transition as the endpoint of chaotic exploration of the energy landscape.

Internal degrees of freedom of cross-linked polymer networks enable compressible hydrogels and microgels to swell or deswell by absorbing or expelling solvent in response to environmental changes. Macromolecules in solution can influence the swelling response by acting as crowding agents, with practical relevance for drug delivery and biosensing. We extend the Flory-Rehner theory of polymer network swelling to incorporate nanoparticle crowders as another implicit species that can perturb a gel through volume exclusion, including the entropic cost of crowder penetration from polymer field theory. Within the free energy landscape of asymmetric ternary mixtures, we numerically solve equilibrium relations equating solvent and crowder chemical potentials inside and outside the gel. Independently, we perform Monte Carlo simulations, including trial moves that allow gels to swell and take up crowders. We investigate how crowder size, solution concentration, cross-link density, and solvent quality influence swelling of polymeric gels, partitioning of crowders between inside and outside, and structural properties of microgel suspensions governed by Hertzian elastic pair interactions. Our results show that nanoparticle crowding promotes deswelling, thereby weakening interparticle correlations, and that, with increasing the concentration of crowders, polymeric gels reach a maximum loading capacity, dependent on crowder size and polymer cross-link density.

Nonreciprocal interactions are a generic source of nonequilibrium dynamics, yet their consequences for nematic topological defects remain unexplored. We introduce a nonreciprocal nematic model on a two-dimensional hexagonal lattice and formulate a continuum theory containing a nematic nonreciprocal torque. In the deterministic limit, simulations and symmetry analysis show that this torque drives +1/2 defects to self-propel along their polar axes. Nonreciprocity modifies the splitting pathway of integer +1 defects. These results identify a symmetry-resolved route from nonreciprocity to nematic defect transport and topological reorganization, distinct from active-stress-driven motion.

The dynamics and stability of a swarm of microswimmers is examined here using a thermodynamically compliant microswimmer model. The theory presented here is a mean-field model in which the swarm is considered to be a uniform solution of swimmers that are moving, on average, in the same direction. The hydrodynamic interaction between swimmers is modeled accurately assuming a crystalline arrangement to the swarm. A swimmer in the swarm can swim up to twelve times faster than when alone in an infinite sea, when the volume fraction of swimmers in the swarm is about 0.14. Moreover we have also studied the stability of the swarm around a uniform crystalline arrangement by calculating the hydrodynamic torques generated by the swarm as a function of the volume fraction of swimmers. The predictions presented here agree with recent multiparticle simulations that have shown that hydrodynamic torques have a stabilizing effect in swarms of pullers while swarms of pushers are generally destabilized by hydrodynamic interactions. The thermodynamically admissible coupling between the swimmer's motion and fuel consumption allows us to study the full dynamics instead of artificially constrained steady-states only. By accounting for fuel consumption and high order hydrodynamic interactions we are able to examine the swarm's stability as function of fuel concentration and the volume fraction of swimmers. We find that at high concentrations of fuel, swarms of pullers are stabilized by hydrodynamic torques for volume fractions of swimmers as low as 0.02 but at lower volume fractions Brownian forces make the swarm unstable.

Structural relaxation in supercooled liquids is influenced by the initial configuration, yet its microscopic evolution exhibits substantial variability. Here, we investigate the interplay between structural constraints and dynamical stochasticity by examining fluctuations of relaxation dynamics across and within isoconfigurational ensembles. We show that fluctuations among trajectories originating from the same configuration constitute a substantial fraction of the total dynamical fluctuations over a broad range of temperatures. At the collective level, the distribution of relaxation times is well described by a stochastic model involving a sequence of effective relaxation events, whose number decreases upon cooling. At the microscopic level, dynamical fluctuations exhibit spatial correlations that grow upon cooling, revealing a spatial organization of relaxation even when the initial configuration is fixed. Remarkably, the characteristic length associated with these fluctuations closely follows the length scale inferred from the stochastic first-passage model, establishing a connection between the spatial organization of dynamical fluctuations and the temporal statistics of collective relaxation. Together, these results suggest that structural relaxation is governed by an interplay between configuration-dependent constraints and stochastic dynamical events: the initial structure influences when and where relaxation occurs, without uniquely determining its microscopic realization.

Self-propelled particles moving through structured anisotropic media such as smectic liquid crystals exhibit transport properties that differ qualitatively from those in isotropic environments. Here we introduce a minimal model of an active Brownian particle whose propulsion axis is coupled to the layer-normal field of a smectic liquid crystal. Using numerical simulations complemented by approximate analytical calculations, we investigate the dynamics of an active particle in three representative two-dimensional smectic microstructures: a uniform planar texture, an isolated toroidal focal conic domain, and a periodic array of toroidal focal conic domains. For the planar and isolated focal-conic geometries, we characterize the crossover from short-time superdiffusion to long-time normal diffusion. In periodic focal-conic arrays, however, transport is controlled by two distinct persistence mechanisms whose relative importance depends on the Péclet number ($\mathrm{Pe}$) and the coupling strength $\varepsilon$ between the particle orientation and the smectic layer-normal field. At small $\varepsilon$, long-time diffusion is governed by the intrinsic persistence time of the active Brownian dynamics. At large $\varepsilon$, repeated scattering by smectic defects generates an emergent persistence time that dominates the transport. These results demonstrate that the competition between the intrinsic persistence of active motion and the mean free time between encounters with smectic defects provides a simple physical mechanism for the emergence of nontrivial diffusive behavior in structured anisotropic media.

Local error correction can preserve classical information against noise, but protection under synchronized updates need not survive when sites evolve at independent random times. Establishing stability is particularly challenging when protection relies on the collective action of competing local rules. Here we develop a spacetime renormalization framework that reveals how independently acting local updates can collectively stabilize memory. We identify sufficient conditions under which the geometry of stable interfaces and suppression of defect propagation produce reliable erosion at large scales. Applying this framework, we prove stability of the asynchronous \textsf{R} squeezing code and introduce robust processes in two and three dimensions. In these systems, both encoded phases persist under sufficiently weak noise, even when the noise favors one phase. Our results provide a criterion for designing autonomous memories sustained by competing local stochastic dynamics.

Odd elasticity extends continuum mechanics to active nonconservative systems containing internal energy sources, such as robotic active metamaterials with nonreciprocal feedback. Modeling these systems as effective continua requires relaxing Maxwell-Betti reciprocity, which results in stiffness tensors lacking major symmetry. In this contribution, we extend this framework to 3D strain-gradient odd elasticity to incorporate the length scales inherent in these heterogeneous systems. By applying the full hierarchy of 3D point-group symmetries along chiral and achiral branches, we derive the exhaustive set of fourth-, fifth-, and sixth-order odd elastic stiffness tensors. Further, utilizing the dynamic principle of virtual work, we formulate the equilibrium equations, higher-order boundary conditions, and the generalized acoustic tensor for elastodynamic analysis. The results demonstrate that nonreciprocal moduli survive even under full isotropy in the sixth-order stiffness, under hemitropy in the fifth-order stiffness, and under cubic symmetry in fourth-order stiffness. In contrast, the elastodynamic analysis reveals that under isotropic and hemitropic limits, despite the underlying odd stiffness moduli, the acoustic tensor remains unconditionally Hermitian. Non-Hermitian elastodynamics is shown to require anisotropy. By numerically analyzing a transversely hemitropic odd elastic continuum, we demonstrate that this symmetry reduction results in non-Hermitian elastodynamic phenomena including exceptional points in the dispersion spectra and active energy exchange through simultaneous amplification and attenuation of the elastic wave components. These results provide the necessary theoretical foundation for future multiscale homogenization frameworks for anisotropic strain-gradient active microstructures, and for the design of nonreciprocal strain-gradient metamaterials.

Nematic liquid crystals confined in cylindrical pores adopt multiple stable director topologies --- radial, escaped, and arches --- each imprinting a distinct optical signature on transmitted circularly polarized light, with topological charge set by the projected director winding number, $\ell = 2m$. Using Landau--de Gennes and Jones-calculus modeling validated against micron-scale experiments, we show that this mechanism persists as the pore diameter shrinks toward the optical wavelength. However, full-wave Maxwell simulations of periodic sub-wavelength pore arrays reveal that the resulting vortex is a near-field phenomenon only: each topology imprints a distinguishable phase-singular signature --- differing in core multiplicity, core width, and ring amplitude --- directly below the pore array, but this signature does not survive propagation into the far field, where diffraction and inter-pore interference erase it within about one wavelength. Landau--de Gennes simulations further demonstrate that an applied electric field switches the pore between topologies, and hence between their near-field optical signatures. Because each topology is locally stable, sub-wavelength NLC pore arrays constitute an electrically reconfigurable, non-volatile platform for topology-encoded near-field optical readout, with potential application to optical labeling and anti-counterfeiting.

Accurately predicting the transport properties of liquid electrolytes is critical for next-generation battery design and requires force fields that are both quantum-mechanically accurate and fast enough for long-timescale simulation. Recent large-scale pretrained machine learning interatomic potentials (MLIPs) approach density-functional-theory accuracy, but remain too slow to access the necessary timescales to converge transport properties. We provide a knowledge distillation procedure to transfer the accuracy of a large-scale "teacher" MLIP into fast, system-specific "students", without any additional ab initio data. Our distilled models run ~40x faster, reproduce teacher-predicted structural observables, and produce stable 20 ns trajectories in days, rather than the months the teacher would require. Across a diverse set of sodium- and lithium-ion electrolytes, student-predicted self-diffusivities, ionic conductivities, and shear viscosities track experiment and outperform classical force-field predictions, establishing distillation as a practical route to accurate, long-timescale simulations necessary for high-throughput electrolyte screening.

A major question in active matter is how interactions between particles are modified by activity. Here, we address this question for Coulomb interactions by considering a charged swimmer immersed in an electrolyte. A static charge is screened by an ionic cloud that decays over the Debye length $\lambda_D$. We show that the persistent motion of the swimmer can qualitatively modify the steady-state ionic charge-density profile. At low activity, the swimmer appears effectively quasistatic to the ions, and conventional Debye-Hückel screening is recovered. At higher activity, the ballistic-to-diffusive dynamics of the swimmer are reflected in distinct spatial regimes. A power-law decay is followed by a stretched-exponential decay at intermediate distances. At sufficiently large distances, exponential screening is restored, but with an increased screening length, $\lambda>\lambda_D$, revealing activity-induced underscreening. Thus, active motion modifies both the spatial form and the range of electrostatic screening. Our results motivate the study of active electrolytes composed of positively and negatively charged swimmers.

Formal relations between scalar dissipation rates and curvatures are developed in the context of non-orthogonal two-dimensional composition spaces. These show that it is possible to achieve general closure of flamelet theory in terms of strain rates only, but that this requires the consideration of at least three different parameters (both in non-orthogonal and orthogonal spaces).

This study introduces a new approach for building surrogate models, in the form of Reduced Order Models (ROMs), for PDE-constrained optimization. A physics-constrained data-driven framework is developed to transform large-scale non-linear optimization problems into ROM-constrained optimization problems. Unlike conventional methods, which suffer from instability of the forward sensitivity function, the proposed approach projects optimization problems to system dynamics optimization problems in Hilbert space to increase stability, diminish memory requirements, and lower computational cost. The present approach is applied to shape optimization of a 2D flapping wing section at $Re=2,400$, where the non-linear interaction of the wing with fluid includes chaotic flow structures. It is shown that the proposed approach can significantly enhance the time-averaged thrust force and propulsive efficiency by 37\% and 40\%, respectively. We also tested this approach for a 3D flapping wing and the results reveal the potential of the proposed approach for more complex optimal designs in the aerospace industry.

We consider classical problem of turbulence of capillary waves. In a series of numerical simulations it is shown that Zakharov-Filonenko spectrum corresponding to direct cascade of energy has a limited dynamic range of realization in a finite system, which shrinks with decreasing level of nonlinearity. Recent hypothesis that this dynamic range scales with average steepness as $\sim\mu^{8/3}$ is confirmed. As a byproduct the Zakharov-Filonenko spectrum was observed for record dynamic range close to or beyond one decade in a variety of simulation configurations.

In the present work, numerical simulation of the evolution of capillary turbulence was performed on the basis of the wave kinetic equation taking into account energy dissipation at small scales. For an isotropic initial condition, the simulation results reproduce the Zakharov--Filonenko power-law turbulence spectrum for the wave action, \(n_k \sim k^{-17/4}\). The main result of the work is the calculation of the evolution for a substantially anisotropic initial condition. The numerical data indicate that, during the evolution of an anisotropic wave-action distribution, a factorized spectrum \(n(k,\phi) \sim k^{-17/4}F(\phi)\) is formed in polar coordinates \((k,\phi)\), where \(F(\phi)\) is a function of the angle in Fourier space. In the regime of a steady power-law distribution in \(k\), the calculated collision integral vanishes with high accuracy in the inertial interval of wavenumbers (the region of the power-law spectrum). Thus, the work provides evidence for the realization of a new strongly anisotropic turbulence spectrum, similar to Kolmogorov--Zakharov spectra.

Wave-mean flow interactions in stratified fluids can drive spontaneous oscillations, yet the mechanisms controlling transitions between periodic and chaotic regimes remain poorly understood. Using a minimal one-dimensional model of wave-driven mean-flow reversals motivated by the quasi-biennial oscillation (QBO), we identify two distinct mechanisms that suppress the formation of multiple extrema in the velocity profile: critical-level momentum deposition by a broad spectrum of undamped small-scale gravity waves, and wave-amplitude growth due to exponential density stratification. Although physically distinct, both mechanisms inhibit the route to chaos and reduce sensitivity to small-scale viscosity, substantially widening the region of periodic behavior in parameter space. These results identify a general internal mechanism for the stabilization of wave-driven oscillations, with direct implications for QBO-like phenomena in geophysical and astrophysical flows.

Causal analysis characterizes directional dependencies in dynamical systems, while such information is not typically used to inform reduced-order modeling of unsteady flows. This study proposes a Granger Causality-informed Dynamic Mode Decomposition (GC-DMD) framework that incorporates such information into data-driven modeling and modal analysis of high-dimensional flow data. The framework uses conditional Granger causality estimates to regularize the identification of the DMD operator, preferentially suppressing weakly supported interactions while preserving dynamically relevant couplings. This regularization promotes sparse operators informed by directional predictive dependencies, leading to improved predictive accuracy and identification of dynamically relevant modes. GC-DMD is evaluated on a linear system with a known coupling structure, lid-driven cavity flows with varying dynamical complexity, and a broadband transonic turbulent jet. Compared with standard DMD, GC-DMD improves operator identification accuracy in the linear benchmark and improves the robustness of the identified spectrum while reducing long-horizon prediction errors in the cavity flows. For the turbulent jet, it yields a sparser operator with improved prediction accuracy. These results demonstrate the potential of incorporating causality information to guide the identification of sparse, predictive reduced-order models of complex flows. The \href{ this https URL }{source codes} \footnote{ this https URL } from this research are publicly available in the GitHub repository.

The nonlinear evolution of a helical vortex with axial flow disturbed by an elliptic or curvature instability mode is investigated by direct numerical simulations. The normalized vortex core radius and reduced pitch are systematically varied to examine a wide range of linear growth rates, revealing two types of nonlinear evolution. At relatively small growth rates, both instabilities exhibit weakly nonlinear saturation, with the vortex and unstable mode structures largely preserved. Together with previous findings for other vortex configurations, these results reveal that weakly nonlinear saturation is a generic feature of short-wave instabilities. At larger growth rates, the instabilities reach higher energy levels and evolve beyond the weakly nonlinear regime, with the vortex and unstable mode structures substantially deformed. Comparison with weakly nonlinear analysis suggests that larger linear growth rates require larger disturbance amplitudes for nonlinear effects to balance linear growth. At these larger amplitudes, higher-order nonlinear effects and modal components not retained in the weakly nonlinear analysis become increasingly important, as demonstrated by the numerical results. This provides a new physical interpretation of the departure from the weakly nonlinear regime. Since helical vortices serve as a model for tip vortices shed from rotating blades, these results offer useful insights for tip-vortex control in wind turbines, which can potentially accelerate wake recovery and thereby improve turbine performance.

Flow transitions in electromagnetically-driven swirl in a cylindrical domain are investigated using three-dimensional simulations for a liquid metal battery electrode. The parameter space considered: applied current $I=11.11-100A$; Current density, $J_0 \approx 4,000-35,000 A/m^2$, domain radius, $R=3-9cm$, domain height, $H=3$ and $4.5cm$). The background magnetic field, $B_0$, strength is varied systematically from 0.1 to 20 G to characterize the route to chaos. \cite{davidson2022swirling} found the onset of chaos occurs around $1-1.5 G$ for aspect ratio $1/6$ and current of 100A, however, this is shifted to $16-17 G$ for a lower current of 16A and aspect ratio $1/2$. Across a range of geometrical configurations and forcing conditions, including variations in aspect ratio, current and current density, a consistent sequence of dynamical transitions is evident from phase portraits, FFT spectrum, 0-1 chaos test, autocorrelation function and correlation dimension. The flow evolution is by the Ruelle--Takens-Newhouse route to chaos, with the strange non-chaotic attractor (SNA) regime providing an intermediate state prior to the onset of chaos. In our results, it is observed that, for a fixed aspect ratio, the transition is governed by a dimensionless group, $Q_m$, representing the ratio of applied Lorentz force to viscous force. The critical value of $Q_m$ at the onset of oscillatory flow is found to be nearly invariant except when the domain height is varied. Moreover, our results follow the $Re \sim Q_m^{2/3}$ scaling law expected from torque balance moderately-forced electro-magnetically driven swirl flows.

This study numerically investigates the effects of geometrical curvature on drop deformation and breakup in shear flow between counter-rotating concentric cylinders. Simulations were performed using a geometric Volume-of-Fluid (VOF) method incorporating plicRDF interface reconstruction and isoAdvector interface advection, combined with adaptive mesh refinement. Three circular geometries with different values of the non-dimensional geometrical curvature, $\kappa_{\mathrm F}$, were considered and compared with a planar shear flow system. At fixed Reynolds and Capillary numbers ($Re$ and $Ca$), the breakup morphology differed substantially between the planar and circular systems. In the planar system, the drop underwent relatively symmetric neck thinning, whereas in the circular systems, the drop exhibited asymmetric deformation and pronounced azimuthal elongation. At higher curvature, the drop formed a thin filament that subsequently fragmented, producing multiple satellite drops. Analysis of the internal velocity field and the magnitude of the rate-of-deformation tensor revealed distinct flow and deformation structures associated with these breakup behaviors. Furthermore, the critical $Re$ for breakup, $Re_{\mathrm{cr}}$, decreased with increasing $\kappa_{\mathrm F}$ at nvestigated $Ca$ values. In contrast, the maximum dimensionless elongation length immediately before breakup at $Re=Re_{\mathrm{cr}}$ increased with $\kappa_{\mathrm F}$. These findings suggest that geometrical curvature affects not only the breakup threshold but also the deformation process leading to breakup, providing insights into drop breakup in curved shear flows.

Direct numerical simulations are performed to investigate supersonic turbulent boundary layers subjected to continuous concave and convex surface curvatures. Scale-resolved spectral turbulent kinetic energy (TKE) budgets, triadic energy-transfer bispectra, spectral proper orthogonal decomposition (SPOD), and global resolvent analysis are employed to elucidate the effects of compressibility and pressure gradients, and to distinguish the linear and nonlinear mechanisms at play. Over concave walls, the destabilizing curvature enhances pressure-strain redistribution, shifting near-wall turbulence toward a two-component state, and induces a shear-driven outer-layer production peak at low spanwise wavenumbers. Bispectral and SPOD analyses reveal that this outer-layer energy feeds a structured, multi-step triadic transfer toward fundamental large-scale and spanwise-uniform modes, which physically manifests as streamwise vortex breakdown rather than a three-dimensional inverse cascade. Global resolvent analysis further demonstrates that while nonlinear triadic interactions select the dominant scale amplitudes, the spatial topology of these coherent structures is dictated by linear mean-flow receptivity and spatially developing convective instabilities. Conversely, over convex walls, stabilizing curvature and dilatation attenuate pressure fluctuations and suppress pressure-strain redistribution, breaking the near-wall turbulent cycle and trapping energy within elongated, one-component streamwise streaks, while a localized resolvent wavemaker energizes the downstream recovery region.

Although vorticity and passive tracers (such as dye) are both transported by fluid flows, there are subtle differences in how this transport happens. This indicates that dye cannot be used to track vortex motion in experiments, even though it has often been used for this purpose. In this manuscript we show that under proper circumstances dye can be used to accurately track the center-lines of vortex filaments. Moreover, we show that a number of important fluid quantities, such as energy and helicity, can be computed in terms of the shape of the vortex center-line. As a result, dye-tracked vortices are a valuable tool for measuring the properties of fluid motion in a variety of experimental situations. Moreover, we discuss techniques by which could be used to extract more detailed vortex information in future work.

We investigate the influence of non-dimensionalization on the trainability and accuracy of physics-informed neural networks (PINNs) for buoyancy-driven flows. Using a differentially heated square cavity at $\mathrm{Pr}=0.71$ and $\mathrm{Ra}=10^3$--$10^5$, we compare thermal-diffusive and free-fall velocity scalings under identical training conditions. The free-fall scaling, with a unit buoyancy coefficient, achieves errors below 1.1\% in the mean Nusselt number for $\mathrm{Ra}\le10^4$, whereas the diffusive scaling, with a buoyancy coefficient of $\mathrm{Ra}\,\mathrm{Pr}$, produces errors of 157--650\% and diverges at $\mathrm{Ra}=10^5$. We identify a coefficient-induced gradient imbalance, with the dominant buoyancy-related contribution to the loss gradient scaling as $(\mathrm{Ra}\,\mathrm{Pr})^2$, and confirm it through direct gradient measurements. Neither sparse-data supervision nor adaptive loss weighting resolves the training difficulties under the tested conditions. For unsteady convection, the free-fall PINN accurately predicts long-time heat transfer but fails to capture the transient Nusselt-number overshoot. These findings establish non-dimensionalization as an important design consideration for improving PINN trainability in buoyancy-driven flows.

Deep lid-driven cavities contain strong motion beneath the lid and much weaker recirculation at depth, so agreement in bulk velocity is an incomplete assessment of a computed flow. We examine data-free physics-informed neural networks (PINNs) for steady, two-dimensional incompressible flow in a cavity of depth-to-width ratio five at Reynolds numbers 100, 250, 500 and 1000. An established hard-constrained streamfunction formulation is combined with prescribed regional collocation, transferred initialization, and selected residual-scaling and envelope variants. Independent spectral/$hp$ calculations with the same Gaussian-regularized lid provide the reference fields. For a cavity of depth-to-width ratio $D/W=5$ at Reynolds numbers $\mathrm{Re}=100$, 250, 500, and 1000, evaluation on a common $121\times605$ grid gives interior relative velocity discrepancies of 5.130\%--7.850\%. Over the same cases, floor-region relative velocity discrepancies remain below 5\%, with absolute RMS discrepancies ranging from $1.255\times10^{-10}U$ to $2.332\times10^{-9}U$, where $U$ is the lid-velocity scale. In a separate $161\times801$ assessment at $\Rey=1000$, the refined workflow lowers interior velocity discrepancy from 5.624\% to 2.658\% and gauge-aligned pressure RMS discrepancy from $2.793\times10^{-3}$ to $1.167\times10^{-3}\rho U^2$. The improvements compare accumulated training workflows and do not isolate regional sampling. Configuration rankings depend on both region and observable. These finite-budget comparisons establish where the retained workflows agree with the reference and where rotational-field discrepancies remain substantial.

Reynolds stress is assembled from correlations among velocity fluctuations; assigning it to named vortical structures additionally requires their velocity fields to be separable. We examine this requirement in homogeneous isotropic turbulence from the Johns Hopkins Turbulence Databases (JHTDB) using a frozen solenoidal expansion of curl-lifted anisotropic Gaussian vorticity functions. The expansion retains locally addressable blob-, sheet-, and tube-like geometry, while its fixed Biot-Savart map carries coefficient covariance exactly into the stress of the represented Gaussian velocity. Principal-angle geometry and self-cross covariance then connect overlap between group velocity spans to stress assembly. At a principal cosine of 0.95, 55% of the sheet-associated directions are also closely represented by the tube-like family, and products within the shared directions carry 99.6% of the covariance cancellation. Removing between-family covariance increases the direct numerical simulation (DNS)-referenced stress error by factors of 53.6 to 87. Orthogonal Fourier and proper orthogonal decomposition (POD) regroupings of the same velocity remove this cancellation, showing that it follows from the local nonorthogonal organization rather than from the represented field alone. The morphology labels remain representation-dependent, but their physical consequence is direct: Reynolds stress in this local description is carried by coupled velocity fluctuations, not by additive component energies. Localized nonorthogonal representations can therefore reveal how turbulent momentum flux is assembled, provided that span overlap and cross covariance are retained.

Modal and non-modal linear stability analysis of incompressible shear flows is performed for the first time by linearizing the Boltzmann equation and its full collision operator. In this kinetic linear stability theory (kLST) the hard-sphere operator and its BGK, ES-BGK and Shakhov relaxation models share the same discretization, so that their results can be compared directly. Written in the peculiar velocity about a Chapman-Enskog base state, the collision operators are independent of the cross-stream coordinate and are formed once. Summation-by-parts Legendre collocation, weak diffuse-reflection wall conditions and a moment-consistent velocity derivative yield an energy-stable discrete operator, verified to spectral accuracy by a manufactured solution. Numerical solution of the four-dimensional problem, comparable in size to a TriGlobal problem (Theofilis 2011), is made feasible by the fast spectral method of Gamba, Haack, Hauck and Hu (2017) for the full operator. Modal kLST uses matrix-free shift-invert Arnoldi iteration, preconditioned by an exact relaxation-model inverse. Non-modal kLST is based on an energy norm containing Chu's disturbance energy, a kinetic Reynolds-Orr equation identifying the mean shear as the only energy source. Transient growth and pseudospectra follow from the same preconditioned solves. For plane Couette and Poiseuille flows, the mixing layer and the Blasius boundary layer at Reynolds numbers 10^2-10^5, all four operators recover the Orr-Sommerfeld eigenvalues (Orszag 1971; Mack 1976) in the incompressible limit to a few parts in 10^7 for the models and 10^6 for the full operator. The optimal growth of Butler and Farrell (1992) and the resolvent norms of Trefethen et al. (1993) are reproduced to 0.1%, while the pseudospectra converge where ill-conditioned eigenvalues do not.

Waves generated by storms gradually disperse, forming swells that can travel thousands of kilometers across the ocean's surface. The evolution of deep-water swells, which are unaffected by the seafloor, can be modeled by the nonlinear Schrodinger (NLS) equation and its generalizations. These models typically assume that the wave trains are comprised of a narrow band of frequencies. We present measurements from a new series of laboratory experiments in which the broadbandedness is increased and show that generalizations of the NLS equation can accurately model these measurements.

High-Péclet-number transport problems give rise to thin boundary layers with steep near-wall gradients whose accurate solution requires high-resolution meshes and could challenge inverse modeling. To address this challenge, we develop an overlapping Schwarz domain-decomposition framework grounded in perturbation theory, in which an inner equation governs near-wall dynamics and an outer equation governs bulk transport, and both subproblems are discretized using the finite element method and assembled into a fully differentiable multidomain physics solver. The formulation permits coarser mesh resolutions, reducing computational cost relative to a single-domain formulation. Exploiting the differentiability of the coupled solver, we formulate inverse problems in which the governing equations and boundary conditions are imposed as hard constraints, with the Schwarz coupling enforcing interface continuity. To accelerate the resulting adjoint-based optimization, we integrate large language models (LLMs) into the inverse workflow in two distinct configurations: a standalone optimizer that proposes successive parameter updates from the adjoint-computed sensitivities and an agentic artificial intelligence (AI) approach with access to the complete solver workflow, enabling it to perform multistage optimization procedures. The agentic AI configuration is shown to be most advantageous when the spatially varying unknown is represented in a functional basis rather than a high-dimensional nodal field representation. In this case, the AI agent grows the library of candidate basis functions during optimization under a prescribed admission policy, admitting predefined families in stages and initializing their parameters. In short, our proposed framework integrates Schwarz-coupled differentiable physics with agentic AI optimization for the inverse modeling of multiscale transport problems.

The main hypothesis of this paper is that inertial effects known from porous-media flow can be observed even in a simple system consisting of a single channel. The strength of inertia is controlled by the Reynolds number, $Re$. We investigated fluid flow through a channel with a cavity in the shape of a Koch leaf. The Koch leaf of level-6 was chosen because it combines regularity, repeatability, and representativeness with a complex multiscale structure and non-trivial hydrodynamic interactions. We analyzed nonlinear effects through the so-called friction factor and show that its deviation from Darcy's law is very subtle. We further examined the influence of inertia on the flow structure, including the participation number $\pi$ and the backward-flow fraction $\rho^{-}$. In contrast to disordered porous media, the participation number decreases with $Re$, indicating that inertia concentrates kinetic energy in the main through-flow, while recirculation (backward flow) increasingly occupies the Koch leaf cavity. The tortuosity varies non-monotonically with $Re$, the apparent permeability decreases, and in the inertial regime the two are related by a power law with an exponent comparable to that found for natural rock. At the lowest and highest Reynolds numbers, the local kinetic energy followed a power-law distribution, $P(\varepsilon)\propto\varepsilon^{-m}$, over several orders of magnitude with the same exponent, $m\approx0.83$; inertia modified only the tails of the distribution. Our research can be regarded as an investigation of transport in an extremely porous system with porosity $\varphi \approx 1$.

The detonation cell size $\lambda$ is known to provide a characteristic scale for the detonation dynamics and serves as scaling parameter for numerous correlations with other dynamic parameters of detonations, e.g., the critical detonation tube diameter for transmission to open space of $d\simeq13\lambda$ across many reactive systems. In the present paper, we address the reason why such scaling works so well. We formulate a macroscopic reaction rate model for cellular detonations relying on the distribution of ignition delays in cellular detonations, conditioned by $\lambda$. The ignition delay distribution is modeled in terms of the cellular dynamics, using the closed form model recently proposed by Radulescu (JFM 2025) for the lead shock dynamics in a unit cell. The distribution of ignition delays obtained in closed form serves as a simple model for the phase-averaged reaction rate in a cell-averaged description. The global reaction rate model is applied to the problem of globally curved cellular detonations. Excellent agreement with experiment is obtained. The paper thus highlights for the first time a simple dynamic closure for cellular detonations and provides the simple answer why the cell size provides the relevant length scale for detonations: it provides the length of the mean detonation structure, or its hydrodynamic thickness.

The localized turbulence in pipe flow, known as puffs, is sustained by their proliferation. This process is crucial to the subcritical laminar-turbulent transition, a century-old fundamental problem related to a wide range of natural and engineered systems. Here, we leverage the nonlinear nonmodal analysis of a reduced-order model to capture the full Navier-Stokes dynamics of the splitting process: from the splitting seed through the edge state to successful splitting, even when the pre-edge evolution is obscured by the puff's intrinsic chaotic fluctuations. Moreover, the optimized evolution provides a splitting-progress coordinate to frame a phase-space representation of the proliferation, resolving the temporal desynchronization among chaotic realizations and thereby enabling dynamically aligned ensemble averaging to uncover the underlying splitting dynamics. The splitting seed is characterized by a strong velocity inflection, and its energy threshold exhibits a power-law scaling with the Reynolds number, giving the optimal solution direct physical consistency in spontaneous puff splitting.

We investigate the steady configurations supported by the inviscid two-dimensional Boussinesq equations in the periodic channel. We show steady laminar velocity fields (closed non-contractible fluid trajectories) coupled to non-decreasing density stratifications are necessarily stratified shear flows. The direction of density monotonicity along level sets is in fact fundamental: in striking contrast with the Euler equations, we exhibit laminar non-stagnant non-shear stationary solutions in the periodic channel. We also provide distinct flexibility and rigidity results (laminar persistence or appearance of islands for nearby non-shear solutions) close to stratified shear flows according to their stagnation points. As a by-product of our analysis, we establish a uniform Crandall-Rabinowitz bifurcation theorem that might be of independent interest.

In the study, the geometry of curved rectangular vortex generators (RVG) has been optimized to enhance heat transfer and overall performance of the analyzed water-to-air finned-tube heat exchanger (FTHE). The developed and validated conjugate numerical model includes a small section of the full-scale heat exchanger representing the computational domain, with fully developed velocity and temperature profiles specified at the inlet boundaries of the water. Four influential geometry parameters of the vortex generator were selected for the optimization; attack angle, curvature angle, axial position in the streamwise direction and height. The optimization process has been performed according to two criteria: maximization of heat transfer solely and maximization of heat transfer while considering the influence of pressure drop. Accordingly, one objective function related to the Colburn factor (j) and two objective functions combining the Colburn factor and the friction factor (f) were defined. The regression analysis has been used and the Central composite design of experiment was selected in order to obtain non-linear regression polynomial functions which were integrated into the investigated objectives. The optimization procedure has been performed using the genetic algorithm. Optimized configurations performance improvement was evaluated through comparison with the performance of the reference FTHE with plain fins. For the RVG configuration optimized according to the objective of maximizing heat transfer, the Colburn factor was enhanced by 53.1%. Optimizing the RVG configuration to maximize heat transfer while accounting for the influence of pressure drop resulted in an enhancement of the FTHE area goodness factor by 14.4% for one set of geometry parameters, and an enhancement of volume goodness factor by 26.5% for another.

Sparse-view computed tomography (CT) reduces the number of acquired projections, but conventional sampling strategies are designed primarily for image reconstruction rather than for downstream physical inference. Here, we investigate optimal task-aware projection selection for directly predicting hemodynamics from sparse CT angiography (CTA) measurements. Using computational fluid dynamics simulations of intracranial aneurysms, we generate synthetic fan-beam CTA projections and train a Fourier neural operator (FNO) to predict two targets: the spatially resolved time-averaged wall shear stress (TAWSS) field and the spatially averaged TAWSS. The FNO was coupled with optimal input selection for simultaneous optimal sampling and training. Our goal was to investigate if agentic AI could discover optimal sampling strategies that outperform current methods. We compared fixed uniform and golden-angle sampling with three task-aware optimal selection strategies: Gumbel-Softmax, a Soft top-K method, and an agentic AI selector. The methods were compared at different view selection budgets. A detailed analysis of the AI agent was performed to understand its reasoning and performance. For spatially resolved TAWSS, Agentic and Soft top-K achieve the lowest mean errors (Agentic performs slightly better) and substantially outperform fixed sampling under extreme sparsity. For spatially averaged TAWSS, optimized selection becomes important at extremely sparse acquisitions. Analysis of the selected masks reveals multiple distinct subsets concentrated around informative regions. Moreover, masks optimized for hemodynamic prediction yield poor image reconstructions, showing that task-optimal acquisition differs fundamentally from reconstruction-optimal acquisition. This work suggests the possibility of designing sparse acquisitions directly around downstream physical quantities.

We study the effect of constant vorticity on the Benjamin-Feir instability of small-amplitude Stokes waves in infinite depth. Working with the full water-wave equations, we rigorously establish a transition between modulational instability and stability as the vorticity crosses a critical value. We consider right-propagating waves with constant vorticity $\gamma$, associated with the background shear current $-\gamma y\mathbf e_x$, and normalize the gravitational acceleration and carrier wavenumber to one. For each fixed $\gamma<2/\sqrt{3}$, we prove that sufficiently small-amplitude Stokes waves are Benjamin-Feir unstable. For each fixed $\gamma>2/\sqrt{3}$, these waves are spectrally stable with respect to longitudinal, long-wavelength perturbations. These results rigorously confirm, away from the critical value, the stability transition predicted by the formal nonlinear Schrödinger approximation of Thomas, Kharif, and Manna.

Geometric Volume-of-Fluid (VOF) on unstructured polyhedral meshes reconstructs the interface orientation from the volume fractions of a stencil of neighbours; on irregular cells and in the presence of wisps it degrades, and the curvature built on it drives the parasitic currents of capillary flows. We transport, consistently to the volume fraction of every cell, the wetted fraction of every face area. From the area and volume fractions, closed-form equations recover the interface normal and position of a cell, for the first time in VOF: the normal from one sum over the cell's own faces, the divergence theorem on the liquid sub-volume, and the plane's position from a second, without neighbours or iteration. Both identities are exact for a plane on hexahedral, perturbed and polyhedral cells. On a sphere and an ellipsoid the normal has the order of the face fractions, the position is second order for every state and mesh, and a quadric through one ring of recovered normals gives a converging curvature where the reference models show none. Transported with the plane clipping, the ring normal, the same identity on the union of the cell's ring, stabilises the state and carries a sphere over 3.3 diameters bounded and conservative, first order in the face fractions as the clipping law predicts, at plicRDF's position and shape errors. A preliminary transport implementation with one paraboloid per cell, its frame from the normal, its curvature tensor from the ring and its position from the volume fraction, carries the sphere bounded and conservative over the resolution ladder with face fractions of order 2.8 per period with the exact normal and 2.1 with the ring quadric's normal over N = 32 to 128. The loop has the order of the normal it is fed; a transported normal of second order is the research goal. This document is the basis on which the further development of the method is documented.

In stably stratified regions of rotating stars, magnetic instabilities play a key role by enabling dynamo and angular momentum transport. In particular, the Tayler instability of wound-up toroidal fields has long been considered to drive the Tayler-Spruit dynamo. However, the nonlinear saturation of the instability is poorly understood, despite its central role in the dynamo loop. In this paper, we use global simulations to verify the recently completed linear theory of the Tayler instability and determine its saturation. We confirm the picture of overstability of magnetostrophic and inertial waves, which grow on similar magnetostrophic timescales but oscillate with different frequencies. We find that magnetostrophic waves saturate with large amplitudes $\delta B/B\sim 1$ and dissipate the toroidal field on magnetostrophic timescales, while inertial waves saturate with $\delta B/B\ll 1$ and erode the toroidal field over much longer timescales. Moreover, magnetostrophic waves efficiently regenerate axisymmetric poloidal fields through nonlinear couplings while inertial waves do not. Our results indicate that the Tayler-Spruit dynamo can operate only through the magnetostrophic wave branch and that its steady-state may follow the scenario proposed by \cite{spruit2002dynamo}, ruling out the small-amplitude saturation scenario proposed by \cite{fuller2019slowing}. Implications for angular momentum transport and magnetic field amplification in evolving stars and nascent neutron stars are discussed.

Two-dimensional (2D) intraglottal particle image velocimetry (PIV) of ex vivo phonation experiments quantifies vocal fold medial surface dynamics and the intraglottal flow field. However, it relies on manual segmentation because residual glare, low tissue-to-flow contrast, and tracer-particle speckle obscure the vocal fold boundaries. This study assessed how deep learning architecture and ImageNet pretraining affect automated vocal fold segmentation in these high-speed images. Four established architectures from three categories were benchmarked: the convolutional neural network (CNN)-based UNet and UNet++, the hybrid CNN-transformer-based TransUNet, and the pure transformer-based Swin-UNet, the latter two trained from scratch and from ImageNet-pretrained weights. Using 16,344 expert-annotated images from 227 phonation trials of excised canine larynges, the six pipelines were trained with five seeds under a standardized protocol and compared on 50 held-out test trials using trial-level Wilcoxon signed-rank tests with Holm correction. Mean Dice similarity coefficient (DSC) spanned only 0.9734 to 0.9764, so the pipelines differed mainly in boundary fidelity. Pretraining significantly improved the boundary F1 score (BF1) and 95th percentile Hausdorff distance (HD95) of the TransUNet and Swin-UNet, about four times more for the Swin-UNet. Once pretrained, the two performed similarly, although the Swin-UNet has only about a quarter of the trainable parameters. Without pretraining, the TransUNet had a significantly higher BF1 and a lower HD95 than both CNN-based pipelines and about half their share of images with HD95 > 50 pixels. To our knowledge, this is the first study to apply deep learning to vocal fold segmentation in 2D intraglottal PIV, and it offers a reference framework for segmenting experimental flow-visualization images with noisy optical conditions or highly deformable objects.

A particle colliding with a moving wall provides one of the simplest mechanical settings in which a small system can exchange energy with its surroundings. In a chaotic time-dependent billiard, repeated elastic impacts may produce Fermi acceleration, with the characteristic kinetic energy growing without bound. This result poses an instructive thermodynamic puzzle: a physical wall maintained at finite temperature should act as a reservoir and drive a dilute gas toward a stationary temperature rather than heat it indefinitely. We use this puzzle to connect nonlinear dynamics with elementary thermodynamics. Under suitable decorrelation assumptions, collision sequences generate effective diffusion in velocity space and the square-root growth associated with normal diffusion. We then introduce two ingredients absent from the conservative accelerator: phase randomisation, which simplifies the statistics of energy exchange, and dissipation, which transfers energy back to unresolved degrees of freedom of the boundary. Their competition replaces unbounded acceleration by a stationary kinetic-energy scale. A recurrence for the second velocity moment yields a stationary kinetic-temperature scale $T_\infty=(mA^2/8k_B)(1+\gamma)/(1-\gamma)$, where $A$ measures the boundary forcing and $\gamma$ is a restitution coefficient. We compare relaxation in collision number with a simple Fourier-inspired heat-transfer model in physical time, emphasising that the two clocks are not interchangeable during transients. The resulting picture shows how fluctuations, dissipation, coarse graining and relaxation can produce an effective thermal state from chaotic dynamics while also clarifying the limits of the thermodynamic analogy.

We investigate the nonlinear dynamics of resistive drift-wave turbulence with a three-wave truncation of the Hasegawa--Wakatani equations, in which the background density gradient either is fixed or evolves self-consistently, fed by an external particle source $P$ (such as neutral beam injection) and eroded by the turbulent particle flux. Two triads that differ only by a small tilt of the long-wavelength mode are compared, in one this mode is zonal and cannot be driven by the gradient, in the other it is a weakly driven drift wave. Period maps in the plane of the adiabaticity parameter $C$ and the drive show that the zonal triad is almost always regular, whereas the non-zonal triad becomes chaotic. The feedback of the flux on the gradient amplifies this contrast: the fraction of aperiodic states grows considerably in the non-zonal triad and remains negligible in the zonal one. Along a line of constant $C$ at low adiabaticity, the non-zonal triad with a fixed gradient enters chaos through torus breakdown with intermittency and leaves it through an interior crisis and a period-doubling cascade. With the self-consistent gradient, a Neimark--Sacker bifurcation leads to a phase-locked torus that breaks down abruptly, with hysteresis, and chaos then persists up to the largest drive, with the gradient driven intermittently above the threshold of the long-wavelength mode. None of these routes to chaos exists when that mode is zonal.

A single resistor moves a discrete analog realization of the forced Aliev-Panfilov excitable oscillator from a chaotic operating point of the model to a regular one. In this model a rate parameter multiplies the complete right-hand side of the excitation equation, forcing term included. The input resistor of the excitation integrator sets that parameter, so no state, delay element, or controller is added. Sampled waveforms were recorded at two resistor values, with two independent runs each. The measured excitation excursion agrees with numerical integration to within three percent at the baseline setting and five percent at the rate-controlled setting. Between the two settings the excitation excursion contracts by a factor of thirteen. At the rate-controlled setting the recovery excursion exceeds prediction by a factor of eight. This excess traces to a displaced operating point on the state-dependent recovery rate. Thermal drift in the multiplier chain and leakage at the high-impedance recovery-rate divider could each produce it, and the present data do not separate them. A tested bipolar input stage strongly loads that divider, a constraint absent from the ideal equations. The divider, not the sub-hertz signal bandwidth, sets the amplifier input-stage requirement.

For a scalar equation $y^{(n)}=\varphi(x,y,\dots,y^{(n-1)})$ the $S$-function of the extended Prelle--Singer method is a vector $S=(S_0,\dots,S_{n-2})$, the null-form vector of Chandrasekar, Senthilvelan, Lakshmanan and collaborators, and the jet gradient of a first integral solves the adjoint of the variational equation. We describe the solutions of the system satisfied by $S$ intrinsically, and determine which of them come from first integrals. Over the field $C$ of first integrals the solutions are exactly the hyperplanes of the $n$-dimensional space $VV$ of symmetry characteristics, recovered from $n-1$ independent characteristics by a Plücker formula; in flow-box coordinates they are the hyperplane fields on the local space of leaves. A solution is the $S$-vector of a first integral if and only if the corresponding hyperplane field is integrable. This Frobenius condition splits into the $S$-system itself plus $\binom n3$ further differential conditions, so it is vacuous for $n=2$ and a genuine restriction for every $n\ge3$, for which we give an explicit non-realisable solution. The same picture explains why $\lambda$-symmetries and $S$-functions coincide only when $n=2$: line fields and hyperplane fields agree only on surfaces. For the computation of $S$ we record that the system is equivalent to one scalar equation for the last component, which is the Riccati form of the adjoint variational equation, and we spell out what this does and does not imply for a rational search.

Early-warning methods can indicate that a system is approaching a loss of stability, but they do not usually reveal whether the approaching bifurcation is supercritical or subcritical. We investigate whether this distinction can be made from noisy pre-transition observations. For this investigation, we extend a regression-based stability method by including the leading cubic nonlinear term, whose sign is used to predict the bifurcation type. We test the method on a stochastic pitchfork model and a spatial stochastic Swift-Hohenberg equation. In both models, classification improves with longer observation horizons, closer proximity to the bifurcation, stronger noise, and larger nonlinear effects. However, these conditions are also linked to a higher risk of noise-induced tipping in the subcritical case. The useful early-warning window is therefore determined by a balance between obtaining enough information to identify the bifurcation type and doing so before noise-induced tipping becomes too likely. In spatially extended systems, we find that observing the full spatial field allows classification over shorter observation horizons, and performance improves when a broader range of spatial modes contributes to the observed dynamics. Altogether, we identify the conditions under which the method can reliably distinguish between supercritical and subcritical bifurcations.

With numerical simulations of the complex Ginzburg-Landau equation in a two-dimensional space, we find that a stationary but non-zero Dirichlet boundary condition with a discontinuity can drive a periodic train of evenly spaced topological defects that drift along and in proximity to the boundary.

We study standing waves of the discrete nonlinear Schrödinger (DNLS) equation by means of perturbative series expansions in the inter-site coupling parameter $\varepsilon$. Power-series approximations are derived for three representative configurations: a single-site soliton and the two two-site ones, namely the in-phase and the out-of-phase configurations. Although higher-order truncations are increasingly accurate for small $\varepsilon$, the expansions possess a small radius of convergence and cease to be useful well before $\varepsilon={\cal O}(1)$. To extend their range of validity we apply the Euler convergence-acceleration method, constructing an optimally transformed series for each lattice site individually. The transformed solution is shown to have substantially better convergence radius and preserves the localization of the solution much better than the original series solution. We then insert the series profiles into the linearization matrix of the DNLS equation in order to obtain improved approximations of the stability eigenvalues, with particular attention to the unstable real eigenvalue of the in-phase configuration. Optimal truncation of the corresponding expansion yields a closed-form ${\cal O}(\varepsilon^{5/2})$ estimate, which significantly extends the known ${\cal O}(\varepsilon^{1/2})$ leading-order result to considerably larger couplings, while the semi-numerical use of the accelerated profiles reproduces the numerically computed eigenvalue to values of $\varepsilon$ of ${\cal O}(1)$. Throughout, both the solution profiles and their stability eigenvalues are benchmarked against the numerical solution obtained through a continuation procedure from the anti-continuum limit.

We investigate linear and nonlinear localization in a disordered electrical lattice composed of coupled LC resonators. In the linear regime, the normal-mode spectrum and spatial voltage profiles are characterized theoretically and experimentally, revealing strongly localized Anderson modes induced by capacitive disorder. Good agreement is found between numerical predictions and experimental measurements of resonance frequencies, spatial profiles, inverse participation ratios, and localization lengths. Nonlinearity is introduced through varactor diodes, allowing the numerical continuation of a selected Anderson-localized mode into a family of discrete breathers. Floquet analysis indicates that these nonlinear localized solutions remain spectrally stable over the investigated frequency range, while their spatial localization evolves with increasing amplitude. Experimental measurements reveal nonlinear resonance bending, frequency shifts, and hysteresis, in qualitative agreement with the predicted nonlinear behavior. These results provide numerical evidence for the emergence of stable, disorder-pinned discrete breathers from Anderson-localized modes, supported by experimental observations of the associated nonlinear resonant response, and highlight the interplay between disorder and nonlinearity in electrical lattices.

The Nikolaevskiy equation is a model of short-wave pattern formation coupled to a neutral long-wave mode, and it is believed that all of its spatially periodic steady states are unstable. Existing results are formal, numerical, or restricted to a small neighbourhood of onset. We give computer-assisted proofs of three results. First, for every wavenumber q in [0.9, 1.1] and every control parameter r between the onset value (1-q^2)^2 and 4, the equation has a nontrivial, real-analytic, odd steady roll; these rolls form a single continuous two-parameter family that bifurcates from the trivial state at onset, with an explicit amplitude bound proportional to the square root of the distance to onset. Second, every roll of this family with r in [0.25, 4] is spectrally unstable on the real line: its linearisation has a Bloch eigenvalue with real part at least 6.7e-4, and at least 0.13 for r >= 0.575. Third, at nine sample points we enclose, at a small Bloch number, the eigenvalue numerically identified with the long-wave (Matthews-Cox) branch; its real part is positive at seven points and negative at two, while strongly unstable eigenvalues exist at all nine. The proofs combine a parametrised Newton-Kantorovich theorem, a desingularisation near onset, Taylor-model bounds on parameter boxes, and a Weyl-sequence argument for the Bloch spectrum; all estimates are evaluated in rigorous interval arithmetic.

Periodic attractors of spatially extended systems possess not one period but a hierarchy of periods, one for each level of observation and symmetry quotient, and this hierarchy separates how a pattern evolves from how it fits the finite domain. For a synchronous threshold model of cyclic dominance on an $L\times L$ torus, equivalent to the three-color cyclic cellular automaton of Fisch, Gravner and Griffeath, we measure for every attractor a \emph{tuple} of periods: that of the populations ($\Tpop$), of the full configuration ($\Tst$), and of the configuration up to color rotations ($\Tcol$), lattice symmetries ($\Tgeo$) and the full space--color group ($\TG$). Equivariance implies exact divisibility relations and the factorization $\Tst=\TG\,m$, where $m$ counts the applications of the symmetry $h$ that maps the configuration onto itself after $\TG$ steps: $\TG$ and the type of $h$ belong to the pattern, $m$ to the lattice, and the attractors are relative periodic orbits whose full period emerges from the interaction between the intrinsic dynamics and the lattice symmetries. A family of attractors built around a pair of counter-rotating spirals, with $\Tpop=24$ and $\TG=8$, persists from $L=9$ to $L=40$ while $\Tst$ takes values from 24 to 960, given in every case by the order of $h$; on a rectangular $9\times12$ torus it takes the value 48, absent from all square tori. With more than $4.5\times10^5$ runs at each of $L=8$ and $L=9$ we estimate the basins of attraction: fixed points take 95--97\% of the configuration space, and no single period is enough to tell the oscillating attractors apart. The same analysis locates local diversity: it is balanced whenever the cycle has a color symmetry and, on large lattices, it is concentrated at the spiral cores.

This paper considers the eigenmode problem for a waveguide with a resistive film. An integral equation for the surface current on the film is formulated. A method for evaluating the kernel is described, and an explicit expression for the kernel is derived for rectangular and circular waveguides.

The linear behavior of micro- and nanomechanical devices has been the topic of intense study over the past years. Their nonlinear behavior, on the other hand, continues to provide new and interesting dynamics. This work leverages a cavity opto-mechanical system whose very high sensitivity and low dissipation rate allows to capture the dynamics of fast transients that occur when strongly-driven nonlinear resonators relax to their equilibrium state. We experimentally study the ringdown dynamics of a nanomechanical Duffing resonator in both the time domain and in phase space. The resonator exhibits very different ringdown dynamics depending on whether it is subject to one or two tone driving. In the former case the ringdown follows a regular exponential decay, whereas the latter case shows exotic dynamics such as libration, slowing-down while scattering in phase-space, and ghost slowing-down. We demonstrate that this distinct difference can be attributed to the structure of the phase space itself. Surprisingly, we find that the energy in the resonator changes non-monotonously and that long delay between turning off the drive and the decay of the motion amplitude results in dynamical meta-states.

We investigate the dynamics of a magnetic Newton's cradle (MNC) using experiments, simulations through forward and inverse data driven models. In the MNC magnetic forces replace the instantaneous elastic collisions of the classical design. We compare point-dipole and finite-current-loop interaction models, identifying their parameters from direct measurements as well as through pendulum trajectories using the method of Optimizing a Discrete Loss (ODIL). For a synthetic three-pendulum twin, ODIL reproduces discretized trajectories to round-off accuracy and infers accurately magnet strength and damping from sparse data even when only one pendulum is observed. Model comparison shows that the point-dipole model compensates for near-field errors by underestimating the magnetic moment and produces structured residuals at each momentum transfer. The current-loop model removes this bias and, on full-precision recordings, also recovers the magnet radius. The continuous magnetic coupling reproduces the classical cradle's key behavior while enabling richer dynamics, including $N$ normal modes and a static repulsion offset. These results demonstrate that ODIL can infer physical parameters, and quantify model-form errors from sparse, noisy observations. Ultimately, this work establishes the magnetic Newton's cradle not merely as a physical curiosity, but as a rigorously quantifiable testbed for computational inverse modeling.

We present a theoretical study of trapping an electron in a two-frequency Paul trap, motivated by future hybrid architecture consisting of a doubly charged calcium ion (Ca$^{2+}$) and an electron. By isolating the electron from ionic-electron interactions, we formulate the equations of motion for the electron in the time-dependent trap potentials and cast them in the Hill form. Stability and dynamics are then analysed in terms of the dimensionless q-parameters, which encode the applied voltages, drive frequencies, trap geometry, and the particle's charge-to-mass ratio. Under the combined action of the two radio-frequency fields, the trapped electron's classical motion is shown to be approximated well by a slow secular oscillation modulated by two distinct motion sidebands originating from the low- and high-frequency RF drives. The approximation method presented here enables a quick evaluation of the relation between the device-design q-parameters and the electron motion. It offers a crucial foundation for developing physical models of electron-ion interactions in electron-ion traps.

Much of the water that matters most - flowing through biological cells and membranes, percolating through soils and rocks, or processed by filtration and desalination technologies - is not bulk water. It is water in nano- and molecular-scale confinement or at interfaces. Nanoscale water is therefore central to many challenges of our time, from the global water crisis and the water-energy nexus to catalysis, electrochemistry, and health. Beyond its applications, nanoscale water has emerged as a rich scientific field in its own right: discoveries are accumulating rapidly, revealing that confinement and interfacial forces produce a range of behaviours absent in the bulk. Sometimes this amounts to a renormalization of bulk properties; in other cases, new and non-intuitive phenomena emerge - exotic phases, anomalous transport, and dielectric responses that defy continuum expectations. A convergence of atomically precise nanofluidic devices, novel spectroscopies and microscopy approaches, and machine-learning-accelerated simulations is now exposing the molecular mechanisms behind these behaviours. This Perspective argues that the recent findings should not be viewed as isolated nanoscale anomalies, but as evidence for a molecular regime of water in which continuum descriptions must be rethought and molecular-level understanding becomes essential. Recognising and exploring this regime should have consequences ranging from fundamental physics to the rational design of future technologies that rely on water and dissolved ions.

In this paper, a multiple-relaxation-time (MRT) total enthalpy lattice Boltzmann (LB) model is proposed for liquid-vapor phase change. The pseudopotential LB method is employed to describe the liquid-vapor multiphase dynamics, while the thermal field is solved using an MRT LB formulation with total enthalpy as the evolution variable, thereby incorporating sensible and latent heat into a unified framework. A latent heat expression based on the equation of state (EOS) is further derived to provide a thermodynamic reference for its specification. Multiscale analysis demonstrates that the proposed model recovers the target macroscopic energy equation without introducing the nonlinear thermodynamic source term commonly required in temperature-based formulations, thereby avoiding the explicit evaluation of $\nabla\cdot\mathbf{u}$. The model is validated through free droplet evaporation, droplet evaporation on a heated surface, and bubble growth and departure during boiling, showing good agreement with published results. Simulations with different prescribed latent heats are further conducted in all three cases, demonstrating that the latent heat can be independently specified according to the physical conditions considered without altering the equation of state.

Immiscible liquid-liquid jets occur in numerous industrial and environmental settings, including oil spill response and liquid-liquid extraction, yet the coupled evolution of turbulence, interfacial instability, and droplet size distribution across transitional to turbulent regimes remains poorly understood. We present a combined experimental and theoretical investigation of a silicone oil jet injected into refractive-index-matched sugar water, employing simultaneous Particle Image Velocimetry (PIV) and Planar Laser-Induced Fluorescence (PLIF). Beyond the breakup region, mean velocity and Reynolds stress profiles exhibit self-similarity. Proper Orthogonal Decomposition (POD) of the volume fraction reveals a systematic shift in the dominant instability mechanism with increasing Reynolds number: axisymmetric Rayleigh-Plateau modes govern breakup at low Reynolds numbers, sinuous and varicose modes coexist in the transitional regime, and Kelvin-Helmholtz-driven shear-layer breakup dominates at higher Reynolds numbers. Droplet sizes are extracted from PLIF images using a convolutional neural network-based segmentation approach. In the transitional regime, a bimodal droplet size distribution is observed, reflecting the coexistence of shear-induced breakup and Rayleigh-Plateau instability. As the Reynolds number increases and turbulent dissipation intensifies, the distribution evolves toward a single mode with smaller characteristic droplet sizes. To predict the droplet size distribution, existing population balance models are extended to include droplet coalescence. Incorporating coalescence substantially improves agreement with experimental measurements, particularly for larger droplets. These findings demonstrate that turbulent dissipation, interfacial instabilities, and droplet coalescence collectively govern the evolution of droplet size distribution in immiscible liquid-liquid jets.

We present a native implementation of the Two/Three-Phase Thermodynamics (xPT, $x \in \{2,3\}$) method within the LAMMPS molecular dynamics framework, termed FixXPT. xPT is an approach for obtaining absolute, quantum-corrected thermodynamics (entropy, enthalpy, free energy, heat capacity, diffusivity) from the density of states function, obtained from the velocity autocorrelation function of an equilibrium trajectory. FixXPT addresses non-trivial integration challenges, including atom reordering, compute scheduling, FFT backends, unit systems, and partitioning of atomic velocities into molecular modes. Two autocorrelators are provided: a Wiener-Khinchin FFT correlator with one cumulative window-end operation, and an in-line multi-tau correlator whose memory footprint grows only logarithmically with the window length, removing the principal scaling bottleneck for long analysis windows. The velocity history of each window is distributed across the MPI ranks, so the memory the fix adds to a node stays nearly constant as ranks are added and its cost falls with the number of GPUs. Replaying identical velocity frames through FixXPT and the stand-alone pyxPT post-processor reproduces every thermodynamic observable of well-sampled groups to within 0.1 to 0.5% across the full analysis-mode matrix; sparsely populated ionic species agree within their statistical uncertainty, and the multi-tau VACF converges monotonically to the FFT result as its buffer grows, from 0.8% to 0.1% drift across a 16-fold buffer sweep. The code is distributed as a drop-in LAMMPS package.

Using an activation model reproducing facilitation mechanisms, we found recently a fluidization transition in supercooled water triggered by the motion of a few active molecules. We investigate here the effect of the activation force on the transition. The activation force increases the probability for active molecules to overcome the energy barrier induced by caging. The induced molecular motions result in an intermittent loose structure leading to a decrease of energy barriers around the moving molecule, thus facilitating the motion of nearby molecules. Therefore we expect the force, if small enough, to increase the facilitation mechanism, and as a result cooperative motions induced by it. As a result the activation force permits to tune facilitation and cooperative motions in active glass-formers. We find an optimum force for cooperative motions that we evaluate to be around 3.5pN, a value in the range of protein motor forces. As expected for a phase transition we observe peaks of cooperative motions (dynamic heterogeneity) on the transition. This result shows that dynamical heterogeneity are the cooperative motions of physical importance for the transition.

The dielectric constant of polar liquids depends not only on the magnitude of the molecular dipole moment but also on short range orientational correlations between neighboring dipoles. How molecular structure determines these correlations, quantified by the Kirkwood correlation factor $g_\mathrm{K}$, remains unclear. Using molecular dynamics simulations of model polar liquids without hydrogen bonding, we show that molecular shape plays a central role. We interpret $g_\mathrm{K}$ as resulting from the combination of dipolar interactions and steric effects, which together favor either alignment or antialignment of neighboring molecules. Depending on molecular shape, $g_\mathrm{K}$ can either increases or decreases upon cooling, or change monotony. A minimal model of dipoles on a cubic lattice reproduces these three regimes and attributes the nonmonotonic case to a competition between the first layer of neighbors, which favors alignment, and the second layer, which favors antialignment.

We carried out molecular dynamics simulations of a mixture of self-propelled particles (SPPs) and passive particles. When the self-propulsion speed was sufficiently high, the system separated into two phases. One phase consists of ordered passive particles, and the other is a disordered mixture of both particle types. The separation arises from the interplay between the self-propelled motion of SPPs and thermal motion of the passive particles, since phase separation does not appear with either particle type alone. As the self-propulsion speed increases, the SPPs push surrounding particles away, effectively increasing their excluded size. As a result, the increase in the effective excluded sizes promotes the accumulation of passive particles and the segregation of SPPs into the dilute phase through a mechanism analogous to the depletion interaction. This mechanism explains the phase separation observed in the present study. Our findings provide insights into the potential applications of SPPs and contribute to our understanding of natural systems composed of elements with different levels of motility.

The structural accessibility and perimeter shell properties of branched macromolecules are studied using Monte Carlo simulations on a simple cubic lattice. Constituent polymer chains of these macromolecules are constructed in an algorithmic way as: a set of collinear monomers; a self-avoiding walk (SAW); tigthly packed monomers. These mimic the ground states for a rigid rod, flexible chain, and collapsed chain conformational states, respectively. We analyzed the set of observables that are related to adsorption, such as perimeter shell size (number of available sites for particle adsorption) per monomer $\langle \bar{n}_a \rangle$, mean coordination number of perimeter shell $\langle n_{\rm bond} \rangle$ (average number of contacts per adsorbed particle), and coordination accessibility per monomer $\langle \bar{n}_s \rangle$. Our results demonstrate that branching reduces the perimeter shell size while it increases mean coordination number of perimeter shell across all conformational states, due to higher local monomer density near branching cores and formation of shared adsorption sites or microcages. Stiff extended structures yield the highest values for $\langle \bar{n}_a \rangle$ (approaching $4$ in the limit of long chains), whereas the flexible ones provide the largest values for $\langle n_{\rm bond} \rangle$. We can note that the collinearity of monomers in constituent chains works in the same direction as reduction of branching ($\langle \bar{n}_a \rangle$ grows), whereas the { tight packing of them} -- in the same direction as the increase of branching ($\langle \bar{n}_a \rangle$ decreases)

Mechanical stress is one of the main characteristics of viscoelastic molecular systems, including vitrifying liquids and amorphous solids which are known to show long-range dynamical heterogeneities. It is therefore important to deal with time- and space-resolved local stress whose correlations can be used to obtain viscoelastic memory functions of such systems, in particular, their wave-vector dependent shear and compression relaxation moduli. However, such memory functions are not directly accessible within standard molecular dynamics (MD) simulations. Here we discuss a new method called the constrained molecular dynamics (CMD) which allows for a direct evaluation of the wave-vector and time dependent viscoelastic moduli. The study is focused, in particular, on the stability analysis of different variants of the CMD, revealing the most efficient stabilization algorithm. Our theoretical predictions for the time-dependence of the most important parameters (like the wave-vector resolved mass current) during the stabilization stage are compared with the simulation data using different CMD algorithms. An excellent agreement is observed, thus confirming the validity of our theoretical approach and its ability to accurately predict the most important initial part of CMD trajectories.

Active materials are driven out of equilibrium at the microscopic scale and display diverse phenomenology; non-reciprocity is a subclass of activity in which action-reaction symmetry is also broken. These models are often grouped by the order of symmetry of their components, such as polar bird flocks or hexatic cellular tissues. However, many biological examples exist in which the components appear to have two or more symmetries simultaneously. To study this effect we introduce two independently controllable symmetries to the non-reciprocal XY model. This lattice model demonstrates wide ranging behavior dictated by the chosen symmetries. We derive a full hydrodynamic description of our lattice model that highlights the mechanisms driving its behavior. Each combination of symmetries can lead to a different hydrodynamic model with one or two simultaneous order parameters with different levels of orientational order that can appear active or not.

Tribocharging of granular materials is a widespread phenomenon ranging from volcanic eruptions and dust storms to pharmaceutical processing, yet its underlying mechanism remains elusive. Recent thermoelectric models have provided a quantitative framework for triboelectric charge transfer, but they have difficulty accounting for charging between identical materials. In this Letter, we propose a theory of granular tribocharging based on the interplay between particle geometry and thermoelectric response. Collision-induced frictional heating produces a size-dependent temperature asymmetry between particles, generating a thermoelectric voltage that drives charge transfer. The sign of the Seebeck coefficient determines the charging polarity, while particle size and thermal properties set its magnitude. Our multi-collision theory explains the experimentally observed size- and material-dependent reversal of charging polarity, as in quartz and nylon.

Filaments are incredible material building blocks that, when entangled together, form robust structures with remarkable adaptive mechanics, from stiff cables to stretchable knits. Basic questions about the mechanism that holds together such structures, especially assemblies like rope, without attractive physical or chemical bonds between constituents are among the oldest considered in materials science. Contradicting a long-standing picture that structural integrity of rope-like assemblies rely on a combination of external loading and inter-filament friction to prevent spontaneous detangling (e.g. fraying of a cut rope), we demonstrate that assemblies of intrinsically-curved filaments can achieve structural integrity purely from the competition of elastic forces that resist shape-change and (traction-free) repulsive forces that prevent overlap. We analyze a friction-free model of assembly of intrinsically-helical filaments, and show that depending on filament number and preferred filament shape, overcrowding in the assemblies generate elastic pre-stresses that give rise to either self-locking entanglement or spontaneous detanglement through propagation of a soliton-like detanglement front through assemblies. We test a generalized fracture criterion for spontaneous detangling and confirm the role of shape-elastic costs to self-locking via experiment and simulation of frictional filaments, demonstrating a range of bundled structures which cannot be made self-locking for any value of friction. The mechanism of ``purely elastic cohesion" illuminated here sheds light on self-locking in a broader class of entangled structures, and further, offers design principles for new classes of active filament materials capable of stimuli-responsive assembly and disassembly.

The dramatic slowing down of liquids approaching the glass transition remains unresolved, partly because competing theoretical explanations are difficult to discriminate. Indeed, several mature, contrasting frameworks account for the main features of glassy phenomenology, making agreement with familiar observations a weak basis for identifying the microscopic mechanism responsible for the slowdown. Recent numerical advances are changing this situation in two complementary ways. Deep equilibration extends controlled equilibrium studies into regimes previously accessible only by extrapolation, allowing established predictions to be stress-tested over a broader dynamical range. At the same time, new numerical methods increasingly provide direct access to theory-specific quantities such as configurational entropy, static lengths, elastic properties, and local activation barriers. I discuss how these developments constrain thermodynamic, facilitation-based, elastic, and excitation-based descriptions. The emerging picture is not yet a unique theory, but a set of increasingly discriminating tests that can reveal where apparently successful laws cease to be universal and identify the microscopic ingredients that causally control the activation barrier.

Interactions shape the properties of many physical and biological nonequilibrium systems, but whether collective operation raises or lowers entropy production remains difficult to predict. Here, we show that strong coupling suppresses irreversible circulation associated with the directly coupled degrees of freedom. In identical two-dimensional systems, this suppression is monotonic for nonzero coupling modes and guarantees a monotonic decrease of the entropy production rate (EPR), with the corresponding probability currents vanishing in the strong-coupling limit. In higher dimensions, suppressing the circulation associated with the coupled degrees of freedom does not generally eliminate all irreversible circulation, since the remaining degrees of freedom can still sustain nonequilibrium currents. The EPR of these residual dynamics sets the strong-coupling limit, providing a criterion for whether a given choice of coupled variables leads to lower dissipation than the uncoupled system. The approach to this limit depends on how the finite-coupling current correction aligns with the residual current. Further, we show that convergence to residual dynamics in the strong-coupling limit also applies to coupled non-identical systems. Finally, we demonstrate the predicted EPR reduction in nonlinear models of vertebrate hair-cell bundles and bacterial chemotaxis.

Understanding the fluctuations and response of particles in potential landscapes is a fundamental problem in nonequilibrium statistical physics. Here, we investigate how negative mobility reshapes the stochastic behavior of a particle moving in a mechanical potential landscape. We consider a one-dimensional overdamped particle subject to additive noise, with mobility that is negative at weak forces and positive at strong forces. In a potential well, negative mobility destabilizes the mechanical potential minimum and produces bimodal localization at two off-center positions. The same stability reversal transforms conventional Kramers escape from a potential well into a two-stage escape process involving an intermediate metastable state. When an additional spatially uniform force is applied, the mechanical perturbation translates rather than tilts the effective double well, yielding a positive response dominated at weak noise by intrawell relaxation, even though slow interwell switching dominates spontaneous positional fluctuations. These findings reveal how negative mobility reshapes the interplay among mechanical landscapes, stochastic stability, and response.

Swarmalators are particles which have internal degrees of freedom in the form of phase oscillators that can synchronize and change the dynamics of the particles. We explore the active matter disk swarmalator model proposed by Adorjáni [Phys. Rev. E 109, 024607 (2024)] where there is an additional attraction or repulsion determined by whether the phases of particles within a certain radius synchronize or anti-synchronize. This model in the absence of swarmalator rules forms a motility-induced phase-separated (MIPS) state at high activity, but when the swarmalator rules are present, a number of additional states appear including an active gel, labyrinth state, frustrated MIPS, and frustrated fluid states. Here we examine ratchet effects for the Adorjáni model coupled to asymmetric substrates. We find that swarmalator interactions can strongly enhance or suppress active matter ratcheting depending on the structural state of the system, and show that the ratchet efficiency depends on the substrate strength, substrate lattice spacing, and the motor force on the particles. The gel state exhibits the weakest ratcheting for small substrate spacing and can even produce a reversed ratchet motion, but shows the strongest ratcheting for large motor forces. The labyrinth state exhibits the strongest ratcheting over a wide range of parameters since the quasi-one-dimensional labyrinth morphology can match the substrate geometry well.

Dynamical coarse-graining of neural networks gives macroscopic observables and enables training to be predicted, and controlled in a state space far smaller than the parameter space. In this paper, we first define the learning operator following the training law of neural networks and establish a descent theorem for the learning operator, which serves to determine whether the operator is sufficient to characterize the learning dynamics. Then the exact closure theorem and the dynamic coarse-graining theorem are presented in sequence. The three theorems established in this paper provide a systematic framework for constructing and assessing dynamical coarse-grained models of neural-network training. Finally, we demonstrate the applicability of the theorems with a finite-width nonlinear ReLU network. Its dynamic coarse-grained model for a fixed pattern is exactly derived and composed of five independent moments. The model exactly predict the training outputs and evolving learning operator. The framework may also guide the development of approximate coarse-grained models for more general neural networks when exact closure is unavailable.

We develop a continuum-thermodynamic model for chemically reacting, multi-velocity and multi-temperature fluid mixtures. Partial balances of mass, momentum and total energy are closed using a single entropy density depending jointly on the constituent mass and nonkinetic internal-energy densities. Its partial derivatives determine the constituent temperatures and chemical potentials. For the chosen entropy flux and separately treated volume deformation, the strengthened entropy principle yields a weighted Euler relation constraining the partial thermodynamic pressures. We construct thermodynamically consistent constitutive relations for viscosity, heat conduction, Maxwell--Stefan momentum exchange, thermal relaxation and nonlinear reaction kinetics. The baseline model includes thermo-diffusion and its reciprocal coupling; a fully coupled reciprocal completion is given within the stated isotropic co-factor class. An alternative formulation couples chemical conversion and energy redistribution through specified elementary processes. We identify the material functions required for closure and admissible shifts of constituent energy zeros. An ionization network with resolved electronic levels yields Saha-type ionization relations and Boltzmann excitation ratios under the stated detailed-balance assumptions, recovering the Saha--Eggert relation at common temperature. Competing electron- and heavy-particle processes can maintain stationary populations while transferring energy between groups at different prescribed temperatures.

The Artificially Thickened Flame (ATF) approach is widely used to render premixed flames resolvable on coarse computational meshes, but thickening alters their interaction with turbulence. While considerable research has focused on the effects of thickening on turbulence-induced flame wrinkling, its influence on the mean local flame propagation speed in turbulent, thermodiffusively unstable hydrogen flames remains poorly understood. More than 200 flame-resolved simulations of premixed flames in homogeneous isotropic turbulence with detailed chemistry and transport are used to systematically isolate and quantify the effects of artificial thickening. Thickening the flame by a factor $F$ increases its effective flame-scale Karlovitz number according to $Ka_{\mathrm{f}}^F = Ka_{\mathrm{f}}\sqrt{F}$, while decreasing its effective Damköhler number according to $Da_{\mathrm{f}}^F = Da_{\mathrm{f}}/F$. In the regime considered here, the former enhances the mean local flame speed, whereas the latter reduces flame wrinkling, resulting in opposing effects on the flame consumption speed; hence, changes in both local flame propagation and flame area must be accounted for. Simulations matched with respect to $Ka_{\mathrm{f}}^F$ and $Da_{\mathrm{f}}^F$ collapse across different thickening factors $F$ until the thickened flame approaches the integral or geometric length scales of the configuration. Based on these scaling relations, a self-consistent efficiency correction is proposed to recover the unthickened flame consumption speed. Since the efficiency factor feeds back on the effective Karlovitz and Damköhler numbers, it must be determined implicitly.

Interfacial turbulence damping is required in Reynolds-averaged simulations of stratified gas--liquid flows when strong interfacial velocity gradients are present. In this work, we develop a target-$\omega$ interfacial damping formulation for the low-Reynolds-number Wilcox-type $k$--$\omega$ model in a one-field RANS/VOF framework. A gas-side target value of the specific dissipation rate $\omega$ is constructed from an effective interfacial wall coordinate determined from the local resolved flow. The constructed target-$\omega$ provides a smooth transition between the viscous and logarithmic limits through power-law blending and requires no calibration of model constants against target data. \textcolor{black}{The formulation is first assessed against three gas-layer DNS cases at $Re_\tau\simeq180$ with different interface velocities. The model reproduces the principal features of the mean velocity, turbulent kinetic energy and Reynolds shear-stress distributions, while showing substantially weaker sensitivity to the near-interface grid resolution than the Egorov-type formulation, although some grid dependence remains on the coarsest mesh. The assessment is then extended to the co-current Fabre stratified-flow experiment at a higher Reynolds number and to the counter-current Stäbler experiment}. In both cases, the present formulation provides generally good predictions of the gas-side mean flow and turbulence statistics without case-specific adjustment. For the Stäbler case, in which the liquid level develops as part of the coupled two-phase solution, the predicted mean liquid depth agrees closely with the measured value. These results indicate that the target-$\omega$ formulation provides a consistent interfacial turbulence-damping treatment for resolved large gas--liquid interfaces over the range of conditions considered.

Quantifying the dissolution and buoyancy-driven transport of CO2-rich water is critical to understanding solubility trapping mechanism in geologic storage. Analog-fluid density driven convection experiments do not represent CO2 dissolution chemistry or the aqueous CO2 density-concentration monotonic relationship. X-ray tomography does not provide enough contrast to directly measure dissolved CO2. Spatial colorimetry provides an inexpensive method to map pH and estimate total dissolved inorganic carbon (CT) via carbonate equilibrium assumptions. However, the effects of experimental conditions such as domain (free fluid and porous), geometry (2D and 3D), and indicator mix concentration on the reliability of pH and CT measurements remain unexplored. We evaluated how these factors affect the reliability of measurements using two different colorimetric models (hue and spherical coordinates ({\theta} and {\phi})). Hue was reliable in all domains whereas {\theta}-{\phi} was reliable in free fluid. Lower indicator mix concentration increased the chromatic sensitivity at low pH in free fluid; however, it did not produce sufficient color contrast for pH calibration and mapping in the porous domain. In the porous domain, {\theta}-{\phi} calibration was 33 times more susceptible to noise than hue. Temporal pH noise was less than 0.01 units; spatial noise changed domain-mean CT by 0.6-4.4{\%}. Both models were able to resolve CO2-rich plumes in free fluid; however, {\theta}-{\phi} had sharper plume boundaries than hue. The temporal evolution of CO2 dissolution resolved by the color models agreed more in 2D than 3D. These findings provide a reliability framework for studying subsurface dissolution and mixing of CO2.

The wake of an airborne wind energy kite is shaped by its crosswind path and, for on-board generation, by the slipstreams of its rotors, and in farms it reaches downstream units. It is computed here by a vortex step method with a time-marching free vortex wake, implemented by the authors in their open-source code OpenFAWE with a lumped-mass tether, actuator-disc rotors releasing vortex rings and several kites. It reproduces an independent vortex step code to 10^-9 on the rigid-wing Makani M600 and within 0.3% in lift and 0.9% in drag on the TU Delft V3 leading-edge inflatable kite, matching its Reynolds-averaged Navier-Stokes lift within 3.1%. For fixed kites the lift deficit of a finite wake is the far field of its starting vortex, which fixes the wake length before a run, and the vortex core must stay below the narrowest panel width. With these settings the helical tip-vortex pair of the M600 on its loop lowers its lift by about 0.5% from 5 to 13 m/s. Free rotor rings do not converge with the time step, whereas an undeformed slipstream tube converges once its rings are refined at the wing and raises the lift by 1.9%. A slipstream deflected by the wing lowers it by 3.5%, so the treatment near the wing sets the sign of the rotor effect. A second unit one loop diameter downstream loses 0.5% of its lift and 2.2% of its aerodynamic power, with or without rotors.

Computed herein are examples of mode-2 internal solitary waves to the Dubreil-Jacotin-Long (DJL) equation. These are localised, fully nonlinear waves in a continuously stratified, inviscid fluid under the Boussinesq and rigid-lid approximations. The equation is solved directly using finite differences on a periodic domain, enabling the computation of both generalised solitary waves, which possess oscillatory mode-1 tails, and embedded solitary waves, whose tails vanish. Two stratifications are considered. The first is a double pycnocline, generalising the three-layer system considered by Doak et al. (2022) by replacing each infinitesimal interface with a pycnocline of finite thickness. The second stratification, a surface mixed layer above an exponentially stratified layer, shows that embedded mode-2 solitary waves are not restricted to double-pycnocline stratifications. These are the first mode-2 solitary waves of the DJL equation computed for stratifications that are asymmetric about mid-depth.

Unsteady flow over a 30 $\mu$m diameter cylinder at Mach 4 is investigated using Direct Simulation Monte Carlo across Reynolds numbers from 270 to 6750, spanning slip-flow to near-continuum regimes. Power Spectral Density analysis at discrete probe locations and Dynamic Mode Decomposition of flowfield snapshots independently characterize instabilities in both the stagnation and wake regions. In the stagnation region, a bow shock pulsation mode at 10-15 MHz frequency is identified across all cases despite a 24-fold variation in number density. In the wake, two distinct instabilities are observed. The canonical vortex shedding mode at Strouhal number St $\approx$ 0.2 dominates at lower Reynolds numbers. A second instability at St $\approx$ 0.5, consistent with previously reported slipline-driven oscillations in supersonic wakes, emerges at higher Reynolds numbers and progressively strengthens, becoming the dominant mode. In the studied Reynolds range, the wake transitions from no clear unsteadiness, to canonical vortex shedding at St $\approx$ 0.20, and reaching a regime where the St $\approx$ 0.5 mode becomes dominant, while also having a distinct independent bow shock pulsation possibly governed by its standoff distance.

A three-dimensional curvilinear lattice-Boltzmann method is introduced for simulations on smoothly deformed grids while retaining exact one-to-one streaming on a uniform computational lattice. The coordinate transformation is represented locally through a metric-Gaussian equilibrium and a Christoffel-connection source in moment space. A dynamically reconstructed homogeneous-state perturbation streaming procedure preserves homogeneous physical states on warped meshes without interpolation in the advection step. The method is implemented on a D3Q27 lattice with a cumulant collision operator, while the geometric construction remains compatible with other local collision models. The formulation is assessed using two sets of tests. First, static non-orthogonal warped-cube cases validate the bulk curvilinear solver through a convected helical shear wave, the Taylor--Green vortex, and Arnold--Beltrami--Childress flow. These tests verify viscous decay, clean freestream preservation, vortex-breakdown dynamics, and the nonlinear inertial--pressure balance induced by geometric acceleration. Second, wall-bounded and moving-boundary demonstrations assess the boundary-compatible extension through warped plane Poiseuille flow, arbitrary Lagrangian--Eulerian (ALE) peristaltic pumping, and a two-way fluid--structure interaction (FSI) case with added-mass frequency shift. The results show that the proposed curvilinear LBM avoids interpolation-based transport, reduces geometry-locked numerical modes, preserves global mass and momentum to round-off accuracy in the tested warped periodic cases, and extends to wall-bounded ALE/FSI configurations with conservative treatment of mass and physically consistent momentum exchange.

Rotating internally heated convection has been studied almost exclusively in laterally periodic domains, which cannot support the sidewall-attached modes that appear for sufficient rotation rates in rotating Rayleigh--Bénard convection in containers. We conduct direct numerical simulations of internally heated convection with isothermal plates and an adiabatic sidewall in cylinders of aspect ratio $\Gamma = 1/2$, $1$, and $2$ at $\Ra = 10^8$ and $\Pran = 1$, comparing them with a doubly periodic layer. When rotation is strong enough to stabilise the flow in a doubly periodic layer at the same $R$ ($\Ek \lessapprox 2 \times 10^{-5}$), the cylinders continue transporting heat via a wall mode down to $\Ek = 5.62 \times 10^{-6}$. This mode consists of a wave attached to the sidewall, with a radial thickness of roughly $0.03$ layer depths independent of $\Gamma$, leaving a stationary interior. Although unstable stratification is confined to the upper half of the conductive state, the mode also penetrates the lower half while retaining stable mean stratification in the measured lower-layer interval. Its azimuthal wavenumber scales roughly with $\Gamma$, yielding a wall parallel wavelength on the order of the layer depth, and it drifts retrograde as a rigid wave slower in wider cylinders and at lower $\Ek$. Analogous to rotating Rayleigh--Bénard convection, the wall modes reported here extend the observed range of sustained convection relative to the periodic reference and may complicate experimental comparisons.

The standing wave problem concerns the space-time periodic motion at the free surface of a two-dimensional, infinitely deep, irrotational flow of an incompressible inviscid fluid under gravity. Although spectrally accurate computations have revealed a rich array of nonlinear wave phenomena, repeatedly evaluating their evolution over large parameter spaces remains challenging, particularly when resolving fine-scale spatial oscillations. We employ a Fourier neural operator (FNO) architecture to learn the solution operator along a numerically computed one-parameter family of symmetric standing waves. Given a wave profile at an instant of rest and a normalized observation time, the learned operator predicts the fluid surface, the velocity potential and the dipole density at the surface at that time. In-distribution tests yield uniformly small relative errors within the training range. Two out-of-distribution experiments characterize extrapolation toward contrasting physical regimes. Toward the free-fall limit, errors concentrate near the sharpening crest, consistent with the spectral truncation in the FNO architecture. Toward the linear limit, absolute errors remain small whereas relative errors increase as the amplitude vanishes. A residual of the governing equations, evaluated independently of reference solutions, complements these tests and provides a diagnostic for exploratory predictions beyond the available data.

In this study, a regularized lattice Boltzmann method is proposed for solid-liquid phase-change simulations. The governing total-enthalpy equation is solved within a regularized lattice Boltzmann (RLB) framework, which enables accurate tracking of the solid-liquid interface while effectively suppressing numerical diffusion. In addition, the multi-relaxation-time RLB (MRT-RLB) model with standard lattices is developed to solve the flow field. To enhance computational efficiency, an efficient multi-GPU (graphics processing unit) implementation based on CUDA C (Compute Unified Device Architecture) is developed, which is particularly suited for computationally intensive three-dimensional phase-change simulations. The proposed model is validated against a series of one-, two-, and three-dimensional benchmark problems. The results demonstrate that the present solver provides a robust, accurate, and efficient framework for simulating solid-liquid phase-change heat transfer.

The flow past a rotating cylinder undergoes substantial changes in its wake dynamics and aerodynamic response with increasing rotation rate. This study investigates these changes in two-dimensional compressible flow at \(Re_\infty=3800\) and \(M_\infty=0.1\), with the rotation rate systematically varied over \(0.1\leq\Omega\leq10\) using 130 high-fidelity simulations. At low rotation rates, conventional periodic vortex shedding is progressively suppressed with increasing rotation. A narrow transition regime around \(\Omega=2.2-2.8\) is identified, where sustained oscillations evolve into intermittent fluctuations before reaching a nearly quiescent state. At higher rotation rates, unsteadiness re-emerges with distinctly intermittent and multiscale characteristics, demonstrating that this instability is fundamentally different from conventional Kármán shedding. The surface pressure and streamwise skin-friction distributions reveal substantial redistribution of aerodynamic loading with rotation, characterized by increasingly intense suction and significant modification of the near-wall shear field. The maximum lift increases systematically with rotation, reflecting the strengthening Magnus-Robins effect, whereas drag exhibits a non-monotonic response with enhanced variability at high rotation rates. Despite the low free-stream Mach number, rotational acceleration produces local Mach numbers approaching 0.5, indicating appreciable compressibility effects in the near-cylinder region. Vorticity-based proper orthogonal decomposition further reveals a transition from wake-dominated coherent structures at low rotation to strongly wrapped, rotation-dominated structures at high rotation. These results establish a direct connection between rotational forcing, surface loading, compressibility, and the suppression and subsequent re-emergence of flow unsteadiness.

Learned flow surrogates are applied recursively, so errors in phase, amplitude and transport accumulate as each prediction feeds the next. During training, however, the realized next state is known. We propose Future-Aligned Motion Inference for Recursive Physical Forecasting (FAMIR), which uses this realized future to shape the signal that drives the update, not only the predicted state. On the latent grid of a frozen autoencoder, a future-conditioned teacher and a history-only student infer motion tensors that condition one shared residual transition. Posterior--Prior Motion Alignment (PPMA) jointly aligns the teacher (posterior) and student (prior) motions, prediction-fed multistep objectives train the student on its own rollouts, and only the student is deployed. On viscoelastic channel flow, Rayleigh--Bénard convection and planetary shallow-water flow, FAMIR achieves lower complete-prefix normalized root-mean-square error than three direct latent predictors of comparable size and a delay-embedded linear reference at ten steps (1.003\%, 1.055%, 0.620%) and twenty steps (1.661%, 1.683%, 1.036%). Its advantage is largest at the first step in the viscoelastic flow and grows with lead time in the other flows. Over forty-step forecasts, FAMIR keeps fluctuation profiles and probability densities closer to the reference than the direct predictors. Without the teacher, the motion-conditioned student already outperforms the direct predictors; in the shallow-water flow, prediction-fed rollouts are decisive and joint alignment is far more effective than distillation toward a fixed teacher (1.036% against 1.874%). Fixed-state interventions show that the trained update relies on the state-specific motion, and the deployed student matches the one-step accuracy of the future-informed teacher.

The prediction of transition remains challenging because the receptivity amplitude is usually prescribed rather than measured. This work uses Direct Simulation Monte Carlo (DSMC) to study an unforced Mach 6 nitrogen boundary layer over a 120 mm flat plate, with no imposed inlet wave, wall signal, modal shape, or disturbance spectrum. The retained unsteady field is the intrinsic finite-particle stochastic fluctuation field carried by the DSMC representation. Changing the DSMC particle count provides an independent numerical control parameter that sets a predictable finite-particle noise floor while preserving the time-averaged boundary-layer flow. Dynamic Mode Decomposition (DMD) is then applied to unforced DSMC snapshots. The DMD eigenvalues and spatial modes estimate the quantities that appear in the LST normal-mode description, including frequency, temporal growth or decay, wavenumber, wavelength, phase speed, mode location, and amplification envelope. LST is used after extraction to test whether the data-derived structures occupy the expected second-mode band. The results show that DSMC data can connect a measured finite-particle stochastic disturbance level to second-mode instability dynamics without imposed disturbance spectra.

We investigate conjugate flows in a two-layer fluid system with a flat bottom and a free surface. These are up- and downstream states consistent with simultaneous conservation of mass, momentum, and energy; and therefore candidate end-states of one-dimensional dissipationless bores. By choosing variables in a specific way, we are able to explicitly parameterize all physical non-trivial conjugate flows in the system, using only rational functions. This two-parameter family can be categorized according to whether the states are compatible with (1) a rising surface, and falling internal interface; or (2) vice versa. In particular, we rule out the existence of monotone bore solutions, consistent with an earlier result due to Chen, Walsh, and Wheeler. However, here we do so already at the level of conjugate flows. Separating these two distinct categories is a one-parameter family of critical trivial conjugate flows. The complete description obtained in the present paper serves as an important stepping stone towards finding actual realizing heteroclinic orbits connecting such conjugate states.

Laboratory experiments in a wave flume investigated the attenuation of shoaling extreme waves by artificial salt marshes placed immediately before an abrupt depth transition. Increasing vegetation density systematically reduced the excess kurtosis of the surface elevation distribution in the intermediate water depth regime. Nonetheless, attenuation exhibits a short saturation regime at low vegetation densities, whereas at very high densities, excess kurtosis decreases significantly across the gauges. However, kurtosis attenuation becomes ineffective as waves approach shallow-water conditions or as second-order nonlinear effects become significant. Furthermore, the highest experimental densities where the kurtosis is tamed exceed typical natural salt marsh stem densities. Thus, in natural settings, salt marshes are likely to provide only partial mitigation of extreme wave statistics in intermediate and shallow water depths, as the wave field retains some hazardous nonlinearity.

We develop the theory of hydrodynamic fluctuations for one-dimensional quantum liquids. At low temperatures the relaxation of interacting electrons in a single-channel wire separates into two classes: equilibration, which changes the numbers of right and left movers through backscattering and is exponentially slow, and thermalization, which redistributes energy and momentum at a fixed number of movers at a power-law rate. This separation of time scales gives the electron liquid a two-fluid description analogous to superfluid $^4$He, with the zero mode of the Luttinger liquid as the superfluid component and the gas of thermal excitations as the normal component. Using Onsager reciprocity and the fluctuation-dissipation theorem, we add Langevin fluxes to the two-fluid hydrodynamic equations, including a mutual-friction noise generated by rare backscattering events that has no counterpart in helium. We apply the theory to Coulomb-coupled quantum wires and calculate the dynamic structure factors, which contain a second-sound peak next to the plasmon doublet; the Coulomb drag resistivity, where intrawire equilibration acts as a bottleneck and turns the hydrodynamic drag into an activated temperature dependence; and the near-field heat transfer between the wires. Mode frequencies, spectral weights, linewidths, and the crossover scales of the transport coefficients are expressed through the thermodynamic properties of the liquid and a few dissipative coefficients, providing spectroscopic and transport probes of two-fluid behavior in one-dimensional quantum systems.

Existing noise mitigation strategies for wind farms usually consist in reducing turbines power output, without accounting for the wake interactions between them and the noise emission directivity. This leads to over-conservative policies and unexploited wind power. Yet, turbine yaw can simultaneously affect wake interactions and the direction of noise emission, offering an additional degree of freedom for farm-level noise control. We therefore propose Noise Steering, a model-free reinforcement learning (RL) strategy that jointly controls turbine yaw angles and power setpoints to maximise farm power while satisfying a local noise constraint in a defined region. To enable training at a reduced computational cost, a low-fidelity acoustic model is coupled with the steady-state FLORIS simulator. The RL agent effectively learns how to redirect wakes and noise directivity away from the protected region while redistributing power across the farm. On a six-turbine test farm, the policy satisfies the 40 dB noise constraint throughout the full range of turbulent winds, with an average power deficit of only 2% relative to greedy unimpeded control, and up to 7.7% at high wind speeds. In comparison, the industry-standard noise-reduced operation (NRO) baseline here generates an average power loss of 17%. When deployed in the higher-fidelity this http URL simulator, the policy largely retains its performance under steady and turbulent inflow, despite differences in simulation fidelity. These results demonstrate the potential of combining yaw control and power derating through RL to improve the power-noise trade-off in wind farm operation.

Recent advances in machine learning (ML) have the potential to substantially accelerate aircraft wing design, a process that has traditionally required extensive high-fidelity simulation and design iteration. Existing public datasets for ML-based wing design have focused primarily on aerodynamic performance, with limited consideration of the multidisciplinary interactions that govern practical aircraft design. In particular, efficient wing design requires simultaneous consideration of aerodynamic performance and structural integrity, yet no publicly available datasets capture this coupled aerostructural behavior at high-fidelity. To address this need, a high-fidelity multidisciplinary dataset for static aerostructural analysis of transonic wings is introduced. The dataset includes 2471 samples, along with three out-of-distribution samples. The wing planform geometry is parameterized by span, sweep, dihedral, tip chord, and tip twist, while the airfoil cross-sections are parameterized using the class-shape transformation method. The analysis is further parameterized by Mach number, angle of attack, altitude, and structural load factor. The utility of the dataset is demonstrated by training state-of-the-art ML models to predict aerodynamic surface quantities, integrated aerodynamic performance quantities, and the failure distribution of the wingbox. ML models achieve at most 0.0309 normalized root mean squared error (NRMSE) in the prediction of aerodynamic quantities and at most 0.1189 NRMSE in the prediction of failure distribution of the wingbox. By providing coupled aerodynamic and structural responses for a diverse set of transonic wings, this dataset establishes a benchmark for developing, evaluating, and comparing multi-physics ML models for wing design. Broadly, it is intended to encourage creation of similar high-fidelity multi-physics benchmark datasets across engineering domains.

We develop a quantum hydrodynamic theory based on Nambu's unpublished note \emph{A New Look at Fluid Dynamics}. The kinetic action defines a metric on configuration space and a mechanical connection coupling an observable cyclic deformation to unobserved fluid modes. Tracing out these modes yields a quantum channel for the observed deformation. We establish a criterion for the exact preservation of coherence between opposite momenta and show how nonzero connection curvature prevents this coupling from being removed. The leading quadratic decay of quantum coherence is determined by the prepared quantum state. For two shear flows, we identify an exact noiseless sign subsystem. Introducing additional generating flows cancels the initial residual of the Euler equations while producing nonzero connection curvature, governed by the same kinetic integrals that determine the classical correction. At fixed mean energy, choosing amplitudes adapted to the dominant coupling flow substantially reduces the initial decoherence, even along the direction that cancels the Euler residual. This advantage gradually diminishes under conditional evolution, eventually leading to a crossing of the decoherence curves. Our example shows that a preparation with a smaller initial coherence-decay coefficient can have a larger maximum sampled loss over a finite readout interval.

Cutting and shuffling (CS) rearranges fluid without stretching, but homogenisation requires diffusion (D); this interaction is not well understood. We show that CSD is a coarsening process, with scale $\bar\ell=L(n_c\mathrm{Pe}/2)^{-1/3}$ rather than the Batchelor scale, and that cutting acts as a fractional Laplacian in wavenumber, giving the exact mixing rate $\gamma=2^{1/3}|a_1'|n_c^{2/3}\lambda\mathrm{Pe}^{-1/3}$ for $n_c$ cuts per event at rate $\lambda$, with $a_1'=-1.0188\dots$ the first zero of $\mathrm{Ai}'$. This holds in any dimension for random and deterministic protocols, extends to finite-time mixing, and places CSD in a known non-equilibrium universality class.

Wind farm layout optimization becomes increasingly difficult as turbine count grows, especially when high-fidelity aerodynamic models are used. Conventional Kriging-based Bayesian optimization often suffers from low sample efficiency in high-dimensional layout spaces because sparse training data provide limited domain coverage. We develop a Graph-informed Kriging framework that embeds reusable aerodynamic interaction information into the surrogate mean function. The wind farm is represented as a directed aerodynamic graph, where pairwise turbine interactions defined in a low-dimensional relative-coordinate space are assembled into a farm-scale mean. This structured mean captures the dominant variation in annual energy production (AEP), allowing the Gaussian process to model only the residual structure and uncertainty. Numerical experiments show that Graph-informed Kriging consistently improves AEP prediction accuracy over ordinary and generic-trend Kriging under sparse-data conditions, with increasing benefits as layout dimension and wake-interaction strength grow. Embedded in Bayesian optimization, it substantially improves sample efficiency and achieves competitive solutions for the IEA Wind Task 37 benchmark with about 280 AEP evaluations. In a controlled 16-turbine case, it also outperforms ordinary and multi-fidelity Kriging under the same high-fidelity evaluation budget. The framework is further extended to a 48-turbine wind farm, demonstrating applicability to large-scale CFD-based layout optimization. These results show that Graph-informed surrogate modeling can enable more efficient use of high-fidelity aerodynamic models for reliable large-scale wind farm layout design.

Effective control of nonlinear complex networks needs to identify not only the intervention sites but also the state variables to be monitored and the locations at which control inputs should be applied. Here, we present a network-scale generalization of an observability-guided, flatness-based control framework. The resulting control laws are implemented using sliding-mode control and evaluated in heterogeneous networks of chaotic oscillators driven toward a prescribed periodic regime. We compare two control architectures: in the node-wise method, oscillators are independently sensed and actuated, while in the pairwise method, measurements acquired from a single node within each dyad are used to synthesize control inputs applied to both nodes. Across the parameter regimes considered, node-wise control generally achieves accurate control over a broader operating region, whereas pairwise control remains effective over a more restricted region while using half as many measurement locations for a given number of actuated nodes. Moreover, network interactions can enhance control by propagating the control influence to non-actuated nodes, creating a cooperative effect between the collective dynamics and the control action. Collectively, these findings quantify the trade-offs among measurement-location requirements, control performance, and control effort in nonlinear complex networks.

We study statistics of transport properties in a system of two quantum chaotic cavities coupled in series through a tunable junction and connected to reservoirs with asymmetric leads. Within the random matrix theory framework and in the absence of time-reversal symmetry, the scattering matrix S undergoes a crossover from two independent circular unitary ensembles to a single CUE as the inter-cavity coupling increases. Modeling this crossover using Dyson's Brownian motion approach, with the junction width acting as a time-like parameter, we derive closed-form expressions for the time-dependent averages and variances of conductance and shot noise power for arbitrary lead asymmetry. These analytical results reduce to known expressions in the symmetric and fully coupled limits. The mapping between the Brownian time parameter and the physical junction width is found to be observable-dependent, reflecting the different eigenfunction correlations probed by conductance and shot noise power, and this dependence is examined and separately calibrated for each observable. Validating against random-matrix simulations and tight-binding transport calculations using Kwant, we find quantitative agreement for ensemble-averaged observables throughout the crossover, while variances, being more sensitive to microscopic fluctuations, show deviations from the Brownian-motion predictions.

We compute the normal mode spectrum and its spectral form factor for a probe scalar wave in smooth horizonless backgrounds. We first consider the BTZ black hole with a brickwall that hides the near-horizon region, which has recently been proposed as a toy model for a finite-temperature semiclassical black hole microstate. In this setup, the spectral form factor may or may not have a linear ramp, depending on the details of the brickwall construction. However, we argue that even in cases that do show a ramp, this ramp does not originate from level correlations associated with quantum chaos. Then we calculate the normal mode spectrum for a genuine microstate geometry (superstratum) and find evidence of chaos, both with a ramp and level repulsion. We conclude that the eigenvalue spectrum of normal modes can indeed serve as a tool for investigating the quantum dynamics of fuzzballs; however, the brickwall models are incapable of capturing this phenomenon.

The Wilson-Cowan model is a classic example of a ``neural mass model'' - a simplified yet powerful way to describe the activity of large networks of neurons. It is particularly interesting because, even in its relatively simple form, it can produce a surprising variety of behaviours, from steady rhythms to complex oscillations. A key factor influencing these dynamics is the presence of time delays, reflecting the time it takes for signals to travel between neurons. This article offers an accessible introduction to the Wilson-Cowan model, focusing on how these time delays affect its behaviour. We explore the core concepts behind the model, survey the existing literature, and introduce some numerical techniques specifically designed for analysing such delay differential equations. We also provide a practical, hands-on tutorial on using the DDE-BIFTOOL software package, demonstrating its application to the Wilson-Cowan model. Downloadable code allows the reader to reproduce our results and to explore the model's dynamics further, including MATLAB code for all computations, using DDE-BIFTOOL for the continuation, and Python versions of simulation codes.

By using suitable ansatz which reduces the problem of obtaining exact solutions of the sine-Gordon equation with nontrivial time dependence to obtaining exact solutions of two first order symmetric $\phi^4$-like coupled equations in $x$ and $t$, we obtain a large number of hyperbolic and periodic solutions of the sine-Gordon equation. In particular, we not only obtain the well-known two-soliton, soliton-antisoliton and the breather solutions but also obtain periodic two-soliton, periodic soliton-antisoliton as well as periodic breather solutions. Besides, we also obtain superposed real and complex (parity-time reversal or) $\mathcal{PT}$-invariant solutions related to the two-soliton, soliton-antisoliton and the breather solutions of the sine-Gordon equation.

In this study, we revisit the subject of optical solitons in non-Hermitian potentials. For the underlying model of the focusing nonlinear Schrödinger equation with a complex localized potential, we offer a classification of such models into four canonical cases. These correspond to (a) $\mathcal{PT}$-symmetric Wadati potentials, (b) $\mathcal{PT}$-symmetric non-Wadati potentials, (c) Non-$\mathcal{PT}$ but Wadati potentials, and (d) complex potentials with neither $\mathcal{PT}$ nor Wadati symmetries. We study the existence and stability of optical solitons across prototypical model variations spanning all four relevant quadrants. We complement such an investigation with a low-dimensional effective description based on a non-conservative variational approximation method. The variational framework is assessed in terms of its ability to represent the structural properties and bifurcations of solutions. {Our results suggest that continuous families of bright solitons persist across sectors (a)--(c). For non-$\mathcal{PT}$-symmetric potentials, small departures from the Wadati limit, corresponding to sector (d), suggest the loss of continuous families of bright-solitons including, more specifically, the possibility of the generic absence of single-humped localized states. The corresponding variational analysis is broadly consistent with these observations. We also highlight the usefulness and limitations for such variational approaches in describing bright solitons in the presence of non-Hermitian potentials.

Dissipative solitons (DSs) provide a prototypical platform for studying nonequilibrium dynamics governed by the interplay between nonlinearity, dissipation, and external driving. In particular, subjected to external potentials, DSs exhibit a rich variety of nonlinear dynamical behaviors. This work investigates DS dynamics in a moving intracavity potential generated by phase modulation whose frequency is detuned from an integer multiple of the cavity repetition rate. Modulation detuning introduces a timescale mismatch between the DS and the moving potential, leading to two distinct dynamical regimes. At large detuning, the DS cannot continuously track the moving potential and exhibits persistent spectral oscillations and temporal meandering, whereas at sufficiently small detuning it enters a synchronized locking state. Furthermore, both the oscillation period and amplitude can be tuned via the modulation detuning and modulation depth. These results reveal how asynchronous driving reshapes DS dynamics and establish a route for controlling their dynamical response in nonlinear optical cavities.

We perform an asymptotic analysis of the biased van der Pol equation $\ddot{x} - \nu\,(1 - x^{2})\,\dot{x} + x = a$, where the dissipation parameter is large $(\nu \gg 1)$ and the bias parameter $a$ is a real number between $-1$ and $1$, corresponding to large-amplitude relaxation oscillations along a stable limit cycle. Using an abridged singular perturbation analysis, the period of relaxation oscillations $T(a,\nu)$ is obtained that is accurate within $0.1\%$ of the numerical results for $\nu \gg 1$.

The Bloch sphere representation, familiar from quantum two-level systems, can also describe classical linear systems whose dynamics are effectively confined to two modes. Here, we experimentally realize this framework in a linear two-mass, three-spring mechanical system by controlling superpositions of its symmetric and antisymmetric eigenmodes. The system is driven from both boundaries at a fixed frequency between the two resonances, so that the steady-state response remains within a two-mode manifold. By independently varying the relative amplitude and phase of the boundary excitations, we generate tunable modal superpositions. Scanning laser vibrometer measurements and frequency-domain analysis are used to extract the complex modal coefficients, which are then normalized and mapped onto Bloch sphere coordinates. This reconstruction reveals planar rotations of the state under phase sweeps and continuous steering between eigenstates under amplitude-ratio tuning. These results provide an experimental validation of Bloch sphere state reconstruction and steady-state geometric state preparation in a minimal linear mass-spring platform, establishing a simple classical testbed for exploring two-mode manifold dynamics.

While classical thin-film hydrodynamics models widely govern macroscopic fluid layers, they fail to capture the molecular-level thermal fluctuations that dictate nanoscale interfacial dynamics. Standard stochastic extensions rely on the long-wave approximation of the continuum fluctuating Navier-Stokes equations; however, this top-down paradigm lacks a formal connection to microscopic particle trajectories and cannot readily accommodate complex, non-equilibrium boundary mechanisms. We resolve this limitation by deriving the stochastic thin-film equation directly from the exact underlying N-particle Hamiltonian dynamics. This is achieved via a systematic, bottom-up coarse-graining framework based on a generalized fluctuating dynamic density-functional theory. Crucially, this first principles formulation offers unparalleled flexibility, enabling the seamless integration of multi-layered interfaces and non-conserved dynamics such as evaporation. For these complex configurations, our framework rigorously yields entirely novel stochastic thin-film equations featuring emergent noise terms that encapsulate microscopic fluctuations missing from classical top-down models.

Active droplets provide a platform for converting microscopic propulsion into macroscopic flow. Previous realizations of bacteria-driven droplet rotation typically rely on nearby solid boundaries, external fields, or dense active nematics. Here, we report autonomous rotation of droplets in a three-dimensional aqueous two-phase system driven by interfacial population of \textit{Pseudomonas aeruginosa}. Combining confocal microscopy with fluid particle dynamics simulations, we show that amphiphilic bacteria accumulate at the dextran--polyethylene glycol interface and preferentially move and orient along the local tangent. Interfacial localization partitions the force-free swimming dipole between the two liquid phases, allowing either phase to experience a finite active torque while the combined system remains torque balanced. The simulated interfacial population is more spatially heterogeneous than in the experiments, emphasizing that both the bacterial distribution and its signed orientational organization can influence the instantaneous torque. Over the accessible size range, the macroscopic angular velocity exhibits an inverse-radius ($R^{-1}$) dependence. We also formulate a theoretical model to rationalize this scaling law, revealing how the macroscopic rotation is governed by collective interfacial swimming and surface coverage. These results identify a fluid-interface-mediated route for converting swimmer activity into macroscopic rotational flow and establish a strategy for harnessing interfacial active matter to regulate droplet dynamics.

In this perspective article, we introduce elasto-plastocapillarity: surface-tension-driven free-surface flows of yield-stress fluids in which capillary stresses compete with yielding and elastic relaxation. We frame the relevant parameter space, and highlight representative problems (drops, bubbles, jets/filaments, thin films, and porous media) that are central to applications ranging from additive manufacturing and coatings to biological flows. We then outline a set of timely open challenges, including surface-tension measurements, breakdown of scale separation near the microstructures, coupled bulk-interface flow experimental diagnosis, interfacial rheology and surface stresses, history dependence, constitutive models and boundary conditions, reduced theoretical models, and the emerging opportunity provided by artificial intelligence and microgravity; aimed at guiding future experiments, theory, and computation.

Under applied forcing, static droplet retention is accompanied by contact angle asymmetry, with unequal apparent contact angles on opposite sides. Yet, the relation between the asymmetry and forcing lacks a common constitutive basis. Here, we show that the asymmetry emerges from minimizing the forcing-dependent free energy. The response of the asymmetry to forcing defines a susceptibility whose zero-forcing value yields a universal constitutive relation between the asymmetry and forcing. The constitutive relation is quantitatively validated across liquids, volumes, and forcing levels.

We examine the linear stability and nonlinear evolution of a heated falling film containing a soluble surfactant and a weakly viscoelastic liquid. The stress response is described by the short-memory Walters model, while surface tension depends on temperature and surface concentration. An Orr--Sommerfeld analysis and its long-wave limit determine how elastic memory and the two Marangoni stresses enter the instability threshold. A five-field weighted-residual model is then derived to describe finite-amplitude disturbances. The bulk and surface transport equations are written with compatible fluxes, which conserve their combined projected surfactant inventory in a periodic domain. The numerical examples show that solutal Marangoni stress suppresses disturbance growth and reduces the amplitude of the nonlinear waves. Thermal Marangoni stress increases the maximum growth rate, although its effect on the width of the unstable wavenumber band is different. Elastic memory changes both the onset and the finite-wavelength response. The nonlinear profiles develop a main hump and capillary ripples, accompanied by variations in bulk concentration, surface concentration, and interfacial temperature. These results describe the competition between thermocapillary forcing, surfactant redistribution and elastic stress within the retained long-wave model. The larger elastic parameters are interpreted as formal predictions of the truncated constitutive equations, rather than as a controlled extension to strongly elastic flow.

Why do bubbles moving through a viscous fluid in a Hele-Shaw cell select a particular velocity, even in the limit of vanishing surface tension? We address this longstanding problem using exact time-dependent solutions for bubble dynamics in a Hele-Shaw channel, including a new class of rational solutions. Our results show that the experimentally observed velocity, twice that of the background flow, emerges as the unique dynamically stable attractor, revealing an intrinsic selection mechanism that does not rely on surface tension.

Particle-filled soft composites generally stiffen as particle loading increases, imposing a trade-off between functionality and compliance. Here, we show that this trade-off can be overcome by designing particles to actively direct gelation rather than act as passive fillers. In a sol-rich elastomer matrix, sol-phase kinetics redirect network formation towards particle-mediated assembly, yielding anomalous softening despite increasing particle content. This response is governed by topological reconfiguration of the load-bearing network during gelation rather than by filler loading alone. A structure-based model captures the composition-dependent onset of this behaviour, and the same response is reproduced across distinct particle systems. The resulting materials combine functionality with softness, energy dissipation, and recoverability under large deformation. These findings establish topology-guided gelation as a general strategy for engineering compliant functional composites for soft robotic actuation, conformal interfaces, and other systems that require both deformability and embedded material functionality.

Synchronization with vibrating boundaries can qualitatively alter the dynamics of confined granular fluids and control the collision-induced transfer of energy to horizontal motion. We develop an Enskog kinetic theory for the active phase of a driven granular monolayer within the framework of the $\Delta$-model, which accounts for the transfer of energy from the vertical to the horizontal degrees of freedom of grains. Synchronization effects are incorporated through a state-dependent effective collision rule governed by the interplay between the local collision frequency and a characteristic synchronization time. A viscous drag force is also included to account for energy dissipation arising from interactions with the confining plates. Within this framework, we characterize the homogeneous active state and use it as the reference state for a Chapman--Enskog expansion. The solution of the Enskog equation to Navier--Stokes order then yields explicit expressions for the shear and bulk viscosities, the thermal conductivity, the diffusive heat coefficient, and the first-order contribution to the cooling rate, consistently accounting for inelasticity, damping, finite-density effects, and synchronization. Event-driven molecular-dynamics simulations show that the theory accurately describes the steady temperature and shear and bulk viscosities over a broad region of the active phase. Close to the discontinuous synchronization-controlled absorbing transition, deviations are mainly attributed to the mean-field coarse-graining of the microscopic synchronization dynamics: fluctuations of the collision-dependent injection amplitude and correlations between synchronization and pre-collisional velocities become increasingly important. These results provide a kinetic description of synchronization-controlled transport and delineate its range of validity near the absorbing transition.

Insect exoskeletons abruptly acquire complex three-dimensional forms during metamorphosis from larva to pupa. This transformation occurs through the unfolding of preformed wrinkle structures inside the larval body under internal pressure. Inspired by this process, we investigate an inverse-origami strategy for fabricating curved surfaces. Whereas conventional origami produces three-dimensional objects by folding a flat sheet, this strategy produces curved surfaces by unfolding preformed wrinkle structures. The central design problem is to derive a wrinkle structure from a prescribed target surface. Our key idea is to regard a wrinkle structure as a unidirectional stretching field, which specifies at each point the stretch produced when the structure unfolds. We first derive such a field from the target surface geometry and then translate it into spatially varying wrinkle directions and spacing, so that the wrinkle structure unfolds into the target. The resulting numerical designs approximate the intrinsic metric of the target surface. We demonstrate the method on multiple target surfaces through numerical construction, mechanical unfolding simulations, and 3D-printed prototypes. This work provides a biologically inspired geometric design principle for encoding prescribed surface shapes in wrinkle structures, as well as a framework for designing and fabricating deployable curved surfaces.

Aqueous dispersions of hydrophobic carbon black (CB) particles can be stabilized by carboxymethylcellulose (CMC), forming CB-CMC hydrogels whose microstructure is controlled by the relative CB-to-polymer content. At low CMC content, CB particles form a percolated, electrically conductive network, whereas at higher polymer content, CB particles act as isolated physical crosslinkers within an electrically insulating polymer matrix [see Legrand \textit{et al.}, Macromolecules 56, 2298-2308 (2023)]. Combining rheology and electrical impedance spectroscopy, we show that these two regimes exhibit markedly different aging dynamics. Conductive hydrogels exhibit logarithmic elastic recovery associated with a percolated CB network, whereas insulating hydrogels exhibit a combination of logarithmic and power-law stiffening, accompanied by dielectric polarization associated with confined ionic motion. The insulating hydrogels further exhibit a time-aging superposition principle, as their viscoelastic spectra measured in a time-resolved fashion can collapse onto a single master curve. Under steady shear, the viscoelastic response measured perpendicular to the flow also obeys a time--shear-rate superposition principle. Remarkably, the scaling between the shift factors under shear is reminiscent of critical-gel behavior, unlike that observed during aging at rest. Finally, time-resolved rheo-USAXS measurements performed during shear-rate cycles reveal structural rearrangements of CB particles and clusters that correlate with rheological hysteresis. These results provide a microstructural basis for understanding the nonlinear rheology of insulating CB-CMC hydrogels and establish generalized superposition principles as a unifying framework for their aging and flow behavior.

Buffer chemistry modulates colloidal impedance critically for label-free biosensing and electrokinetic diagnostics, yet classical models neglect buffer-specific interactions. We studied carboxylated polystyrene (PS) microspheres in conductivity-matched zwitterionic 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES) and phosphate-buffered saline (PBS). Two concentration-dependent regimes emerged: oscillatory at ultradilute concentrations (<0.02 w/v%; Region 1) and monotonic at higher concentrations (Region 2). In Region 1, HEPES at pH 6.9 (approximately 80% zwitterionic) produced the largest deviation of delta Z from the O'Brien prediction. The conductivity increment was opposite in sign to classical expectation. We attribute this to zwitterion-driven interfacial ordering that enhances local conductivity and promotes self-limiting particle clustering. Dynamic light scattering detected cluster formation at 0.008 w/v%, well below aggregation thresholds. Changing pH from 6.9 to 8.1 strongly altered impedance amplitude; DLS profiles remained invariant. This indicates zwitterions modulate electrochemical polarization, not physical assembly. Molecular dynamics simulations showed pH-dependent HEPES organization at the PS surface. At pH 6.9, interfacial charge- and number-density profiles showed comparable oscillatory periodicity. At pH 8.1, anionic HEPES produced a more diffuse profile with increased Na+ compensation. These results support interfacial ordering as a contributor to enhanced conductivity but do not establish discrete layers or registry. Zeta potentials distinguished stable HEPES interfaces from PBS, where magnitude increased with ionic strength, contrary to classical screening theory. These nonlinear signatures and mesoscale organization underscore the role of buffer selection in high-sensitivity impedance biosensing.

Micro- and nanoswimmers diffusing in a fluid flow confined to microchannels are often described by overdamped active Brownian particle dynamics, in which viscous effects dominate and inertia is negligible. Here, we investigate the diffusive behavior of chiral self-propelled particles in a two-dimensional microchannel with oscillatory Poiseuille flow. Using numerical simulations, we show that the effective diffusion coefficient strongly depends on the oscillation frequency, flow strength, intrinsic angular velocity, and rotational diffusion rate. Interestingly, the effective diffusion coefficient can oscillate with oscillation frequency and flow strength, exhibiting distinct maxima and minima. The enhanced diffusion peaks arise from resonant diffusion associated with the matching between the flow oscillation time scale and the intrinsic characteristic diffusion time scale. Moreover, we identify an additional vorticity matching mechanism, leading to alternating channel wall accumulation of particles during successive flow half-cycles. Additionally, chiral particles strongly amplify the resonant diffusion, producing diffusion enhancements of several orders of magnitude compared to nonchiral particles. The results of this study could have implications for controlling the diffusion of self-propelled particles in microfluidic channels using time-dependent flow.

Many industries rely on models of colloidal gelation and phase behavior to predict how processing equipment will handle new product formulations. In colloidal systems with nearly uniform particle size it is possible to predict the formation of a gel from only three state variables; however, the extension of this model to bimodal and multimodal systems is not well described. Here we present a systematic simulation study of the attractive bimodal depletion gel phase diagram. For these systems, we find that gelation is highly dependent on total volume fraction, attraction conditions, and bimodal composition. Attraction and composition can be effectively collapsed into a single parameter using the contact-weighted second virial coefficient. This successfully projects the bimodal phase diagram onto the established monodisperse phase diagram, including accurately describing most bulk assembly properties; however, the underlying network structure of these gels remains highly dependent on the details of bimodal composition and attraction.

Enabled by their controllable optical anisotropy, liquid crystals form a cornerstone of linear optical and display technologies. Bringing the versatile platform into the nonlinear regime, we explore its nonlinear optical anisotropy by high-order harmonic generation spectroscopy. Through a comprehensive study targeting gas, liquid, nematic, and crystalline phases, we present a semi-empirical tight-binding approach that provides insight into the intermolecular character of ultrafast light-driven electron dynamics across soft-matter mesophases. We demonstrate how intermolecular electron hybridization enables spectroscopic access to structural properties, such as the nematic director and order parameter. Outlining such foundational mechanisms opens avenues towards nonlinear liquid crystal devices and ultrafast soft-matter spectroscopies.

The stress tensor resolved in wavevector $\qvec$ and time $t$, $\sigma_{\alpha\beta}(\qvec,t)$, gives access to the elastic moduli of amorphous solids as a function of the probed length scale, and to the long-range stress correlations that distinguish an amorphous solid from a liquid. Its evaluation requires the contribution of every interacting pair and therefore an interface to the force loop of the molecular dynamics code. In the current work, we present: i) an optimized implementation of the LAMMPS~\cite{lammps} module for calculating $\sigma_{\alpha\beta}(\qvec,t)$, in which trigonometric functions are calculated only for the basic wavevectors and, in addition, all the relevant wavevectors are supplied as an explicit list rather than generated as a full grid, so that only the wavevectors of interest are computed and stored, and ii) a validation protocol for the code illustrated for a two-dimensional polydisperse Lennard-Jones (2DpLJ) glass-forming liquid. Based on these technical achievements we elucidated how the affine moduli for the 2DpLJ model depend on the norm $q$ of the wavevector. In particular, we demonstrate that the longitudinal affine modulus shows a minimum near $q_\text{max}$ corresponding to the main peak of the structure factor. Our data also point to the peaks in the $q$-dependencies of vibrational frequencies well below $q_\text{max}$ for both transverse and longitudinal modes. The potential relevance of this feature to the ``boson peak'' is discussed as well.

The Discrete Element Method (DEM) is an indispensable tool for modeling and understanding the basic mechanical behaviors of (dry) granular media, a class of disordered material systems of significant interest to multiple scientific domains from (geo-)physics to (chemical) engineering. At the core of all present DEM frameworks is a phenomenological friction law--commonly chosen to be of the Amontons-Coulomb type--that models the frictional interaction among constituent grains. Here, inspired by research in the tribology community, we present an alternative, fundamentally different framework, termed surface-roughness-based DEM (SR-DEM), in which contact friction is handled in a more physics-based manner. In this framework, instead of using a friction law, we explicitly resolve the surface topography of each grain and let friction emerge from collective frictionless interactions of surface asperities. In essence, we trade phenomenology for physics at the cost of an increased computational demand. To mitigate the cost, we introduce an FE$^2$-like algorithm and a feature-wise linear modulation (FiLM)-based neural network surrogate, both of which are parallelized on GPU to accelerate contact computation. Crucially, using this framework in 2D, we (1) demonstrate the possibility of recovering a two-body-based Amontons-Coulomb-type friction behavior using a simple representation of surface topography, and (2) identify many-body-based frictional behaviors--more specifically, the angle of repose values--that cannot always be captured by current DEM frameworks under the same level of model complexity. We conclude by discussing future directions for SR-DEM, as well as exciting new opportunities it could unlock for a wide range of emerging applications, including (designing) suspension rheology and metamaterial mechanics.

We employ reinforcement learning algorithms to develop control strategies for manipulating synthetic jets on an elliptical cylinder, targeting robust flow control across varying aspect ratios (Ar). Our results show that for high aspect ratios (Ar = 1 and 0.75), the learned strategies effectively mitigate vortex shedding, achieving drag reductions of 13.4% and 20.1%, respectively. As the Ar decreases, more complex wake dynamics challenge flow control. For Ar = 0.5 and 0.25, drag reductions of 26.88% and 30.37% are achieved, though vortex suppression becomes increasingly difficult. For extremely slender cylinders (Ar = 0.1), we enhance control performance by enriching dynamic feature representation and using Kalman filtering for state estimation. Unlike conventional methods, our approach successfully achieves complete vortex shedding suppression, a maximum drag reduction of 32.2%, and eliminates periodic oscillations, stabilizing the flow. These results demonstrate the efficacy of state-enhanced RL in controlling highly slender geometries.

This study enhances the performance of flow control across various synthetic jet configurations by improving deep reinforcement learning techniques. The training results based on the foundational deep reinforcement learning framework indicate that as the Reynolds number increases, the effectiveness of synthetic jet control becomes increasingly sensitive to the position of the jet. When synthetic jets are positioned near the flow separation region, the control strategy consistently exhibits excellent performance. However, when synthetic jets are located farther from the separation region, the flow control performance diminishes, and the consumption of external energy increases. By enhancing dynamic state features and reshaping the reward function, we significantly improve control performance across various Reynolds numbers and synthetic jet positions. With the optimized framework, we achieve significant drag reduction effects ranging from 8% to 34% within the Reynolds number range of 100 to 400. The flow control strategy is capable of simultaneously achieving multiple control objectives, including reducing drag, suppressing lift, eliminating vortex shedding, and decreasing energy consumption. These findings highlight the potential of optimizing deep reinforcement learning frameworks to achieve more adaptive flow control strategies for various flow scenarios.

Multi-fin bioinspired propulsion systems have seen a rise in interest recently due to natural occurrence in animal systems and emerging technology. These systems make use of fin-fin interaction to improve swimming performance where the downstream fins use the wake of the upstream fin to their benefit. While 2-fin systems are relatively well understood, it is unclear how performance is impacted as the number of fins grow. Using an immersed boundary method solver, we model the multi-fin systems to analyze performance across several key parameters: spacing between fins, phase offset, freestream velocity, and number of fins per system. We characterize performance via system thrust and propulsive efficiency. We show that a dimensionless phase parameter incorporating inter-fin spacing, oscillation frequency, and freestream velocity approximately collapses the thrust response across different operating conditions, providing a useful predictor of favorable wake-interaction timing. As more fins are added ($>2$), they can further enhance the group thrust and efficiency without modifying the performance of the fins upstream. Through optimization, we found this enhancement to peak with a 3-4 fin system, after which performance diminishes with additional fins due to the growing wake complexity. Optimal conditions led to boosts in thrust or efficiency of 30% and 20%, respectively. From this study, we show that there are performance gains realized in larger fin systems (though with diminishing returns) and optimizing system performance of multi-fin systems can be done sequentially to save computational resources.

The Stochastic Transport in Upper Ocean Dynamics project introduced a new paradigm for representing uncertainty in geophysical fluid dynamics through stochastic transport models calibrated from data. This paper provides a synthesis of the principal theoretical and data assimilation developments achieved as part of the project. The central theme of the paper is the transformation of stochastic transport models from a modelling paradigm into a mathematically rigorous framework equipped with analytical, variational, calibration and Bayesian data assimilation methodologies suitable for geophysical fluid dynamics. We describe the development of the theory of stochastic transport equations, including well-posedness, regularity and approximation results, together with their geometric foundations based on stochastic variational principles, rough paths and fractional transport models. We further review methodologies for calibrating stochastic transport structures from observational and high-resolution simulation data, ranging from reduced-order stochastic models to modern generative approaches. Finally, we discuss Bayesian inference and high-dimensional data assimilation techniques developed for stochastic transport models, including particle filter methodologies and machine learning uncertainty quantification. Taken together, these developments establish a coherent framework linking stochastic transport modelling, rigorous analysis, calibration and Bayesian inference, thereby providing a foundation for uncertainty quantification and forecasting in geophysical fluid dynamics.

Developing interpretable full-profile relations for mean velocity and effective mixing length remains challenging because the near-wall, overlap, and outer regions exhibit distinct scaling behaviors. In this paper, physics-constrained symbolic regression is used to construct analytical relations for incompressible zero-pressure-gradient turbulent boundary layers. Classical logarithmic and Prandtl mixing-length scalings provide the starting points, while the regression identifies near-wall transition functions under asymptotic constraints and Reynolds-number-dependent outer corrections. The resulting expressions retain the prescribed leading-order near-wall exponents, reproduce the principal overlap-region behavior, and describe finite-Reynolds-number variations. The mean-velocity relation agrees well with 35 profiles from direct numerical simulations, large-eddy simulations, and experiments spanning friction Reynolds numbers from 252 to 72,526, while the mixing-length relation captures the principal trends in the simulation-derived data. These results illustrate how physical scaling knowledge can guide symbolic regression toward compact, interpretable analytical descriptions of canonical wall turbulence.

Godin (\textit{J. Fluid Mech.}, vol. 767, 2015, pp. 52--64) showed that compressible fluids in a uniform gravity field support finite-amplitude incompressible wave motions, in which every parcel conserves pressure and density, and constructed exact Gerstner-type surface and edge waves, possibly carried by currents. Using the short-wavelength instability method for compressible flows, we show that these waves are linearly unstable above a critical steepness. The stability of each fluid level reduces to a Floquet problem depending on two parameters: the steepness $\mathfrak{e}=e^{ka_2}$ and $\nu^2=(1-\mathfrak{e}^2)\nu_0^2$, where $\nu_0^2=\cos^2\alpha\,N_0^2/\Omega^2$, $N_0$ is the buoyancy frequency of the hydrostatic reference state, $\alpha$ the inclination of the plane of motion and $\Omega=(gk\cos\alpha)^{1/2}$ the intrinsic orbital frequency. In an isentropic fluid, a level is unstable if $\mathfrak{e}>1/3$, recovering Leblanc's threshold for Gerstner waves (\textit{J. Fluid Mech.}, vol. 506, 2004, pp. 245--254) and extending it to compressible surface and edge waves; weak stable stratification lowers the threshold to $\frac13-\frac{32}{81}\nu_0^2+O(\nu_0^4)$. In an isothermal atmosphere, $\nu_0^2=\kappa\cos\alpha/(kH)$, where $H$ is the pressure scale height. For horizontal wavelengths near $5.5\,H/\cos\alpha$, principal subharmonic resonance makes the critical steepness vanish. For the fast airglow wave observed by Hecht et al. (\textit{J. Geophys. Res.}, vol. 107, 2002, D20, 4444), which Godin interpreted with his solution, the lidar temperature places the layer in which this interpretation is consistent on this resonance, where the critical steepness is typically 0.1 instead of $1/3$. Instability is confined to a layer beneath the free surface of surface waves and to a wedge at the shoreline of edge waves.

Numerical stability has long constrained the application of lattice Boltzmann methods to high-Reynolds-number and high-Mach-number flows. Improving the stability and accuracy of collision models has therefore remained a major challenge for nearly three decades. Regularized collision models constitute an important class of lattice Boltzmann collision models and have recently undergone substantial theoretical development. They are now widely used for high-Reynolds-number turbulence, high-Mach-number compressible flow and aeroacoustics. This article systematically reviews their development and establishes a unified theoretical framework that clarifies the relationships among the principal formulations. The analysis identifies the underlying principle of the regularized multiple-relaxation collision model: higher-order kinetic moments that cannot be represented by the discrete lattice are rapidly relaxed in a coordinate-independent, self-similar moment space, thereby preventing spurious modes from contaminating the hydrodynamic equations.

Generative AI offers new approaches to turbulence problems in which incomplete observations or unresolved d.o.f. admit multiple physically plausible solutions. Potential applications include stochastic closures, super-resolution, data assimilation, uncertainty quantification, and the generation of Eulerian and Lagrangian flow ensembles. However, turbulence is not a conventional image-generation problem. Its multiscale dynamics, intermittency, extreme events, rough velocity fields and intrinsically stochastic transport make visual realism, pointwise error, and low-order spectral agreement insufficient measures of physical fidelity. We examine where generative AI provide novel capabilities with emphasis on diffusion models, score-based methods, and related probability-transport formulations. We discuss their use in unconditional generation, probabilistic reconstruction, reduced-order modeling, temporal evolution, and mesh-free representations. We argue that validation must address turbulence properties: energy transfer, structure functions, anomalous scaling, pdf tails, coherent structures, conservation laws, temporal consistency, ensemble diversity and generalization. Finally, we discuss potential limitations in validation, baseline, data availability and reproducibility, and the need for a benchmark ecosystem combining open data, standardized challenges, hidden tests, physics-aware metrics, and documented failures. This paper serves as a bridge between two communities. For AI practitioners, we provide a fair and accessible introduction to turbulence, essential for appreciating the challenges posed by the field and for assessing the physical relevance of generative models. For turbulent practitioners, we provide an introduction to the key technological aspects of Generative AI, clarifying what these tools actually do, and where their potential and current limitations lie.

The classical formulation of Gill's theorem establishing the linear stability of the buoyant flow in a vertical porous channel subject to transverse diffusion and bounded by impermeable walls is here reconsidered from the perspective of anomalous mass diffusion. Anomalous diffusion is a physical effect implying a more general formulation of the governing equations of mass transfer either in a fluid or in a fluid-saturated porous medium. Anomalous diffusion is mathematically modelled via a diffusion equation with a time-dependent mass diffusivity. In this study, the stationary and parallel buoyant flow in a vertical porous layer saturated by a fluid is investigated. The implications of the anomalous diffusion model for the proof that such a flow is always linearly stable are analysed.

Classical gravity--capillary theory locates the restoring-force crossover, but the wave amplitudes and depths for which energy losses remain measurable depend on the constitutive response and on where viscous dissipation occurs. We develop a weak-loss mechanical-energy model for small-steepness progressive surface waves in memoryless power--law liquids. The full invariant of the leading inviscid strain field yields the deep-water bulk law $\dd A/\dd t=-C_tA^n$, with $C_t=4Kk^2(2k\Omega)^{n-1}/[(n+1)\rho]$, and the corresponding spatial law $\dd A/\dd x=-(C_t/v_g)A^n$. For finite depth we calculate bulk dissipation using a phase- and depth-resolved quadrature $J_n(kh)$ and formulate a separate oscillatory power--law bottom layer. We solve the latter numerically in periodic state, obtaining dimensionless integrated wall losses $I_{0.6}\simeq0.5432$ and $I_{1.4}\simeq0.4708$ and recovering the exact Newtonian benchmark $I_1=1/2$. These values make it possible to evaluate conditional finite-depth bulk--wall dominance boundaries rather than only their amplitude exponents. The theory is organized into restoring-force, attenuation, local propagation-length, and dissipation-mechanism regime maps; at fixed wave steepness it additionally predicts a capillary-side maximum of normalized temporal damping for $0

Reduced-order models simplify fluid simulation by representing complex flows with a small number of spatial modes. Building on Laplacian Eigenfluids, we introduce Neural Eigenfluid Bases (NEB), a neural representation whose basis functions can be evaluated anywhere in space. We enforce incompressibility and impermeable boundaries directly through differential lifts and potential boundary conditions. Geometry-local orthogonalization and Rayleigh minimization then learn an ordered basis. We connect learning in potential and velocity spaces, and derive a spectral-variance relation explaining why these objectives weight approximate modes differently, even though their exact positive spectra agree. Gauge fixing reduces the number of spatial derivatives needed for potential learning, while a Dirichlet energy loss learns independent circulation fields around obstacles. With 1024 modes, both objectives keep velocity errors below 1% in periodic vortex merger. For random flows around obstacles, potential-based learning captures more initial energy and gives lower final errors than numerical Laplacian bases of the same size. The reduced state is about a thousand times smaller than the full reference model. Three-dimensional tests separate spatial reconstruction errors from errors in coefficient evolution. Precomputed Galerkin operators allow millisecond-scale updates when the same basis is reused across simulations. This provides a physically constrained basis for continuous flow reconstruction and efficient reduced-order simulation.

We analyze scale-by-scale budgets of velocity and buoyancy second-order structure functions using Large Eddy Simulation of the BOMEX trade-wind cumulus layer. The simulation utilizes a $10\,\mathrm{m}$ grid resolution under the anelastic approximation, incorporating moist thermodynamics to capture phase changes. The analysis of derived turbulence kinetic energy (TKE) and turbulence potential energy (TPE) budgets reveals four regions of distinct turbulence dynamics. For three of these regions, approximate balances holding over wide range of length scales are identified, highlighting the importance of interspace and pressure transport. Above the lifting condensation level ($\approx 800\,\mathrm{m}$), phase changes introduce forcing across all resolved scales, leading to an inverse TPE cascade spanning all scales. The TKE, inter-scale transfer is inverse above the vertical velocity integral length scale but below the horizontal velocity scale. In the upper cloud layer ($>1400\,\mathrm{m}$), forward inter-scale transfers are recovered despite ongoing phase changes. A phenomenological interpretation of these features, referring to the different formation stages of convective updrafts, is also proposed. Finally, 1D horizontal subsamples from the simulation show good agreement with recent airborne measurements, validating the numerical framework and confirming the departure of moist convective turbulence from standard energy cascade models.

A frequency-domain response analysis of a wind turbine rotor requires the complete hub-load spectrum, but the customary scalar thrust and torque spectra retain neither the four in-plane components nor the coupling between them. This paper derives the full six-degree-of-freedom (6-DOF) rotor-load cross-spectral-density (CSD) matrix from the IEC Kaimal turbulence model. By decoupling the spatial order of inflow coherence from the temporal Doppler shift, the formulation introduces a two-index rotational-sampling kernel. Rotor symmetry and azimuthal averaging constrain the observed Doppler carrier strictly to blade-passing harmonics $pBf_{\mathrm{rot}}$, while the azimuthal aerodynamic transfer shifts the spatial coherence order to $pB+s$. A convergence study of the retained azimuthal order $s$ shows that $\lvert s\rvert\le4$ suffices, the assembled CSD then deviating from the full-band result by less than $10^{-5}$ in relative norm. The formulation is compared with OpenFAST simulations of a rigid floating wind turbine over nine wind speeds: the six auto-spectral densities agree closely below 1~Hz, and the present theory over-predicts the spectra near the 6P and 9P rotational harmonics.

We propose an improved version of the $k$-$\omega$ shear-stress transport Reynolds-averaged Navier-Stokes model that supersedes our prior work (Griffin et al. 2024 J. Turb.) with an updated pressure-gradient sensor that generalizes well across geometries and to laminar, transitional, and turbulent flows alike. The model is based on a composite pressure gradient criterion that uses the solution of an intermittency transport equation to synthesize the separation criteria of the Falkner-Skan theory for laminar flows and the continuously critical theory for turbulent flows. The proposed model is applied to various airfoils including the thick airfoils representative of wind turbine applications (DU00-w-212, S809 and S814) and thinner airfoils used in aerospace applications [NACA23012 and NLF(1)-0416]. For all airfoils, the proposed model is found to preserve or improve the predictions of the baseline model for both fully turbulent and transitional airfoils as demonstrated with results for the lift and drag coefficients. The model is also found to improve the prediction of separation on the NREL Phase VI rotor in a preliminary study, suggesting that the model will generalize to other complex three-dimensional flows.

Thermal-fluid field distributions underpin the analysis and operation of energy infrastructure, from nuclear-reactor cooling channels to industrial heat exchangers, but resolving these distributions through computational fluid dynamics requires prohibitively large simulation ensembles. Their complex geometries also demand unstructured meshes that are poorly accommodated by generative models developed for regular grids. Here we introduce FlowMesh, a generative framework that combines permutation-invariant mesh encoding with deterministic latent flow matching and an l1 penalty on the learned transport velocity. FlowMesh generates full-field realizations directly on fixed unstructured meshes without auxiliary grid interpolation or a stochastic denoising chain. Across lid-driven-cavity, pressurized-water-reactor subchannel and heat-exchanger datasets, evaluated over six matched training seeds, FlowMesh achieves macro-averaged probability-density-function coverage of 91.7%-97.0%, exceeding an architecture-controlled latent diffusion model by $11.6$--$45.4$ percentage points. Latent-velocity regularization increases coverage by $3.8$ percentage points for reactor flows and 1.1 points for heat-exchanger flows, while reducing temperature-field Kullback--Leibler divergence by 1.7-2.4-fold. Each full-field realization requires 1.23 \pm 0.15 s, providing a 585--1902-fold wall-clock acceleration over computational fluid dynamics. FlowMesh therefore makes large-scale generative characterization of thermal-fluid states computationally feasible, providing a foundation for data-driven analysis and digital-twin development in fixed-geometry energy systems.

Direct Numerical Simulation (DNS) of the deterministic Navier-Stokes (NS) equations is widely used to provide benchmark solutions of turbulent flow, but its accuracy and reliability have not been rigorously inspected from a mathematical viewpoint. Here we prove a spatial symmetry invariance theorem (SSIT) of three-dimensional NS equations whereby an exact solution of deterministic NS equations under periodic boundary conditions maintains the same spatial symmetry as its symmetric initial flow, forever. SSIT provides an absolute benchmark test for computational fluid dynamics (CFD). It is shown herein that traditional DNS of NS turbulence quickly violates SSIT, revealing that the spatiotemporal trajectory of NS turbulence predicted by DNS soon becomes badly polluted by numerical noise. Importantly, it is found that even the statistical results of DNS might be unstable, i.e., exhibit sensitivity dependence on the initial flow conditions. In other words, the loss of spatial symmetry in traditional DNS of NS turbulence is not a physical instability but instead a numerical artifact caused by the chaotic nature of the flow. Using the SSIT, it is straightforward to deduce several key properties of NS turbulence, including `ultra-chaos', the so-called `noise-expansion cascade', `permanent memory of symmetric initial flow conditions', and so on. Note that permanent memory of symmetric initial flow conditions suggests that NS turbulence governed by deterministic NS equations subject to symmetric initial flow should have no `mixing', corresponding to non-ergodicity, although ergodicity is one of the most fundamental assumptions of turbulence theory.

The interaction of strong ($a_0>1$), superluminal X-mode electromagnetic waves with magnetized pair plasma falls into two regimes set by $\varepsilon_{\rm B}\equiv a_0\omega_{\rm B}/\omega_0$, the ratio of the wave strength parameter to its frequency, in units of cyclotron frequency. For $\varepsilon_{\rm B}<1$ the wave propagates until induced scattering disrupts it. Using analytical theory and kinetic simulations, we show that the background magnetic field introduces a restoring frequency $\Omega_{\rm B}$ to scattering; when $\Omega_{\rm B}$ exceeds the scattering rate, the unattenuated length grows from $\simeq\varepsilon_{\rm p}^{-2/3}$ to $\simeq\varepsilon_{\rm B}^{1/2}/\varepsilon_{\rm p}$ wavelengths ($\varepsilon_{\rm p}\equiv a_0\omega_{\rm p}/\omega_0$; $\omega_{\rm p}$ is the plasma frequency). When $a_0^2>\varepsilon_{\rm B}>1$, the plasma current is nonlinear, and the wave is damped while riding a motional electric field, so one half-cycle appears attenuated. This framework has implications for the duration of fast radio bursts and whether they can escape their surroundings.

We investigate the three-dimensional unforced Navier-Stokes equations through the interaction between spatial analyticity and the geometric sparseness of regions of intense fluid activity (i.e., regions where the fluid's motion varies sharply). Interpreting higher-order derivative ratios as turbulence scales, we introduce time-weighted bridge inequalities that quantify the relationship between lower- and higher-order derivative norms. The time weights give the derivative ratios greater flexibility while ensuring that the resulting lower bound on the radius of analyticity dominates the sparseness scale of the super-level sets, indicating that the flow has entered the dissipation regime. Combining this scale comparison with a harmonic-measure maximum principle on one-dimensional sparse sets yields a contraction in the relevant derivative norm, thereby excluding a class of strongly turbulent blow-up scenarios. Consequently, the strong solution extends analytically beyond the candidate blow-up time.

Hyperbolic partial differential equations (PDEs) transport information at finite speed along characteristics, often producing shocks and discontinuities that are challenging to capture numerically. Graph neural networks (GNNs) offer learned update rules, but neighbor aggregation alone does not tell a GNN how far information must travel and along which edge. As a result, when a GNN model takes a time step larger than what was used in training, shock fronts smear and oscillations grow. In this work, we ask whether making the scale of transport explicit as an edge-local Courant-Friedrichs-Lewy (CFL) signal can enhance GNNs' ability to model hyperbolic PDEs. Holding the architecture fixed, we vary only the information given to each edge, from a raw edge form to forms that progressively expose the edge-local transport interaction through direction, length, and wave speed. Because all of these are computed from the same ingredients, what changes is not the amount of information but its form. The results show a consistent pattern, in which feature count is not the limiting factor, and appending CFL directly to a raw edge form produces almost no benefit. The CFL conditioning proves most effective when the edge information already exposes the transport interaction, reducing final-step error by 10.4-14.4%, and the improvement widens as the step size grows larger. Notably, this improvement arises not from smearing the solution but from suppressing oscillations near shocks. These results point to a specific design principle that CFL conditioning is most effective when the edge representation already separates the direction of interaction from spatial scale, so that the CFL value has a well-defined quantity to modulate.

The conditions governing the existence and evolution of trapped sausage waves in photospheric magnetic pores are investigated, with particular emphasis on the limitations of analytical cut-off criteria and the role of viscous dissipation. A pore is modelled as a cylindrical magnetic flux tube with smoothly varying radial profiles of magnetic field and density, subject to the constraint that its temperature is lower than that of the surrounding atmosphere. For finite plasma-$\beta$, the linearised equations governing sausage-mode perturbations are derived, and an initial-value problem is solved numerically to obtain the full spatio-temporal evolution of the waves. The applicability of the analytical cut-off relation derived for a flux tube with step-function equilibrium profiles is examined, revealing that its predictions depend on the equilibrium parameters. The simulations reveal distinct wave behaviours across different parameter regimes, including the simultaneous excitation of trapped fast and slow sausage waves for a representative photospheric parameter set. Viscous damping is further investigated through the temporal evolution of the wave energy. Energy dissipation increases with decreasing viscous Reynolds number, increasing longitudinal wavenumber, and increasing radial magnetic-field contrast. These trends are consistent with enhanced viscous damping associated with increasingly fine spatial gradients generated through phase mixing. The findings highlight the importance of radial equilibrium structure in assessing sausage-wave trapping and demonstrate the sensitivity of wave-energy dissipation to the physical parameters of photospheric magnetic pores.

This article revisits entropy and related magnitudes (entropy density, effective measure complexity, and informational distance) for the analysis of sequential data. We present their mathematical foundations within information theory and ergodic theory, establishing connections between probabilistic Shannon entropy and algorithmic Kolmogorov complexity. A central result, Zivs theorem, demonstrates the asymptotic equivalence between the normalised number of distinct words and entropy density, providing the theoretical basis for estimation via Lempel-Ziv factorisation. We examine the convergence properties of these magnitudes and introduce estimation procedures for finite sequences, including a method for the effective measure complexity and the transfer entropy rate. An open-source software library implementing parallel algorithms for efficient Lempel-Ziv factorisation is presented. The practical utility of the framework is illustrated through three case studies: functional brain connectivity analysis from fMRI data, characterisation of spatiotemporal dynamics in coupled nonlinear oscillators, and electrocardiogram-based classification of atrial fibrillation, demonstrating how entropic measures capture meaningful structural and dynamical properties across diverse domains.

Forecast-error growth in multiscale chaotic systems involves both advancement toward saturation and evolution of the error's scale distribution. We introduce Logit--Koopman coordinates to describe these processes together. For error energies normalized by fixed reference levels, logistic growth has exponential odds as exact Koopman eigenfunctions and affine logits as growth clocks, with an explicit inverse to error energy. Several band clocks define a longitudinal coordinate for shared advancement and transverse coordinates for departures from the reference band-growth relation. An exact transformed error-energy budget resolves production, conservative redistribution, interlevel exchange and dissipation into contributions to clock speed and transverse motion; an equivalent reference-law decomposition exposes the effect of ensemble heterogeneity. In uncoupled and coupled three-level Lorenz-96 regimes, 200 forecasts per regime exhibit nearly affine band-mean logits ($R^2=0.965$--$0.993$), alongside distinct timing, residual and launch-anomaly correlations. Recovered error fields reveal net slow-to-fast interlevel error-energy exchange in the coupled control, which removes slow-level error energy at a nearly steady relative rate near 1.2 per model time unit. Fast-only initial perturbations nevertheless seed slow-level errors immediately; after this transient, their mean approximately follows the control growth curve delayed by about 0.7 model time units. The slower middle-band clock reflects the full physical balance and an error deficit maintained at the dominant wavenumbers, rather than the strongest transformed interlevel sink. The contribution is a prescribed reference geometry in which growth timing, relative scale-evolution and signed physical exchange become separately measurable.

Out-of-time-ordered correlators (OTOCs) measure the scrambling of information and are a powerful diagnostic of chaos. In chaotic quantum systems with a classical analog, their relaxation towards equilibrium is dictated by the classical Ruelle--Pollicott resonances. We investigate higher-order OTOCs in quantum maps, prototypical one-body systems with a classical limit showing all the essential features of chaotic dynamics. We demonstrate numerically that in the intermediate-time regime they decay exponentially at a rate that depends only on the parity of the order: odd-order OTOCs decay at the same rate as classical correlations, given by the leading Ruelle--Pollicott resonance, and even-order ones at twice that rate. Both are far slower than the naive expectation, under which the rate would grow in proportion to the order. We then mimic the effect of an environment by defining a coarse-grained superoperator whose effect is to introduce decoherence into the system, and find that the expected proportionality between rate and order is thereby restored. Finally, we show that at long times each higher-order OTOC becomes dominated by a single free cumulant, whose saturation value falls off inversely with the dimension of the Hilbert space, signalling the emergence of asymptotic freeness and highlighting the relevance of free probability theory as a framework for the study of quantum chaos.

Predicting dynamics across bifurcations by extrapolating trained models is crucial in diverse fields of physics. Generalized synchronization provides a framework for understanding dynamical reconstruction by neural networks, especially in the context of reservoir computing. Building on this framework, we derive a formula combining pretrained readouts to reconstruct unseen chaotic dynamics. Using classical Lagrange interpolation theory, we derive rigorous bounds on readout errors and conjugacy residuals. Numerical examples demonstrate accurate prediction of chaotic dynamics across bifurcations.

Amrita Pritam (1919-2005) was a prominent writer of modern Indian literature, particularly in Punjabi and Hindi. Her literary-biographical context provides a setting for exploring memory, longing, companionship, and emotional regulation through simple dynamical models. This study develops three single-state ordinary differential equation models centred on two important relational references in her life: Sahir Ludhianvi, associated with memory, absence, recollection, and longing, and Imroz, associated with companionship, care, continuity, and support. The first model describes Sahir-related longing through memory-driven excitation and natural emotional decay (fading); the second models Imroz-related companionship through nonlinear stabilisation around a preferred emotional state; and the third unifies both influences within a single-state framework. Analytical solutions, equilibrium conditions, local stability analysis, and numerical simulations are used to examine emotional-state decay and persistence, convergence to stable equilibria, and threshold effects on system behaviour. The results indicate that memory-related reinforcement may sustain the modelled emotional state under suitable stimulus conditions, whereas Imroz-related companionship may drive the system towards a stable upper equilibrium when initial conditions lie within the admissible range. The unified model illustrates how memory-driven longing and companionship-driven stabilisation associated with Sahir and Imroz can jointly shape a modelled emotional trajectory. This study is conceptual and mathematical, not empirical or psychological. It neither measures private emotions of Amrita Pritam nor estimates parameters from biographical data. Instead, it introduces a simple nonlinear framework for exploring memory, fading, companionship, equilibrium, and threshold effects in a literary-biographical context.

Understanding how complex networks respond to perturbations is key to uncovering their functional organization. We show that, for a maximum-entropy perturbation prior, standard diffusion cannot increase response entropy, a measure of the diversity of the system's response. To overcome this limitation, we develop a density-matrix-based information thermodynamics of perturbation responses along arbitrary dynamical trajectories. We show that this framework is grounded in an information-theoretic principle of least dissipation and introduces a generalized free energy that quantifies deviations from an instantaneous diffusive reference. We then illustrate the formalism using nonlinear complex networks, revealing regimes of enhanced response diversity that cannot be captured by standard diffusive descriptions.

Coherent sets-regions of phase space that resist mixing-organize transport in stochastic dynamical systems and are encoded in the leading singular functions of the stochastic Koopman operator. These are typically computed numerically and globally; a local, analytic theory near a fixed point has been missing, although fixed points and the transitions between them organize the flow. We supply the local theory for a saddle, the transition state through which probability flows between basins. Naively the construction fails-probability escapes along unstable directions, the invariant measure is non-normalizable, the singular functions leave $L^2$, and singular values exceed one. We show that conditioning on non-escape (a Doob's $h$-transform) repairs this; that the required $h$ is the unique stabilizing solution of an algebraic Riccati equation; and that the resulting slow modes decay at the escape rate along the unstable manifold. We obtain these modes in closed form-products of Hermite polynomials in canonical coordinates times the $h$-function-and use their unitary structure to derive a data-driven estimator: canonical correlation analysis on conditioned trajectories. When a single unstable direction dominates, the leading mode is the reaction coordinate, locally recovering the stable manifold and committor of transition-path theory. The construction connects coherent sets to transition-path theory, to the stabilizing Riccati solution of linear control, and to the time-reversed dynamics of generative diffusion models.

The triangle map is an area-preserving, piecewise-parabolic map of the torus with vanishing Lyapunov exponent. We study the symbolic process $X_n=\pm1$ given by the two halves of the torus, whose partial sums $S_n$ are the transport of the lifted momentum, with an integrator free of accumulated rounding errors and exact computations on polygonal cylinder sets. We prove that the Koopman operator has no non-constant $H^1$ eigenfunctions, that the symbol is not an $H^1$ coboundary, and that runs of equal symbols are uniformly bounded. For generic parameters the walk is normally diffusive and Gaussian, but its diffusion coefficient is not that of a coin: away from the edges of the parameter square it varies between $0.2$ and $14$ times the Bernoulli value, and for a benchmark pair, with $D=3.09\pm0.01$, the excess is produced by the order of the bounded inter-event intervals, not by their distribution. The first-passage exponent is $1/2$ with a non-Bernoulli amplitude, and worst-case Birkhoff averages decay as for a uniquely ergodic system. For $\beta=0$ the Green-Kubo sum cancels, $D=0$, yet $\mathrm{Var}(S_n)$ keeps growing slowly, sign changes are rare and the correlations of Fourier modes decay as $n^{-0.2}$. We identify the zero-sum words, which become pure twists at $\beta=0$, as resonances that trap orbits with a computable $1/\ell$ law, set the crossover time $\beta^{-1/2}$ at small $\beta$, and, in an asymmetric deformation of the symbol, produce a logarithmic term in the variance whose coefficient we compute exactly. We formulate conjectures on unique ergodicity, mixing, the central limit theorem and the cohomology of the symbol.

Tipping points---abrupt, potentially irreversible reorganizations of a system's statistical state---are commonly anticipated through critical slowing down: recovery slows, autocorrelation and variance rise, and spectra redden. This paradigm is powerful near simple equilibrium bifurcations but is not a general theory for stochastic, multistable, or metastable systems. We develop such a theory from the Ruelle--Pollicott (RP) spectrum of Kolmogorov generators of hypoelliptic Itô diffusions. Resolving the sensitivity of invariant statistics on RP spectral blocks shows that each contribution factorizes into a spectral denominator and a residue coupling the block to both the observable and perturbation direction. Small denominators permit large responses; residues produce them. Thus a closing RP gap is not sufficient for an early warning, while growing residues can generate the classical signature with no gap closure. An early-warning signal is therefore a property of a triple: RP block, observable, and perturbation direction. We demonstrate this on a stochastic non-normal system whose RP spectrum is exactly frozen, yet classical indicators become more alarming than during genuine gap closure. The RP decomposition attributes this to residue growth and yields an index $\mathcal{N}(f)$ satisfying $\mathcal{N}(f)\leq 1$ for reversible dynamics; hence $\mathcal{N}(f)>1$ certifies residue-driven amplification. For metastable systems, one killed problem yields two complementary spectral objects: the Doob $Q$-process isolates in-well recovery, while escape clocks and committor-weighted destination probabilities govern interwell transitions. In a one-dimensional fold, these scale as $(\epsilon_c-\epsilon)^{1/2}$ and $(\epsilon_c-\epsilon)^{3/2}$, separating bifurcation-induced from noise-induced tipping. Doob drift also connects to optimal Girsanov sampling.

Unlike kink solitons with nonzero topological charge, pulse solitons cannot be driven by the experimentally most easily implemented constant force because of their zero topological charge. Here, we focus on a vector soliton with two polarization components: a pulse soliton component (rotation) and a kink soliton component (translation). We apply a constant force at the mass centers of the units, thereby driving the translational component with a constant force. Numerical simulations show that energy injected into the translational component can be transferred simultaneously to the rotational component through coupling, thereby achieving equal amplification of positive and negative pulses. Next, we change the application of this constant force to eccentric loading and find that the initially symmetric amplification of positive and negative solitons gradually becomes asymmetric over time. These phenomena are all explained by a theoretical model based on the adiabatic approximation, which gives a quantitative relation for the amplitude evolution, while the higher-order correction terms arising from the coupling effect also explain the origin of asymmetric transmission under eccentric driving. Our results demonstrate that vector solitons possess a unique capability for pulse soliton amplification by a constant force through polarization coupling and that this coupling can further modulate the symmetry between positive and negative pulses.

Previous studies have indicated that the local defocusing nonlinear Schrödinger equation (NLSE) is modulationally stable. Therefore, superregular solitonic solutions characterizing the nonlinear evolution of modulational instability under weak localized perturbations do not exist. In this work, we study the nonlinear stage of the modulation instability of a condensate in the framework of the defocusing nonlocal NLSE. By using the dressing method and Joukowski transformation, we systematically derive the general $N$-solitonic solution of the defocusing nonlocal NLSE, and the explicit expressions for one-solitonic, two-solitonic and superregular two-solitonic solutions are provided. Then dynamics of these solutions is also examined. We find that these solutions show a much wider variety than those in the local NLSE, such as the one solitonic solution composed of two interacting wave components and the two-solitonic solution containing four wave components. Finally, the accuracy and noise robustness of the analytical solutions are confirmed by numerical simulations. Such results advance the theory of superregular solitonic solutions in nonlocal systems and offer new physical understanding of wave propagation in nonlocal nonlinear media.

In extended electrodynamics, the Lorenz condition is not imposed and $C=\nabla\cdot\mathbf{A}+\mu_0\varepsilon_0\partial\Phi/\partial t$ is a dynamical field, which adds a scalar-longitudinal (SL) family to the TE, TM and TEM modes of a cavity. With $C=0$ on the wall of a closed perfectly conducting cavity, the classical resonances remain unchanged, while the SL modes are the Dirichlet eigenmodes of the volume, with $\mathbf{B}=0$ and an electric field along $\nabla C$. In uniform cavities they share the frequencies of the TM modes that vary along the axis, and for a connected wall the fundamental remains classical. Matching at a conductor described by its constitutive laws gives $\partial C/\partial n=0$ instead and couples the scalar-bearing modes to the Maxwell field. The results belong to the $C=0$ problem, the condition that separates the sectors and the one divergence cleaning imposes. The rectangular, circular cylinder and coaxial cavities provide benchmarks, together with the damping time that gives the slowest scalar mode its fastest decay.

In this work, an enriched model describing the longitudinal wave propagation is established based on Mindlin's Second Strain Gradient (SSG) theory, which can describe the heterogeneity caused by the micro-structure interactions in the frame of continuum mechanics. The governing equation and associated boundary conditions are derived based on Hamilton's principle, then the dispersion relation of non-classical longitudinal wave together with the extra-waves appearing exclusively in SSG theory model are investigated. The investigations are based on the modal density, energy flow, and forced response of the rod. Wave transmission and reflection through planar interfaces based on the proposed model have been calculated. Finally, the results of the enriched model are well interpreted by comparing with the classical theory results, and some useful conclusions are derived on the SSG theory based model in the wave propagation characterization.

The amplification of large-scale magnetic fields via the Tayler-Spruit dynamo has been invoked to explain the slow rotation of stellar cores and the formation of magnetars. The existence of this mechanism has recently been proved via 3D MHD numerical simulations of a differentially rotating stably stratified fluid. Using the same setup, we show that the dynamo can produce a wide variety of magnetic field dynamics, including reversals and hemisphericity, by varying thermal stratification. In a fiducial simulation, we interpret the appearance of reversals as the result of the coupling of two large-scale magnetic modes with opposite equatorial symmetries by the symmetry breaking of the flow.

Interactions between ultrasound and microbubbles underlie a range of biomedical and industrial applications, yet predicting how the physical parameters of the medium and bubbles govern nonlinear wave propagation remains difficult. This study proposes a parameter estimation framework that combines a Korteweg-de Vries-Burgers (KdVB) equation, describing weakly nonlinear wave propagation in a bubbly liquid, with a physics-informed neural network (PINN). The contributions are threefold. First, the PINN reproduces the reference solution of the governing equation in the forward problem, with a near-zero prediction error at the initial time that confirms the initial condition is enforced exactly as intended. Second, prior to inverse estimation, a sensitivity analysis is introduced that quantifies, at both the coefficient and solution levels, how each of eight physical parameters influences the KdVB equation, allowing the expected difficulty of estimating each parameter to be assessed in advance. Third, based on this assessment, single-parameter inverse estimation is performed for seven of the eight parameters using the PINN. Liquid viscosity, bubble initial radius, liquid density, sound speed, and liquid pressure are estimated with errors of 0.8-2.1%, the polytropic exponent converges only partially, and the surface tension coefficient cannot be estimated at all, consistent with the sensitivity analysis. These results establish a general framework for identifying and estimating the physical parameters governing nonlinear wave propagation in bubbly liquids from observed waveform data.

Physics-informed machine learning has become a major direction in predictive modeling of fluid dynamics, combining governing physics with learned representations. Yet prevailing formulations neither guarantee that small PDE-residual losses imply small solution errors nor scale effectively with increasing problem size. Here we present the neural basis method (NBM) as a new approach for Navier--Stokes dynamics. NBM is built on a ``representation-then-projection'' principle: fixed neural bases define the representation space, while projection of the governing equations determines the expansion coefficients. The same bases define common coordinates for the parametric solution manifold, recasting operator learning as a parameter-to-coefficient mapping and enabling scalability by removing explicit spatial dependence. For incompressible flow, NBM yields a velocity-only formulation whose residual provides an a posteriori velocity-error estimate, establishing a certified, data-free training objective for coefficient learning. Theoretical analysis and numerical experiments demonstrate the accuracy, efficiency, generalization, and scalability of NBM, with substantial improvements over baselines.

Inertial microcavitation rheometry (IMR) characterizes the high-rate mechanical response of soft materials from the rapid expansion and collapse of a microscopic bubble. In a typical IMR experiment, high-speed imaging provides the bubble radius as a function of time, R(t), and material parameters are identified by comparing the measured response with simulations that couple bubble dynamics to a constitutive description of the surrounding medium. This inverse analysis requires repeated forward simulations and careful control of experimental inputs, material parameters, and fitting settings. IMRFit is an open-source Python desktop application that brings these steps into an interactive environment for forward simulation, parameter identification, and constitutive-model comparison. Users can import experimental radius-time data, select a bubble-dynamics formulation and constitutive model, inspect simulated responses, fit material parameters, and organize batch fitting and parameter-sweep jobs. IMRFit includes Neo-Hookean Kelvin-Voigt and generalized Maxwell-Ogden-based models, among other constitutive options, and supports additional models through JSON descriptors and Python solver entry points. It also integrates fitting-window selection, visualization, and data export into a single workflow.

In a zero-gravity cylindrical container, a meniscus can span a square or equilateral-triangular cross-section only at contact angles at or above the respective Concus-Finn critical angles of 45 degrees and 60 degrees. We study strong-form physics-informed neural networks (PINNs) across these thresholds under fixed collocation and optimization budgets. Classical capillary flux balance yields a lower bound on the combined interior and wall residual loss for arbitrary positive sampling densities. In the tested nonexistence regime, several degrees below the critical angles, independently evaluated network losses are 1.6-1.9 times this bound. A polynomial least-squares comparison supports the same geometric interpretation. The PINNs still return smooth graphs with finite axial extent, even though the prescribed equilibrium problem has no spanning graph solution. Their small interior residuals coexist with wall-flux deficits near corners, where adjoining contact-angle conditions demand more flux than a finite-slope graph can supply. Residuals vary on both sides of the critical angle, while the bound tends uniformly to zero at threshold for fixed wall weight. These results give a geometric scale for interpreting the computed loss and locate the incompatibility that a small interior residual can conceal.

High-fidelity Reynolds-averaged Navier--Stokes (RANS) simulations remain a standard tool for aerodynamic analysis, yet each solve on an unstructured mesh is computationally expensive, making many-query tasks such as design exploration, optimization, and multi-condition evaluation costly. Neural operators provide mesh-flexible surrogates for mapping geometry and operating conditions to flow fields; however, in many existing architectures, global parameters such as the freestream state and design variables are concatenated with pointwise inputs, leaving their influence on intermediate features implicit. This paper proposes CoPiT, a \textbf{Co}nditional \textbf{P}osition-induced \textbf{T}ransformer that builds on the Position-induced Transformer (PiT) as its geometric backbone and injects a global condition vector through multi-stage feature-wise linear modulation (FiLM), thereby making parametric modulation explicit while preserving geometry-based attention weights. The model is evaluated on two-dimensional AirfRANS airfoil fields, including scarce-data and extrapolation regimes, and on three-dimensional BlendedNet++ blended-wing-body surfaces. On the AirfRANS full-data test set, CoPiT reduces surface and volume losses by approximately 54\% and 24\% relative to Transolver, respectively, and achieves the lowest overall normalized test MSE among the compared baselines on BlendedNet++. Matched ablations show that FiLM conditioning generally improves upon input concatenation, while the preferred placement is task-dependent. CoPiT thus provides a practical operator-learning surrogate for parametric aerodynamics on unstructured meshes.

Controlling the folding of biopolymers in crowded and confined environments, such as the interior of biological cells, remains a significant challenge. Macromolecular crowding and spatial confinement can strongly influence transition pathways between folded and unfolded states of proteins. Such environments can be mimicked in experiments by confining polymers within soft, tunable media, such as hydrogels -- cross-linked polymer networks that swell by absorbing solvent and exhibit stimulus-dependent responsiveness. Here, we develop a self-consistent mean-field theory for the equilibrium swelling and internal composition of a hydrogel immersed in a solution of free polymer coils. The theory extends the Flory-Rehner framework by incorporating free polymer coils, modeled as fluctuating ellipsoids, whose sizes and shapes are characterized by the eigenvalues of the gyration tensor. Confinement of the coils within gel pores is characterized by an effective free-volume fraction, parametrized from numerical calculations for self-avoiding-walk chains between hard walls. Coupled chemical potential equilibrium conditions are solved numerically over ranges of coil molecular weight and free polymer concentration. We find that free polymers drive a non-monotonic swelling response of hydrogels, with osmotic swelling at low concentrations followed by deswelling at higher concentrations, in qualitative agreement with experiment. We further demonstrate that confinement within gel pores reduces the radius of gyration and asphericity of embedded polymer coils, driving them toward compact, globular conformations analogous to folded protein states. These results establish a theoretical foundation for using responsive hydrogels as tunable, artificial chaperone-like systems capable of inducing and controlling biopolymer folding.

Inferring constitutive laws from transient response data is a central inverse problem in soft condensed-matter physics, particularly when the relevant relaxation spectrum extends beyond the time window of a single experiment. Time-temperature superposition (TTS) constrains this problem for thermorheologically simple materials in the linear viscoelastic regime by allowing temperature to rescale the characteristic relaxation time without changing the underlying shape of the relaxation spectrum. We incorporate this constraint into a physics-informed machine-learning framework for time-resolved mechanical spectroscopy via chirp rheometry. We encode compact fractional viscoelastic models as causal convolutional features derived from the Boltzmann superposition principle, and we jointly fit multi-temperature chirp records using sparse variational Gaussian process regression. The model infers horizontal shift factors, constitutive parameters, and an observational-noise scale directly from time-domain stress-strain signals measured in the linear viscoelastic regime, without first extracting frequency-domain spectra or manually shifting separate curves. For synthetic Fractional Maxwell data, the method recovers the generating constitutive law from a prescribed model library and latent shifts over stress-noise levels from 3% to 25%. Applied to a DGEBA-IPDA epoxy dataset spanning the glass-transition regime, the pooled likelihood distinguishes competing fractional rheology models using the Bayesian information criterion. These results recast TTS master-curve construction as probabilistic inference over latent time rescaling and linear viscoelasticity, while also identifying limitations, such as homoscedastic noise and weakly informative spectral regimes.

We investigate the field-directed assembly of patchy colloidal particles composed of magnetic hematite cubes encapsulated in TPM shells. These Pacman-like particles exhibit specific interactions via their magnetic patch, enabling tunable structures under external fields. A magnetic field drives patch-to-patch interactions, while an AC electric field induces stacking and spreading. By using this multi-field combination and by varying field parameters, such as frequency and amplitude, we achieve programmable transitions between distinct assembly modes. Our work offers a versatile platform for designing reconfigurable colloidal architectures with potential applications in micro-robotics and smart materials.

Many solvated materials, from nanoparticles to polyelectrolytes, acquire charge through the dissociation or association of surface groups, a phenomenon known as charge regulation (CR). Recent methods use hybrid charge regulation Monte Carlo (CR-MC)/molecular dynamics (MD) to evolve the system while dynamically adjusting charges on the surface groups. However, this approach is computationally expensive, as Monte Carlo sampling can be as costly as the accompanying MD. In this work, we introduce charge regulation machine learning (CR-ML), a graph attention network that predicts the ionization probability of every surface site from the instantaneous configuration, the dissociation constant of surface groups, and the solution conditions. We show that CR-ML reproduces the equilibrium conformations and degree of ionization obtained with CR-MC for a hydrophobic polyanion. We further test CR-ML on the more complex system of two nanoparticles mediated by a polyelectrolyte, where it accurately predicts the charge asymmetry that develops between the two particles. Across these systems, CR-ML updates charges an order of magnitude faster than CR-MC while accurately reproducing its equilibrium properties. This framework opens a path toward large-scale simulations of charge-regulating materials for understanding and designing their responsive behavior.

Understanding the microscopic behavior of materials in response to mechanical perturbations is a central challenge in soft matter, yet existing methods, which typically rely on microscopy-based imaging, often struggle with spatial heterogeneity and low signal-to-noise that are characteristic of many soft and biological materials. Additionally, many existing rheo-optical methods focus on the response to macro-scale forces rather than localized perturbations despite the importance of local stresses in biological and industrial applications of soft materials. Here, we present STroboscopically Averaged, time-Resolved Differential Dynamic Microscopy (starDDM) to investigate a sample's deformation across time and distance due to a cyclically applied local force. As proof-of-principle, we use this model-independent and tracer-free approach to map the motions of active cytoskeleton composites imposed by the movement of an optically trapped probe particle embedded within the complex network. We reveal how motor-driven restructuring and varying strain rates tune the magnitude and propagation of the response, which we further show decays with distance from the perturbation. This analytical platform fills a critical gap in micro-rheology, offering a versatile tool for probing the non-equilibrium dynamics of soft materials ranging from biopolymer networks to 3D-printed materials and soft robotics.

Various types of electrohydrodynamic instabilities in liquid crystals (LCs) are a recurring theme in LC research. The nonlinear stage of the flexoelectric instability in nematics remains the least studied aspect of this phenomenon. This work highlights a key advancement in nonlinear physics, providing a compelling example of nonlinear dynamical system behavior. By solving the system of nonlinear equations for a nematic in an alternating external field, we derive from first principles the unique "dancing" behavior of truly two-dimensional patterns above the flexoelectric instability threshold. Our analysis is restricted to liquid crystals with negative dielectric permittivity and electrical conductivity anisotropies. The resulting solution represents a stable limit cycle near above the Hopf bifurcation, valid within the parameters range where the solutions characteristic exponent is complex. The generalized two-dimensional Ginzburg-Landau-like phenomenological theory of the phenomenon is developed.

While defect dynamics in condensed matter systems is widely studied and several methods are available to track the defect position over time, the formulation of dynamical models for the coupled evolution of both defect and background field quantities seems to be more challenging. Yet, the overall behavior of a system containing moving defects is strongly influenced by this defect-field interaction. Here, we propose a modeling framework for the conservative coupled evolution of the defect density and the background fields upon focusing on two relevant cases of study: the Gross-Pitaevskii theory of quantum fluids and the Ericksen-Leslie model of nematic liquid crystals. To achieve the coupled evolution, we combine the Euler-Poincaré variational setting of continuum dynamics with the gauge theory of topological defects. While the latter allows us to overcome certain ambiguities in definition of the defect density, the Euler-Poincaré method provides a unified modeling approach in the absence of defect reconnection.

We derive a mechanically consistent Ginzburg-Landau theory for the metastable heterogeneous G state reported in deeply undercooled metallic liquids. The central result is that type-II-like mixed-state physics can emerge structurally with the random internal stress field playing the role of the magnetic field. Frozen eigenstrain due to elastic incompatibility between ordered cores and the amorphous matrix generates incompatible stress, while the non-affine internal strain in the liquid-like matrix in between the ordered cores relaxes that stress over a finite screening length $\lambda_\sigma$ (analogous to the London length in the superconducting problem). Structural order heals over a distinct mechanically-dressed length $\xi_G$; their ratio $\kappa_G=\lambda_\sigma/\xi_G$ provides the structural counterpart of the Ginzburg-Landau parameter. Because the matrix is transiently rigid yet locally relaxational only over an intermediate time window, the same mechanism selects crystal for slow protocols, a heterogeneous G state at intermediate rates, and a homogeneous L-like glass under rapid arrest. Residual incompatibility frustrates coarsening, allowing finite ordered cores and screened, orientation-dependent core interactions. The resulting texture is an inverted Abrikosov analogue: structural order resides in the cores, whereas incompatible-stress screening is carried by the surrounding disordered matrix. The theory yields direct simulation and experimental tests through stress-decay, structural-healing, non-affine-susceptibility, and kinetic measurements.

Classical chemotaxis models consider the directed motion of cells in response to a chemical gradient. Recent experiments suggest that biological microswimmers such as bacteria can perform chemotaxis toward multiple chemicals, which dynamically evolve depending on the distribution of the microswimmers. In this Letter, we consider a mass-conserving chemotaxis model in which pattern formation is driven by two competing chemicals, autoinducers and nutrients, where the former acts as an activator and the latter as an inhibitor for coarsening. We show that this can give rise to diverse patterns including long wavelength uninterrupted coarsening, Turing-like arrested coarsening, traveling waves as well as a novel class of mixed multi-scale oscillatory coarsening patterns, where a dense aggregate coexist with a dynamically spreading part of the population. We analytically derive the conditions for the onset of such patterns and discuss their physical implications, which significantly broadens our understanding of signaling active matter and pattern formation in general.

We investigate how the shape and arrangement of high-stiffness regions govern stress redistribution in two-component triangular elastic spring networks subjected to spatially correlated and uncorrelated random prestress. We compare boundary roughness, partitioning into disconnected regions, and graded transitions between regions of different stiffness. Our simulations identify interface bonds as channels for energy transfer: increasing their number provides additional transfer paths and reduces stress concentration in mechanically rigid regimes, while offering little benefit in compliant subnetworks. This is analogous to defects in naturally occurring crystal structures, where the defects themselves isolate stress. At a fixed fraction of high-stiffness material, partitioning reduces stress concentration for both correlated and uncorrelated prestress. The benefit diminishes with further subdivision as the number of interface bonds becomes comparable to the number of interior nodes. Stress reduction, however, depends on the spatial correlations of the imposed prestress: random prestress generally yields a stronger effect, though the difference diminishes in some regimes. Graded interfaces further reduce peak stress by distributing the stiffness transition over a broader region. Together, these results suggest design strategies based on increasing interface area, matching subdivision scale to prestress correlations, and grading stiffness transitions. This minimal framework identifies how internal structure controls energy transfer and stress redistribution, suggesting design principles for mechanical robustness under both internal and external loading.

Phenomena responsible for emerging technologies originate from novel molecular states at buried interfaces. Yet quantitatively resolving these features is out of reach in most cases. Resonant scattering has demonstrated sensitivity to these local states but is limited due to a lack of accurate interpretive models. We leverage a machine learning (ML)-optimized optical model to analyze polarized resonant soft X-ray scattering (RSoXS) from molecular thin films. This new analysis establishes the direct and quantitative interpretation of molecular orientation, chemical identity and packing states as a function of depth with sub-monolayer resolution - reaching beyond the diffraction limit via locking energy and polarization through the optical model. From our analysis, we discover a gradient evolution of molecular orientation and packing emerging from the interface, indicative of competing surface versus bulk growth dynamics and contradicting hypotheses of substrate patterning. This nondestructive insight into buried interfacial formation and final state opens possibilities in controlling interfacial states and phenomena in next-generation technologies.

Conventional particle tracking velocimetry (PTV) has been the standard diagnostic tool for studying fluid and granular flows. However, in dense granular systems, the average distance moved by particles between frames can approach or exceed inter-particle spacing, demanding ultra-high frame rates. Furthermore, neighbouring particles may move together, and common velocity-based prediction fails after energetic collisions. Existing methods struggle to track granular particles without losing identities or swapping. We present Colour Bean Tracking Velocimetry (CBTV), a training-free multi-pass method leveraging multicoloured particles to achieve enhanced tracking. CBTV first matches constellations of neighbouring coloured particles as single units, guided by a cross-correlation motion prior, and only then assigns the remaining particles individually. We compare it with 12 baseline tracker configurations, from classical linkers to graph-neural-network and transformer models, on 59 cases from 15 simulated discrete-element granular flows with exact ground truth (0.006-9 diameters/frame). CBTV matches or exceeds every tracker tested on an impulsive collision at every displacement. Its advantage lies in dense flows in which particles move between about half and twice their spacing per frame, where links between frames are ambiguous. On agitated shear flow, a colour relaxation tracker, which also uses neighbour context, matches or narrowly exceeds CBTV. Where links are unambiguous, CBTV is close to the best tracker, and beyond about two to three particle diameters per frame, the range of its motion prior, trackers that compensate for bulk motion are more accurate. For experimentalists, dense granular flows of coloured particles can be tracked at displacements per frame where trackers without neighbour context lose identities, easing the demand for ultra-high frame rates without training data.

The three-dimensional Navier-Stokes equations govern fluid turbulence, a chaotic and non-linear physical phenomenon characterized by complex eddies interacting across vast spatial and temporal scales. A numerically accurate modeling of this multi-scale energy cascade requires fully resolving both the fine spatial structures and the continuous temporal evolution of the flow field. In this paper, we leverage massive, time-resolved direct numerical simulations, which exceed 28 TB per run, to assess how numerical choices govern the resolved (3+1)-dimensional physics of turbulent flows. Building on this analysis, we study how neural networks represent the recorded turbulent motion. Our results highlight that spatial and temporal assessments can disagree for both numerical records and learned representations. We therefore call on the machine learning community to treat (3+1)-dimensional turbulence as a four-dimensional phenomenon.

The fidelity of direct numerical simulation now outpaces the storage and data-movement capacity available for the resulting fields. We present an open, distributed, GPU-accelerated low-rank compression framework for large turbulent flow databases. We assess it using two direct numerical simulations of a controlled diffusion compressor cascade under laminar and turbulent inflow conditions. Compression is formulated using a correlation operator over space and time, which is two orders of magnitude larger than that of snapshot POD. Its dominant range is extracted with a randomized range finder based on communication-avoiding hierarchical QR. The compressed databases are evaluated through a hierarchy of increasingly strict diagnostics, from instantaneous reconstruction and second-order statistics to the modal turbulent kinetic energy budget and its nonlinear interscale transfer. The budget terms are far more sensitive to compression than fieldwise or one-point errors. They remain accurate at conservative compression and degrade sharply once the retained energy is relaxed. The near-wall dissipation and the interscale transfer degrade the most and set the admissible compression level. An aggressive reduction preserves every one-point statistic to within a few per cent while corrupting both by an order of magnitude more. The dissipation error is confined to the viscous sublayer and grows with the development of the boundary layer. It is carried by the high-order modes. For both inflows, the linear budget terms scale with the discarded energy to the power $0.8$ and the triadic transfer to a power above one.

From a novel fluid-dynamical perspective, the present study investigates the heat-current vortices and heat vorticity in heat conduction process of solid materials. The heat vorticity $\bm{\omega}$, defined as the curl of the heat-flux field, is decomposed into the orbital-rotation $\bm{R}$ and spin $\bm{S}$, which collectively constitute the heat-vorticity triplet $(\bm{R},\bm{S},\bm{\omega})$, extending beyond the existing single-vorticity research paradigm. As an illustrative example, kinetic phonon transport in a 2D porous solid structure is examined based on the numerical solutions of the Peierls-Boltzmann equation under the Callway dual-relaxation-time approximation. The physical characteristics of heat vortices and the vorticity triplet patterns are analyzed across different kinetic regimes in the phase diagram of the normal (N) and resistive (R) scattering processes.... In the hydrodynamic limit, the boundary generation mechanism of heat vorticity is further elucidated based on the Guyer-Krumhansl (G-K) equation generated from the truncated Chapman-Enskog (C-E) expansion. The boundary heat vorticity flux (BHVF) is proposed as a new concept for describing the local rate at which heat vorticity is generated at the boundary of a solid material. The general expression for the BHVF is rigorously derived for phonon hydrodynamics, and for the 2D steady hydrodynamic phonon transport case, we find that the BHVF is solely attributed to the tangential component of the net heat flux deviating from the classical Fourier heat flux. Furthermore, we show that the total vorticity contained in a control volume arises from the spatiotemporal accumulation of the BHVF, weighted by the memory kernel arising from the R scattering. The proposed theory and findings herein could be valuable for understanding the diverse vortical-flow phenomena in condensed matter systems.

Accurate simulation of atmospheric flows is challenging. Low-Mach-number dynamics often need to be resolved in the presence of a dominant, nearly hydrostatic background state. Conventional upwind numerical fluxes can introduce excessive acoustic-speed-based dissipation in the low-Mach regime. Discretization errors in the balance law can also generate spurious motion. This work investigates these two issues within a high-order Direct Flux Reconstruction (DFR) framework coupled with a third-order exponential time integrator for the 3D compressible Euler equations with gravity. Low-Mach-number accuracy is addressed using a modified AUSM$^+$-up flux, denoted AUSM$^+$-upH. Preservation of the background equilibrium is improved through a deviation-based formulation. The resulting approach is assessed using a hierarchy of idealized atmospheric test cases. The results show that AUSM$^+$-upH preserves low-Mach flow structures more effectively than the more dissipative Rusanov flux. However, reduced numerical dissipation also makes AUSM$^+$-upH more sensitive to residual errors in the discrete hydrostatic balance. The deviation formulation substantially suppresses these errors by several orders of magnitude, with the strongest improvement observed for flows over orography. Overall, AUSM$^+$-upH exhibits greater robustness when combined with the deviation formulation across the atmospheric test cases considered.

Molecular clouds exhibit complex, multi-scale dynamics driven by the interplay of turbulence, self-gravity, and gas pressure. Modelling these systems with conventional grid-based methods becomes increasingly expensive as spatial resolution and dimensionality increase. Physics-Informed Neural Networks (PINNs) offer a mesh-free alternative by incorporating the governing equations directly into the training objective, but their ability to model realistic turbulent self-gravitating flows remains largely unexplored. We apply PINNs to isothermal molecular clouds initialized with astrophysically motivated turbulent velocity fields, considering subsonic and supersonic evolution in two and three dimensions. We benchmark the predicted density and velocity fields against the finite-volume code Athena++. PINNs accurately recover the global evolution of the flow over multiple free-fall times across turbulent realizations, Mach numbers, and dimensionalities. Their training cost also exhibits weak dependence on spatial resolution, increasing by less than 25% from 128^3 to 1024^3 in our experiments. These results demonstrate that PINNs can model substantially more realistic self-gravitating turbulent flows than previously explored and provide a promising complementary framework for studying these systems.

Chaotic attractors are typically visualized in an abstract phase space. Here we show that an orientable active particle moving through a steady, two-dimensional, multivortex flow can trace a Lorenz-like chaotic attractor in its real space trajectory. Despite the flow being strictly time independent, coupling between particle position and orientation creates a three-dimensional nonlinear dynamical system. For suitable particle shape and swimming speed, the trajectory organizes into a striking two-lobed geometry reminiscent of the classical Lorenz attractor. A structured first return map, positive largest Lyapunov exponent, and a broadband power spectrum establish that the underlying motion is chaotic. Varying the swimming speed reveals a rich sequence of dynamical regimes as self-propulsion breaks streamline confinement and reorganizes the particle motion. Our results demonstrate how an internal orientational degree of freedom can make chaotic dynamics directly visible in physical space, allowing a single active particle to trace a chaotic attractor as it moves through an otherwise steady flow.

Computational Fluid Dynamics (CFD) is increasingly used to resolve wind, heat, and pollution patterns in cities with high fidelity but high computational cost. Thermal effects and vegetation are often neglected despite being important drivers, yet their influence may be masked by variability from other uncertain inputs. This work determines how precisely model parameters and boundary conditions must be known for these effects to govern output uncertainty in the velocity, temperature, and concentration fields of a two-dimensional street canyon. A global Sobol analysis of 24 parameters is made tractable by a surrogate trained on Reynolds-Averaged Navier--Stokes (RANS) simulations, combining principal component analysis (PCA) with multilayer perceptrons (MLPs). Two ventilation regimes assess the variance due to thermal and vegetation parameters as uncertainty in all other inputs is progressively reduced. At typical uncertainty levels, turbulence closure constants and inflow turbulence profiles govern variability in all three fields in both regimes. Under weak ventilation, solar forcing becomes the main source of temperature variability once the remaining uncertainties are halved, and of concentration variance once they are reduced to a quarter (about $\pm11\%$ for the dominant closure constant and $\pm12\%$ for the emission rate). In contrast, vegetation contributes significantly at typical uncertainty levels. Under strong ventilation, however, the canopy never overtakes the closure constants, even when the dominant one is known to $\pm5\%$. Spatially, both effects peak at road level and along canyon walls, which influence outdoor exposure and indoor infiltration, suggesting that high-resolution exposure studies should account for them.

We present an HLLD Riemann solver for a multicomponent hypoelastic diffuse-interface model of compressible fluid-solid interaction, with no separately computed interface and a deviatoric stress advanced by an objective hypoelastic rate law outside conservation-law form. The difficulty specific to this model is that the stress evolution is nonconservative and, unlike the familiar volume-fraction terms of Kapila-type models, cannot be left outside the Riemann solve once the shear waves are resolved. The shear coefficient $\rho(G+\tau_{xx})$ sets the impedance of the resolved shear waves and so belongs to their eigenstructure. Anchored HLLD carries it inside the solve by evaluating the HLLD fan twice at each face, anchored in turn to each adjacent cell-centered state, with every cell advancing from the flux anchored to its own state. HLL, HLLC, and anchored HLLD form a three-tier hierarchy of increasing wave resolution in one framework. We prove local structural properties: consistency at the reconstruction order, exact species-mass conservation, and tangential-momentum and energy drift vanishing under refinement at the reconstruction's face-jump order on smooth fields, with one-dimensional tests illustrating these structural properties and demonstrating first-order drift convergence on discontinuous fields. Across one-dimensional tests and two-dimensional production simulations in the open-source solver MFC, anchored HLLD resolves both the material contact and the shear waves, HLLC the contact alone, and HLL neither sharply. Where refinement studies are shown, anchored HLLD converges toward exact or semi-analytic solutions. A three-dimensional shock-ellipsoid interaction demonstrates the solver with all six stress components active.

In this work, we develop a nonlinear continuum model for wave propagation in two-dimensional granular materials, building on key ideas from Nesterenko's work. Starting from the Hertzian contact law and neglecting contact friction, we derive an effective continuum description through homogenization, assuming spherical, monodisperse grains, local periodicity, and the Cauchy--Born hypothesis. The resulting strain-gradient model depends on both the first and second gradients of the displacement field. We analyse the hyperbolicity of the leading-order system through its eigenvalues and eigenvectors, establishing conditions for hyperbolicity within a restricted deformation domain. The model is solved using an explicit finite-volume method to investigate gravitational settling and wave propagation. We derive analytical expressions for the longitudinal and transverse wave speeds and highlight their dependence on depth. Finally, the predictions of the continuum model are compared with existing discrete-element simulations. This formulation allows several extensions, including more complex packing geometries, contact laws, and large-deformation regimes in which the contact network can evolve.

This brief tutorial review examines the operation of reservoir computing from the standpoint of nonlinear dynamics and provides a concise overview of recent advances in the field. We begin by delineating the predictive capabilities of reservoir systems, followed by a succinct yet sufficient introduction to the nonlinear dynamical systems techniques that will be employed throughout this article to elucidate reservoir functioning. Subsequently, we describe reservoir operation using these techniques in the context of successful prediction, accompanied by all necessary implementation codes. The objective of this article is to offer a practical guide to the implementation of reservoir computing while, from a nonlinear dynamics perspective, explaining the mechanisms by which reservoirs achieve accurate predictions.

We investigate the dynamics of Conway's Game of Life (GoL) through the lens of Ordinal Pattern analysis. Each GoL generation is transformed into a one-dimensional time series, from which ordinal patterns are extracted to characterize its underlying dynamics. The resulting ordinal distributions are then represented in the Entropy--Statistical Complexity ($H \times C$) plane, enabling a quantitative analysis of the system's evolution. We evaluate different encoding strategies, including patch sizes and linearization methods, and assess their impact on the resulting $H \times C$ trajectories. Finally, we characterize the emergent dynamics in terms of convergence behavior, trajectory patterns, and statistical complexity, showing how the proposed entropy--complexity framework provides insights into the dynamics of cellular automata.

Feeding a pretrained language model the expected embedding of its own next-token distribution turns it into a discrete-time dynamical system with continuous states. Across Qwen2.5, OLMo-2 and Llama-3 models from 0.5B to 72B parameters, temperature and activation steering move this loop between repeating text and chaos, with positive finite-time Lyapunov exponents. The loop's derivative factorizes into the inverse temperature, the covariance of token embeddings under the next-token distribution (a cross-covariance for untied embeddings) and the network's Jacobian. In one model studied in detail, along recorded orbits, the growth that steering adds comes mainly from the readout, where next tokens compete. The periodic windows show the quantitative signatures of low-dimensional maps, from saddle-node scaling and Feigenbaum's constant to shrimp-shaped domains; passage times predicted in advance from the model's derivatives came within one return-map iterate of the measured passage times in 42 of 48 cases over two prospective stages (24 and 18 of 24), and interval arithmetic proves attracting periodic orbits of the full transformer map. Numerical reproducibility depends on the dynamical regime: changing only the batch layout changed the text of 173 of 192 chaotic float64 loops in the smallest model, compared with only 7 of 192 periodic ones. These results show that bifurcation theory can make quantitative predictions about continuous language-model feedback, with rigorous guarantees for selected periodic orbits of the full transformer.

Reduced-order models of nonlinear structures are often evaluated using mechanical response errors, while the signals of interest may also pass through dynamic readout channels that modify their amplitudes and phases. We develop an offline validation framework that distinguishes mechanical source error, readout-model prediction error, and physical distortion of a normalized two-component modal state. We couple a Galerkin reduced source to two calibrated resonant channels and evaluate modal amplitudes, relative phase, and state fidelity using consistent complex coefficients. For the linear readout model, an exact output-error decomposition distinguishes source and interface modeling contributions, while a two-channel identity relates differential channel transfer to normalized-state distortion. For the ten-mass nonlinear lattice, the two-mode source and coupled-output errors over the two-resonance interface band are $3.069 \times 10^{-2}$ and $2.448 \times 10^{-2}$. At $F_0=0.04$, the relative-phase mean absolute error increases from $9.82 \times 10^{-3}$ rad for the linear interface to $1.74 \times 10^{-2}$ rad for the nonlinear interface. At the strongest forcing, a four-coordinate proper orthogonal decomposition model gives a source error of $2.05 \times 10^{-2}$, compared with $8.03 \times 10^{-2}$ for four linear modes on the same held-out test set. The noise analysis shows that accurate in-band output prediction can coexist with substantial parameter error, while a constrained linear approximation of nonlinear readout data produces a substantial residual. We use these findings to assess reduced-model adequacy for the specified outputs, forcing levels, and validation frequencies.

This paper investigates integrable turbulence and the mechanism for generating rogue waves in the complex modified Korteweg--de Vries (mKdV) equation through numerical simulations and statistical analysis. We solve the Lax pair eigenvalue problem using the Fourier collocation method and establish a correspondence among solitons, breathers, and rogue waves on the spectral plane. We generate chaotic wave fields by simulating the complex mKdV equation using the split-step Fourier method, starting from a plane wave with superimposed random noise. We analyze the effects of the standard deviation \(\mu\) and the correlation length \(L_c\). The results show that increasing \(\mu\) drives a transition from breather turbulence to soliton turbulence, increasing the probability of rogue-wave this http URL contrast, \(L_c\) primarily influences the spatial scale of the structures. As the constant background of the complex mKdV equation is modulationally stable, its integrable turbulence does not depend on modulational instability. Compared with the nonlinear Schrödinger (NLS) equation under identical initial conditions, the complex mKdV equation attains comparable amplitudes under strong perturbations, but exhibits a higher spatial gradient. This suggests that third-order dispersion and derivative nonlinearity alter the excitation mechanism and steepen the waveform.

The state of a quantum particle confined to a spherical surface is commonly described using spherical harmonics, which play a crucial role in solving many scientific problems featuring spherical symmetry. A mean-field description of a system of many interacting quantum particles confined to a spherical shell naturally leads to nonlinear generalizations of spherical harmonics. In this study, we analyze the emergence of such nonlinear modes in a shell-shaped Bose-Einstein condensate with both repulsive and attractive two-particle interactions. We find several classes of nonlinear modes. The first kind is an analytical continuation of a single spherical harmonic or their superposition for nonvanishing atom-atom interaction. Some of these solutions have planar counterparts in the form of Townes solitons and Townes vortices, which either appear stable even in the case of attractive interactions or can be stabilized by three-particle interactions. The second kind originate from symmetry-breaking bifurcations in the case of a repulsive interaction, and therefore have no linear counterparts. Moreover, we demonstrate the existence of a breathing dynamics that oscillates primarily between an unstable soliton and a stable vortex necklace state. Our findings show that the physics of nonlinear matter waves on curved geometries differs substantially from that in planar systems, suggesting the feasibility of observing these unconventional wave patterns experimentally.

Dynamic mode decomposition (DMD) is a powerful tool for uncovering coherent flow dynamics, yet the need for time-resolved data often limits its experimental use. We show that the evolving gaps between tracer particles in standard, non-time-resolved particle image velocimetry (PIV) images contain enough dynamical information to recover velocity-associated DMD modes. The proposed gap-based DMD approach extends modal analysis to measurements that would otherwise be considered temporally under-resolved.

Non-destructive early detection of water stress is critical for precision agriculture, yet current detection methods are often labor-intensive or destructive. We propose a rapid, non-invasive method based on Spectral Submanifold (SSM) reduction to analyze the nonlinear vibration dynamics of soybean plants. Unlike traditional linear modal analysis, our data-driven approach reveals a distinct transition in the dominant dynamics of the plant stem as drought progresses. Specifically, we uncover a sign reversal in the nonlinear damping coefficient within SSM-reduced models of full plants. Our finding reveals a fundamental transition in the plant's dissipative mechanics from a pressurized, fluid-rich vessel exhibiting superlinear (viscoelastic) damping to a dry, cellular solid dominated by sublinear (frictional) damping. This transition is closely correlated with the onset of physiological stress indicated by a significant decrease in the values of mature-leaf soil plant analysis development (SPAD) and colorimetric metrics. In contrast, traditional metrics, such as linear frequency and leaf wilting, do not provide consistent statistical signals of water stress. This study provides the first experimental evidence that SSM-based nonlinear model reduction can detect the changing internal state of a living organism, offering a physics-based metric for high-throughput plant phenotyping.

Active phase separation in living systems is ubiquitous, yet the microscopic origins of the non-equilibrium terms in active field theories remain largely unknown. Here, starting from stochastic mass-conserving reaction-diffusion dynamics of two interacting chemical species, we perform a systematic slow-mode reduction and derive the complete Active Model B+ field theory, with all phenomenological coefficients expressed in terms of microscopic parameters. We identify concentration-dependent diffusivities and asymmetric inter-species chemotactic couplings as the minimal microscopic ingredients generating the genuinely non-equilibrium coefficient responsible for microphase separation, cluster phases, and arrested coarsening. Our framework recovers the equilibrium limit consistently and is validated by stochastic numerical simulations. These results establish a direct, bottom-up link between the architecture of chemical reaction networks and the universality class of their emergent large-scale dynamics.

The co-condensation of DNA and proteins plays an important role in genome compaction, including heterochromatin formation and chromosome segregation. Meanwhile, transcription and replication continuously generate DNA supercoiling, yet how the resulting torsional stress affects co-condensation remains poorly understood. Here, by coupling DNA elasticity to a protein concentration field, we show that supercoiling acts as a topological catalyst for co-condensation through a mutually reinforcing interplay with protein wetting. Specifically, protein wetting facilitates twist-to-writhe conversion, generating highly writhed DNA conformations that in turn promote capillary collapse into a protein-rich droplet. In the absence of supercoiling, DNA remains kinetically trapped in metastable extended states within our model, whereas sufficiently strong supercoiling removes the nucleation barrier and enables spontaneous co-condensation. These results establish topology as a distinct control parameter for biomolecular condensation and provide a mechanical framework for how active genomic processes can dynamically regulate large-scale genome organization.

Nozzle-free droplet generation eliminates the need for a dispensing orifice, but useful printing also requires control over where droplets are deposited. Here we demonstrate predictable droplet deposition using a nozzle-free, angle-controlled surface acoustic wave jetting platform. Opposing focused interdigital transducers steer droplets from a pendant parent drop toward a collection substrate, with the ejection angle set by the time-integrated acoustic acceleration imbalance. The overall acceleration ratio identifies the operating window for single-droplet ejection and separates it from no-ejection, satellite-droplet, and multiple-droplet regimes. We then connect ejection angle to landing position through a geometric deposition model referenced to a balanced shot in each experiment. At a 5.2 mm parent-drop-to-substrate spacing, 80 steered shots across twenty experiments show strongly anisotropic relative placement scatter: 0.59 mm in the steering direction and 0.06 mm transverse to it. In tests conducted independently over several days, a model calibrated on six earlier collection dates predicted landing positions on two later dates with a root-mean-square error of 0.71 mm; bootstrap resampling placed the 95% confidence range for this error between 0.41 and 1.01 mm. The results establish a practical framework for predicting relative droplet landing in angle-controlled surface acoustic wave jetting and identify the limits imposed by steering angle, separation distance, and actuation regime from an orifice-free, clog-free droplet ejection method.

The rotating detonation engine (RDE) faces severe thermal protection challenges. This study numerically investigates a head-end dual-purpose injection configuration in which the film-cooling holes act as both fuel and coolant injectors. An Eulerian-Lagrangian framework is employed, in which the turbulence closure, the film-cooling effectiveness prediction, and the droplet evaporation model are validated against experimental benchmarks. The validated framework is then applied to examine the effects of coolant flow rate, atomization quality, and the fuel allocation between the main flow and the cooling system. Beyond a threshold coolant flow rate the wall temperature drops substantially, whereas an excessively low flow rate elevates it by intensifying local deflagration, revealing a competition between evaporative cooling and secondary combustion that is inherent to this dual-purpose configuration. Fine droplets cool effectively but only over a limited distance downstream, and fuel allocated to cooling weakens the detonation wave and reduces thrust. A moderate coolant flow rate combined with fine atomization is therefore recommended.

Trained network weights are increasingly treated as data, but there is rarely ground truth about what a population of models should encode, which hampers systematic validation of weight-space methods. This makes parametric dynamical systems a natural test-bed: the dynamics change qualitatively at submanifolds of parameter space that are, in well-studied families, known analytically or numerically. Fine-tuning a forecasting network at each point of a parameter grid yields a model zoo indexed by a physical parameter, against which weight-space diagnostics can be checked. We build such model zoos for four dynamical systems and analyse them with JEPAWG, a recently proposed joint-embedding hypernetwork built around a learned parameter--weight representation. It was first introduced for neural samplers for lattice field theories, where its latent geometry located the phase transition and estimated the 2D Ising critical exponent. Applied to dynamical systems, JEPAWG is competitive on forecasting with a hypernetwork trained directly for that task, despite being supervised on the parameter--weight correspondence rather than on forecasts. Beyond forecasting, the norm of the parameter-derivative of the decoded weights locates Hopf points and curves, tracks a period-doubling cascade closely enough to give a qualitative estimate of the Feigenbaum constant, and detects a global bifurcation, which has no eigenvalue signature and is therefore invisible to linearisation. As such, JEPAWG provides interpretable insight into the dynamics that is not available from other hypernetworks. Together, these results indicate that JEPAWG is a workable instrument for reading physical structure off a population of trained networks.

Biomedical devices, wearable interfaces, and soft robots require compliant soft materials with reliable mechanical performance, yet the molecular principles needed to design such materials are not always fully understood. Thus, there is an urgent need to understand how to design novel stretchable and soft hydrogels with enhanced toughness, i.e. resistance to breakage. Slide-ring gels (SRGs) are a class of unconventional soft materials formed by polyrotaxanes (PR) building blocks whereby sliding cyclodextrins (CD) replace traditional chemical and physical crosslinks and in turn enhance toughness and stretchability by several orders of magnitude. The rational design of SRGs re- mains challenging due to a lack of a mechanistic understanding of the role played by individual components. In this work, we implement simple synthetic perturbations that individually target polymer-CD and CD-CD interactions in unstoppered pseudopolyrotaxanes (pPR) solutions and measure the consequent changes in viscoelastic properties. Weakening the intermolecular interaction between CDs abolishes crystallisation and significantly weakens the gel. At the same time, thermodynamically favouring threading by using azobenzene-modified PEG chains favours the formation of stable and long-lived networks even at remarkably low CD stoichiometries. We rationalise these observations with coarse-grained Molecular Dynamics simulations which clarify the structure-function relationship of the components forming these materials. Our work contributes to guiding the rational design and development of enhanced SRG hydrogels and elastomers.

Collective decision-making requires individuals to reconcile diverse, often conflicting opinions to reach a common course of action. However, within a group, they rarely exert equal influence, leading to non-reciprocal communication patterns manifested as leader-follower relationships and social hierarchies. Here, using homing pigeon flocks as a model system, we develop a trajectory-based framework to infer and quantify hierarchy within navigating living collectives. We find that while small flocks exhibit pronounced hierarchy, increasing flock size progressively weakens it, driving the collection toward more egalitarian decision-making. We provide a physical basis of this observation using a thermodynamic framework in which non-reciprocal communication between birds carries an information-entropy cost. Our calculations reveal that hierarchy weakening observed in larger flocks is a direct consequence of maintaining a constant per-individual entropy production rate across flock sizes. Together, these results suggest that constraints on information-processing capacity may play an important role in the collective dynamics of living organisms.

Improving the particle surface frictional behavior is of considerable importance in several industries so as to manipulate the powder flowability and handling. In this work, we have studied the lubrication phenomena in an assembly of flowing bulk powder particles in presence of a fine powder lubricant. Experiments were conducted in two different shear environments, for two different levels of confinement and using three different bulk powder particles having distinct surface morphology. The added lubricant particles tend to adhere to the surface of bulk particles thereby altering their surface morphology. This results in altered inter-particle friction, which typically reduces for small addition of lubricant, but increases on its excess addition, thereby altering the particle flowability. While this behavior is generally understood through previous studies, the current work explores how the effect of confinement, shear environment and particle surface characteristics combine in a unique manner to provide modified flow behavior for different lubricant concentrations. Extended shear duration seems to extend the range of lubricant concentrations for improved flowability. On the other hand flow confinement seems to limit the extent of lubrication for these range of concentrations. Both these opposing effects also exhibit a unique dependence on the particle surface morphology and its seeming affinity with the lubricant particle. The parameter types and ranges explored comprise most conditions encountered in industrial systems, the outcome thereby providing a basis for designing of applications handling lubricant-particle mixtures.

Chemical reactions can sustain polymer motion without necessarily generating the compression required for buckling. Theory and simulations show that tension-dependent chemical transitions coupled to bond elasticity generate finite-wavelength traveling strain waves in a semiflexible polymer. In the straight chain at fixed axial span, the waves reduce mean active contraction while leaving mean elastic tension unchanged, generating compression that drives bending above a threshold. Releasing the mean load allows longitudinal waves to persist while transverse perturbations decay.

We present a phenomenological, mean-field model for condensates of intrinsically disordered proteins that describes inverse phase transitions and qualitatively predicts reentrant phase behavior as a function of salt concentration. The model is based on a matrix-based formulation of the Flory-Huggins free energy, in which the enthalpic interaction parameter and the protein valence, defined here as the number of effective "sticky patches", are treated as free parameters. Its central insight is that integrating out dynamics of fast-moving molecular species generates an effective entropic force that increases the free-energy barrier to mixing, even within a mean-field description. We account for this by linking Gaussian integration of co-solutes to the Schur complement of the matrix-based Flory-Huggins free energy. This provides a general thermodynamic framework illustrating how enthalpic interactions that increase the number of available microstates necessarily induce effective entropic forces. We demonstrate the expressiveness and predictive power of the model by qualitatively reproducing recent experimental observations on the rabies virus phosphoprotein.

In sheared aggregating suspensions, flow drives both the formation and breakage of particle clusters, whose dynamic evolution influences transport and rheological properties. Understanding these mechanisms remains challenging due to the complex interplay between interparticle forces, hydrodynamic interactions, and shear flow. Using parallelized Accelerated Stokesian Dynamics (PASD) simulations, we investigate cluster microstructure and rotational dynamics, and how their coupling produces suspension stress in sheared, attractive non-Brownian suspensions. When interparticle attraction dominates over separating shear forces, clusters grow until mechanical loading balances maximum interparticle bond strength. We examine how the cluster stresslet depends on cluster size, with both quantities normalized by their mechanical yielding scales. Scaled cluster stresslets collapse onto a master curve exhibiting three distinct regimes: cubic, quadratic, and linear with respect to the scaled radius of gyration $R_g$. In the cubic regime, small, compact clusters behave as rigid bodies, whose hydrodynamic stresslet scales with cluster volume $R_g^3$. As clusters grow into the quadratic regime, low-aspect-ratio clusters preferentially yield under flow, driving a proportional increase in average aspect ratio with size. High-aspect-ratio clusters follow Jeffery rotational dynamics within the flow-gradient plane, spending longer durations aligned with the flow and thereby reducing their time-averaged hydrodynamic stresslet to scale as $R_g^2$. In the linear regime, clusters approach the maximum size sustainable by the interparticle bonds. The internal tension is bounded by the maximum bond strength, limiting the stresslet to an $R_g$ dependence. These findings establish a mechanistic framework connecting microscale cluster morphology and dynamics to macroscale rheology.

Data-driven reduced-order modelling (ROM) of turbulent flows is based on an efficient and physical low-dimensional representation of the flow process. Such a dimension reduction can be achieved using proper orthogonal decomposition (POD) or non-linear autoencoders. Capturing the inherent non-linearities in turbulent flows offers the potential for improved compression rates. This work proposes the local tangent residual (LTR) as an a priori estimate of the potential benefit of non-linear dimension reduction for a given dataset. The LTR is based on the local geometry of the data points, requiring neither prior model training nor the definition of a threshold parameter. For all datasets investigated in this work, namely, two vortex street cases and the turbulent wake flow of a wind turbine, the dominant trends in autoencoder compression performance are reproduced by the proposed LTR. The results are further contextualised through the decoder linearisation error (DLE). The DLE quantifies the non-linearity of the trained decoder by comparing it to a linearised surrogate model, which enables physical interpretability of the non-linearities. Together, a large non-linear compression potential in the turbulent flow, as quantified by the LTR, is corroborated by a large DLE, i.e., a pronounced non-linearity captured in the trained autoencoder. The LTR thus enables practitioners in turbulent flow modelling to determine a priori whether non-linear compression is worthwhile, avoiding the substantial computational cost of autoencoder architecture search and hyperparameter tuning in cases where POD already suffices.

We developed a machine learning (ML) surrogate trained on instantaneous large eddy simulation (LES) data filtered using proper orthogonal decomposition (POD) to predict mean flow fields in natural rivers with complex geometries. The surrogate enables efficient prediction of mean flow fields downstream of marine hydrokinetic (MHK) turbine arrays at a fraction of the computational cost of high fidelity simulations, facilitating turbine layout optimization in natural waterways where bathymetry, turbulence, and turbine interactions influence the available energy resource. We demonstrate the capabilities of the model at a real world tidal river site under ebb tide conditions. Complex bed bathymetry and planform geometry generate substantial background turbulence that can obscure turbine wake signatures. POD is employed to extract relevant flow structures, improving the ability of the ML model to learn wake dynamics. First, LES is performed at the tidal site to generate training data. POD is then applied to decompose the instantaneous LES fields into spatial modes. Selected modes are used to train a three dimensional convolutional encoder decoder network to predict time averaged velocity fields. This selective filtering reduces the influence of dominant background fluctuations while preserving information relevant to turbine wakes. At equivalent network size and training cost, the POD filtered surrogate reduces the mean squared error by three orders of magnitude compared with the same network trained on unfiltered LES data.

Twin tandem jets in crossflow are examined by 40\ kHz time-resolved particle image velocimetry (PIV) over nine spacing--velocity-ratio conditions ($L=2d$--$4d$, $r\approx3$--7; 68 twin cases, 11 single-jet records). The front jet is diluted: its trajectory lies below the single-jet reference, with a near-field segment up to 40\% shorter, and its velocity ratio falls to an effective value $r_{\mathrm{eff}}

We construct a second-order, linear, and fully decoupled scheme for Rayleigh--Bénard convection between Navier-slip walls. The nonlinear terms are treated explicitly and multiplied by a scalar with exact value $1$ and no energy contributed to the continuous problem. As a result, each BDF2 step, with a rotational pressure correction, solves only constant-coefficient linear problems. For the time discretization, we prove that, for any time-step, the energy decays when the walls have equal temperatures, under a condition on the thermal weight, and the energy is bounded on finite time intervals when heated from below. Relaxing the scalar towards $1$ preserves both estimates. Energy stability does not control the accuracy of the scalar; the velocity and temperature fields are computed with its unrelaxed value, whose deviation from $1$ scales like $(E/C)(\delta t/\tau)^3$ for kinetic energy $E$, time-scale $\tau$ of the flow, and weight $C$ of the scalar equation. In our tests, choosing $C$ comparable to $E$ keeps this deviation small and doubles the largest time-step for which steady rolls are reproduced to a relative difference of $10^{-8}$. With Taylor--Hood elements, we observe second-order convergence in time, recover the critical Rayleigh numbers, and match published Nusselt numbers to within $0.5\%$. A three-dimensional implementation passes corresponding validation tests.

Structures with large global contributions to a flow field are not necessarily those that are most closely associated with a specified engineering observable. We propose a time-lagged cross-correlation (TCC) ranking criterion to extract target-related dynamical structures from a fixed modal expansion while preserving existing spatial modes and temporal coefficients. The criterion ranks mode groups by the mean squared norm of cross-responses between their flow contributions and the observable over a lag window. It is tested separately using dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD). TCC-DMD analysis shows that TCC recovers three low-contribution target structures from a dominant background in a synthetic flow. The reconstruction error for the target subfield is 2.15\%. In the cylinder wake, different force observables select structures associated with the vortex-shedding fundamental, slow drag variations, and the second harmonic. In the cavity case, selected modes connect two main frequency bands of the target observable to distinct spatial amplitude and phase distributions. TCC-POD analysis shows that the criterion minimises the weighted truncation error of the correlation operator among equally sized subsets of the fixed orthogonal basis. A comparison with canonical correlation decomposition further reveals differences between fixed-direction selection and correlation-based basis construction in the spatial structure and retention of flow information. Lag aggregation can improve structure identification when zero-lag association is insufficient. The gains depend on the cross-response distribution and window selection. TCC separates target-related ranking from mode-set construction, enabling comparison of spatial structures associated with different observables within the same modal expansion.

We present a thorough theoretical investigation of the shear force exerted on a horizontal plate undergoing fast (MHz range) longitudinal oscillations in presence of a spherical particle suspended in the liquid at close proximity to the plate. This hydrodynamic problem is relevant toward the analysis of frequency response (i.e., complex impedance) of Quartz Crystal Microbalance (QCM) to discrete (particulate) adsorbates. For low areal density of adsorbates, the contributions of individual particles remain additive, rendering the theory applicable towards quantitative interpretation of the experimental measurements. For adsorbates much smaller than the viscous penetration depth, the closed-form analytical expressions for the complex impedance were derived for particles of arbitrary density, assuming a lubricated contact (i.e., non-localized adsorption). The theoretical predictions were shown to be in an excellent agreement with accurate Finite Element numerical computations. The validity of the theoretical approach was confirmed by QCM measurements conducted for polystyrene nanoparticles in a broad range of sizes, from 32 nm to 510 nm, adsorbing onto gold/silica sensor upon varying the oscillation frequency.

Scientific machine learning provides a promising framework for solving complex problems in science and engineering. Notably, physics informed neural networks (PINNs) have shown considerable potential for solving differential equations and modelling engineering systems. Solving time fractional Navier Stokes equations (TFNSEs) on complex domains is challenging due to temporal nonlocality, nonlinear flow dynamics, geometric complexity, and incompressibility constraints. To address these challenges, we propose a geometry gated, divergence-free Gaussian radial basis function Kolmogorov Arnold network (GeoDiv KAN). The proposed architecture uses geometry dependent feature gating and a streamfunction formulation to preserve incompressibility by construction. GeoDiv KAN is evaluated for the time fractional incompressible Navier-Stokes equations on square, circular, and star-shaped domains. Numerical experiments show that GeoDiv KAN achieves higher predictive accuracy than PINN, PIKAN, RBF KAN, and DF RBFKAN across the considered benchmark problems. To establish practical relevance, GeoDiv KAN is applied to two data driven CFD cases: unsteady flow past a circular cylinder using the \href{ this https URL }{Zenodo dataset} and turbulent RANS flow through a complex U bend using the \href{ this https URL }{U-bend dataset}.

The evolution of long wavelength perturbations of traveling wave 2-soliton solutions of the Kadomtsev-Petviashvili II (KP) equation are investigated using modulation theory. An initial-boundary value problem for a system of hyperbolic conservation laws is formulated for amplitude and slope perturbations to soliton legs of the resonant (Y-shaped) and X-shaped KP traveling wave solutions. The vertex where individuated soliton legs coalesce is modeled as a moving free boundary where information between the soliton legs can pass. The linearized hyperbolic system is proven to be well-posed under suitable initial conditions and is solved exactly. In the case of the resonant Y-shaped soliton, all admissible simple (rarefaction) waves of the nonlinear system are characterized. Specific perturbations of Y-waves can lead to the dimensionality of the modulated solution changing, corresponding to a physical geometric change to the multi-soliton pattern. Spontaneous leg deletion and leg creation can occur. The conditions under which the Y-wave modulation system can experience gradient catastrophe are given. Gradient catastrophe is regularized by the formation of a new leg, with an augmented modulation system proposed to describe the growth of the new leg. On the other hand, the X-wave system can be reduced to two independent line soliton modulation systems. These findings reinforce the prevalence and generality of resonant Y-shaped vertices in the KP II system and this http URL theoretical modulation predictions are supported by direct numerical simulations of KP II, which show good agreement with the analysis.

We formulate anisotropic relativistic spin hydrodynamics in a parity-even magnetized medium using an Israel--Stewart entropy-current construction. Treating the magnetic field at leading order in the gradient expansion reduces the rotational symmetry to $SO(2)$ and separates spin susceptibilities and dissipative transport into longitudinal, transverse, and mixed channels. A restricted quadratic entropy current yields transient equations for the retained dissipative stresses and spin fluxes. We analyze a minimal linear closure around an unpolarized homogeneous equilibrium, retaining dynamical magnetic-flux perturbations but no explicit spin-magnetization coupling; spin and magnetic fluctuations mix through the fluid variables. Infrared coefficient equations and ultraviolet characteristic expansions organize the magnetosonic and Alfvén-like spectra together with spectator spin-flux poles. The first-order truncation exhibits unstable boost-sector poles and superlinear large-wave-number branches, interpreted as diagnostics of the truncated equations rather than microscopic dispersion predictions. For the baseline parameters, finite relaxation times yield asymptotically linear propagation branches and finite relaxation poles, with no growing modes found on the sampled grid. The characteristic speeds depend nonmonotonically on spin transport and provide necessary light-cone diagnostics, without establishing general stability or strong hyperbolicity.

Regularized lattice Boltzmann methods improve numerical stability by projecting the nonequilibrium distribution onto its hydrodynamic second-order Hermite sector and filtering the remaining kinetic modes. We introduce a separate relaxation time for the complete complementary kinetic subspace. The resulting extended-regularized lattice Boltzmann method (E-RLBM) interpolates continuously between the Bhatnagar-Gross-Krook and regularized collision operators while retaining a two-rate implementation. A Chapman-Enskog expansion shows that the isothermal Navier-Stokes equations are recovered with kinematic viscosity $\nu=c_s^2(\tau-\Delta t/2)$, independently of the kinetic relaxation time $\tau_{\rm nh}$, whereas $\tau_{\rm nh}$ changes higher-order truncation errors. For linear transverse shear, its first effect is a fourth-derivative term whose coefficient depends on the direction of propagation relative to the lattice. This fourth-order coefficient is affine in $\tau_{\rm nh}$. For linear shear on D2Q9 and $\tau_{\rm nh}$ between $\tau$ and $\Delta t$, it lies between the corresponding BGK and RLBM values in every propagation direction. Stability maps for the decaying Taylor-Green vortex and flow past a rectangular obstacle show that an appropriate kinetic relaxation substantially enlarges the stable parameter domain. In a Taylor-Green convergence test with consistent initialization, all three operators converge at second order, and their error differences follow the hyperviscous coefficient for diagonal shear waves: the E-RLBM error is about 6% above the BGK error and about 40% below the RLBM error; in a double shear layer at Re = 80000, the E-RLBM follows the RLBM convergence curve. The proposed collision operator therefore provides a low-cost means of controlling nonhydrodynamic modes without introducing a full multiple-relaxation-time basis.

ADER-DG numerical method with the LST-DG predictor, when used to solve hyperbolic equations with stiff source terms, exhibits properties characteristic of IMEX computational schemes. With increasing stiffness, characterized by the parameter $z = \nu{\Delta t}^{n} < 0$, the maximum of the Courant number $\mathrm{CFL}_{\rm max}$ of the ADER-DG numerical method increases. In the region of strong stiffness $|z| \gg 1$, a linear increase in the Courant number $\mathrm{CFL}_{\rm max}(z) \sim |z|$ occurs. In the region of small source terms $|z| \ll 1$, the results $\mathrm{CFL}_{\rm max}(z)$ transform into known results for the problem $\mathrm{CFL}_{\rm max}(0)$ without source terms. In the transition region $|z| \sim 1$, a range of insignificant decrease in the Courant number $\mathrm{CFL}_{\rm max}(z)$ is discovered. In the linear case, instability is violated precisely when one of the matrix eigenvalues reaches $\lambda = -1$, regardless of the phase $\theta$ of the numerical solution. A rigorous stability theory of the ADER-DG numerical method for stiff problems for arbitrary degree $N$ of basis polynomials is constructed. The stability condition is simplified to solving a polynomial equation for the Courant number $\mathrm{CFL}$. Highly accurate dependencies of the Courant number $\mathrm{CFL}_{\rm max}(N, z)$ of the ADER-DG method on the parameter $z$ are obtained. A rigorous direct proof of the approximation of the ADER-DG method is presented. Approximation orders $p = N+1$ for arbitrary degrees $N$ are rigorously derived. A set of numerical experiments is carried out to apply the ADER-DG method to solving both a linear advection-reaction equation and the system of Euler equations for a two-component reacting medium. The results obtained in these calculations confirm the theoretical results well.

When the parameter of a PDE surrogate is the flow domain itself, the key/value set of an attention model must encode that domain. We present CARS (Coronary Artery Rapid Surrogate), a learned surrogate for the finite-volume solution map of the steady incompressible Navier-Stokes equations on coronary lumens built from image-derived centerlines. CARS maps a centerline with per-point lumen radius and a scalar inlet flow rate to pressure and velocity at arbitrary query points. The attention focal set is the case's own centerline, so geometry fusion costs $O(N n_f)$ rather than $O(N^2)$ in the number of evaluation points. Trained per territory on $2{,}700$ OpenFOAM solutions with synthetic focal lesions, CARS reaches relative $\ell_2$ errors of $0.120/0.149$ (pressure/velocity) on left-coronary and $0.063/0.119$ on right-coronary test sets, in $87$~ms per case against a solver wall-clock of $572$-$1{,}063$~s. It outperforms four parameter-matched neural operators, and accuracy saturates eightfold below the operating focal count. Fractional flow reserve derived from the predicted pressure matches the CFD label at Pearson $r = 0.941/0.993$ and reproduces the $\mathrm{FFR}\le 0.8$ decision in $97.7\%/96.3\%$ of held-out cases. The predicted velocity does not satisfy continuity closely enough for derived quantities, and the weights are territory-specific.

We study the problem of finite time singularities in the isentropic compressible Euler equations in multiple dimensions with radial symmetry. Our initial data consists of the radially symmetric Kidder self-similar implosion with a continuous constant density cutoff. Motivated by our recent work on the one-dimensional problem, we present high-resolution radially symmetric adaptive mesh refinement simulations that when combined with asymptotic similarity solution analysis present a full picture of the ensuing dynamics of the implosion. From the cutoff point in the initial data, an expanding wave emerges. The endpoints of the wave follow the "imploding" and "exploding" characteristic speeds associated with the system of hyperbolic conservation laws. This wave has much more complex structure than the exact non-centered rarefaction wave that emerges in the one-dimensional problem. As in the one-dimensional case, the inner Kidder solution is swallowed up by the expanding wave as time approaches the singularity time. However, unlike the one-dimensional case, a blowup occurs along the point where the `imploding' side of the expanding wave attaches to the Kidder solution. This composite blowup has an asymptotic self-similar form that has an interpretation in terms of the Gurderley-type self-similarity structure. The numerical method for the PDE necessitates a Lagrangian scheme to avoid the numerical diffusion inherent in Eulerian methods. We use a leapfrog method coupled to recursive refinement of the mesh near the blowup, which allows for very high resolution simulations, resolving many orders of magnitude of the self-similar blowup. Consistent with prior rigorous results for these equations, the blowup does not involve mass concentration and exhibits a critical $L^p$ space for the concentration of the density, depending on the dimension of space.

Higher-order interactions create a combinatorial space of candidate dynamical terms, making network reconstruction difficult when node dynamics, coupling functions and interaction topology are unknown. Here we identify a regime in which weakly coupled higher-order chaotic networks admit a higher-order interaction reduction. Weak coupling largely preserves the statistical structure of intrinsic chaotic motion, while dense higher-order neighborhoods provide repeated sampling of weakly correlated multi-node inputs received by hub nodes. Consequently, the aggregate interaction field can be represented by a compact function of the hub state, together with a node-dependent offset and finite-neighborhood fluctuations. We exploit this reduction to learn dynamically relevant coupling forms and reconstruct interactions of different orders by sparse regression. Numerical experiments validate the effectiveness of the framework within an effective region of the tested coupling-parameter space, including representative weak-coupling settings. Reconstruction remains stable at the larger network sizes and higher hub-neighborhood densities examined. Additional tests on networks constructed from empirical topologies show that structural priors reduce data requirements and that the framework remains applicable to heterogeneous chaotic dynamics. These results identify reduction of aggregate higher-order inputs as an interpretable route to dimensional compression and joint dynamical and structural reconstruction.

We study the dynamics of recurrent neural networks with random couplings, sublinear odd activation functions, and temporally correlated noise. Using large N methods, we determine stationary correlations and distinguish the loss of local linear stability from the onset of chaos, characterized by a positive largest Lyapunov exponent. These thresholds delimit an intermediate regime in which local instability coexists with asymptotic stability under a common noise history. Their separation depends on both the noise correlation time and the asymptotic growth of the activation function. We show that internal noise with any finite correlation time cuts off the divergence of the network's intrinsic correlation time tau_corr at the edge of chaos; it exhibits a critical scaling tau_{corr,max} propto 1/sqrt{D_0}, where D_0 is the integrated noise strength. Static random input instead produces coincident thresholds and a divergent correlation time. We also calculate the frequency-dependent participation dimension from a four-point correlation function. Its zero-frequency value is inversely proportional to the fourth power of the network correlation time, predicting a smooth minimum at the weak-noise chaos threshold. Numerical simulations support the large-network predictions and reveal appreciable finite-size effects.

Collective behaviors such as synchronization transitions are emergent properties of coupled oscillator systems, and how to reproduce them from data for large-scale systems remains an open problem. Here we propose a model-free coupled reservoir computing (CRC) architecture for constructing digital twins of coupled oscillator systems. The CRC decomposes the twin into three modules that mimic the nodal dynamics, the coupling function, and the coupling network, respectively, so that the modules can be reassembled for different coupled systems. Importantly, it is found that the trained CRC reproduces not only the collective states, including complete synchronization, phase synchronization, and chimera states, but also the synchronization transitions as the coupling strength varies, and the predicted collective behaviors are practically identical to those obtained by direct simulations of the original system. Moreover, the CRC is trained only on the time series of an isolated oscillator and of a pair of coupled oscillators, and the trained modules can be reused for different complex networks and for non-identical oscillators. Our findings establish the CRC architecture as a promising platform for digital twins of complex systems.

We investigate the non-linear magnetization dynamics of two identical anisotropic macrospins coupled by dipolar interaction and subjected to periodic transverse excitation. The coupled Landau- Lifshitz-Gilbert equations are solved numerically using a fourth-order Runge-Kutta method. By combining bifurcation diagrams, local-maxima analysis, Lyapunov exponents, and two-dimensional stability maps, we characterize how dipolar coupling, transverse driving amplitudes, and uniaxial anisotropy govern the long-time dynamics. The results reveal a non-monotonic reorganization of dynamical regimes, with alternating intervals of enhanced and suppressed instability. Analysis of symmetric and antisymmetric coordinates distinguishes the collective and relative spin responses, while Fourier spectra and three-dimensional trajectories provide complementary frequency-domain and geometrical characterizations. Simultaneous positivity of the two largest Lyapunov exponents identifies parameter regions consistent with hyperchaotic dynamics. Finally, analytical linearization and ferromagnetic-resonance calculations reveal the distinct coupling dependence of the collectivemode frequencies and clarify the limitations of the linearized description beyond the stability thresholds of the collinear reference state. These findings establish a unified framework for understanding the interplay of dipolar coupling, anisotropy, and periodic excitation in the non-linear dynamics of a minimal interacting-spin system.

We predict that quantized transport of dark solitons and domain walls can be observed in mutually sliding optical lattices in both focusing and defocusing nonlinear materials. Two different classes of underlying periodic backgrounds are considered here -- unstaggered and staggered -- which are accurately represented, respectively, by the in-phase and out-of-phase trains of Wannier functions. The nonlinear excitations formed on top of these backgrounds -- dark solitons and domain walls -- are sustained by defocusing or focusing Kerr nonlinearities of the optical medium. Despite non-zero asymptotics, dark solitons and domain walls can still undergo quantized topological transport in dynamically changing refractive index landscape when they and background on which they are constructed are dynamically stable. The extended intervals of propagation constants (and, correspondingly, of the background amplitude) and lattice depths, where stable quantized transport occurs, are identified for both dark solitons and domain walls. Outside these intervals, the quantized transport regime is found to be unstable. Our results extend the concept of nonlinear topological transport from bright to dark soliton states.

The attenuation of weak aerodynamic pressure fluctuations in porous trailing edges affects up to which frequency trailing-edge noise reduction is achieved. Hence, very large eddy simulations are used to analyze the frequency-dependent relationship between the local pressure gradient and flow velocity for a weak pressure wave in low Reynolds number flow through a structured porous material. This frequency response compares favorably to the unsteady Darcy equation and indicates that the response has two regimes where viscosity dominates the high-frequency regime, whereas the low-frequency regime shows more clearly flow paths with locally higher inertia.

Band-ensemble Spectral Proper Orthogonal Decomposition (SPOD) computes modes from bands of neighboring Fourier modes of the full-length Fourier transform. Compared with the commonly applied Welch-based SPOD algorithm, this allows the number of modes to vary with frequency, enabling an adjustable bias–variance trade-off across the spectrum. Additionally, the resulting expansion coefficients allow precise frequency estimates to be attributed to individual modes, enabling improved detection of tonal modes in broadband–tonal flow cases.

When an obstacle moves through a compressible medium, it creates a density perturbation. Theoretical arguments regarding the shape of this density wake in Brownian suspensions either suppose infinite dilution or describe only the far field. Here, we study via experiments and numerical simulations the closing of the density perturbation just behind a circular obstacle in dense 2D suspensions of particles that are thermal or self-propelled. In the thermal case, we show that the characteristic length of the wake is a non-monotonic function of density, decreasing then increasing. We rationalise the scalings of both regimes by analytical arguments that highlight the role of the compressibility factor of the suspension. Based on this new understanding of the passive case, we show that the influence of self-propulsion observed in experiments and simulations can be understood as if the obstacle is effectively larger in an active bath, with non-trivial and distinct roles of the self-propulsion velocity and of the persistence time.

Airborne transmission of biological matter is likely to cause numerous respiratory distress in coastal populations during certain harmful algal blooms. While we know that dissolved algal toxins aerosolize, the contribution of particle-associated toxins is still unknown. The observation of microalgae in the atmosphere suggests that cells or cell debris could be a carrier. Exchange of particulate matter between ocean and atmosphere is driven by sea spray: microplastics and bacteria aerosolize in jet droplets, following the bursting of air bubbles. However, current models for particle capture only consider surface effects, which fail to explain how large microalgal cells (5-50 um) can be entrapped in jet drops (100-800 um). Here, we demonstrate with a variety of species that microalgae are consistently captured in jet drops, and derive a new particle capture model based on the hydrodynamics of the jet. Using the enrichment factor, which measures the increase in concentration in the first jet drop relative to the bulk, we uncover two regimes. The transition between regimes strongly depends on cell size. In addition, we highlight the dynamics of particles within the jet and derive an enrichment model based on hydrodynamics rather than surface considerations. This work widens and generalizes established results on bacterial and microplastic entrapment in jet drops, resolving discrepancies found in the literature. Finally, we demonstrate that sea spray can aerosolize toxic Ostreopsis cf. ovata cells. This reveals a potential particulate pathway for airborne toxicity during harmful algal blooms and raises the question of the relative contribution of particles to that of dissolved toxins.

This experimental study demonstrates MHz-order acoustic control of Rayleigh-regime liquid-jet breakup using a compact through-hole lithium niobate thickness-mode transducer integrated at the nozzle exit and driven near its 6.7 MHz resonance. Jet dynamics were measured by high-speed shadowgraphy at 50,000 fps, and breakup lengths were obtained from instantaneous jet-length records using an autocorrelation-based method that identifies statistically separated breakup events. Acoustic actuation produced visible interfacial corrugations and reduced the normalized breakup length, $L_b/d$, for both water and glycerol--water jets. In water, the response was threshold-like at low Weber number and weakened as the jet velocity increased to We ~ 50. A reduced-order threshold correlation, fit to the water amplitude and velocity sweeps, captured this abrupt shortening and the subsequent loss of actuation efficacy. More viscous glycerol--water mixtures shortened immediately at low forcing, indicating a distinct acoustic-coupling regime rather than a universal collapse of the water response. A wetting-control experiment showed that liquid spreading at the nozzle base can also shorten the jet, so the measured response reflects coupled radiation-pressure forcing, capillary-wave feedback, and wetting-mediated disturbance injection. Resolved droplet tracking further showed that MHz excitation changes the visible gate-crossing droplet population, although sub-resolution mist and micron-scale atomization were not measured. These results establish through-hole MHz actuation as a compact route for modifying free-surface jet breakup and provide a repeatable image-analysis protocol for experimental-fluid-mechanics measurements.

The fragmentation of a liquid jet in a crossflowing airstream arises from a complex interplay between aerodynamic forcing and interfacial instabilities acting across a wide range of length scales. We examine the spatial evolution of droplet size distributions along the jet trajectory using a combination of high-speed shadowgraphy and digital in-line holography, allowing simultaneous characterization of jet morphology and volumetric droplet size distributions. The results demonstrate a clear progression of breakup mechanisms, from near-field bag rupture to downstream rim, ligament, and node disintegration, each associated with distinct characteristic length scales. This evolution is reflected in the droplet size distributions, which broaden and become increasingly polydisperse downstream relative to the near-field distributions. By systematically varying the liquid-jet and airstream Weber numbers, we identify distinct breakup modes, and construct a regime map that delineates the column-breakup, isolated-bag-breakup, and interacting-bag regimes. Furthermore, by incorporating the dominant instability mechanisms, including Rayleigh-Taylor and Rayleigh-Plateau instabilities associated with the observed column, bag, and multi-bag breakup modes, we develop a theoretical framework for jet atomization in crossflow. The framework relates instability wavelengths to characteristic droplet sizes, and reasonably captures the experimentally observed trends. We found that stronger aerodynamic forcing induces earlier breakup, decreases the characteristic instability length scales, and generates finer droplets dispersed over a wider spatial region. Overall, the study establishes a quantitative relationship between instability-driven fragmentation dynamics and droplet size distributions, thereby connecting interfacial instabilities with measurable spray characteristics.

Bubble size, depth, and spatial distribution govern transport and uniformity in multiphase flows. A single shadowgraphic view cannot separate bubble diameter from focal-plane displacement, as image signatures depend on both, while multicamera systems add optical access, calibration, and cost. We develop a single-camera physics-guided framework combining direct numerical simulation (DNS), validated Monte Carlo ray tracing, preprocessing, and focus-conditioned multitask deep learning to recover three-dimensional bubble position and physical-equivalent diameter from two-dimensional shadowgraphs. DNS-resolved bubble label images rendered at multiple focal-plane settings. The ray tracer reproduces shadowgraphic signatures with errors below $3\%$ (intensity), $1\%$ (apparent size), $15\%$ (blur), $6\%$ (numerical aperture), and $4\%$ (edge-spread-function shape), running $\sim30\times$ faster than the CPU implementation. The dataset has $900$ frames and $87{,}728$ labeled instances, partitioned by DNS timestamp to prevent leakage and expanded to over $10^{5}$ crops by broad-depth controlled-density rendering. A multitask network predicts signed depth and diameter from crops and focal-plane coordinates, achieving $\sim97.6\%$ normalized depth accuracy on held-out data; a closed-loop DNS-to-image-to-reconstruction test of $180$ bubbles gives diameter error below $9.71\%$ ($\sim90.29\%$ accuracy). On experimental images at four radial planes ($142$--$971$ bubbles each), PDF overlap is $68\%$--$92\%$ and log-PDF correlation is $0.72$--$0.87$. At the focal reference plane ($11{,}679$ bubbles), overlap is $\sim86\%$, correlation is $0.93$, and full-distribution, $D_{99.8}$, and composite errors are below $7.7\%$, increasing with focal-plane distance and defining a recoverability limit. Without stereoscopic hardware, the framework offers a scalable diagnostic for dense bubbly flows.

A circular cylinder undergoes drag crisis beyond the critical Reynolds number via formation of a laminar separation bubble (LSB) downstream of each shoulder. We investigate the dynamics of these LSBs at low intensity free stream turbulence (FST). We report, for the first time, a synchronization between formation of LSB and the Karman vortex shedding for a stationary cylinder, albeit only at the lowest FST investigated. Increasing the FST to mimic the background FST in some of the past studies completely alters the transition dynamics, as several subregimes observed at the lowest FST disappear at higher FST. The findings provide a valuable benchmark of unperturbed transition dynamics.

We study the response of compressible microtubule-based active fluids to sinusoidally varying activity patterns, using experiments and theory. Microtubules accumulate in low-activity regions and are depleted from high activity ones, with the density difference controlled by the wavelength of the activity pattern. To explain these observations the continuum model needs to account for both active stresses that are proportional to nematic order tensor and the isotropic active pressure. At short wavelengths, active vortices spanning adjacent high and low activity regions suppress density modulation. At larger wavelengths, vortical flows confined to the low or high activity region allow for the emergence of the density contrast. Our work shows that a minimal theoretical model of active compressible fluids accurately reproduces experiments, while elucidating the fundamental constraints on control protocols that seek to tame their chaotic dynamics.

Macroscopic phase segregation in binary active mixtures can emerge solely from clutter noise: local, composition-dependent stochasticity, without repulsion or anti-alignment torques. Using an agent-based Vicsek model, we show that clutter noise alone destabilizes the mixed state, producing multi-stripe, co-moving band, and metastable counter-propagating morphologies, as well as a stable phase-segregated polar fluid. Our hydrodynamic theory shows that clutter noise suppresses local polar order and transport efficiency, consistent with the demixing observed in the agent-based model.

Polymerized membranes are paradigmatic fluctuating systems in which geometry, elasticity, and statistical fluctuations combine to produce anomalous long-distance behavior. In the disorder-free flat phase, bending rigidity increases at long wavelengths while in-plane elastic moduli soften. Quenched random metric and curvature introduce competing thermal and disorder-induced fluctuations. We review perturbative and nonperturbative field-theoretical approaches to these systems, from pure membranes to their disordered counterparts. Early one-loop studies identified a disorder-free fixed point, $P_4$, and a zero-temperature disorder-dominated fixed point, $P_5$. A subsequent nonperturbative renormalization-group analysis revealed a third fixed point, $P_c$, at finite temperature and disorder, governing a continuous wrinkling transition between the thermally dominated flat phase and a disorder-dominated glassy phase. Higher-order perturbative calculations also recover a $P_c$-like fixed point, with anomalous dimensions remarkably close to the reexpanded nonperturbative predictions. This scenario connects naturally with the wrinkling transition observed in partially polymerized lipid membranes. The three experimental scaling regimes of height fluctuations can be associated with $P_4$, $P_c$, and $P_5$, with theoretical exponents showing good quantitative agreement with measurements, particularly at criticality. Finally, we discuss the status of the glassy scenario, the unresolved discrepancy between perturbative and nonperturbative fixed-point stability predictions, and possible extensions to defective graphene and related two-dimensional crystalline materials.

Molecular modelling of electrochemical systems at larger than atomic scales poses particular challenges, not least the ability to represent correct thermodynamic, hydrodynamic and dielectric properties while still being computationally viable for large scale applications. In the case of aqueous electrolytes such as those used in vanadium-based batteries with oxidation-reduction (redox) reactions, both a background medium that can respond to localised electric fields due to high-valence ions and control over ion transport properties are crucial to embed consistently in the model. To this end, we propose the use of Dissipative Particle Dynamics (DPD) combined with a newly-devised highly coarse-grained polarisable water model with pairwise interactions designed to produce realistic thermodynamic behaviour as the basis for the aqueous electrolytes found in vanadium redox flow batteries (VRFB). We consider how the core water model can be modified to incorporate the ionic species found in VRFB catholytes and anolytes, as well as how the DPD pairwise thermostat forces can be parameterised to attain realistic diffusivities for those species.

We study cyclic shear in a lattice elastoplastic model of amorphous materials. The model displays a threshold shear amplitude $\gamma_{\rm c}$, which increases with sample annealing. For imposed amplitudes $\gamma_0\lesssim\gamma_{\rm c}$, it shows slow progression to an absorbing elastic state. For $\gamma_0\gtrsim \gamma_{\rm c}$, it shows slow fatigue and delayed material failure. Our key contribution is to elucidate a mechanistic understanding of this behaviour. We show that progression to an absorbing state maps to single element diffusion on a finite interval with two absorbing boundaries. We derive expressions for the decay rate of the fraction of active elements, and the survival distribution. The diffusing variable is the local elemental strain, which takes two jumps stroboscopically per cycle. Once the value at any site diffuses below its yielding threshold, the element behaves elastically. This leads to a gradual accumulation of strains just below threshold. For $\gamma_0\lesssim \gamma_{\rm c}$ this diffusive behaviour is preceded by many cycles in which cooperativity between elements via stress propagation is also important. For $\gamma_0 > \gamma_{\rm c}$, stress propagation dominates and precipitates failure. For $\gamma_0\gtrsim \gamma_{\rm c}$, the same accumulation of elements just below local threshold that led to an elastic state for $\gamma_0\lesssim\gamma_{\rm c}$ accounts for the fatigue that brings the system to the brink of failure. We evidence this via simulations in which the strain amplitude artificially exceeds $\gamma_0 $ in each half cycle, before reverting to the system's actual state at $\pm\gamma_0$ and resuming the next half cycle. During fatigue, the stress-strain slope $d\sigma/d\gamma$ evolves towards unity at $|\gamma|=\gamma_0^-$, signifying perfect elasticity within cycle, yet towards zero at $|\gamma|=\gamma_0^+$, precipitating failure.

The Kovacs effect, characterized by nonlinear, path-dependent structural recovery, is a hallmark of glassy systems. In soft colloidal microgel glasses, the stiffness of the constituent particles governs their deformation, swelling, rearrangement, and response to external stimuli, thereby dictating the path-dependent structural recovery of these jammed non-equilibrium systems. To investigate this influence, microgels of different stiffnesses were synthesized by adjusting the concentration of the polar crosslinker, N, N'-methylenebisacrylamide (MBA). The relaxation of the storage and loss moduli was measured using oscillatory rheology under diverse temperature ramp rates, and cryo-FESEM imaging provided direct visualization of the underlying particle packing. While the rapid adaptability of soft particles and the kinetic arrest of stiff ones suppresses Kovacs asymmetry, intermediate-stiffness particles exhibit moderate thermoresponsivity, traversing distinct energy landscapes on heating and cooling to maximize asymmetry and dissipation. Cryo-FESEM micrographs, displaying gel-like networks in soft particle suspensions, dense packing in stiff particle suspensions, and disordered, compact structures in intermediate-stiffness systems, corroborate these findings. Our results demonstrate that intermediate-stiffness PNIPAM microgels optimize structural recovery, rendering them promising candidates for forming colloidal glasses and establishing Kovacs asymmetry as a robust probe of non-equilibrium dynamics in glassy systems.

Several filamentous biopolymers exhibit unusual polymerization-depolymerization kinetics where continued elongation (shortening) is possible only in an `active' (`inactive') state while occasional random transition (switching) between the active and inactive states takes place. Here, we present a minimal stochastic model capturing only the key features of random elongation-shortening-switching kinetics of a generic filament. The structure and/or function of the filament ends when its length hits a critical value during its shortening; the time to reach this critical length can be formulated as a first-passage time (FPT) and for its calculation the critical length is treated as an absorbing boundary. Moreover, the lengths of the filaments that inspire our model are constrained to a finite maximum value $\mathcal{N}$; therefore, in our model we impose a reflecting boundary beyond which the filament cannot grow. We determined the distribution of the FPT and derived its first two moments. We identify a critical point where the drift of the tip of the filament vanishes making its movement purely diffusive; at this critical point, in the limit $\mathcal{N} \to \infty$, the fluctuations in the FPT diverges and MFPT becomes infinite indicating `critical slowing down'. Our analytical results will serve as the testing ground for the accuracy of the approximate theoretical results of more realistic models for polymerization-depolymerization kinetics of specific bio-filaments.

The solid-liquid equilibrium and solubility of NaCl in water were investigated using molecular dynamics simulations with the NaCl/Madrid force field and the TIP4P/05 water model. Particular attention was given to the influence of the intermolecular cut-off radius, rcut, used to identify ions belonging to the crystalline phase. Simulations were initiated from a NaCl crystal immersed in an aqueous NaCl solution, following the configuration proposed by Manzanilla-Granados et al. After equilibration, the system was analysed over an extended simulation trajectory. The radial distribution function, g(r), was used to establish a physically motivated criterion for distinguishing the crystalline and aqueous phases. Specifically, the first minimum following the principal Na-Cl correlation peak was used to characterise the ionic coordination environment and constrain the range of meaningful cut-off radii. The number of ions remaining in the crystalline phase was then evaluated as a function of rcut, allowing the corresponding solubility to be estimated. The resulting curve exhibits a well-defined inflection point, providing a criterion for identifying the transition between predominantly crystalline and dissolved ionic populations. This approach offers a structural basis for determining NaCl solubility directly from the evolution of the solid-liquid system, avoiding the arbitrary selection of the cut-off distance. The results demonstrate that combining radial distribution functions with cut-off-dependent analysis provides a useful framework for characterising solid-liquid behaviour and estimating the solubility of ionic crystals through molecular dynamics simulations.

Understanding the behaviour of moving objects within confined granular media is important in many technical applications. In this work we study the vertical pullout of a plate-like intruder buried at different depths within a dense granular aggregate from the onset of motion to flow around the intruder in the steady state by means of a two-dimensional polygonal Discrete Element Method. We find that the peak and steady-state drag forces depend differently on their embedding depth for different friction coefficients. Depending on the strength of friction the plate may interact with the domain walls, which enhances the drag force until failure of the aggregate, but not in the steady-state as dilation around intruder directs the force chains emanating from the plate upwards and away from the walls. If the inter-particle friction is weak, it is possible for the overhead pressure to overcome frictional resistance beyond a certain embedding depth. This prevents the formation of dilated failure zones above the intruder and changes the failure mode of the aggregate, leading to a slower decay of the steady-state drag forces with pullout distance.

The CHQ model describes viscoelastic phase separation in a polymer--solvent mixture: a Cahn--Hilliard equation for the polymer volume fraction $\phi$ is two-way coupled, through a phase-dependent cross-diffusion flux, to a damped relaxation equation for a scalar bulk elastic stress $q$. We propose a scalar-auxiliary-variable (SAV) time discretisation of this system, combining the SAV reformulation of the double-well potential with a second-order backward differentiation formula (BDF2) and a second-order extrapolation of all phase-dependent mobilities: a linear, computationally cheaper complement to the reference scheme's fully nonlinear Newton solve. The resulting method is (i) linear at every time step, with a coupling structure we prove has exactly one solution at every step, for every choice of time-step size; (ii) mass conserving, exactly, as an algebraic identity of the discrete equations themselves (the only drift ever seen numerically traces to the finite tolerance of the iterative linear solver, not a failure of the conservation property); and (iii) unconditionally stable for a modified discrete energy, via an exact one-step energy--dissipation identity. We show the energy identity extends to this filtered variant as well, with two explicit extra non-negative terms. Hence, the scheme actually producing the physics results is itself provably stable for the same energy. A Fourier--Galerkin implementation verifies that the energy identity holds at every time step to within floating-point round-off. It also confirms second-order temporal accuracy, including in the steep-interface regime, and agreement with an independently implemented nonlinear Newton--BDF2 solver. Compared with that independent nonlinear Newton--BDF2 solver, at equal grid resolution, the SAV method uses $2.5$--$3.0\times$ fewer linear-solver iterations and $1.7$--$2.0\times$ less wall-clock time.

We present a lattice gas model with random interactions quenched in space and spins quenched to the particles. The vacancy-mediated diffusion is studied in equilibrium. A two-stage slowdown is witnessed in both the mean squared displacement and the spatial overlaps. We demonstrate that the plateaus are due to anti-correlation at the corresponding length scale. The anti-correlation diminishes quickly with increasing lag time. A broad and yet finite distribution of the survival function of vacancies suggests their normal diffusion at large time limit. Our model can serve as a new playground for understanding hierarchical dynamics in glassy-like dynamical systems.

Estimating position-dependent diffusivity with the residence-time approach (RTA) requires choosing an interval width that resolves spatial variation while probing time scales compatible with a local diffusion model. We develop a selection criterion that combines bulk diffusivity convergence with local model agreement measured by the Kullback-Leibler divergence between observed and predicted first-exit-time distributions, and assess global model agreement through independent propagator analysis against unbiased molecular dynamics. Applications to water in a fluid phospholipid bilayer and three permeants in a model skin lipid barrier show that local agreement alone does not ensure global fidelity: in the skin barrier, narrow intervals minimize exit-time mismatch but predict excessive spreading, whereas requiring bulk convergence selects wider intervals with better longer-time predictions. In propagator tests, RTA profiles at the selected interval widths outperform velocity-autocorrelation-based profiles and generally improve agreement relative to position-autocorrelation-based profiles in the skin barrier, while phospholipid-bilayer rankings depend on lag time and discrepancy metric; both autocorrelation methods use harmonically restrained simulations.

The static relative permittivity is an important property in thermodynamic modeling, electrochemistry, and solvent design, but predicting it directly from molecular structure remains challenging because both electronic polarization and molecular dipole orientation contribute to the measured response. Here, we introduce CRAFT-{\epsilon} (Conformer-Resolved Atom- and Fragment-based Theory for {\epsilon}), a conformer-resolved molecular descriptor model for predicting the static relative permittivity of neutral pure liquids. Conformer free energies, molecular dipoles, and atom-resolved polarizabilities are obtained from a GFN2-xTB/ALPB 10 workflow. The molecular dipole is decomposed into chemically defined polar-fragment vectors, allowing fitted corrections to retain both the magnitude and relative orientation of local dipolar contributions. Electronic and orientational polarization are combined with a group-contribution molar volume in the Onsager-Kirkwood-Fröhlich relation. A staged parameterization with 41 parameters is applied to nonpolar, polar, and hydrogen-bonding compounds. For 1393 liquids with permittivities between 1.5 and 183, CRAFT-{\epsilon} reaches a five-fold cross-validated average absolute deviation of 2.40 ({R^2} = 0.93). Conformational averaging 15 is essential for liquids with several polar groups. Compared with an established fragment-based model with 139 parameters, it reaches a similar cross-validated RMSE (3.65 versus 3.41) with about a quarter of the parameters and applies to every liquid of the dataset. The resulting framework provides a computationally inexpensive route from molecular structure to liquid dielectric response and forms a basis for later application to solvent mixtures and electrolyte systems.

Traditional turbulence-model development relies heavily on expert knowledge and is time-consuming. This study develops an agentic AI framework, DEScover (automated Discovery of DES closures), to explore subgrid length scales for detached eddy simulation (DES). The user provides only a modeling idea: the length scale is the grid width normal to the local vortex axis. Four large language model (LLM) agents then propose, review, implement, and evaluate candidate formulations and generate scripts for CFD simulations. The Discovery Agent infers the vortex axis from various vortex-identification methods. The candidates are tested on four cases spanning canonical and engineering flows: a flat plate, a backward-facing step, a free shear layer, and an iced airfoil. For all test cases, the best candidate consistently outperforms the standard length scale based on the maximum cell size. Its accuracy is similar to, or slightly better than, that of the expert-designed shear-layer-adapted length scale. Each agentic discovery run takes about 25 minutes on average, excluding the CFD simulations. These results show that LLM-based reasoning can significantly accelerate the discovery of physically interpretable turbulence models and reduce reliance on manual expert formulation.

Successful prediction of the interaction between turbulent flows and river ecosystems is essential for flood management, development of mitigation strategies, and infrastructure protection. Natural riverbeds consist of bed materials of multiple grain sizes that interact with turbulence differently, leading to spatial classification of particle sizes. Such particle sorting processes can only be captured by models capable of handling multiple grain sizes. We present a numerical framework that couples large-eddy simulation with a multi-grain-size sediment transport module to track multiple grain size classes, their local fractions within the bed-load layer, and bed evolution. A laboratory experiment was conducted in a flume with multi-size bed material to examine sediment particle redistribution and sorting. Measured sediment grain size distributions and bed elevations were used to validate the numerical framework. The results of the multi-grain-size sediment transport model for bed deformation were then compared against those of a uniform sediment transport model, demonstrating that the former reduces the prediction errors relative to the experimental measurements from 37.98 to 3.83 percent for maximum scour depth and from 48.35 to 11.54 percent for maximum deposition height. The validated numerical framework was also applied to large-scale meandering rivers with multi-grain bed material, simulating their bed deformation and sediment sorting. The simulation results revealed the formation of particle sorting patterns in meandering rivers, with coarser and finer sediment particles accumulating near the erosional depression (scour) and depositional (point bar) regions, respectively. These findings support the coupled framework's ability to predict sediment particle sorting and highlight the importance of representing bed material heterogeneity in numerical modeling of meandering rivers.

This paper presents a grey-box framework for a robust deterministic, real-time prediction of coupled surge-heave-pitch motion in waves. The approach combines a physics-based online system identification with a nonlinear pseudo-spectral potential flow solver. Rather than prescribing a complete hydrodynamic model from captive model tests or relying on a black-box surrogate, three coupled compact, dynamics equations are identified with constrained ridge-regression of a short time-history of free-running body motion data in waves. The PSPF solver is then used to provide the future incident wave at the body's location. The PSPF and dynamic system models are coupled for continuous real-time future motion prediction in a receding horizon architecture, while the model coefficients are re-identified online to enable robust prediction to changing wave-conditions. This novel framework is demonstrated based on CFD data that has been validated for a freely floating two-dimensional rectangular box in waves. The results demonstrate a feasible framework for accurate motion forecasting up to around eight wavelengths into the future utilising data that can be gathered onboard a ship in real operations. Furthermore, it is shown that the framework is robust to changing sea-states and agnostic to underlying model geometry.

Matrix-product-state (MPS) and quantized tensor-train (QTT) representations offer a promising framework for computational fluid dynamics, with logarithmic run time and memory scaling in mesh size when bond dimensions remain bounded. Existing MPS-based solvers are Eulerian: they compress velocity fields and enforce immersed-body boundary conditions through static masks or body-fitted coordinates. Moving or flexible bodies complicate this approach: deformation requires updating MPS masks every time step, while filamentary vorticity in high-Reynolds-number flows may resist low-rank compression. We propose a complementary approach: compress the Biot--Savart kernel rather than the flow state, evolve vorticity using Lagrangian vortex particles, and represent immersed bodies by bound vortex sheets on Lagrangian surface points. Our main theoretical result is a lifting theorem: QTT rank $r$ of the kernel implies matrix-product-operator (MPO) rank at most $2^d r$ for the corresponding convolution operator in $d$ dimensions, independent of grid resolution. This bound is sharp for our interleaved ordering. With quantics tensor cross interpolation, the moment-to-local stage of a single-level fast multipole method becomes a precomputed tensor-network contraction with quasi-linear complexity, retaining Lagrangian flexibility for immersed bodies. Our PyTorch implementation (\texttt{DiffVortex}) is end-to-end differentiable, runs on GPUs, and handles $6.7\times10^{7}$ particles on a single device. We validate against reference vortex-method results for an impulsively started cylinder and exact and reference solutions for inviscid elliptical vortices. We also demonstrate two-dimensional flows past rigidly moving, multiple, and deforming bodies, including gradients propagated through the full time integration.

We present Swarmlet, a GPU solver for the unsteady aerodynamics and flight dynamics of one or many multirotor vehicles. The wake is a meshless, evolving-core vortex particle field in the reformulated (rVPM) large-eddy formulation, coupled to rotor models of three fidelities, six-degree-of-freedom vehicles and flight control. Particles carry a smooth core of compact support whose field outside four core radii is exactly the singular Biot-Savart field, so the multipole far field of the treecode carries no regularization error. The subfilter closure is a dynamic eddy viscosity on a fixed filter width, applied by core spreading with a Lagrangian exchange of its local excess under an explicit stability bound, and the strengths are relaxed by projection; global corrections make both the exchange and the relaxation conserve total vorticity and linear impulse. All rotor models shed connected bound circulation, the disks along the arcs swept in each step however long, so the wake receives the lift impulse. The solver agrees with direct summation to $5\times 10^{-7}$ and converges at third order in time. Without calibration, an actuator-line model that includes its own near sheet predicts the hover thrust of a DJI 9443 propeller within 2%. With calibrated section polars it reproduces a Crazyflie propeller's thrust and torque within 3.2% at three speeds and the near wake of a hovering quadrotor with relative $L^2$ differences of 0.08-0.21 against particle image velocimetry, while the wake keeps the delivered impulse. A closed-loop formation of 100 quadrotors, run at a coarser setting on one GPU, illustrates the coupled method at swarm scale.

We investigate how boundary geometry controls the coexistence of regular and chaotic motion in a static, eye-shaped billiard. A single control parameter continuously deforms the smooth, strictly convex boundary between two singular geometric limits. Across the sampled parameter range, chaotic layers coexist with regular islands and invariant curves that restrict phase-space transport. We derive analytical conditions for the existence of diagonal period-two orbits and determine the stability transitions of the axial period-two trajectories. We also establish the existence of invariant caustics near the boundary for every finite positive value of the control parameter. Numerical simulations reveal a nonmonotonic dependence of the average maximal Lyapunov exponent on the control parameter, withthe strongest sampled instability occurring at an intermediate geometry. The mean squared-angle envelope width associated with the sampled chaotic component decreases toward both singular limits, following power laws with fitted exponents of opposite signs and magnitudes close to two thirds. We further characterize a geometric response function and discuss the resulting analogy with continuous critical behavior. Our findings show how geometric deformation governs orbital stability, barriers to chaotic transport, and scaling properties in conservative billiard dynamics.

We investigate analytically and numerically stochastic resonance in an underdamped active (Ornstein--Uhlenbeck) particle confined in a bistable potential with time-delayed feedback and subjected to an additional (non-thermal) white-noise source. Restricting the analysis to the active-noise-dominated bistable regime, with sufficiently short delay and active-noise correlation times, we develop a perturbative theory that yields analytical expressions for both the escape rate and the spectral power amplification within the framework of linear-response theory, without invoking detailed balance. The analytical predictions are in qualitative agreement with direct numerical simulations throughout the perturbative regime. We show that a moderate increase in the active-noise correlation time can enhance the stochastic-resonance response, in marked contrast to previous results for overdamped passive systems driven by colored noise. Conversely, the addition of white noise weakens the resonant response and shifts its optimum toward lower active-noise intensities. Time-delayed feedback further alters the matching condition between the escape rate and the driving frequency while preserving the resonant mechanism. Beyond the perturbative regime, we find that finite-memory effects progressively broaden the resonance profile and substantially decrease its amplitude. Overall, these results provide new insight into the combined role of inertia, activity, environmental fluctuations, and time delayed feedback in stochastic resonance in nonequilibrium systems.

Autonomous navigation independent of Earth-based tracking remains a challenge for spacecraft operating in cislunar space. This paper proposes onboard eclipse detection as an opportunistic measurement set to supplement the state estimation of cislunar trajectories. Penumbral and umbral entry and exit times detected from standard power telemetry are formulated as implicit zero-measurements on the boundaries of second-order shadow cones computed from planetary ephemerides. These observables are processed in an unscented Kalman filter. The event-time uncertainty that weights each measurement is derived from physical sources excluded in the spherical body model, including telemetry sampling, Earth's atmosphere, and topography/oblateness of the occulting body. The approach is demonstrated both in simulation for an $L_1$ halo orbit and with flight telemetry and orbit determination products from the CAPSTONE spacecraft during the January 2026 lunar eclipse, where umbral contacts timed directly from the power telemetry agree with the geometric contacts to within one sample interval. In both cases, hardware-free eclipse event timing shows utility in uncertainty reduction, especially as the initial solution quality is degraded.

Individuals within a cellular or ecological population can exhibit substantial variation in their traits or phenotype. Such heterogeneity can fundamentally alter population-level behaviour, including the ability to aggregate and form spatial patterns. We investigate these effects by extending nonlocal aggregation models, widely used to model cell--cell adhesion and collective animal movement, to incorporate phenotype structure. We characterise how heterogeneity and switching between phenotypes affect whether patterns form, how phenotypes are distributed within them, and whether they are stationary or exhibit spatio-temporal oscillations. We show that pattern formation is promoted when phenotypes that produce stronger interaction signals also respond more strongly to them, whereas specialisation towards either signal production or response inhibits pattern formation. Increasing rates of switching between phenotypes dampen these effects. Heterogeneity can also enable weakly interacting, and even repulsive, individuals to pattern as part of the collective. Furthermore, movement in phenotype and physical space can interact to restructure patterns and generate spatio-temporal oscillations. A further key message of this study is the value of considering both discrete $N$-phenotype and continuous phenotype formulations. We develop both in parallel, demonstrating formal correspondences, but also advantages to each framework in terms of mathematical analyses and interpretability.

Soliton pumping enables controlled transport of localized wave packets through the interplay between nonlinearity and band topology. Interactions between such wave packets provide an additional means to manipulate their localization and subsequent motion. Here, we investigate collisions of solitons in a driven bichromatic lattice, where solitons associated with bands of opposite Chern numbers are pumped toward one another. For intracomponent collisions, the soliton that dominates the collision survives as a localized outgoing wave packet, while the weaker one can lose its distinct localized identity. For intercomponent collisions, attractive interaction produces spatial locking, whereas repulsive interaction induces redistribution toward the lowest band and reverses the motion of the initially excited-band wave packet. Remarkably, for collisions between vector solitons with comparable initial intensities, the difference between their internal relative phases controls the collision outcome, favoring capture for in-phase preparation and re-separation for out-of-phase preparation. These results connect nonlinear scattering with subsequent topological pumping and identify initial intensity, intercomponent interaction, and relative phase as control parameters for manipulating localized transport within the same pumping protocol.

Torque ripple in electrical machines is a wellknown source of noise and vibration. While numerous studies focus on control strategies to mitigate this ripple, the feedback mechanism by which the resulting mechanical oscillations influence the electromagnetic forces remains less explored. This paper presents a detailed investigation into the impact of torque ripple on the rotor angular dynamics and the subsequent generation of new harmonics in the Maxwell pressure distribution. We first develop an analytical model for a rigid rotor subjected to a single torque harmonic, revealing the inherently non-linear nature of the angular response. This analysis demonstrates the creation of new harmonics in the rotor motion and a slight reduction in the mean rotational speed. The study is then extended to a flexible rotor model incorporating torsional modes, solved using the Finite Element Method. Finally, we introduce a strongly coupled magneto-mechanical model, based on the subdomain method, to quantify how these rotor oscillations modulate the air-gap magnetic field. The results show a new modulated spatio-temporal harmonic distribution in the Maxwell pressure spectrum, which is not predicted by conventional uncoupled models. These findings are crucial for high-fidelity Noise, Vibration, and Harshness (NVH) analysis, as these additional pressure waves can excite stator structural modes.

Extended electrodynamics keeps the scalar combination $C=\nabla\cdot\mathbf{A}+\mu_0\varepsilon_0\partial\Phi/\partial t$ as a dynamical field rather than imposing the Lorenz gauge condition, and this scalar adds a scalar-longitudinal (SL) family to the TE, TM and TEM modes. With $C=0$ on the wall of a closed perfectly conducting waveguide, the classical modes are unchanged. The SL modes have $\mathbf{B}=0$ and an electric field along $\nabla C$, and their cutoffs are the Dirichlet eigenvalues of the cross-section, the same as the TM cutoffs, with no coaxial TEM counterpart. Charge-conserving sources with zero scalar data do not excite them. Matching at a conductor described by its constitutive laws gives $\partial C/\partial n=0$ instead and couples the scalar-bearing modes to the Maxwell field. The results belong to the $C=0$ problem, the condition that separates the sectors and the one divergence cleaning uses, with benchmarks for the rectangular, circular cylinder, coaxial and L-shaped guides.

Acoustic "ping" testing of bullion is empirical: it compares a coin's ringing frequency with frequencies recorded for the same coin type, so it cannot assess a specimen absent from the reference library. This work replaces the comparison with an absolute measurement, computed from the measured resonance and geometry through a physical model rather than retrieved from a library. Free-plate flexural resonance is calibrated on five machined aluminium discs ($a/t=2.58$--$10.75$), recovering an empirical finite-thickness coefficient $\beta=0.895\pm0.047$ that reduces the worst-case departure from thin-plate theory from 8.9% to 0.75%. A fill factor, the ratio of a coin's displaced volume to its nominal cylinder, supplies the effective thickness that relief hides from calipers, extending the calibration to struck coins. The readout is the plate wave speed $c_{p}=\sqrt{E/\rho(1-\nu^{2})}$, a material constant, conditioned on an assumed Poisson's ratio. On six struck 0.999 copper rounds not used in the calibration it recovers a Young's modulus of $119.1\pm6.7$ GPa, inside the accepted 110 to 128 GPa. The recovered wave speeds form distinct observed groups across the measured specimens, with the strongest independent validation provided by these copper rounds. The $(3,0)/(2,0)$ mode ratio falls below its thin-plate value in thirteen of sixteen specimens (one-sided sign test, $p=0.011$), as finite-thickness theory predicts. Weighing displaced mass to 0.1 mg rather than 0.1 g cut per-specimen volume uncertainty from 1.6% to 30% to 0.5% to 2.6% and shrank an apparent 11% design-dependent bias to a 4.7% residual on one deeply relieved silver design. The readout is now limited by tabulated elastic constants and the assumed Poisson's ratio, not by the acoustics, which are reproducible to 0.15%.

Horizontal convection is often modeled with a linear temperature-density relation. Two-dimensional simulations show that a density maximum, such as that of water near 4°C, can generate full-depth mixing plumes, reorganize the circulation, and enhance heat transport. An energy-budget analysis suggests that plume height controls an additional potential-energy transfer associated with this enhancement.

Unstable periodic orbits are thought to form the backbone of turbulence, yet their computation in thermal convection remains scarce near the onset of chaos. We compute a steady state and three families of periodic orbits in two-dimensional Rayleigh-Benárd across nearly two decades of Rayleigh number, and use Floquet analysis to characterize every bifurcation in the route to chaos. Additionally we find that all symmetries are broken before this onset, and the heat-transport scaling is unaffected throughout.

This study presents a numerical investigation of flow in a curved channel with a low height-to-width aspect ratio. By independently varying the Reynolds number, channel curvature and aspect ratio, we identify two distinct scaling laws for the intensity of secondary flows, each corresponding to a different flow regime: one governed by a balance between viscous and curvature forces, and the other by an equilibrium between inertial and centrifugal forces.

Particles and drag-reducing polymers can each strongly alter turbulent transport, but what happens when the two act together? Experiments in Taylor-Couette turbulence uncover a transition from particle-dominated to polymer-dominated dynamics as flow strength increases. The coupling is also shape dependent, with spherical particles producing a stronger drag response than oblate and prolate particles.

Turbulent flows contain a wide range of vortical structures, from the tiny to the large. One of the central tasks of turbulence theory is to provide a simple yet reliable means of identifying how much kinetic energy is, on average, held at each scale. Traditionally, Fourier analysis is used for this purpose. However, a decomposition into sine waves is somewhat artificial. Here we provide a real-space diagnostic, quite unrelated to Fourier space, which measures the scale-by scale distribution of kinetic energy.

What governs the formation of scalar gradients essential for mixing in turbulent flows? Using high-resolution Direct Numerical Simulations (DNS) at high Reynolds and Schmidt numbers, we show that intense scalar gradients arise primarily from near-optimal alignment with the most compressive strain direction, rather than unusually strong strain alone. These gradients organize into thin sheets within shear layers between vortex tubes, where their amplification is ultimately arrested by molecular diffusion. Remarkably, their structure and dynamics exhibit near-universal behavior across Reynolds and Schmidt numbers, revealing a robust picture of small-scale turbulent mixing.

Acoustic levitation enables objects to be suspended and manipulated without physical contact, providing a versatile platform for studying the dynamics of freely suspended matter. Yet levitated objects, from droplets and thin films to particle assemblies, frequently rotate spontaneously, and this axial rotation often remains difficult to predict or control. There is no general understanding of how the shape of a levitated object determines whether it rotates, in which direction, or how its rotation changes with acoustic amplitude. Here, we establish how particle geometry and acoustic amplitude govern spontaneous rotation of acoustically levitated objects. We work with a family of shapes we call ``chiral stars'', within which we systematically vary handedness and number of arms. In a symmetric acoustic field, stars that preserve in-plane mirror symmetry do not rotate, while those that break it spontaneously rotate with a direction set by handedness. Beyond this symmetry requirement, we demonstrate that geometry, as encoded by the number of star arms, couples with acoustic amplitude to produce complex, nonlinear dynamics, including spontaneous reversal of rotation direction. To explain these behaviors, we develop a minimal torque model constrained by independent measurements of rotational drag, which captures the observed responses across all star geometries. We then demonstrate predictive power by designing a ``hybrid star'' with a prescribed amplitude-dependent response and reversal voltage. Our results not only establish how particle geometry and acoustic amplitude combine to govern rotation in acoustically levitated systems, but also reveal unanticipated higher-order couplings with the acoustic field. Beyond explaining spontaneous rotation, they open a route toward programmable rotational dynamics in acoustically levitated matter.

We report results from an experimental investigation on the role of intrinsic curvature in the spontaneous entanglement of elastic rods subjected to controlled tumbling. We examine two distinct entanglement mechanisms, knotting and locking, in a statistical ensemble of straight and helical rods with varying arc length and natural curvature. Our primary finding is that natural curvature exerts a dominant, non-monotonic influence on knotting, with a critical curvature that suppresses knot formation and significantly reduces the probability of knotting relative to equivalent straight rods. In contrast, locking is largely insensitive to curvature and scales primarily with rod length. These results, obtained for the macroscopic experimental system studied here, identify geometric parameters that govern distinct entanglement modes in tumbled elastic rods and may inform entanglement processes in microscopic filamentary systems such as DNA.

The kinetic energy budget of a laminar separation bubble on a compressor blade is formed mode by mode in frequency and spanwise wavenumber from a direct numerical simulation at a Reynolds number of $2.5\times10^{5}$ based on the axial chord. The nonlinear transfer between modes is evaluated as a triadic tensor that gives the energy exchanged in every triad, the roles of its three modes, and the location of the exchange. Nine dominant tonal modes are identified: the flapping of the bubble, the Kelvin-Helmholtz mode with its sidebands, a pair of modes near reattachment, and their sum, difference, and harmonic. They hold 8% of the fluctuation energy, and their triads are responsible for 19% of the energy exchanged. Every tonal mode is fed by the mean shear and exports 69 to 82% of the energy it takes from the mean flow. The Kelvin-Helmholtz mode sends 45% of the energy it sheds to lower frequencies. The largest of these transfers is a triad in which it acts as a catalyst. The exchange in each triad is split into nine channels by velocity components. In every triad of spanwise-uniform modes, one channel dominates: the wall-tangential velocity of the donor advected by the wall-normal velocity of the catalyst. For a pair of oblique modes, the same advection by the two-dimensional Kelvin-Helmholtz mode exchanges their spanwise velocity, which the mean flow cannot produce. The rollers thus become three-dimensional through the advecting velocity of the Kelvin-Helmholtz mode, which supplies no energy to the exchange.

Simulating high-pressure transcritical flows with phase change is critical for advanced propulsion, yet traditional first-principles approaches, vapor-liquid equilibrium (VLE) calculations, consume most of the runtime and frequently fail to converge. Standalone machine learning models introduce heavy evaluation overhead across large grids, while dynamic tabulation still relies on fragile iterative solvers. To resolve these limitations, this study introduces a hybrid In-Situ Adaptive Tabulation and Artificial Neural Network (ISAT-ANN) framework. A pre-trained ANN replaces the iterative solver during table expansion to guarantee crash-free operation, while ISAT enables rapid data retrieval via local linear interpolation. To eliminate parallel load imbalances, an O(N) greedy load-balancing algorithm redistributes computational tasks across cores. Coupled with Adaptive Mesh Refinement (AMR), the framework was validated on a Mach 5 shock-droplet interaction benchmark. It accurately captured shock-interface dynamics without instability, achieving a 2.30 times speedup in thermodynamic calculations on a single core and 2.62 times in parallel over standalone ANNs, with AMR providing an additional 2.92 times overall efficiency boost. This plug-and-play framework offers a stable, scalable path for high-fidelity multiphase flow simulations.

Sand-laden cavitation spans solid particles, macroscopic vapor cavities, and microbubbles, yet existing simulations rarely resolve their coupled multiscale dynamics. We develop a two-way coupled Eulerian-Lagrangian framework that simultaneously captures cavity evolution and discrete particle-bubble motion. The simulations reveal that sediment particles accelerate cavity shedding and weaken the re-entrant jet, while increasing the Hinze scale by reducing turbulent dissipation and suppressing the breakup cascade from large to small bubbles.

Lateral fluorination has emerged as a powerful design variable in the design of polar liquid crystals, but its interplay with terminal-group identity remains poorly understood. Here we report a 40-member matrix of biphenyl-ester-phenyl mesogens that independently varies lateral core fluorination and terminal-group identity. Increasing lateral fluorination generally suppresses apolar mesophases and clearing points, however this same change can enable polar nematic phase behaviour in conjunction with suitable terminal units. Graph Fourier analysis of conformer averaged atomic charges shows polar materials occupy a high-frequency region of charge-spectral space, consistent with a bond-scale electrostatic motif. Different terminal units can bias this towards higher or lower frequencies, and in doing so can enable polar order to emerge.

The flow of molecularly confined water has attracted considerable interest in recent years. Yet despite their exquisite character, current nanofluidic devices cannot probe molecular water flow beyond the linear-response regime, while nanomechanical force- based approaches have produced markedly inconsistent results. Here, using tuning- fork-based atomic force microscopy, we tackle these limitations by measuring the full linear-to-nonlinear, shear-dependent viscoelastic rheology of molecularly confined water at various two-dimensional material interfaces -- demonstrating pronounced rate effects in water flow response. The observed rheological behaviors are remarkably analogous to that of macroscopic soft glassy yielding materials and fully captured by a non-linear model accounting for the shear-induced acceleration of the dynamics -- a hallmark of disordered supercooled and metastable systems. We further unveil a pronounced pressure-induced slowdown in nanoconfined water dynamics, with relaxation times extending into the microsecond range and marked material dependence. These results reveal non-linear, glassy rheology as a general feature of interfacial water and offer a route to tunable, non-linear nanofluidic elements.

Can high-harmonic generation track how microscopic intermolecular interactions give rise to macroscopic order? We address this question in the thermotropic liquid crystal 4-cyano-4'-n-pentylbiphenyl, a model system with a well-defined nematic-to-isotropic transition. Using a temperature-controlled flat jet, we show that polarization-resolved high-harmonic generation driven by mid-infrared strong-field pulses is highly sensitive to liquid-crystal order. In the nematic phase, the harmonic yield forms a four-lobed angular pattern with twofold rotational symmetry and is strongest when the driving-field polarization is perpendicular to the molecular director; this anisotropy vanishes in the isotropic liquid. A tight-binding model parameterized by first-principles calculations attributes this response to intermolecular orbital hybridization in short-range antiparallel molecular arrangements. Temperature-dependent measurements across multiple harmonic orders resolve the same first-order phase transition, with each harmonic order exhibiting a distinct optical sensitivity. A multiscale model combining the microscopic response, Landau-de Gennes orientational correlations and phase matching explains this behaviour through the interplay between orientational correlation lengths and harmonic coherence lengths. High-harmonic generation therefore links local electronic coupling to mesoscopic order and macroscopic propagation, providing an all-optical probe of multiscale organization in soft matter.

Weakly hydrated anions tend to partition to macromolecular surfaces, leading to salting-in at low salt concentrations. Recent studies have linked this partitioning to disruption of the interfacial water network. Here, we investigate the role of interfacial-water-network disruption as an indirect driving force for the adsorption of weakly hydrated anions and its interplay with direct solute-anion and anion-cation interactions using computer simulations. We study the adsorption of SCN$^{-}$ and I$^{-}$ ions on a model extended solute that interacts with water and ions only via van der Waals interactions. To probe the indirect contribution, we increase the effective solute size while simultaneously decreasing the attractive solute-water and solute-ion interactions, resulting in progressively greater disorder in the interfacial water network in pure aqueous solutions. Our results show that iodide adsorption increases despite weaker direct solute-iodide interactions and correlates with greater disruption of the interfacial water network, although iodide remains depleted overall. In contrast, preferential adsorption of SCN$^{-}$ decreases, but the rate of decrease becomes smaller at higher levels of interfacial-water-network disorder. This suggests that the indirect contribution associated with interfacial-water-network disruption partly compensates for the decrease in SCN$^{-}$ adsorption caused by weaker direct solute-SCN$^{-}$ interactions. Our results highlight that the indirect contribution associated with interfacial-water-network disruption promotes the adsorption of weakly hydrated anions on macromolecular surfaces, while the extent of adsorption also depends on direct solute-ion interactions and anion-cation pairing. This interplay may be particularly important in mixed-salt solutions, where the presence of strongly hydrated anions can also disrupt the interfacial water network.

Particle shape plays a fundamental role in the dynamics and pair interactions of active particles. Yet, experimental measurements of anisotropic active particles are largely lacking. Here, we introduce an experimental system that allows us to observe and measure the effective pair interactions of self-propelled active colloidal polyhedra. We realize such a system by 3D micro-printing quasi- 2D polyhedral colloids with edge number N= 3,4,5,6 and infinity and induce propulsion by partially coating them with an iridium catalytic cap and dispersing them in hydrazine. Despite their different geometries, all shapes exhibit similar single-particle positional dynamics. Stochastic Force Inference reveals predominantly radial, non-reciprocal pair interactions with similar attractive and repulsive regimes for all particle shapes at center-to center distances of about two particle diameters. A minimal plausible phoretic active-Brownian-particle model with a disc shape reproduces the experimentally observed behavior and identifies the physical origins: concentration-dependent slowing down sets their dominant angular symmetry, while the spatial geometry of the chemical coupling and phoretic attraction recover their relative magnitudes and angular dependence. We find that the shape anisotropy present in experiments only modulates the magnitudes and angular dependence of these interactions, and that these variations become more pronounced the stronger the anisotropy. Our results demonstrate the interplay of chemically mediated interactions and particle geometry-induced effects at intermediate interaction distances.

The coil-to-globule transition is a paradigmatic phenomenon in polymer physics and biophysics, in which polymer chains evolve from swollen to globular conformations upon decreasing solvent quality. At equilibrium, this transition can be rationalized in terms of a thermal blob length that diverges at the so-called $\Theta$ condition, marking the crossover from self-avoiding to globular conformations. How activity modifies this conformational transition and affects the fundamental length scales at play remains poorly understood. Here, we address this question for tangentially driven polymers using Brownian dynamics simulations, systematically varying both intrachain attraction strength and activity. We find that polar activity smears out the crossover from swollen to globular conformations. Between self-avoiding and $\Theta$ conditions, activity dominates by introducing an emergent folding length scale, which acts as an active blob length. In this regime, we demonstrate that the ratio of thermal to active length scales provides a new scaling variable that leads to a universal master curve for active polymer collapse.

Topological defects in nematic liquid crystals have recently received renewed interest due to their important role in non-equilibrium active materials and developing biological systems. While many studies have focused on simulating defect behaviors in these non-equilibrium situations, there has also been recent progress in our analytical understanding of defect morphology and behavior in a number of complicated regimes, such as intricate boundary conditions, anisotropic elasticity, or the presence of flows. Here, we review the analytical theory of disclination structure and dynamics in two-dimensional nematic liquid crystals, highlighting recent methods and results.

Soft modes of a shell are one-parameter families of non-trivial deformations that preserve the elastic energy. We identify all soft modes of the soft shells described by the variational theory of put forward by Sonnet and Virga (2025). They are seen to be strictly connected with the Bonnet families, a special class of solutions to the problem posited by Bonnet, who asked whether there exist non-trivial isometries that preserve the mean curvature. Differential geometry deems as equivalent all surfaces in one and the same Bonnet family, but continuum mechanics is interested more specifically in soft deformation modes and the shapes they traverse, as they may describe ways to ignite fluctuations of soft shells that ideally require no energy to be activated. We give a general criterion for the existence of soft modes and a method to construct them based on a cascade of path integrations. We apply both criterion and method to some exemplary cases.

We investigate quasi-2D active-passive colloidal mixtures with electric field-mediated non-identical interactions: unlike species attract and like species repel. Mapping the steady states across total area fraction and active particle area fraction identifies the regime of active percolated network formation among active fluid and clustered states. Within the percolated network regime, relaxation speeds up with increasing density, contrary to expectations for dense particulate gels. Particle-resolved dynamics and microstructure link this acceleration to activity-driven rearrangements enabled by asymmetric interactions.

SAXS/SANS determine the size and structure of particles and macromolecules in solution. However, the conventional low-angle determination of the radius of gyration, Rg, cannot separately resolve its scattering-weighted mean and the width of its distribution. Because the apparent Rg includes a contribution from ensemble variance, the distribution width is required even to recover the mean Rg. Here, we introduce TENOR-SAXS, a method for estimating the scattering-weighted width of an Rg distribution by applying two anisotropic digital smearings to a single 2D scattering image. Comparing the smeared images provides curvature information unavailable from the conventional radial profile. The resulting observables require no explicit model of the native instrumental point-spread function and show only weak sensitivity over the range of native resolutions typical of SAXS measurements examined here. Analytical expressions are derived in the low-angle and narrow-distribution limits for ensembles described by a known or independently constrained single-particle form factor. For verification, we simulated scattering by particles with several form factors and ensembles with different size distributions, all agree well with the analytical theory. To leading order, the principal observable depends on the scattering-weighted mean and variance rather than on the distribution's functional form or higher moments. For simulated data corresponding to feasible synchrotron exposure times for biological samples, the distribution width and, expressed as a fraction of its mean, was recovered with a typical discrepancy of ~0.1, while the scattering-weighted mean Rg was recovered with ~2% relative discrepancy. TENOR-SAXS thus provides a framework for estimating ensemble width from existing 2D scattering data without explicit instrumental desmearing and for correcting the variance contribution to the apparent radius

Mean First Passage Time (MFPT) is a crucial quantity that characterizes stochastic processes in various stochastic dynamical systems across different disciplines. The inverse of the MFPT, known as the escape rate, is helpful in the context of Brownian motion and chemical processes. The MFPT dynamics of a passive particle in the presence of active noises presents a fascinating avenue. In this work, we study the dynamics of two different systems: first, a single Brownian particle and second, a dimer (two Brownian particles connected by a spring). In both cases, the systems are kept in contact with a thermal bath and an active bath, and are trapped in a bistable potential. The active bath produces kicks that follow the Poisson distribution. The MFPT of the particle and the dimer is investigated in various scenarios. Analytical results are presented for the small kick variance approximation only. In this approximation, we formulate the MFPT in two scaling regimes: a weak-noise regime characterized by classical Arrhenius scaling for escape rate and a strong-noise regime in which the MFPT scales as a power law in the effective noise strength. For the general case, the problem is solved numerically. Next, under the same approximation, the MFPT of a dimer in the small-bond-strength regime is studied using a sequential-hopping mechanism, and in the large-bond-strength regime, the MFPT is formulated using the adiabatic elimination approach. Motivated by recent studies on speeding up the escape mechanism, the MFPT of the particle and the dimer in the presence of an intermediate barrier is also examined. We deduced from the numerical results that the MFPT can be enhanced and further optimized by selecting a suitable intermediate potential profile.

A graph neural network (GNN)-based autoencoder is leveraged to produce reduced latent graph representations of detonation-containing flows. In a two-dimensional hydrogen-air channel configuration with a uniform fuel-air mixture, it was found that latent graphs with effective resolutions of twice the induction length are capable of reconstructing both the wavefront and the post-shock region of the cellular detonation wave structure. Extrapolation studies using stratified and three-dimensional detonation configurations revealed an intrinsic property of GNN-based reconstruction from reduced latent graphs -- a representational hierarchy, rooted in the local nature of message passing, that tends to prioritize features at the detonation front (i.e., the wavefront profile and triple points) over the downstream deflagrative regions. In particular, it was found that at a fixed ambient condition, the information contained in uniform two-dimensional detonations was sufficient to reconstruct the wavefront structure of both stratified and three-dimensional detonations. Overall, this work demonstrates the utility of GNNs for both reduction and information overlap extraction in detonation-containing flows, opening promising pathways for accelerated simulations of these flows.

Cross helicity, the velocity--magnetic-field correlation, is an ideal invariant of incompressible magnetohydrodynamics and constrains energy cascades and magnetic-field generation. Although cross helicity typically decays via visco-resistive effects, we analytically demonstrate that it grows exponentially in sheared inhomogeneous turbulence. This cross-helical shear instability is confirmed using three-dimensional numerical simulations. Growth requires a nonzero gradient of the Reynolds--Maxwell stress to produce turbulent cross helicity; this production overcomes effective losses when shear exceeds a threshold set by the ratio of turbulent magnetic to momentum diffusivities.

We study coherent structures extracted from time-resolved particle image velocimetry (TR-PIV) measurements of isothermal elliptical jets with aspect ratio of 1:2, at Mach numbers 0.4 and 0.7. The velocity snapshots are decomposed according to the D$_2$ symmetry. Spectral proper orthogonal decomposition (SPOD) is then used to identify coherent structures. Modelling is performed using three-dimensional parabolised stability equations (3D-PSE) based on linearisation about the time-averaged mean flows. A comparison between SPOD and 3D-PSE results shows alignment of SPOD and single-mode PSE structures of up to 70\%. A linear combination of PSE solutions, obtained from the family of initially unstable local modes, leads to SPOD-PSE alignment of up to 90\%. Limitations are observed at low frequencies and near the nozzle and are attributed to the existence of non-modal amplification mechanisms. The study shows that coherent structures in turbulent elliptical jets can be educed using the D$_2$-SPOD approach, and modelled using 3D PSE.

The spatial evolution of a turbulent boundary layer at $Re_\tau = 652$ developing across a finite spanwise oscillating wall is investigated with normalised oscillation period of $T^+ \approx 101$ and amplitude $A^+ \approx 7$, yielding a drag reduction of 32\%. The spatial distribution of skin friction is estimated adopting a recently introduced near-wall data nonlinear regression method based on the arctangent function, which circumvents the requirement of high wall-normal resolution to capture the viscous sublayer. The method viability is assessed against reference DNS data, and the trends of measurement errors from experimental data are well reproduced. The local impact of the control action is examined by evaluating the spatial development of scalar fields of turbulence statistics as well as conditional quadrant analysis to link the onset and recovery transients to turbulence events. The boundary layer response is observed to follow an exponential decay law for the skin friction spatial evolution. The decay length-scale corresponds to $0.6$ boundary layer thicknesses $\delta$ for the onset transient and $0.9\delta$ for the recovery one. The same exponential fit applied to the Reynolds stresses yields a response within $0.5\delta$, with the exception of the shear stress peak, that requires a significantly longer distance.

Accurate prediction of low-frequency responses is important for the dynamic assessment of floating offshore wind turbines (FOWTs), as second-order difference-frequency wave loads can contribute substantially to platform motions and mooring loads. Their relative importance, however, remains less well established when aerodynamic and hydrodynamic low-frequency excitations coexist under operating conditions. This study develops an efficient time-domain formulation for full difference-frequency quadratic transfer function (QTF) loading using bandwidth truncation and integrates it into a fully coupled model of the IEA 15 MW turbine on the VolturnUS-S semi-submersible platform. Numerical predictions are compared with 1:70-scale real-time hybrid wave-basin experiments covering both irregular wave-only and combined turbulent wind-wave conditions. Three hydrodynamic formulations are compared: linear wave excitation, Newman's approximation, and the full-QTF model. Under wave-only conditions, second-order difference-frequency loading substantially improves the prediction of surge and the associated mooring response, particularly in energetic sea states, with the full-QTF model generally providing the closest agreement with measured low-frequency spectra and peak-amplitude distributions. Under combined wind-wave conditions, low-frequency thrust fluctuations dominate near rated wind speed, reducing the relative importance of difference-frequency wave excitation, whereas its contribution becomes more apparent at higher wind speeds as thrust fluctuations diminish. Overall, the full-QTF model provides the most consistent improvement over the linear and Newman models, with maximum surge standard deviation discrepancy from measurement under the most energetic wave conditions less than 18%, with smaller discrepancies for heave, pitch, and mooring tensions.

Porous aerostatic gas bearings are commonly modeled using the ideal-gas law, although non-ideal thermodynamic behavior may become relevant for alternative working fluids. This study quantifies the influence of the thermodynamic closure on the stationary and dynamic response of porous aerostatic journal bearings. A finite-volume formulation couples the compressible Reynolds equation with three-dimensional Darcy flow, retaining transient gas storage in both domains. Density is used as the primary thermodynamic variable, allowing the ideal-gas, van der Waals, Soave--Redlich--Kwong, Peng--Robinson, and multiparameter Helmholtz equations of state to be evaluated within an otherwise unchanged bearing model. Air, R1234yf, and R1234ze(E) are considered. For air, EOS-induced differences remain negligible over the investigated range. For the refrigerants, the ideal-gas approximation produces several-percent deviations, with supplied mass flow and dynamic force response being particularly sensitive. The cubic equations substantially reduce these deviations, with the employed Peng--Robinson formulation providing the closest agreement with the Helmholtz reference for both refrigerants at a computational cost comparable to the other cubic models. The results identify density and differential compressibility as the main thermodynamic quantities governing the propagation of EOS errors into mass transport and transient gas storage.

The evolution of finite-amplitude disturbances is critical in the prediction of laminar-to-turbulent transition. To analyze the transient growth of disturbances, Pralits et al. (J. Fluid Mechanics, 2015) proposed a weakly nonlinear optimal perturbation (WNLOP) analysis that accounts for the effect of mean-flow distortion on the fundamental wave. The present study formulates a WNLOP analysis via Picard--Chebyshev iteration for compressible parallel flows to predict streak breakdown. The formulation incorporates the non-modal amplification of disturbances and their nonlinear interactions for polychromatic waves, considering all the possible nonlinear interactions starting from a finite set of initial wavenumber components. The nonlinear interaction is tracked as a monotonically increasing set of wavenumber components; specifically, the first-order approximation recovers the linear disturbance equation, the third-order approximation corresponds to the amplitude equation of weakly nonlinear theory, and further iterations systematically approach DNS results in the weakly nonlinear regime. By applying the proposed formulation to a subcritical plane Poiseuille flow at Mach number $\mathrm{M}=0.3$ and Reynolds number $\mathrm{Re}=3000$, the proposed formulation demonstrates high predictive accuracy in comparison with DNS calculations and succeeds in identifying the optimal perturbation restricted to a planar wave that causes streak breakdown in full nonlinear simulation. The proposed method predicts the nonlinear interaction between the streak and the planar wave, which generates an oblique wave and subsequent harmonic waves characterized by an alternating streamwise vortex structure, whose amplitude determines whether further nonlinear interactions are induced to trigger the turbulent transition.

In this work, building on previous studies of plane-parallel flows, we investigate the rapid growth of the frozen-in vorticity field in an axisymmetric poloidal flow. We present the results of numerical simulations performed using supercomputing resources. We show that exponentially growing velocity gradients can develop on the axis of symmetry, while vorticity gradients grow superexponentially. These results are qualitatively similar to those previously obtained for vorticity in a simpler two-dimensional flow.

The multiscale nature of turbulent reacting flows and the importance of fine-scale structures pose challenges for super-resolution. We investigate a 3D super-resolution framework inspired by Neural Radiance Fields (NeRF), called Neural Field Super-Resolution (NFSR), to reconstruct fine-resolution fields from coarsened reacting-flow fields. The proposed formulation adapts the continuous coordinate-conditioned representation of NeRF to physical flow-field reconstruction by conditioning spatial coordinates with local coarse-grid thermochemical information, while eliminating radiance prediction and volume rendering. Principal component analysis is used to provide a compact and low-dimensional representation of the thermochemical state, and a hierarchical extension, H-NFSR, progressively reconstructs the solution through intermediate resolution levels. The framework is evaluated using three-dimensional direct numerical simulation data for a turbulent premixed hydrogen-air flame, with an overall spatial coarsening factor of eight in each coordinate direction. The results demonstrate consistently better prediction measures and a higher ability to reconstruct fine-scale information than tricubic interpolation on the unseen test realization. The hierarchical formulation reduces visible coarse-cell imprinting. In contrast, biased sampling mainly benefits the most localized structures. Three-dimensional isosurface comparisons further show that H-NFSR recovers much of the small and intermediate features of the flow, including surface wrinkling and local flame curvature effects. These results highlight the potential of coordinate-conditioned neural fields as a flexible framework for three-dimensional coarse-to-fine reconstruction of reacting-flow simulations.

We present a perturbation-based theoretical framework, together with its immersed boundary/volume penalization implementation, for long-time simulations of fully resolved rigid-particle dynamics in acoustically actuated flows. A perturbation formulation separates the fast acoustic time scale from the slow mean dynamics, avoiding long-time direct integration of the fully compressible Navier-Stokes equations. The immersed rigid body is represented through a Brinkman penalization term in equations posed over a unified fluid-solid domain. The coupled fluid-particle system is decomposed into a time-harmonic first-order problem governing the acoustic response and a time-averaged second-order problem. A central challenge in this decomposition is the treatment of the moving fluid-solid interface. We derive order-consistent expressions for the structural velocities, comprising rigid-body and Stokes-drift contributions, and formulate the corresponding first- and second-order rigid-body equations of motion. For a circular particle in two dimensions, the simulations reveal substantial differences in the magnitude and structure of acoustic streaming around fixed and freely moving particles, highlighting the importance of two-way fluid-structure coupling. The results also show that particle-density effects are more complex than suggested by simplified descriptions based solely on the acoustic contrast factor. The framework captures the mean particle dynamics using time steps associated with the slow particle-motion scale rather than the much smaller acoustic time scale. Finally, simulations of an elliptical particle demonstrate the ability of the method to capture coupled translational and rotational motion. The proposed approach therefore provides an efficient route to fully resolved, long-time simulations of acoustically driven rigid-particle motion while retaining two-way fluid-structure coupling.

We present a novel framework for reconstructing fine-resolution scalar fields from coarse-resolution data in 2D unsteady flames using an extension of neural implicit flow (NIF). The framework leverages the novel architecture of NIF to develop an efficient representation of scalar fields in spatio-temporal reacting flows. Different strategies are adopted within the proposed framework to establish super-resolution for multiscalar fields in combustion. They include 1) a reconfiguration of the input and output fields, 2) the use of a latent composition space based on nonlinear principal component analysis (NLPCA) to reconstruct the fine-resolution fields, and the conversion from nonlinear principal components (NLPCs) to species and temperature contours, and 3) the adoption of multiple ParameterNets in the NIF architecture, each accommodating one of the NLPCs. The framework was validated on a 2D unsteady Bunsen-stabilized lean premixed methane-air flame with forcing at the inlet. The results, using a coarsening ratio of 8 in a given direction, show that the adoption of multiple ParameterNets yields more accurate super-resolution than a single ParameterNet without any additional cost in the hyperparameters.

We present DeHNSSo-v2, a major update of DeHNSSo-v1 (Westerbeek et al., Comput. Phys. Commun. 302, 2024), the open-source Delft Harmonic Navier-Stokes Solver for nonlinear stability analysis of shear flows. The new release adds a compressible formulation on general two-dimensional body-fitted geometries, automatic grid generation, linear-cost sparse assembly, reusable per-mode factorizations, and Newton pseudo-arclength continuation for high-amplitude nonlinear solutions. The curvilinear formulation preserves the fourth-order accuracy of the discretization on strongly distorted grids, and the compressible solver is confirmed to reproduce DeHNSSo-v1 in the incompressible limit. Validation spans published benchmarks for linear instability of compressible flat-plate boundary layers from $\mathrm{Ma}=0.5$ to $\mathrm{Ma}=4.5$, nonlinear oblique-mode breakdown at $\mathrm{Ma}=1.6$, nonlinear swept-wing crossflow compared with direct numerical simulations, and linear Tollmien-Schlichting wave interaction with a modeled surface-embedded Helmholtz resonator compared with experimentally validated linearized Navier-Stokes simulations. On the nonlinear test cases of DeHNSSo-v1, the computational developments result in a speed-up of approximately one order of magnitude. By broadening the scope and reducing the cost of DeHNSSo-v1, DeHNSSo-v2 provides the boundary-layer-transition and flow-control community with an accessible tool for studying receptivity, nonlinear disturbance evolution, and instability interactions with complex surface geometry and metamaterials across compressibility regimes.

Solving dynamical systems in complex and diverse geometries remains challenging for both numerical solvers and learning-based surrogate models. We propose Neural Operator Splitting, a framework for learning fluid dynamics while preserving the physical structure of fractional-step numerical schemes. Instead of learning the full-step evolution monolithically, we decompose each time step into physically interpretable steps, and learn each operator separately using intermediate states from the underlying numerical solver. Guided by the linearity properties of the fractional steps, we introduce a conditional-linear Fourier neural operator (CL-FNO) whose linear state mappings are modulated by nonlinear conditioning on inputs such as boundary geometry. We further introduce two complementary strategies, symmetry sampling and corrective cycling, to mitigate error accumulation during autoregressive rollout. Experiments on 2D and 3D fluid flows with varying geometries and initial conditions show that our full model reduces mean relative $L^2$ rollout error by 68\% in 2D and 40\% in 3D compared with a single full-step neural operator. At comparable error levels, neural-operator inference is approximately $10^3$ times faster per step than the Monte Carlo solver.

Model order reduction has the potential to enable real-time patient-specific assessment of cardiovascular flows. However, it still faces significant challenges stemming from the geometric variability of vascular anatomies. Building upon the SynthAorta dataset (Bosnjak et al., IEEE Trans. Med. Imag. 45(1), 2026) of physiological aortic geometries, we generate an extensive dataset of physiologically consistent computational fluid dynamics solutions through an automatic boundary-condition adjustment procedure. A common reference geometry allows all patient-specific anatomies to be represented by displacement fields, providing point-to-point correspondence without the need for geometric registration. Based on this dataset, we develop Graph U-Net and Transformer U-Net surrogate models to predict velocity and pressure fields at peak systole. We further investigate two strategies to enhance data efficiency and prediction accuracy: active learning and differentiable physical consistency constraints based on the finite element residual. The results show that active learning is strongly regime-dependent: while it offers little benefit over random sampling during early training, it improves performance during fine-tuning through gradient- and subspace-based acquisition strategies. Similarly, physical consistency constraints prove to be substantially more effective as a fine-tuning objective than as a regularizer applied throughout training. Finally, out-of-distribution studies demonstrate that the primary limitation of surrogate models lies in the geometric support of the underlying parametrization rather than in the neural network architectures themselves. The proposed framework combines synthetic dataset generation, geometry-aware surrogate modeling, physics-informed optimization, and active learning into a scalable workflow for inter-patient hemodynamic prediction.

At industrial scale the cost of resolvent analysis is set by the linear solves and the assembly and storage of the Jacobian. We present a matrix-free resolvent framework in the Reynolds-averaged Navier-Stokes solver ADflow: automatic differentiation supplies the action of the shifted Jacobian and its Hermitian transpose, preconditioned Krylov solves recycle subspaces across a Lanczos bidiagonalization, and every gain is certified by a backward error. It is applied to the NASA Common Research Model wing at Mach 0.85 and 4.2 degrees on three grid levels of 0.45, 3.6 and 28.8 million cells, the finest with 1.73x10^8 complex unknowns, 2.3 times the largest reported resolvent computation. On the coarsest level an unstable buffet mode makes the gain peak a resonance; on the finer two the operator is stable and the peak, 1.33x10^4 at omega = 6.4 and 3.0x10^3 near omega = 7.7, is a pseudo-resonance of damped modes whose buffet cells travel outboard at about 0.3 times the free-stream speed. Refinement turns an oscillator into an amplifier of the same mechanism, as forced simulations confirm. A certified frequency costs 3.6 minutes on 128 cores at 2.7 million unknowns, with 14 to 34 kB per unknown, nearly four orders of magnitude below a sparse factorization.

Gradient descent with momentum can be viewed as a particle moving with friction in the loss landscape. In deep learning the learning rate is usually large, so training is a discrete dynamical system: in many full-batch experiments the sharpness grows to the optimizer's stability limit, the edge of stability (EoS), and training continues there. Physics-inspired optimizers change this motion; Velocity-Regularized Adam (VRAdam), for example, shrinks the step at high speed. We study kinetic maps, in which the step is the gradient of a kinetic energy of the momentum, and ask what they do beyond the EoS. (i) In a reduced model, a kinetic map creates a symmetric period-two orbit beyond the edge, strictly linearly stable if and only if the map's elasticity (the log-log slope of step length versus momentum) lies between 0 and 1; on it, training sits at an effective edge of stability. VRAdam's damper fails above twice the critical learning rate, where its kinetic energy is not convex; the Legendre dual of VRAdam's own Lagrangian is convex and passes at every learning rate. (ii) Because the sharpness rises gradually, the loss of stability is delayed, as in Neishtadt's theory of slowly swept bifurcations. In a network with a controlled sweep, the dynamics match this theory without fitted parameters, including the memory of where the sweep started and its erasure by noise. (iii) With momentum, reaching the oscillation also requires elasticity at large momentum: maps that bound the step have competing period-four and chaotic attractors already at beta1 = 0.9, while the cubic-Legendre map reached the oscillation from every sampled start up to beta1 = 0.99. Experiments on an exact quadratic problem, a full-batch MLP and ResNet-32 support the theory; on ResNet-18, much of the apparent benefit of the maps is reproduced by matching the effective learning rate.

Quantum batteries can outperform their classical counterparts through collective quantum effects, yet the conditions enabling such advantage remain unclear. Using a generic class of free-fermionic chargers we prove that global operators are insufficient for scalable superextensive charging and that a cumulative hierarchy of many-body operators is required, with the structure of the battery determining the degree of advantage. This is obtained by relating the charging power to the norm of the commutator between the battery and charger Hamiltonians and deriving an upper bound only capturing noncommuting terms. Moreover, we revisit the concept of participation number and propose an effective definition that accounts for the relative strength of the contributing terms, correlating it with the charging power scaling. Not limited to quadratic Hamiltonians, our results establish cumulative locality as a key resource for quantum charging advantage.

Identifying the quantum signatures of classical chaos remains a central question in quantum physics, and quantum scrambling provides a new perspective on this correspondence. We study two distinct limits of the same model to examine how the correspondence between chaos and scrambling changes across different regimes. The thermodynamic-limit anisotropic Dicke model exhibits a close correspondence between chaos and scrambling, whereas this correspondence breaks down in the large-frequency-ratio limit of the anisotropic Rabi model (ARM). The contrasting chaotic behavior in the two limits originates from the different numbers of classical degrees of freedom, whereas their similar scrambling behavior stems from eigenstate delocalization. This implies that, in the large-frequency-ratio limit, eigenstate delocalization alone is insufficient to qualify the ARM as a classically chaotic model. This finding suggests that identifying chaos in quantum systems requires jointly considering the classical degrees of freedom and eigenstate delocalization.

Early studies on the Dicke model linked superradiance to quantum chaos, whereas later anisotropic Dicke and Rabi studies reached apparently conflicting conclusions. We resolve this tension by distinguishing global chaos from local instability. Along the isotropic Dicke path, a sweep at fixed low excitation energy crosses both the superradiant boundary and a nearby chaotic window, explaining the reported correlation. However, the anisotropic Dicke model can be chaotic in the normal phase and regular in the superradiant phase, making superradiance neither necessary nor sufficient for global chaos. A fidelity out-of-time-order correlator (FOTOC), in contrast, probes the local stability of the stationary point selected by the initial wave packet. The superradiant transition destabilizes the origin, whereas a change in anisotropy can restore its stability and create displaced saddles. Wave packets centered at these saddles exhibit exponential FOTOC growth even on a classically regular Dicke energy shell with Poisson statistics. This local sensitivity also enables quantitative spectroscopy: combined with the topology of stationary points and local density of states relations, FOTOC dynamics reconstructs the absolute amplitudes of spectral singularities in both models without fitting the density of states.

Inspired by Fermi's model of radiation-matter interaction, we investigate the classical dynamics of a closed, finite-energy system, in which matter is coupled to an electromagnetic field. We find that energy is progressively transferred to increasingly high-frequency field modes, so that the effective temperature of both matter and radiation approaches zero in the long-time limit - in sharp contradiction with the finite-temperature equilibrium assumed by classical blackbody thermodynamics. Requiring consistency with the Stefan-Boltzmann and Wien laws identifies a characteristic time $t_L$, at which both laws are simultaneously satisfied. Strikingly, classical spectra obtained for different energies and cavity sizes collapse onto the universal Planck distribution at $t_L$. We conjecture that quantum dynamical localization arrests the classical energy cascade at $t_L$, and that the Planck distribution emerges as a dynamical consequence of this arrest - without invoking any a priori statistical assumption.

Friston's free energy principle holds that a system separated from its environment by a Markov blanket---a boundary whose states statistically screen its interior from its exterior---can be treated as performing approximate Bayesian inference, and that such blankets arise wherever coupling is short-range. We test this blanket condition in a concrete nonlinear pattern-forming system: self-replicating spots in a reaction-diffusion model that persist, compete, and reproduce. Directed boundary exchange and timescale separation hold up reasonably well, with qualifications. A flux-defined blanket does not screen interior from exterior. Flux removes only part of the linear dependence, and a nonlinear test shows that conditioning on flux \emph{increases} the dependence, consistent with conditioning on a collider, since flux is a joint function of concentrations on both sides of the boundary. The dependence is concentrated within about one organism radius of the boundary. A band of the surrounding field that thick screens the interior from the exterior beyond it, as any short-range field would, which is not evidence of inference.

We develop and compare enhanced neural-network solvers for one-dimensional ground-state profiles, which are solutions of $$ Q^{\prime\prime}=bQ-\gamma Q^{p},\quad Q>0,\quad p>1, \quad b, \gamma >0, $$ the stationary profile equation for the nonlinear Schrödinger, generalized Korteweg-de Vries, and nonlinear Klein-Gordon equations. Its explicit sech-type solutions serve as exact reference for error computation and benchmark hyperparameter selection. We improve on the standard Adam-trained physics-informed neural network (PINN) baseline by introducing higher-order optimization via Gauss-Newton/Levenberg-Marquardt and L-BFGS refinements, as well as Fourier-feature PINNs, and constrained Deep Ritz (DR) formulations. In DR approaches we introduce two new neural-network formulations, which implement two classical variational characterizations: a Nehari-constrained Deep Ritz method, in which the height is learned by projecting onto the Nehari/Pokhozhaev manifold, and a Weinstein Deep Ritz method, in which a normalized profile minimizes the Weinstein quotient. The Deep Ritz formulations perform best overall, in particular, the Weinstein variant gives the best error-runtime balance. The neural-network based solvers remain less accurate and efficient than classical Petviashvili iteration in 1D, however, the current study provides a proof of concept: the mesh-free formulation, non-reliance on exact profiles or the related features make them promising in higher dimensions and for more complicated nonlinearities and dispersive operators.

Let $F(x,y)=(f_2(y),f_1(x))$ be a Cournot map of the unit square, $\varphi=f_2\circ f_1$ and $\chi=f_1\circ f_2$. Linero Bas and Muñoz Guillermo proved that an $\omega$-limit set of $F$ with nonempty interior is connected if and only if \textup{(C1)} its two projections are connected and \textup{(C2)} $\omega_{F^2}(z)\cap\omega_{F^2}(F(z))\neq\emptyset$, and conjectured that this holds for every $\omega$-limit set. We prove the conjecture for every point $z=(x,y)$ such that $\omega_\varphi(x)$ or $\omega_\chi(y)$ is finite, and for Lebesgue almost every point $z$ of the square whenever $\varphi$ is metrically regular (every metric attractor is a periodic orbit, a solenoid, or a cycle of intervals carrying a well-behaved absolutely continuous invariant measure). Over a periodic orbit the $\omega$-limit set is a \emph{comb}, whose sections are rigid; when one projection is connected it is a point, a \emph{lattice} $(P\times J)\cup(K\times Q)$ with $P\subset K$, $Q\subset J$ and $\#P=\#Q$, or an \emph{alternating comb} of $2m$ disjoint segments. Conversely, every lattice and every alternating comb is an $\omega$-limit set of a Cournot map with piecewise linear reaction functions; the construction rests on a lemma producing exact compositions of piecewise linear maps with prescribed values. This answers, for this class, the question of Balibrea, Linero and Cánovas of which nowhere dense sets are $\omega$-limit sets of Cournot maps. For instance, the letter H is not an $\omega$-limit set at any such point, and for metrically regular $\varphi$ the points whose $\omega$-limit set is connected, infinite, nowhere dense and not a lattice form a Lebesgue null set.

We derive the Runge-Lenz vector of the five-dimensional Kepler problem from the eight-dimensional harmonic oscillator through symplectic reduction. By rewriting the moment maps of the harmonic oscillator in terms of five-dimensional gamma matrices and the $\mathfrak{su}(2)$ generators associated with the symplectic reduction, we identify the moment map expected to yield the Runge-Lenz vector. We then perform the reduction with respect to the SU(2) symmetry, derive the five-dimensional Kepler Hamiltonian, and show explicitly that the identified moment map reduces to the Runge-Lenz vector.

This study presents several novel approaches to improve the efficiency of a single-stage coil gun. Conventional designs typically feature a uniformly wound solenoid and a ferrite projectile. For our research, we constructed a microcontroller-based prototype to test several new enhancements, including the use of a bipolar current pulse, a stepped multilayer coil with non-uniform winding densities, and the replacement of conventional ferrite projectiles with a neodymium permanent magnet. These modifications were designed to reduce energy loss and improve projectile acceleration by changing magnetic field strength and effectively controlling the magnetic flux. The experimental results show that the proposed methods resulted in significant efficiency improvements, with the varying current pulse and stepped coil design providing enhanced magnetic force at key points in the projectile's path, and the permanent magnet projectile contributing to higher velocities and efficiencies by leveraging the current pulses. Our findings suggest that combining these enhancements significantly improves coil gun performance, achieving higher velocities and efficiencies. These findings can be applied to future coil gun developments, such as multi-stage coil gun systems.

Standing Alfvén waves develop in a poloidal channel of a liquid-metal blanket of a fusion reactor during the first few milliseconds of a plasma disruption event. The waves are characterized by high-frequency oscillations of velocity, electric current, and induced magnetic field, with Lorentz forces exceeding, in some cases, 10 9 N/m 3 .

Motivated by the underground storage of hydrogen and CO₂, we use analytical approximations to study the evolution of a gas current injected into porous, axisymmetric, dome-shaped channels. Unlike flow in flat channels, where injection dominates, flow in bell-shaped channels can remain influenced by buoyancy. In parabolic-shaped channels, slopes steepen with distance from the injection point, leading to distinct stages of spreading with different flow patterns along the channel. These results show how geological curvature can alter gas spreading and suggest that, under suitable conditions, parabolic-shaped aquifers may offer more efficient use of storage volume than flat aquifers.

Flow-induced vibrations are often classified by frequency synchronization, but this alone can obscure changes in the coupling between fluid forces and structural motion. Simulations of an inclined D-section cylinder at low Reynolds number reveal a finite interval in which lift and motion separate in frequency and their phase difference wanders. This transitional response connects lock-in to low-amplitude, nearly antiphase motion without developing into sustained galloping.

A spinning rotor can drive a free neighbor to turn either against it, like a gear, or with it, like a belt, as a recent quasi-two-dimensional experiment showed. Using direct numerical simulations of strictly planar flow, we compute the torque-free spin of the passive rotor across gaps, Reynolds numbers, and corral sizes. The planar model reproduces the observed gap-driven sequence of vortex rearrangements and the order of magnitude of the coupling, and it contains an inertia-driven spin reversal, but at a narrower gap than in the experiment, leaving finite-depth effects as candidate contributors to the difference.

In Newtonian turbulence, velocity fluctuations exhibit a complex, multifractal hierarchy of scaling laws. Here in polymeric turbulence, experiments reveal a simpler, bifractal-like scaling for longitudinal velocity structure functions in the polymer-dominated elastic range, with distinct branches for low- and high-order moments. The results suggest that sheetlike flow structures govern the rare, intense fluctuations, providing insight into how polymer elasticity reshapes turbulent intermittency.

Vortex stretching is regarded as the engine of three-dimensional turbulence, yet the separate roles of its two components, vorticity amplification and vortex tilting, remain unclear. By selectively suppressing vorticity amplification in the Navier–Stokes equations, we show that it is essential for the forward energy cascade and the dissipative anomaly: without it, energy dissipation vanishes at high Reynolds number and the flow switches to a forward enstrophy cascade with anomalous enstrophy dissipation. Yet intermittency and multifractality persist, revealing that the geometric reorientation of vortex lines by tilting alone is sufficient to sustain them.

Coupled level-set and volume-of-fluid methods combine the mass conservation of a transported volume fraction with the smooth interface description of a signed-distance function. In the simple coupled variant, the level set is rebuilt from the volume fraction during every time step rather than transported, and it supplies the interface curvature and the fluid properties. This paper presents an implementation of the simple coupled method in OpenFOAM and sets out four conditions that such an implementation must satisfy to stay consistent. The density in the time derivative and in the convective mass flux of the momentum equation must be the same field, the curvature in the surface tension force must come from the level set, the blended kinematic viscosity must reproduce the blended dynamic viscosity, and the smoothed fields must be evaluated on boundary and processor patches as well as in the cells. The solver is tested on the second two-dimensional rising-bubble case of Hysing et al. on two meshes. Up to t= 1.75 s, while the three reference codes of that benchmark agree, the rise velocity differs from the reference by at most 0.0064 and 0.0073 m/s on the two meshes, and its first maximum is 1.3% and 2.0% below the reference. These differences grow slightly with refinement. The same happens when the curvature and the properties are taken from the volume fraction, which reproduces the standard OpenFOAM solver, so their cause lies outside the coupling. Over the same interval the level-set coupling stays closer to the reference than this volume-fraction coupling, with a largest velocity difference of 0.0073 against 0.0094 m/s on the finer mesh. The bubble volume is conserved to the printed precision, and a run on four processors matches the serial run. The solver is released under the GNU General Public License.

The properties of colloidal suspensions and granular matter change drastically upon adding a small amount of liquid capable of forming capillary bridges between the solid particles. The attractive forces exerted by these liquid bridges induce the formation of particle aggregates and networks, which radically changes the macroscopic mechanical and rheological behaviour. Predicting these forces across bridge sizes, particle separations and wettability is therefore central to particle-scale modelling of capillary suspensions and wet granular matter. While the Young-Laplace equation governing the properties of the liquid bridges is well known, it lacks a convenient analytical solution. Current simulations therefore employ approximate analytic expressions, typically developed for contact angles below ~40° and bridge volumes below ~2.5% of the solid particle's volume. We compare several frequently used expressions from the literature with numerical solutions of the theoretical capillary forces. An overall good agreement is observed in the aforementioned parameter ranges, while the approximate expressions start to deviate outside their intended domains. We propose accurate and computationally efficient expressions for the capillary force that model this behaviour, for contact angles from 5° to 80° and bridge volumes from $10^{-6}$ to 0.15. We also explore mesoscopic 'fluid-scale' simulations of bridges by Multi-body Dissipative Particle Dynamics (MDPD), to ascertain whether this coarse-grained fluid model faithfully captures the continuum capillary forces. Remarkably, a good agreement is observed even for liquid bridges described by a mere few dozen fluid particles. Together, these results offer two approaches, at different resolution scales, for simulating bridges over a wide range of bridge volumes and contact angles.

Predicting the dynamics of anisotropic mixtures of different species is a challenging theoretical task. We show that Dynamical Density Functional Theory (DDFT), a theory predicting time evolution of the one-particle-density through a free energy functional, can be simplified to a diffusion equation. To quantify the dynamical relaxation behavior, we deduce corrections to the regular long-time collective diffusion coefficients from the direct correlations between the interacting particles and determine these effective diffusion coefficients analytically for a number of hard-particle systems, including mixtures of hard spheres, as well as isotropic and nematic phases of uniaxial spherocylinders and biaxial spherotriangles. Finally, we discuss how to generalize our approach to systems with positional order and suggest a possible application to predicting relaxation times of orientational order parameters.

A liquid crystal elastomer (LCE) exhibits a two-way coupling between its mesogen order and network elasticity: the mesogen order sets the undeformed network conformation, and the network deformation reorients the mesogens. This coupling gives rise to large, reversible stimuli-responsive actuation, as well as to soft elasticity, a finite deformation at nearly zero stress. This article reviews the elastic theory of ideal LCEs, bridging single-chain statistics and continuum constitutive models. The "ideal" elastic behavior rests on the assumption of anisotropic Gaussian chains that retain no memory of the crosslinking state, such that rotating the director costs no free energy. The corresponding neo-classical free energy of a monodomain LCE is non-quasi-convex, with a continuous family of stress-free ground states, leading to thermally induced spontaneous deformation and soft elasticity accommodated by coexisting stripe domains. The quasi-convex relaxation of the free energy classifies the behavior of polydomain LCEs into three phases, each with a distinct macroscopic mechanical response depending on the stretch state. The ideal elastic theory can be further extended to incorporate additional behaviors and physical processes, including thermo- and photomechanical coupling, Frank elasticity from director distortion, semi-soft or non-soft behavior arising from network nonideality, and temperature- and rate-dependent viscoelasticity.

Modeling self-propulsion as an emergent diffusiophoretic effect, we come back to the dynamic clustering experiment of active Janus colloids. Working in the original three-dimensional geometry, and using the chemical solute concentration as a control parameter, we find that the dynamic clustering region occupies a robust fraction of the phase diagram. This behavior is rationalized using a linear stability analysis that efficiently captures the instability of the gas phase to dynamic clusters. We also find that dynamic clustering results from the combined effects of a Keller-Segel collapse and of a motility-induced phase separation, either being arrested by the orientational coupling to the chemical field in agreement with previous work.

In systems with coupled order parameters, the relaxation of existing order can modify subsequent transitions, while cooperation and competition between emerging modes can produce complex phase sequences. We develop a modular Landau analysis that locally relaxes noncritical parent-phase variables to obtain effective one- and two-mode free energies. The resulting coefficients quantify relaxation-induced changes in transition characteristics and mode coupling, including changes in transition order for even-symmetry modes. The resulting modules are assembled successively along parent branches, and the equilibrium phase sequence is selected by comparing the fully relaxed free energies of the admissible branches. We apply the framework to ferroelectric liquid crystals, where orientational, polar, smectic, and tilt orders interact and give rise to multiple competing pathways, using a uniaxial model with longitudinal polarization. We fit the model to the measurements reported by Strachan et al. [Adv. Sci. 12(3), 2409754 (2025)]. A single thermodynamic parameter set reproduces the observed transition temperatures, transition types, and phase sequence, while capturing the main birefringence trend. Smectic layer spacing is reconstructed separately through a fitted observation map based on the calculated equilibrium tilt.

Obtaining defect-free single-crystals is of crucial importance in soft matter and materials science, spanning both fundamental interests and practical applications. Active crystals, encompassing diverse dense systems from living organisms to artificial metamaterials, can offer a promising platform for autonomous structural reorganization. We demonstrate that increasing spatiotemporal orientational fluctuations around the mean polarized state can enhance crystallographic order in active crystals. Poly-to-single-crystal transformations in defect-rich, self-aligned active Brownian crystals with coupled translational-rotational dynamics are investigated. We show that long-lived persistence with slow alignment controls the defect-annealing capability. By disentangling activity magnitude from associated timescales, we reveal activity-assisted annealing. Tuning the persistence length enables overcoming thermal energy barriers. Simultaneously adjusting persistence and alignment timescales can tune relaxation from `fast' to `slow', yielding defect-rich and defect-free crystals, respectively. Furthermore, active crystals of point particles are found to exhibit similar defect annealing when flocking is delayed by tuning the timescale of the velocity relaxation towards the polarized state. These findings suggest that the mechanism may extend to a broader class of active crystals. Our results intersect statistical physics of living soft matter with the mechanics of defects and microstructures, proposing a nonequilibrium route towards reconfigurable materials.

Our experiments demonstrate the strong stabilizing effect of a viscoelastic shell on flow-focused viscous jets. The results suggest that stabilization occurs when the polymer viscosity, $\eta_p$, exceeds a critical threshold, provided the extensional relaxation time, $\lambda$, is large enough to allow the polymer molecules to undergo the coil-stretch transition. Under these conditions, substantial extensional viscoelastic stresses develop as the liquid accelerates. Since both $\eta_p$ and $\lambda$ increase with shell viscosity, the polymer concentration required to stabilize the viscous jet decreases accordingly. Remarkably, moderately to highly viscous jets can be stabilized with very small polymer concentrations, for which no beads-on-a-string (BOAS) instability is observed.

Fiberboids are filaments that self-propel by rolling along a surface due to a flux normal to that surface. In the last few years, fibers using several materials and driving mechanisms have been developed that are able to roll persistently. Here we show using thermally driven nylon fibers on a slightly curved glass surface, that fiberboids also come in another state, that we call ``twitching'': the fiber rolls for a short time and then switches direction, implementing on large scales a diffusion-like motion. We rationalize the occurrence of this effect and experimentally quantify this new dynamic state. We then analyze ensembles of twitching fiberboids and by confining the fibers inside a circular arena to allow them to roll on a single axis only, we implement a simple, table-top realization of a one-dimensional non-equilibrium active gas. We study experimentally active cluster formation, their non-equilibrium dynamics and we rationalize the observations by a simple lattice model. This model takes into account a Viscek-like alignment of the velocity directions of the individual particles within clusters to yield good qualitative agreement with the experiments. Overall our work opens the path to study collectives of self-rolling fibers as an interesting new class of active matter.

The measurement of guided wave propagation is an effective approach for evaluating arterial wall stiffness. A more comprehensive characterization of viscoelastic material properties could yield more informative biomarkers; however, this additionally requires estimation of wave attenuation. Furthermore, spatially local estimation is necessary for localized pathologies, such as atherosclerotic plaques. To this end, we propose an original two-stage high-resolution method to recover local viscoelastic properties from guided waves in artery-like soft tubes. First, the local frequency-wavenumber dispersion relation including losses is estimated using a high-resolution complex wavenumber identification method. Second, assuming a fractional Kelvin-Voigt rheological model for the tube wall, we estimate the viscoelastic material parameters by fitting the dispersion relation computed with a spectral element method to this estimate. We experimentally validate the proposed approach on flexural wave propagation along water-filled soft tubes, measured with a high-speed camera coupled with digital image correlation. Owing to the high resolution of the method, the axial modulus variation of a graded phantom is recovered. Finally, a Cramér-Rao analysis indicates that the complex wavenumber estimator operates near its theoretical limit, and reveals why local attenuation is intrinsically difficult to recover.

We construct a hydrodynamic theory of the effect of chiral and active force densities on three-dimensional uniaxial solids. We show that in a fixed background medium active chiral force densities---that arise at lower order in gradients than odd elasticity---generically destabilise the solid state. We further show this active instability also affects isotropic chiral solids in an anisotropic medium, a situation that is relevant for cell clusters moving through the extracellular matrix. Interestingly, the instability is eliminated in a higher-symmetry solid, known as the polar elastomer; indeed, we show that chirality does not affect the leading-order mechanics of such materials. We further demonstrate that momentum-conserving polar active solids have two chiral odd elasticities in contrast to the one discussed for two-dimensional solids. However, we again find that the higher symmetry of polar elastomers eliminates one of these with the remaining one being equivalent to the two-dimensional odd elastic force density. Our results should apply to numerous biological and condensed matter systems.

We examine the effect of chiral activity on nematic and polar uniaxial elastomers and solids by constructing the general hydrodynamic equations for these phases. We start with the elastomer, which is not only invariant under rigid rotations but also under an independent rotation of the uniaxial direction, and show that this higher symmetry strongly constrains the effects of chiral activity. We then break the elastomeric symmetry by adding a symmetry-breaking term to the free energy but still retain invariance under rigid rotations. The resulting state has the symmetry of a uniaxial solid, and we show that in a fixed background medium chiral activity generically destabilises it. The force density responsible for this {instability} vanishes as the field that breaks the elastomeric symmetry goes to zero. Further, the presence of the symmetry-breaking field also allows for an additional odd elastic force density that generically destabilises momentum-conserved chiral and uniaxial solids in the inertial regime.

Annually about one billion tires reach the end of life. Rubber from waste tires can be ground into particles and incorporated into a matrix. In practice, the resulting composites are commonly not recycled into new tires, but downcycled into low-value products such as sport surfaces, indoor flooring, and rubberized asphalt. Recycling waste tires into new tires remains a challenge. In particular, such composites typically have low strength, especially when the particle content is high or the particles are large. A single waste tire particle may act as a flaw to initiate macroscopic fracture and knock down the strength of the entire composite. Here we propose the principle of flaw-tolerant recycling. Rather than requiring every particle to be reliable and small, the matrix is designed so that flaw-like particles do not initiate macroscopic fracture. We demonstrate a flaw-tolerant matrix consisting of two intertwined networks: a network of densely entangled and sparsely crosslinked long natural rubber chains, and a percolated network of carbon aggregates. When the flaw-tolerant matrix is incorporated with up to 80 wt% of commercially available waste particles, the resulting composites still maintain strength. The principle of flaw-tolerant recycling may aid the development of recycling waste tires into new tires.

Does a collection of magnetically driven rotors necessarily rotate in the same direction as its individual members? We show that rotors driven by a rotating magnetic field self-assemble into clusters whose collective rotation can oppose the self-rotation of every rotor within them. The reversal arises from competition between rotation-translation coupling and dipolar interactions, which favor opposite directions of collective rotation. Their balance varies with system size and driving frequency, producing a transition between the two handed states, while hydrodynamic interactions shift the transition boundary. Collective handedness can thus emerge opposite to the field-imposed single-rotor rotation without reversing the external field, and can be tuned through system size and driving frequency.

Recent research revealed the orientation-dependent propulsion of a cone-shaped colloidal particle that is exposed to a planar traveling ultrasound wave. Here, we extend the previous research by considering nano- and microcones with different aspect ratios and studying how the propulsion of a particle depends on its orientation and aspect ratio. We also study how the orientation-averaged propulsion of a cone-shaped particle, which corresponds to an isotropic ultrasound field, depends on its aspect ratio and identify an aspect ratio of 1/2 where the orientation-averaged propulsion is particularly strong. To make our simulation results easier reusable for follow-up research, we provide a corresponding simple analytic representation.

Mode-coupling theory (MCT), one of the most prominent models of the glass transition, also makes various specific predictions for the molecular dynamics in the liquid state of matter. They can be best experimentally tested by evaluating susceptibility spectra covering a broad frequency range. In the present work, we clarify whether the most recent broadband dielectric-spectroscopy results on water, whose glass transition is highly disputed, are compatible with MCT. The so-called fast beta process, expected within this theory, should be detectable at low temperatures only, inaccessible in water due to its inevitable crystallization upon cooling. Therefore, we also investigate data on aqueous LiCl solutions, which can be easily supercooled. We find that all the available broadband dielectric data on these solutions and pure water are well consistent with MCT. Notably, this includes the expected interrelation of the critical temperature dependence of the alpha relaxation to its often-neglected non-Debye spectral shape. Moreover, the available data on the fast beta process, detected in a 14.8 mol% LiCl solution, are also well consistent with the theory. We find a smooth development of the derived MCT parameters with salt concentration which supports the validity of the critical temperature Tc = 222 K and system parameter lambda = 0.55 deduced here for pure water. We also compare the current dielectric relaxation-time results to those determined by other experimental methods and address the question whether information on the controversial fragile-to-strong transition of water can be obtained from such data. Finally, we discuss the significance of the dominant dielectric relaxation process of water for the glass transition as described by MCT, especially considering scenarios questioning its association with the alpha relaxation.

In a liquid--liquid transition (LLT), a single-component liquid transforms into another liquid with different density and viscosity. Flow therefore couples to the transition, but the effect of shear flow is not understood. Here we investigate the LLT under shear with a two-order-parameter hydrodynamic model in which the viscosity depends on the non-conserved structural order parameter. Under shear, a fluctuation of the order parameter drives a compressional flow through the viscosity, and the resulting density change enhances the order parameter fluctuation. In a linear analysis, this feedback destabilizes the metastable liquid above a critical shear rate $\dot{\gamma}_{\rm c}$ for wavevectors in particular directions. Because the flow rotates the wavevector, a fluctuation grows only for a finite time duration, and its amplification is determined by the dimensionless shear rate $\dot{\gamma}/\dot{\gamma}_{\rm c}$ and the second dimensionless number $\Lambda$, the ratio of the thermodynamic relaxation rate of the order parameter to $\dot{\gamma}_{\rm c}$. In hydrodynamic simulations, shear above about $\dot{\gamma}_{\rm c}$ induces the transition in the metastable region when $\Lambda\gtrsim1$. The transition proceeds by nucleation of domains whose morphology becomes anisotropic. The incubation time decreases and the onset of the viscosity increase is accelerated as $\dot{\gamma}$ and $\Lambda$ increase. These results imply that the shear rate is a control variable of LLT in addition to temperature and pressure, selecting whether and how a metastable liquid transforms.

How compression changes both the magnitude and organization of cell motion remains unclear. Using a three-dimensional active vertex model, we examine how tissue state and active dynamics shape the response of confined spheroids to uniaxial compression. With polarity alignment switched off, compression enhances transverse motion in solid-like spheroids throughout the tested activity range, whereas the fluid-like response reverses from acceleration at low activity to slowing at high activity. Changes in contact persistence organize these responses along a common empirical trend. Passive five-cell calculations reveal how compression reshapes local rearrangement barriers: the response depends on geometry and loading direction, and a high-strain increase in the fluid-like mean coexists with many low-barrier paths. In a separate high-alignment regime, strong compression induces coherent rotation in solid-like spheroids, while fluid-like spheroids show no comparable collective rotation. The rotating solids have a higher contact-persistence index than the fluids and exhibit tangential peripheral cell organization. Controlled perturbations reveal compression-induced softening of a differential-twist mode and slower relaxation with activity. Together, these results identify an activity-dependent reversal of the motility response and compression-induced coherent rotation as two distinct outcomes of loading, linking them to contact persistence, local rearrangement costs, and active coordination.

For Brownian hard spheres without hydrodynamic interactions, we obtain a conditional enclosure between 1.8266948 and 1.8267157 for the third-order zero-shear Brownian viscosity coefficient. It applies when the physical three-body correction coincides with the finite-energy weak solution and the remote remainder in the pair adjoint identity vanishes. Kirkwood superposition gives zero because three nonzero pair contributions cancel exactly. An elementary radial identity exposes this cancellation, and a common contact-stress convention allows direct comparison of closure predictions. Although superposition solves the bulk equation, it leaves a shared-contact flux error. Correcting this error defines a unique weak response with positive Dirichlet energy. Explicit symmetric trials yield a variational lower bound and a residual upper bound using the rotational structure of shear and three-sphere geometry. Exact integration and outward interval evaluation enclose the fixed-trial functionals. Under the stated physical conditions, the resulting interval excludes all closure coefficients compared here and supplies a quantitative benchmark for dilute three-body Brownian stress.

Nearby relaxation rates make two membrane viscosities difficult to distinguish from a shape transient. We show how calibrated preparation removes this loss of local sensitivity in a linear Kelvin-Voigt sphere with finite area elasticity and intrinsic membrane dissipation. Two independent releases, with a known signed amplitude ratio and calibrated relative gain and timing, yield normal-displacement records whose fixed linear combination separates the shear and dilatational rates. Their common amplitude remains unknown. For fixed sampling, positive-definite weights, bounded positive rates and nonzero excitation, the amplitude-projected sensitivity has a positive lower bound even at rate coincidence. Without relative calibration, the paired sensitivity decreases linearly with the rate gap; the single tangential-release record decreases quadratically. The calibrated bound is compatible with fixed finite initial energy. A positive local bound also persists with independent ratio calibration of fixed positive precision under a Gaussian error model. Supplied elastic coefficients convert the recovered rates into the two surface viscosities. An unbounded spherical Stokes extension quantifies how bulk dissipation changes the modal patterns and provides a sufficient full-Jacobian criterion for retaining local material sensitivity.

We study the phase behavior of binary blends of polymers with oppositely charged termini using an ion-correlation-augmented self-consistent field theory (IC-SCFT). Under the low dielectric conditions typical for organic polymer melts, strong ion correlations drive association of multiple chain ends, leading to emergent multichain architectures that go beyond a simple ion-paired diblock copolymer picture previously used to interpret recent experiments. At moderate to strong polymer segregation, the resulting phase diagram differs considerably from this effective-diblock prediction: ion clustering broadens the lamellar and cylindrical windows while suppressing the network phases, the reverse of the trend for end-charged diblock copolymers. At weak segregation, the two polymers remain miscible even as ion clustering persists, and decreasing chain length drives the clusters themselves through a sphere-to-cylinder-to-lamella shape transition, connecting continuously to the aggregation behavior of classical terminally charged ionomers in the limit when one of the polymer species shrinks to just the charged end. These results reveal that ion clustering -- beyond simple pairwise bonding -- shapes the self-assembly of end-charged polymer blends.

Models of colliding self-propelled rods are abstractions of many real systems such as gliding bacteria and biofilaments displaced by molecular motors. They have been studied mostly in two space dimensions and shown to display a wealth of different collective regimes with many parameters involved in the ensuing phase diagrams. Continuum-level theories faithful to this phenomenology are largely lacking since coarse-graining models of explicit rods is notoriously difficult. Here we study collections of particles in which the rods geometry is taken into account effectively, by implementing the nematic alignment of their velocities and two types of repulsion. These Vicsek-style models are simple enough to be starting points for systematic coarse-graining. We thus derive hydrodynamic equations that we show to have solutions qualitatively faithful to their particle-level origin.

Motivated by gaps in our current knowledge of the Vicsek model, we present a major update of its phase diagram in two space dimensions, summarizing comprehensive numerical simulations at length- and timescales never explored before. Our main conclusions are that multiple phase separation scenarios are at play, not just the simple microphase separation put forward in [Phys. Rev. Lett. 114, 068101 (2015)], and that the coexistence phase is subdivided in two. We also map out the region of metastability of the homogeneous Toner-Tu liquid phase.

The Vicsek model continues to be central in statistical physics studies of active matter, with major recent surprises such as the partial metastability of the famous Toner-Tu flocking phase. Here we report on the diversity of band patterns observed in its coexistence phase --some of them never observed before--, but we also argue that most disappear in the infinite-size limit, leaving nevertheless a different picture than anticipated previously. We finally show that these rather regular, globally ordered band configurations can be destroyed by a localized perturbation: the coexistence phase is also at least partially metastable, and thus must be, asymptotically, a disordered phase made of a variety of chaotically interacting traveling bands.

We investigate whether cyclically varying the class composition of training batches can modify both the performance and the internal organization of neural networks. Motivated by nonequilibrium systems, in which cycling between related sub-goals can make switching between their solutions increasingly efficient, we introduce Dynamical Batching (DB), a sampling protocol that periodically emphasizes each class while leaving the loss and the optimizer unchanged, and compare it with Uniform Batching (UB), in which every mini-batch has equal class proportions. In the regime where standard training fails, DB changes the outcome: on a three-arm spiral, a capacity-limited MLP that plateaus far below perfect accuracy under UB fits the training data under DB. Tracking individual weights, we find that under DB the change between class-specialized states is carried by a smaller set of weights than under UB, and that this set is markedly more persistent from cycle to cycle, on every synthetic dataset we test and in a wider network that fits the data under both protocols. This organization is a signature of the protocol rather than a predictor of its benefit: it appears equally where DB leaves accuracy unchanged. On CIFAR-10, the same protocol modestly improves the test accuracy of a channel-narrowed ResNet-10, a standard residual architecture, and of a second capacity-limited convolutional network. These results show that how class emphasis is distributed in time can shape both the solution a network reaches and the internal structure of the network.

A method for integrating the Langevin equations of motion for run-and-tumble particles is introduced to compute the joint distribution of their position and active velocity, with and without a harmonic external force field. The key step is the construction of the moments of the distribution and the correlation functions, conditional on the particles being in a specific state at the final time. For one-dimensional run-and-tumble particles in a harmonic external potential, the exact steady-state distributions for the tumble state, as well as for the run state conditional on a specified velocity direction, are obtained. This enables us to demonstrate their equivalence to the exact solutions of the corresponding Fokker-Planck equations.

The desert-dwelling sandfish (Scincus scincus) moves within dry sand, a material that displays solid and fluidlike behavior. High-speed x-ray imaging shows that below the surface, the lizard no longer uses limbs for propulsion but generates thrust to overcome drag by propagating an undulatory traveling wave down the body. Although viscous hydrodynamics can predict swimming speed in fluids such as water, an equivalent theory for granular drag is not available. To predict sandfish swimming speed, we developed an empirical model by measuring granular drag force on a small cylinder oriented at different angles relative to the displacement direction and summing these forces over the animal movement profile. The agreement between model and experiment implies that the noninertial swimming occurs in a frictional fluid.

The glass-forming ability (GFA) of a metallic liquid can be quantified by the critical cooling rate $R_c$, below which it crystallizes upon cooling. $R_c$ is determined by the competition between $R$ and the crystallization rate $\mathcal{K}_{\rm X}$. Here, we calculate $R_c$ and $\mathcal{K}_{\rm X}$ in model pure metals and alloys with BCC/B2 and FCC equilibrium crystal structures. Using classical nucleation theory and independently calculated crystal growth rates, we evaluate $\mathcal{K}_{\rm X}=(IU^3)^{1/4}$ at $T=0.8T_m$, where $I$ and $U$ are the nucleation and growth rates and $T_m$ is the melting temperature. We find a strong positive correlation between $\mathcal{K}_{\rm X}$ and $R_c$ over eleven orders of magnitude. We decompose $\mathcal{K}_{\rm X}$ into a product of a kinetic contribution, involving atomic cluster attachment and diffusion, and a thermodynamic contribution. We show that the thermodynamic contribution to $\mathcal{K}_{\rm X}$ dominates the kinetic contribution over the range of cooling rates that we consider. The nucleation barrier $\Delta G_c \sim \tilde\gamma^3/\Delta\tilde\mu^2$, where $\tilde\gamma$ is the reduced effective liquid--crystal interfacial free energy and $\Delta\tilde\mu$ is the reduced bulk driving force, determines the magnitude of the thermodynamic contribution. The relative importance of $\tilde\gamma$ and $\Delta\tilde\mu$ depends on the material: a large interfacial free energy can suppress nucleation in some systems, whereas a weak bulk driving force can inhibit crystallization in others. Analyses of the structural and chemical order show that better glass formers have enhanced structural frustration, more icosahedral-like and less crystal-like local environments, and a larger chemical-order mismatch between the supercooled liquid and crystal phases.

Discrete adjoint methods give the sensitivities that aerodynamic design and data assimilation require, but they remain hard to obtain for flow solvers that run on graphics processors. This paper presents CuAD, a source-to-source automatic differentiation tool that reads CUDA kernels and writes their tangent and adjoint versions as ordinary CUDA source. Its reverse mode is organised around the GPU thread and exploits the structure of flow-solver kernels: pure accumulations need no tape, the remaining intermediate values are recomputed rather than stored, and adjoint updates are atomic only where several threads reach the same memory. We evaluate CuAD on four kernels from simple flow models: a viscous Burgers residual, a two-dimensional advection-diffusion residual, a quasi-one-dimensional Euler residual and a Biot-Savart summation over point vortices. All generated derivatives agree with finite differences and pass adjoint dot-product tests to round-off, while the adjoint kernels cost two to six times the primal kernels. Compared with the compiler-based tool Clad under the same compiler, CuAD gives identical results at identical cost on the stencil kernels and is 16 to 470 times faster on the summation kernel because it stores no tape. A steady Burgers study shows that in single precision the adjoint gradient of a finite-difference Jacobian reaches errors of 45 to 75 per cent once the condition number grows to $2.5\times10^{5}$, whereas the CuAD Jacobian keeps the error below $5\times10^{-5}$. Four applications complete the evaluation: adjoint fields of the Burgers shock, the sensitivity of a scalar sensor in a cellular vortex, the inverse design of a transonic nozzle whose area is recovered to $2\times10^{-8}$, and an unsteady adjoint of the roll-up of a vortex sheet over 400 time steps.

We derive discrete moment equations exactly equivalent to the lattice Boltzmann method (LBM) and identify the general moment closure shared by kinetic methods based on the discrete-velocity Boltzmann equation. This closure provides a route to correct lower-order dynamics without requiring accurate reconstruction of the higher-order moments, thereby substantially broadening the scope of existing closure strategies that seek increasingly accurate representations of these moments. These advances establish a unified moment framework bridging LBM and moment methods. The framework enables efficient simulations across all Knudsen regimes, overcoming the prohibitive complexity of existing moment methods at high Knudsen numbers. It further provides a common basis for integrating and extending key features of diverse kinetic methods.

This work presents the development and assessment of a hybrid framework coupling numerical simulation, experimental samples, data assimilation (DA) and machine learning (ML) to investigate the flow within an axial compressor stage. The methodology first implements a Multi-Fidelity Ensemble Kalman Filter (MFEnKF) which integrates experimental PIV data with a two-fidelity numerical simulation setup, combining steady-state RANS on a fixed grid with unsteady hybrid RANS/LES simulations on a moving grid. This data assimilation step successfully reduces discrepancies between experiments and CFD realizations. Besides, it provides additional high fidelity samples when compared with the available PIV data. This enriched database is used to train machine learning (ML) tools, with the objective to obtain black-box forcing terms to be included in the discretized form of the Navier-Stokes equations. These models are expected to preserve the accuracy of the DA results while not longer requiring the input of experimental data. The neural network architecture used here maps local physical features such as the velocity, the velocity gradients and the turbulent viscosity, to obtain the volume forcing terms. The analysis of the performance of such ML models shows that global accuracy is preserved but localized increased errors in specific regions of the compressor, such as close to the blade tips, can exceed those observed from the baseline RANS simulations. To resolve this issue, a Mixture of Experts (MoE) method is employed, which classifies and combines the trained ML tools for different flow regions. The discrepancy with experimental data of this method is systematically lower than the one observed for the baseline RANS solution and very similar to the one obtained with the MFEnKF.

Stagnation curves of arbitrary shape (zeros of $\mathbf v(\mathbf x,t)$) are non-generic yet common; we derive their motion. Differentiating $\mathbf v=\mathbf0$ gives $\mathbf L\mathbf U=-\mathbf a$ ($\mathbf U$ curve velocity, $\mathbf a=\mathbf v_t$, $\mathbf L=\nabla\mathbf v$ kills tangent, acts on normal plane via $2\times2$ block $\mathbf K$); dynamics enters only via $\mathbf a$. Normal velocity: $-\mathbf K^{-1}$ times normal $\mathbf a$; tangential solvability: scalar condition $\Sigma=0$ per point ($\Sigma$: part of $\mathbf a$ outside range $\mathbf L$). Potential flow: $\mathbf K$ is strain rate, normal velocity pressure gradient over principal strain rate $\epsilon$, persistence needs uniform pressure on it. Stokes flow: tangential vorticity enters $\mathbf K$ (centre lines), $\Sigma$ involves normal vorticity. Navier-Stokes: $\Sigma$ set by instantaneous flow via nonlocal pressure, viscosity. If $\Sigma\ne0$, line becomes, to first order in $t$, isolated points at zeros of $\Sigma$ (critical points of $\varphi_t$ if potential; maybe none in Stokes flow: loops vanish). Symmetry (line an orbit of rigid-motion group, no velocity along it) suffices for persistence, not necessary: flows steady in rigidly moving frame have $\Sigma\equiv0$. Incompressibility enters via $\mathrm{tr}\mathbf K=0$; for inviscid irrotational homentropic compressible flow, line dilatation is $\varphi_{tt}/c^2$, so lines can be nodes, persistence needs uniform enthalpy, singular $\mathbf K$ arises at ordinary points, acoustic standing waves give exact examples (node line breaking into alternating sinks, saddles); also degenerate $\mathbf K$ (pairs born at distance $O(\sqrt t)$), curvature, torsion evolution, closure for moving-singularity-driven flows, helical and elliptically conical stagnation-point flow, exact Navier-Stokes example: saddle, centre lines split into four points per period.

The settling of particles in a fluid medium can trigger complex collective dynamics, dramatically affecting the distribution of energy across flow scales. In this work we present the first fully-resolved observations of the turbulence induced by large particle structures, also known as cluster-induced-turbulence (CIT), obtained through particle-resolved direct numerical simulations at high volume fractions and density ratios in large domains. We find that particles arrange in macroscopic fractal structures, exciting turbulent fluctuations at scales much larger than the individual constituents. By virtue of their fractal nature, these clusters force the continuous-phase in a multiscale, self-similar way. We further show that these cluster-driven, vertically decorrelated fluctuations at large scales coexist with, but are fundamentally distinct from, the established particle-driven high-wavenumber scaling. Beyond unveiling a different form of clustering in particle-settling, these results highlight a naturally arising, self-assembling path to fractal-generated turbulence.

We investigate the microstructural dynamics of wormlike micellar (WLM) solutions based on CPyCl/NaSal/D\(_2\)O under shear flow using spatially resolved rheo-diffusion NMR, velocity-compensated diffusion measurements, and rheo-optical imaging in a Taylor--Couette geometry. Two viscoelastic systems were examined: a non-shear-banding WLM with a molar salt-surfactant concentration ratio of \(R=0.4\) and a shear-banding WLM with \(R=0.53\). Rheo-optical and velocity measurements confirm homogeneous flow for the non-shear-banding system and the coexistence of low- and high-shear bands within the stress-plateau regime for the shear-banding system. Despite the pronounced heterogeneity in velocity and shear rate associated with shear banding, the local surfactant self-diffusivity remains spatially uniform across the gap and throughout the stress-plateau regime. Furthermore, analysis of the mean-squared-displacement scaling reveals no measurable difference between the high- and low-shear bands. These results demonstrate that the micellar microstructure remains largely unchanged despite the formation of shear bands and provide direct experimental evidence that flow-induced micellar chain scission is not a dominant mechanism governing shear banding in this WLM system.

Longitudinal dispersion in a yielding fluid depends on the velocity distribution and on how the flow is maintained. We study a neutral tracer in pressure-assisted electrokinetic and magnetohydrodynamic flow of a Casson fluid through a slit microchannel. The nonlinear stress and velocity equations determine the yielded layers, the unyielded core and the axial flow. Mei's multiple-scale homogenization of the advection-diffusion equation then separates transverse relaxation, mean drift and longitudinal spreading, yielding the Taylor-Aris auxiliary problem and effective diffusivity. An exact pressure-driven solution gives cubic decay of the mean velocity and eighth-power decay of the dispersion enhancement near flow arrest. Under fixed pressure and electrical forcing, increasing the yield parameter from $Y=0$ to $0.7$ moves the optimum Hartmann number from $Ha_p=0.696$ to $2.634$, while the corresponding normalized diffusivity decreases from $D_T^{\mathrm C}=1.454$ to $1.015$. At fixed mean throughput and $Ha_p=1$, the trend reverses: $D_T^{\mathrm C}$ increases from $1.000433$ to $1.002311$. The homogenized energy identity traces this difference to the velocity departure from the sectional mean, including that within the unyielded core. Analytical limiting solutions, direct concentration calculations, numerical convergence studies and a coupled Casson shear test support the reduced-flow predictions. An electrolyte-based dimensional assessment identifies the magnetic optima as theoretical forcing states for representative aqueous microchannels. These results are relevant to predicting longitudinal tracer spreading in microchannels carrying fluids with a yield stress, whether pressure or throughput is controlled.

A mechanistic interpretation for baroclinic normal mode instability with exponential growth is the interaction arising from Counter-propagating Rossby Waves (CRWs), where pairs of CRWs phase-lock and interfere constructively. On the other hand, an arbitrary initial condition can lead to finite transient growth as long as there is constructive interference. The present work investigates the characteristics of finite time transient instabilities and its description in terms of CRWs in a baroclinic system with asymmetric interaction, in contrast to usual settings where there is an inherent symmetry that leads to equal and opposite CRWs. A sloped Eady problem on a $f$-plane is considered here, which has the benefit that there are only two CRWs in the system, and the presence of a bottom topographic slope can be formulated in a such a way that only one of the CRW is affected and controlled by a single parameter representing the asymmetry, via modifying the bottom background potential vorticity gradient. We derive conditions where the instantaneous growths have key CRW properties that are independent of the asymmetry parameter for a reasonably general family of norms, and that the instability characteristic in the total energy norm is entirely independent of the asymmetry parameter. For finite time transient growth, the optimal initial condition is in some sense counter to that of the exponential growing normal mode: where the bottom slope is such that it is strengthening the bottom CRW, the normal mode has a larger bottom CRW, but the finite time optimal initial condition wants the bottom CRW to be weak instead, and vice-versa. While the results presented here are for the sloped Eady problem, the same results were also found for an analogous Phillips problem, and we speculate the instability characteristics may have origins in the underlying symmetries that are common to those two problems.

Bolus formation is one of the most distinctive features of peristaltic transport, yet the mechanisms governing its development remain incompletely understood. In this work, axisymmetric peristaltic-wave-driven flows under zero-pressure-gradient conditions are investigated using a high-fidelity lattice Boltzmann framework over a broad range of wave amplitudes, wavelengths, and Reynolds numbers spanning the Stokes limit to Re=100. In the Stokes limit, bolus formation is governed by the classical trapping mechanism and exhibits a remarkable wavelength-normalized similarity, with both bolus morphology and transport characteristics approaching common asymptotic behaviors as the wavelength increases. As fluid inertia becomes significant, this similarity progressively breaks down and wavelength-dependent trapping behavior emerges. In the short-wavelength regime, the pronounced geometric bending of the wave reorganizes the local flow structure and produces a distinct off-axis bolus associated with a curvature-induced trapping mechanism. The influence of this mechanism expands toward longer wavelengths with increasing Reynolds number and occupies an increasingly large portion of the parameter space considered in the present study. The results reveal that bolus formation cannot be described by a single universal mechanism. Instead, the observed trapping behavior arises from the competition between classical trapping and curvature-induced trapping, whose relative importance is controlled by wavelength, wave amplitude, and Reynolds number. These findings establish a unified physical framework for understanding bolus formation and transport in peristaltic-wave-driven flows.

A sudden loss of vacuum in a superconducting radio-frequency (SRF) accelerator drives warm gas into the evacuated beamline, where it propagates through interconnected SRF cavities cooled by liquid helium, causing surface contamination, intense heat deposition, and dangerous pressure buildup. Yet predicting how such a failure propagates through realistic multicell cavities has remained difficult because compressible gas dynamics, condensation and cryogenic heat transfer are strongly coupled. Here we develop and experimentally validate a multidimensional computational framework that resolves these processes, and apply it to a full-scale nine-cell SRF cavity. We find that the repeated cell geometry produces staircase-like gas-front propagation, as impingement, recirculation and localized cryopumping strongly retard the bulk flow within each cell. Across a broad range of breach sizes, the cavity traversal time follows a robust power-law scaling with leakage area, providing quantitative guidance for the response time of beamline isolation and protection systems. The simulations also reveal a geometry-confined Mach disk whose position and size track the advancing gas front, suggesting that its acoustic emission could potentially enable rapid, non-invasive detection and localization of vacuum failures. These findings pave the way for a new generation of predictive diagnostics and protection strategies to safeguard large-scale superconducting accelerators.

We present a simple and robust method for generating freely suspended liquid sheets by directing a single laminar liquid jet onto the sharp edge of an inclined plate. By optimizing liquid composition, impact geometry, and flow conditions, we identify a 60:40 ethylene-glycol-deionized-water volumetric mixture for stable sheet formation. The resulting sheets span 8 mm in height and 3 mm in width, with thicknesses from 1.1 to 4.8 micrometers measured by spatial and spectral interferometry. Operated in vacuum as continuously renewed plasma mirrors, these targets demonstrate stable performance from 0.5 to 10 kHz using 175-fs Yb:KGW laser pulses, reaching a maximum S-polarized reflectivity of 66.5% at an intensity of 4 x 10^14 W/cm^2. At higher intensities using 25-fs Ti:sapphire pulses at 1 kHz, maximum S-polarized reflectivity reaches 77% at 2 x 10^16 W/cm^2. The reflected beam exhibits high temporal stability, with angular pointing fluctuations of 18.19 +/- 0.53 microradians. Our results demonstrate a tunable, continuously renewed liquid-sheet target for multi-kHz laser-plasma experiments.

Residual stress remains in an object even in the absence of external forces or thermal pressure, which, in turn, may cause significant plastic deformations. In case the residual stress creates unwanted effects on the material and so is undesirable, an efficient solution is necessary to track and eliminate this stress. Smoothed Particle Hydrodynamics has been extensively used in solid mechanics simulations and the inherent colour-field generation approach is a promising tracker for the residual stress. In this paper, we propose a way to use the colour-field approach for eliminating the residual stress and prevent the undesirable premature failure of solid objects.

Integrating condensed noble gases with superconducting circuits offers new opportunities for operating hybrid quantum devices. In particular, electrons on solid neon have recently emerged as exceptionally coherent charge qubits, however the growth of the underlying neon films on patterned devices remains poorly controlled. We monitor neon films near the triple point using a multimode resonator fabricated from high-$T_c$ YBCO, which remains superconducting at temperatures where the liquid phase exists and whose geometry sets a thickness-sensing window near 1 $\mu$m. In the liquid state we observe rich film dynamics: uniform wetting that saturates near 20 nm, drainage of thicker films, and spontaneous thickness oscillations, reflecting the extreme sensitivity of thick films in this regime. A galvanic connection to our sensing volume enables in-situ electrostatic tuning of the liquid film thickness. Statistics of freezing the neon across various liquid levels reveal variations of the solid film thickness by approximately an order of magnitude. We also observe a two-fold increase in the quality factor of the resonators at the level of $10^3$ with added neon and rule out dielectric loss as the limiting factor. Our results demonstrate that hermetic packaging facilitates the investigation of both rich non-equilibrium fluid dynamics and the impact of condensed noble gas films on microwave loss in superconducting circuits, but may not be the best modality for growing solid neon films with precisely controlled thickness.

Low-order Carleman embeddings replace nonlinear dynamics by a larger linear system, but truncation errors can accumulate even when the underlying nonlinear model is accurately approximated by a quadratic equation. We construct a residual Carleman lift (RC2) of lattice Boltzmann dynamics in which an independently evolved spectral background supplies the coefficients and forcing of a second-order residual lift. In a double-shear-layer test, conventional fixed-rest Carleman reaches $87.3\%$ final error, whereas prepared RC2 achieves $0.136\%$ through vortex roll-up, without restarting the lift or using fine-reference feedback. The results demonstrate control of the finite-time accuracy of a fixed-order linear embedding through nonlinear preparation.

We propose using a directional time-varying (rotating) driving magnetic field to suppress magneto-Rayleigh-Taylor (MRT) instability in dynamic Z-pinches. A rotational drive magnetic field is equivalent to two magnetic-field components, {\Theta} and Z, that alternate in time, referred to as an alternate Theta-Z-pinch configuration. We consider the finitely thick cylindrical liner configuration in this paper. We numerically integrate the perturbation equation to stagnation time based on the optimal background unperturbed trajectories. We assess the cumulative growth of the dominant mode selected by some mechanism at the beginning of an implosion. The maximum e-folding number at stagnation of the dominant mode of an optimized alternate Theta-Z-pinch is significantly lower than that of the standard Theta- or Z-pinch. The directional rotation of the magnetic field contributes to suppress the instabilities, independent of the finite thickness. The finite thickness effect plays a role only when the orientation of the magnetic field varies in time whereas it does not appear in the standard Theta- or Z-pinch. The rotating frequency of the magnetic field and the thickness of liner are both having a monotonic effect on suppression. Their synergistic effect can enhance the suppression on MRT instability. Because the MRT instability can be well suppressed in this way, the alternate Theta-Z-pinch configuration has potential applications in liner inertial fusion. This work is supported by the NSFC (Grant Nos. 11405167, 51407171, 11571293, 11605188, and 11605189) and the Foundation of the China Academy of Engineering Physics (No. 2015B0201023).

The Labyrinthic map is a two-dimensional area-preserving map that features a robust transport barrier known as the shearless curve. In this study, we explore a dissipative version of this map,examining how dissipation affects the shearless curve and leads to the emergence of quasi-periodic or chaotic attractors, referred to as shearless attractors. We present a route to chaos of the shearless attractor known as the Curry-Yorke route. To investigate the multi-stability of the system, we employ basin entropy and boundary basin entropy analyses to characterize diverse scenarios. Additionally, we numerically investigate the dynamic periodic structures known as "shrimps" and "Arnold tongues" by varying the parameters of the system.

We consider a class of noisy dynamical systems on the two-dimensional torus whose phase evolution is governed by Mobius transformations. In the deterministic limit, these systems favor phase-locking that is described by the band-gap structure of an associated Schrodinger equation with a periodic potential. We use the Wentzel-Kramers-Brillouin method to characterize this structure in the slow-fast limit. Then we show that large-deviation theory describes fluctuations of the finite-time rotation number, whereas weak-noise escape actions determine the exponential scale of rare phase slips. These estimates provide quantitative criteria for metastable phase-locking and melting of Arnold tongues over a prescribed observation time. We derive sufficient conditions for stochastic trajectories to follow prescribed canard segments. With controlled entrance errors, exponential amplification of fluctuations along repelling branches leads to an exponentially small sufficient noise scale for canard persistence in the slow-forcing limit.

A herd of animals often follows a leader who sets the direction of travel. The leader sometimes turns unexpectedly and the followers reshuffle. Yet the herd regroups itself and stays coherent. Our work aims to understand the herding behavior mathematically. We construct a minimal discrete-time nonequilibrium dynamical system with one-way coupling, and the minimal structure allows an exact analysis. Take the location of each follower in the frame of the leader. The recorded locations form a distribution. The limit of the distribution is the asymptotic spatial measure, whose geometric representation we study. The dynamics of the herd have an exact operator representation with two factors, the operator of a fixed leader-follower pair and the operator of the interaction rules, which reshuffle the pairs. We show that the influence of the leader passes through some follower more than once. As a result, two followers can have reciprocal influence, despite the one-way coupling.

We construct vector (two-component) asymptotic Akhmediev breathers in the Manakov system, matching generalized modulational-instability (gMI) eigenmodes to decaying tails of the breather states. The branch-resolved matching provides analytical results linking the gMI-perturbation envelopes to the positions of the emerging breathers. Numerical simulations of the system with the focusing and defocusing nonlinearities corroborate the analytical predictions for each MI branch. We further develop the asymptotic theory for two-breather solutions generated by two independent gMI modes, linking their temporal separation to the input envelopes and interaction-induced shifts. Further numerical simulations reveal that breather patterns exhibit robustness in the presence of weak nonintegrable perturbations. These findings establish a framework relating experimentally controllable input modulations to the branch-selective formation and positioning of breathers in multicomponent nonlinear systems.

We investigate three-dimensional spatiotemporal optical vortex solitons (light bullets with a toroidal shape) carrying higher-order orbital angular momentum in Kerr media with anomalous group-velocity dispersion and a transversely localized Gaussian profile of the linear refractive index. Stationary vortex bullets with topological charges (winding numbers) $1\leq \ell \leq 4$ are obtained as numerical solutions of the three-dimensional nonlinear Schrödinger equation, and their existence, structure and stability are systematically analyzed. In terms of atomic Bose-Einstein condensates, these solutions represent matter-wave solitons with embedded vorticity. We examine the dependence of the solution families on the propagation constant, the depth and width of the guiding profile, and $\ell $. It is found that the increase of $\ell $ requires one to use a stronger or wider waveguiding potential to sustain localized states satisfying the Vakhitov-Kolokolov (VK) stability criterion. VK-complying and non-complying branches of vortex-soliton families are separated by a degenerate Townes branch. Direct simulations reveal that, although the guiding profile substantially suppresses the collapse and extends the propagation distance of vortex bullets, their robustness is ultimately limited by azimuthal instabilities, whose growth is enhanced for values of $\ell $. These results demonstrate that engineered refractive-index landscapes significantly enlarge the stability domain of spatiotemporal vortex bullets and provide guidelines for supporting optical bullets carrying large orbital angular momenta.

A spherically symmetric standing wave confined within a finite-radius ball, with weak radiative exchange between its core and boundary, provides a model for an intermediate stage in the adiabatic evolution of the $\phi^4$ oscillon. We employ a multiscale variational framework to derive an approximate description of these standing waves and their energy-frequency relation. The resulting dispersion curve is compared with that obtained from numerical solutions of the boundary value problem for the $\phi^4$ equation on a two dimensional (time and radius) domain. The agreement between the numerical and variational results is excellent near the endpoint of the continuous spectrum but deteriorates as $\omega$ is reduced below $0.85 \omega_0$. We attribute this discrepancy to the growth of the radiation wing, which is neglected in the variational ansatz.

In the framework of vibrational analysis of 2D periodic waveguides, Floquet-Bloch theorem is widely applied for the determination of wave dispersion characteristics. In this context, the Wave Finite Element Method (WFEM) combines Periodic Structure Theory (PST) with standard FE packages, enabling wave dispersion analysis of waveguides involving structurally realistic unit-cells. For such applications, the computational efficiency of the WFEM, depends on the choice of the formulation and can lead to numerical issues, worsened by extensive computational cost. This paper presents a coupled wave-mode approach for the determination of wave dispersion characteristics in structurally advanced periodic structures. It combines two scales of model order reduction. At the unit-cell's scale, Component Mode Synthesis (CMS) provides the displacement field associated with local resonances of the periodic structure, while the free wave propagation is considered using a spectral problem projection on a reduced set of shape functions associated with propagating waves, thus providing considerable reduction of the computational cost. An application is provided for a bi-directionally stiffened panel and the influence of reduction parameters is discussed, as well as the robustness of the numerical results.

This paper presents an improved numerical strategy for the broadband analysis of wave propagation in composite or complex cross-sectional waveguides using the wave finite element method (WFE). Numerical analysis of such structures require highly discretized finite element models and leads to extensive computations. The proposed formulation relies on a projection of the cross-sectional transfer matrices on a reduced set of shape functions associated to propagating waves. Dispersion curves are then predicted only using a reduced number of eigenvectors. The performances and stability of this method are evaluated using the wavenumbers and wave shapes. Validations are provided for a sandwich composite beam and a cylindrical elasto-acoustic waveguide.

This paper investigates the use of a wave-based method in the framework of structural optimisation of composite panels involving advanced components. The wave/finite element method (WFEM) is used to evaluate the influence of a core's geometry on the transition frequency of a sandwich panel involving composite skins. This transition occurs is a sandwich panel when the transverse shear stiffness has a significant influence on the flexural motion, compared to the bending stiffness. It follows that the modal density and the acoustic radiation will considerably increase above this frequency. The periodic waveguide is modelled at the mesoscopic scale using a 3D finite element model of the unit-cell. Therefore this method does not require an homogenisation of the core based on Gibson and Ashby formulations to provide the wave dispersion characteristics. Although the cellular cores compared in this study share the same mass-to-stiffness ratio, a significant alteration of the transition frequency and modal density can be observed compared to honeycomb cores. A periodic octagonal core is designed, providing up to 70 % increase of the transition frequency and a significant reduction of the modal density.

In the "chair challenge" a person stands several foot lengths from a wall, bends forward until the head touches the wall, lifts a chair and tries to stand up. Online videos suggest that women can do this and men cannot, supposedly because women have a lower centre of mass or men have larger feet. We model the body as a planar chain of rigid segments with standard biomechanical parameters and search all postures allowed by the rules for the one that places the combined centre of mass of body and chair furthest back. As a rule of thumb, the largest toe-wall distance is roughly the trunk-plus-head length minus the distance from hip to centre of mass. For a slow, static rise this limit is 2.36 foot lengths for the male and 2.49 foot lengths for the female reference model, just short of the customary 2.5 foot lengths. The limit is set mainly by trunk-plus-head length relative to foot length, not by the height of the centre of mass; in centimetres the male model actually has more room. With the body proportions of 6068 participants in the 2012 US Army anthropometric survey, the sex difference shrinks from 0.13 to 0.03-0.05 foot lengths, half to one European shoe size. Individually, only 13% of men and 22% of women would pass statically, and predicting sex from the outcome is right in 54-68% of cases (for equal numbers of men and women), against 50% for a coin and 83% for a tape measure. Shoes, age and momentum matter more than the residual sex difference. The problem suits first-year undergraduate mechanics, combining static equilibrium of an articulated body, scaling and units, an inverted-pendulum estimate and a simple classification problem. The chair challenge is a fine demonstration of static equilibrium and a lousy sex predictor.

Consider several cavity resonators whose resonant frequencies and electromagnetic fields are known, and suppose that they are coupled through apertures. How can the resonant frequencies and resonant electromagnetic fields of the resulting coupled-cavity resonator be expressed in terms of the original resonant frequencies and electromagnetic fields? This is a problem frequently encountered in radio-frequency systems for accelerators. One example is a multicell cavity used in high-energy electron accelerators. In this note, the resonant frequencies and resonant electromagnetic fields of such coupled cavities are examined as generally as possible, based only on Maxwell's equations and boundary conditions. Specifically, the response function of a cavity as viewed from its coupling ports, namely, its admittance matrix, is derived, and a formulation is developed to express the coupled resonant electromagnetic fields using this matrix. The resulting formulation shows that the coupled resonant modes can be described in terms of overlap integrals between the resonant modes of the cavities and the waveguide modes at the coupling apertures. It also shows that the coupled resonant frequencies are given by the zeros of the determinant of a matrix constructed from the admittance matrices. The results thus obtained are applied to simple systems to confirm the validity of the formulation. Numerical calculations based on this formulation are also carried out for periodic systems in an attempt to derive dispersion relations.

We obtain an exact closed-form total photon count for a prescribed Newtonian Kepler parabola, with a fully relativistic treatment of its radiation. We also obtain closed expressions for the angularly resolved photon spectrum and elementary expressions for the total radiated energy and momenta. The count is finite, scale-independent, and analytic in subluminal speed at closest approach. At large maximum rapidity $\eta$, $N\sim(7\alpha/\sqrt6)\eta$, while $E\propto e^{3\eta}$ at fixed passage timescale: the radiation chiefly hardens. For slow motion at fixed coupling and closest distance, a nearby ellipse emits fewer photons but more energy and angular momentum per orbit. The hyperbolic photon count remains IR divergent arbitrarily close to threshold, while the count at the exact parabolic threshold is finite.

The steady-state temperature predicted for an ideal point heat source diverges in conventional heat-conduction theory, but no physical thermometer measures a point value. We derive a sharp, shape-independent upper bound on the quasi-steady temperature rise of a sensor with thermometric volume $V_\mathrm{s}$, placed anywhere inside a region enclosed by an isothermal reference surface. The bound requires only the total heat power generated in the region $\dot{Q}$, a lower bound on its thermal conductivity $\kappa_\mathrm{m}$, and the value of $V_\mathrm{s}$. It is otherwise independent of the heat-source distribution, domain shape, and source--sensor distance. For $\dot{Q}=50~\mathrm{pW}$, $\kappa_\mathrm{m} = 0.1~\mathrm{W\,m^{-1}K^{-1}}$, and $V_\mathrm{s}=10^{-22}\mathrm{\,m^3}$, approximately the volume of a $60~\mathrm{nm}$-diameter sphere, the theorem permits a maximum temperature rise of approximately $2~\mathrm{mK}$ above the reference level. The result applies directly to nanodiamonds, upconversion nanoparticles, fluorescent polymer particles, and core-shell quantum dots. It shows that neither source localization nor uncertain source-sensor separation can account for kelvin-scale readings under steady-state heat conduction.

Stern-sculling is a traditional form of human-powered boat propulsion in which a single oar is oscillated laterally at the stern. In this study, we investigate this propulsion technique from a hydrodynamic perspective by continuously measuring the oar kinematics, the boat motion, and the forces acting on the oar across a broad range of boat speeds. During the lateral strokes, lift serves as the main propulsive force, whereas during the backward strokes, propulsion is primarily associated with added-mass effects. These measurements allow us to determine the propulsive efficiency as a function of boat speed. The efficiency peaks at approximately 65\% at an intermediate speed and then decreases progressively to approximately 25\% at higher speeds. These results provide insight into the hydrodynamic mechanisms governing this traditional mode of propulsion and highlight the effectiveness of stern-sculling at moderate speeds.

The impact of droplets, such as rain and sea sprays, on wind turbine blade surfaces can cause severe damage through leading-edge erosion (LEE). Current industrial practice has largely relied on empirical fatigue models to predict damage progression and guide maintenance. However, an important limitation of existing models is the assumption on ideal impact conditions, including perfectly spherical droplet and normal incidence, which rarely occur in reality. This study develops a fluid-structure interaction (FSI) model that couples incompressible multiphase flow simulations with finite element (FE) analysis of blade materials. Using this framework, we investigate the impact dynamics of droplets with arbitrary shapes and orientations. The results reveal a positive correlation between the peak impact pressure, the influential area at the pressure peak, and the peak impact force. In contrast, the time of peak force scales inversely due to momentum conservation. From these findings, we propose a $\textit{universal scaling law}$ that relates all key impact loadings to the simple parameter of the droplet $\textit{projection area}$, which can be determined solely from the initial droplet geometry and orientation. This law provides a predictive framework for impact loading dynamics of non-ideal shapes, offering new insights into the mechanisms of LEE and improving the accuracy of erosion predictions for wind turbine blades.

Collective synchronization is a common response of interacting magnetic particles subjected to rotating external fields. Here we demonstrate a distinct nonequilibrium state in a two-dimensional cluster of magnetic colloidal particles in which the ordered crystalline core rotates, on average, opposite to the direction of the applied rotating magnetic field, while the defect-rich outer region continues to rotate with the drive. We term this state anti-synchronized collective rotation. By combining structural, spectral, bond-resolved, and layer-resolved torque analyses, we show that anti-synchronization is associated with a broader defect-rich interface, enhanced and dynamically heterogeneous bond deformation, and a reorganization of torque transmission between the surface and the crystalline interior. In the synchronized state, steric torques compensate the opposing dipolar contribution in the outer core, maintaining a positive net interaction torque. In the anti-synchronized state this compensation becomes insufficient, producing a negative net torque in theouter core and enabling core-surface rotational decoupling. Increasing the driving frequency restores coherent rotation through a transition characterized by competing positive- and negative-angular-velocity populations and hysteresis, consistent with a discontinuous, first-order-like dynamical transition. These results demonstrate how deformation and spatial redistribution of interaction torques can generate counter-rotating collective states in driven colloidal matter.

Dense active--passive mixtures are often described within an effective-temperature picture, in which active dopants promote cage breaking and fluidize an arrested amorphous host. However, at sufficiently large persistence, the same dopants drive stress accumulation and localized void formation. Here we investigate the avalanche dynamics across this progression, focusing on the intermediate regime between dynamic arrest and void formation, where the system remains structurally homogeneous on average but relaxes through intermittent collective rearrangements rather than as a simple activated liquid. Using overdamped simulations of dilute active dopants embedded in a dense amorphous solid, we show that the avalanche dynamics separates into distinct spatial and temporal controls. For a given system size, the active fraction sets the size of the largest stress-release events, with a cutoff that grows as the square root of the fraction of dopants, $S_c\sim \phi_a^{1/2}$, i.e., with the number of mean dopant spacings across the system, whereas persistence controls how avalanches unfold in time at fixed released stress. A decomposition of the stress into active and passive contributions, together with measurements of avalanche participation and morphology, shows that the active minority provides a localized and persistent driving channel while the surrounding amorphous packing carries the collective stress release. While the active minority controls the cutoff of the avalanche size statistics and the timing of the stress releases, the long-range elastic response and the building correlations in the passive host sets the size exponent, $\tau_S\simeq1.1$, that is shared with externally sheared and uniformly active amorphous solids.

We develop a theory for the plastic shear rate $\dot{\gamma}_i$ on each slip system $i$ of face-centered cubic (FCC) single crystals, by integrating the shear rate contributions $\dot{\gamma}_i(l)$ from dislocation links of length $l$. A generalized Orowan equation expresses $\dot{\gamma}_i(l)$ in terms of the link density $n_i(l)$ and the average link velocity $v_i(l)$. This model accurately reproduces the discrete dislocation dynamics (DDD) shear-rate data for all 12 slip systems across 99 loading orientations. In particular, it explains why the plastic shear rate depends exponentially on the resolved shear stress $\tau_i$, as reported previously, in the absence of any thermally activated mechanism. This dependence arises from the exponential tail of $n_i(l)$ filtered through the threshold-like velocity function $v_i(l)$. Furthermore, $v_i(l)$ is well approximated by a single two-dimensional function $v(\tau_i,l)$ for all these slip systems. The link velocity is therefore governed mainly by $\tau_i$ and $l$, with only a minor effect from the complex interactions between slip systems. These interactions instead manifest themselves mainly through $n_i(l)$. As a demonstration of the effect of the link-length distribution on the slip rate, we show that even when $\tau_i$ is limited to a narrow window, the shear rates still span two orders of magnitude. The supply of long links is therefore the dominant factor controlling slip-system activity, outweighing the direct effect of $\tau_i$ on the link velocity.

We investigate phase separation in a binary fluid subjected to a moving Gaussian cooling source and externally imposed material flow. Unlike conventional homogeneous quenches, the moving thermal field initiates phase separation at different times across the system, creating a spatially varying thermal history and local age. The interplay of a moving cooling source, phase separation and external flow field introduces directional bias, resulting in anisotropic pattern formation. Using an advective Cahn-Hilliard-Cook model coupled to a spatially and temporally varying temperature field, we examine how front propagation, thermal diffusion, phase separation, and material transport jointly select the evolving morphology. In the absence of flow, increasing the cooling-source velocity drives a transition from nearly symmetric structures to asymmetric spiral-like patterns and, at higher velocities, to narrow elongated domains as the thermal front increasingly lags behind the source. Advection reorganizes the phase-separated domains by transporting, stretching, and reorienting them. At low flow velocities, competing thermal and advective histories produce distinct regions of flow-aligned and vertical layers. A stronger flow aligns the domains predominantly along the flow direction. Our results demonstrate that a moving thermal history can encode a spatial record of non-equilibrium phase separation. This work provides a route to controlled morphology selection through the competition between front propagation, thermal diffusion, and material flow.

Conventional centrifugal sedimentation cannot readily separate particles with the same sedimentation velocities. Density gradient centrifugation, although highly selective, exposes delicate particles such as drug delivery system (DDS) nanoparticles and exosomes to high osmotic pressure that can cause shrinkage, rupture, or expansion. To separate particles with equal or similar sedimentation velocities while preserving their properties, we propose two methods that exploit thermal fluctuations (Brownian motion): the centrifugal Brownian ratchet method, which uses asymmetric structures, and the centrifugal wavy-channel method, which uses geometric barriers. Two-dimensional Brownian dynamics simulations combining Stokes-Einstein diffusion with centrifugal sedimentation were performed, and particle transport was analyzed using the Péclet number. In the ratchet method, particles with identical sedimentation velocities but different Péclet numbers showed statistically distinct mean arrival positions and times. In the wavy-channel method, periodic entropic barriers interacting with differences in transport properties produced arrival-time differences, achieving temporal separation even for particles with identical sedimentation velocities or Péclet numbers. Both methods separate particles without relying on sedimentation-velocity differences and are expected to preserve particle properties. Because they neither depend on electrical properties nor require a change of medium, they may also be applicable to particles in liquid metals, oils, organic solvents, and ionic liquids.

With growing interest in environmental conservation, polymer composites incorporating wood-derived materials have attracted significant attention. While research has focused extensively on hard composites utilizing delignified wood or cellulose nanofibers (CNF) and soft composites reinforced with CNF, there have been a limited number of studies on the development of soft composites that utilize the porous cellular structure of wood, with few exceptions. In this study, we fabricated soft composites by infiltrating delignified wood with polyacrylamide hydrogel and subjected them to uniaxial compression tests. The results demonstrated that these materials exhibited far superior strength and toughness compared to either delignified wood or polyacrylamide hydrogel alone. Through systematic investigation and theoretical analysis, we identified the mechanisms underlying these enhancements in strength and toughness. Specifically, in addition to the sacrificial bond breakage known to enhance toughness in double-network hydrogels, we propose that mechanical confinement, arising from the soft, incompressible hydrogel filling the hollow cell lumens, generates excess stress and acts to resist compressive deformation. This approach, which utilizes the cellular structure as a filler, suggests the potential for creating a new class of high-toughness composite materials.

Entropic repulsion between polymer chains under confinement in a narrow channel tends to induce segregation. Recent computer simulation studies have provided indirect evidence that internal cross linking of ring polymers, which creates internal loops, enhances the entropic force. Such topologically enhanced entropic forces are thought to contribute to the segregation of bacterial chromosomes during replication. In this study, we use Monte Carlo computer simulations of a coarse-grained hard-sphere chain model to measure the configurational free energy of two cross-linked ring polymers as a function of the separation distance between the polymer centers of mass. We examine the effects of varying the polymer architecture as well as the confinement dimensions on the free energy functions. In addition, we use the results to make a quantitative assessment of the accuracy of a simple theoretical model built on the de Gennes blob model that has been used in past studies to estimate the overlap free energy of confined polymers. Consistent with indirect evidence from previous simulations studies of segregation dynamics, we find that increasing the number of internal loops and selecting binding sites to enforce a side-loop configuration tends to increase the overlap free energy. Analysis of the whole-polymer and interior-loop extension and overlap lengths reveal a sequence of overlap domains that explain subtle variations in the free energy functions. For all architectures examined, the theoretical model provides a reasonably accurate prediction for how the cross linking and degree of confinement affects the free energy, with quantitative discrepancies comparable to those observed in previous studies using linear polymers and ring polymers without cross links.

The 150--235 K ``no man's land'' (NML) of deeply supercooled water is a highly debated regime where rapid crystallization hinders experimental observation of the hypothesized liquid-liquid phase transition. Using TIP4P/2005 molecular dynamics simulations, we uncover a structurally and dynamically heterogeneous state at ambient pressure that exhibits novel physical features. Our results demonstrate that this low-density state ($\rho \approx 0.925$ g/cm$^3$) is a unique supercooled liquid, distinct from both glassy and spinodal states. Specifically, it emerges as a stable, structurally arrested phase driven by a self-generated ``soft skeleton'' of nanoclusters. This network forms an intrinsic nanoporous structure that imposes nanoconfinement on the remaining fluid, proving that NML confinement can be an entirely self-driven phenomenon. Finally, we resolve the temperature-dependent, nonlinear behavior of density and compressibility, highlighting a structurally driven anomaly that clarifies the thermodynamics of deep supercooling. Collectively, this work provides a transformative structural framework for understanding the anomalous nature of water within the NML.

Despite a vigorous effort, a comprehensive and satisfactory understanding of the dynamics underlying the glass transition in finite-dimensional systems has not yet emerged. One key hallmark of supercooled liquids approaching the glass transition is the breakdown of the classical Stokes-Einstein (SE) relation, manifested as the decoupling between the self-diffusion coefficient and structural relaxation time, commonly described by a fractional SE relation. Whether and how the fractional SE exponents vary remains an ongoing debate, even for the simplest supercooled liquids. In this work, we numerically establish a universal relation between the self-diffusion coefficient and structural relaxation time by introducing characteristic scales that are revealed under the condition of constant dynamical heterogeneity. Moreover, this universal relation could also capture literature data for supercooled water and silica. Remarkably, we find that the fractional SE exponent is invariant across various supercooled liquids studied spanning a wide range of fragility, thereby challenging the prevailing view that the fractional SE exponent is correlated with fragility. Our study demonstrates that investigating dynamical heterogeneity yields more valuable insights into understanding glassy dynamics than expected.

We analyze the stability and non-linear dynamics of extended domain walls (DWs) with Dzyaloshinskii-Moriya interaction (DMI) driven by an external magnetic field in the clean limit (i.e., in the absence of disorder and thermal fluctuations). We show that for moderate DMI strengths, the dynamics in both the low- and high-field regimes are accurately described by a rigid-wall Walker model that neglects flexural degrees of freedom. At intermediate fields, however, the system undergoes a transition into a non-trivial spatio-temporally chaotic regime characterized by dynamically roughened domain walls displaying single- or multi-valued profiles. The phase boundaries delimiting this regime in the magnetic field-DMI phase space are computed using a linear stability analysis based on Floquet theory applied to the extended domain wall, explicitly accounting for DMI and internal phase dynamics. Our theoretical analysis and predicted phase diagram are fully supported by numerical micromagnetic simulations solving the full Landau-Lifshitz-Gilbert equation.

We present GINNGER (GENERIC-Informed Neural Network for GEnerative Rheology), a framework for discovering thermodynamically admissible constitutive equations from microstructural flow data. Unlike existing approaches that learn constitutive operators, GINNGER reformulates constitutive discovery as the learning of the underlying thermodynamic generators from which constitutive equations emerge. Embedding the GENERIC formalism into the learning process restricts the search to constitutive models that satisfy the first and second laws of thermodynamics by construction, eliminating the need to prescribe phenomenological constitutive equations a priori. A second conceptual advance is a spectral formulation of constitutive discovery in the intrinsic eigenspace of the polymer conformation tensor. This provides a kinematics-independent thermodynamic state space in which the thermodynamic generators depend only on the instantaneous microstructural state, while flow kinematics acts solely as an external driver transporting the system through this space. Consequently, data from shear, extensional, and mixed flows contribute to the discovery of a single constitutive model that generalizes across deformation protocols and flow geometries. By learning thermodynamic generators rather than high-dimensional constitutive operators, GINNGER substantially reduces the complexity of the discovery problem while preserving thermodynamic consistency, material objectivity, and physical interpretability by construction. The framework is validated using high-fidelity simulations, accurately reconstructing constitutive behavior and predicting complex flow fields across previously unseen geometries. GINNGER establishes a new paradigm for constitutive discovery by combining generative, spectral, and thermodynamically grounded learning within a unified framework for data-driven modeling of complex fluids.

Red blood cells carrying intracellular vacuoles, called pocked cells, are a sensitive marker of splenic function: about 0.5% of cells in healthy people, 20 to 70% after splenectomy. Vacuoles too small to see are common, and visible ones are thought to grow when small ones merge. We tested that idea with a particle model that resolves the cell's membrane, its contents and every vacuole, and with an inventory of the vacuole volume a cell can make. In tube, shear and vascular flows, a cell's vacuoles met within a second, and, allowed to fuse, ten merged into one to five. Meeting is not what limits growth; material is. At the rate measured after splenectomy, all the vacuoles an average cell makes in its 120-day life fuse into one body 0.6 $\mu$m across, the size healthy cells carry, but 16 times smaller in volume than the 1.5-$\mu$m bodies of patients without a spleen. Taking vacuole size as set at formation, a population model in which vacuoles are made mainly in young cells, and far faster in a small minority that alone makes material for a large one, accounts for the published counts, sizes and age profiles and, on first-hand measurements, favours a splenic clearance that rises several-fold as cells age; letting that minority's vacuoles fuse fits nearly as well. At a model splenic slit, the cell's spare surface decided passage, and a vacuole mattered only when it led. A slit experiment would test whether brief encounters fuse vacuoles.

The influence of spanwise convex curvature on hypersonic boundary-layer transition over a streamwise-concave surface is investigated using direct numerical simulation and Mach 7 experiments. Smooth doubly curved geometries with fixed streamwise concavity and increasing spanwise convex curvature isolate the effects of three-dimensional wall curvature on a centrifugally unstable boundary layer. Increasing spanwise curvature delays transition while preserving a Gortler-dominated route to breakdown. As spanwise curvature increases, the boundary layer thins, reducing the effective Görtler number and weakening centrifugal amplification of streamwise vortices. Consequently, growth of the primary Görtler instability is reduced, vortical structures remain closer to the wall, and secondary instability and turbulent breakdown shift downstream. Spectral proper orthogonal decomposition confirms that low-frequency vortical dynamics remain dominant in controlling transition, with sinuous secondary instability of Görtler vortices providing the principal route to breakdown. Meanwhile, boundary-layer thinning modifies acoustic instability dynamics: the second Mack mode shifts to higher frequencies and higher-frequency supersonic disturbances become increasingly prominent near breakdown as spanwise curvature increases. These acoustic disturbances remain subdominant and do not replace the Görtler-sinuous mechanism as the primary transition pathway. Numerical and experimental results exhibit consistent trends in transition location, thermal-streak organisation and disturbance evolution, supporting a common physical interpretation. These findings demonstrate that spanwise convex curvature stabilises hypersonic Görtler-dominated boundary layers, primarily by suppressing centrifugal amplification and delaying secondary instability, while leaving the transition pathway qualitatively unchanged.

Large-scale offshore wind development will intensify wake interactions between wind farm clusters in the North Sea, increasing uncertainty in regional energy estimates. We assess HARMONIE-AROME mesoscale simulations, ASPIRE large-eddy simulations (LES), and three engineering wake models based on Jensen, Bastankhah Gaussian, and TurbOPark formulations for a 100.7 GW 2050 offshore wind scenario. We find that LES and mesoscale simulations accurately represent observed local free-stream wind conditions. Moreover, all engineering wake models predict higher mean wind speeds than LES in every month, with biases reaching 0.60-0.70 m/s at 10-40 km downstream. These differences also vary systematically with atmospheric regime: the Bastankhah Gaussian model remains positively biased across wind speed and stability conditions, whereas Jensen and TurbOPark shift from underprediction in unstable and near-neutral conditions to overprediction in stable conditions at 8-12 m/s. These results show that agreement in annual capacity factor can conceal substantial differences across space, time, and atmospheric regime, highlighting the importance of including sensitivity to model formulation in regional wind energy assessments.

Isogai's case A, a pitch-plunge aerofoil whose elastic axis lies half a chord ahead of the leading edge, has a folded transonic flutter boundary in inviscid flow: near the bottom of the transonic dip several flutter speeds coexist at one Mach number. We map this boundary, and the family obtained by moving the elastic axis, with coupled unsteady Euler simulations, a Gaussian-process surrogate of the damping coefficient trained by batch active learning, and split conformal prediction on independent random simulations, which turns the surrogate into stability calls with a distribution-free error rate. Three failure modes of time-domain damping labels that leave no trace in the residuals are documented, and the half-degree mean incidence left by the common one-degree start is shown to raise the flutter speed at the dip by 2.8%, more than any numerical setting. With 80 simulations the learned case A boundary labels 64 of 65 independent runs correctly, and calibrated calls are wrong in at most 1.6% of cases. Over Mach number, elastic axis and flutter speed index, 193 simulations and 40 calibration runs show that the fold exists only for elastic axes more than about 0.4 chord ahead of the leading edge; it closes between 0.39 and 0.33 chord ahead, on two meshes. Chordwise energy budgets, closed against the solver loads and the growth rate within a few per cent, explain the boundary. The lower branch is crossed through the reduced frequency at unchanged shock phase. On the upper branch the shock is pinned at the trailing edge, and moving the elastic axis aft brings the pivot of the flutter mode towards the section, so that the damping of the supersonic surface falls faster than the residual shock input and the fold closes.

Reactive solute transport in shear flows is of broad importance in chemical engineering, liquid--solid chromatography, and environmental mechanics, particularly in flow reactors and fluidic devices involving interphase mass transfer. Based on the recently developed streamwise dispersion theory for inert solutions (Guan & Chen, 2024, J. Fluid Mech., vol. 980, A33), we present an analytical model for reactive dispersion of chemically active solutes characterized by first-order, irreversible surface reactions. The extension is not a simple perturbation because the reactive boundary destroys mass conservation with streamwise and radial derivatives coupled. The model establishes how the microscopic kinetic reactivity and radial eigenmodes combine to determine a newly defined (effective) local exchange rate. We derive rigorous explicit solutions for the local moments, concentration, and phenomenological transport coefficients at arbitrary reactivity, in quantitative agreement with numerical simulations across all regimes. For tube Poiseuille flows, we reveal pre-asymptotic behaviours including sign-changing radial exchange, reactivity-enhanced drift, reactivity-reduced dispersivity, and non-Gaussian concentration profiles. Small- and large-Damköhler-number asymptotics for the local and global transport coefficients identify the reaction-limited and diffusion-limited regimes, connecting the conservative case to the Dirichlet limit at infinite reactivity. This streamwise perspective could advance our understanding of macroscale transport in chemically active systems.

This paper investigates the dependence of azimuthal mode growth rate of oscillating liquid laminar jets on the Weber number. The oscillating liquid laminar jets were simulated over a range of Weber numbers. The simulation setup was validated by comparing the instantaneous interface shapes and the visible azimuthal mode from experimental measurements. As the Weber number increases, the spreading angle rises due to the small surface tension, and higher azimuthal modes are observed. Fourier Transform analysis is used to find the exact azimuthal mode of the simulation results. The dominant azimuthal mode increases as the Weber number increases. A power-law dependence of the growth rate on the Weber number is identified, with the obtained exponents showing good agreement with linear instability analysis. Furthermore, the rescaled Fast Fourier Transform (FFT) results collapse onto a single growth curve for each azimuthal mode, validating the proposed power-law for predicting the growth rates of oscillating liquid jets.

Reconstructing flow fields from sparse and noisy measurements becomes particularly challenging when data are completely absent from dynamically critical regions, such as the vortex-formation region of a wake. Conventional interpolation and numerical reconstruction methods generally require sufficient spatial or boundary information, while physics-informed neural networks (PINNs) can also face difficulties when sparse and noisy observations provide little or no supervision in the region of interest. To address this gap, we propose a Fourier-feature-embedded complex-valued physics-informed convolutional residual network (FCV-PICRN) for sparse, gappy, and noisy flow-field reconstruction. The framework integrates Fourier features for oscillatory and multiscale structures, complex-valued representations for coupled amplitude--phase learning, and convolutional residual blocks constrained by the Navier--Stokes equations. The method is first verified using the Taylor--Green vortex at $Re=100$ and then evaluated for the cylinder wake at $Re=100$. Three severe missing-data configurations are imposed in the dynamically sensitive wake: a large hole, a large truncation, and a plus-shaped gap extending in both streamwise and transverse directions. These gaps are further combined with additive Gaussian and multiplicative speckle noise. Despite having no supervised velocity data inside the excluded regions, FCV-PICRN reconstructs velocity, pressure, and vorticity with high structural similarity index (SSIM) and peak signal-to-noise ratio (PSNR), and remains robust under Gaussian noise up to $20\%$. Finally, for forced two-dimensional Kolmogorov turbulence with $5\%$ Gaussian noise, FCV-PICRN yields lower reconstruction errors than a conventional PINN. These results demonstrate robust physics-informed reconstruction of severely incomplete and noisy flows across laminar and turbulent regimes.

Nonlinear interactions in incompressible magnetohydrodynamic (MHD) and Navier-Stokes turbulence involve three spatial fluctuations conservatively exchanging, e.g., energy. The mathematical structure of a triad interaction does not allow to unambigously determine the specific contribution of each of the participating fluctuations to the resulting exchanges. Presently, only additional assumptions allow for the deconstruction of triad interactions into a sum of pair exchanges. This work proves that in incompressible MHD the simultaneous nonlinear transfer of cross-helicity sufficiently constrains the triad dynamics such that a mathematically unique pair-exchange representation of nonlinear energy and cross-helicity transfer is possible.

Finite-time and finite-size Lyapunov exponents (FTLE and FSLE) characterise material stretching and transport barriers over prescribed time intervals and separation scales, but their evaluation from three-dimensional velocity sequences requires large computational costs. We introduce SCP-FTLE and SCP-FSLE, two modules of StreamCenter+ for CPU- and GPU-accelerated Lagrangian analysis. The modules support structured and native unstructured meshes, selectable integration and interpolation schemes, and graphical and command-line workflows. Rolling snapshot reuse, memory-bounded FTLE batching, device-resident trajectory state and active-set FSLE advancement reduce data movement and redundant computation, achieving the state-of-the-art (SOTA) computational performance among peer packages. For a billion-seed benchmark, strong-scaling efficiencies on 32 GPUs reach 86.3% for FTLE and 95.2% for FSLE. FTLE is verified with published steady and unsteady Arnold-Beltrami-Childress (ABC) flows and stationary concentrated vortex model (SCVM), while FSLE is verified in linear stretching and rotational shear flows. As examples, applications reveal the spanwise reorganisation of stretching layers in a shear-thinning lid-driven cavity, and resolve three-dimensional stretching structures associated with contrasting tracer dispersion around an urban building canopy at NUS campus. These results demonstrate a scalable workflow in large-scale Lagrangian diagnostics and analysis of flow data.

In geothermal systems, injected fluid flows along preferential fracture pathways and exchanges heat with matrix blocks. Reduced models often neglect temperature-dependent viscosity and assume unlimited matrix storage, although the thermal capacity accessible to the flow is finite. This work analyzes thermo-viscous feedback in a planar fracture-matrix system where viscosity controls discharge through the integrated hydraulic resistance, while finite capacity enters through an effective single-timescale memory fixed by initial uptake and total capacity. The reduced model gives parsimonious semi-analytical predictions with physically based parameters, verified against the nonlinear solution. A perturbation hierarchy separates matrix storage from the hydraulic response it induces, while an exponential velocity reconstruction preserves the exact terminal discharge and bounds front-moment errors within the front-moment limit model. At fixed pressure difference, heating accelerates and broadens the front, whereas cooling delays and sharpens it. The terminal discharge depends only on the endpoint viscosity ratio, while matrix uptake, storage and contrast determine its approach time. At fixed rate, viscosity alters only the pressure drop, not the thermal response. Finite thickness controls the transition to capacity-limited equilibration, and strong matrix uptake collapses the isoviscous response onto a two-variable similarity surface.

Rarefied nonequilibrium flows are described by the Boltzmann equation, which can be solved using stochastic particle or deterministic methods. With advances in computing, data-assisted physics-informed neural networks have been widely used for flow prediction by combining governing equations with measured or computed data. Data-free PINNs do not require such training data and have been widely studied for continuum flows, but their application to rarefied flows remains limited. This study develops a data-free Fokker-Planck physics-informed neural network (FP-PINN) to describe rarefied nonequilibrium flows. The physics loss is constructed from the ellipsoidal statistical Fokker-Planck (ES-FP) equation using a velocity distribution function (VDF) closure and moment projection. The FP-PINN is evaluated for a steady one-dimensional Mach 10 normal shock. The FP-PINN results agree with the numerical ES-FP results, with errors below $1\%$. Compared with the particle ES-FP results, the FP-PINN predicts a sharper shock structure with errors up to $17\%$. This difference is attributed to the VDF closure and moment projection.

We propose a regularization of stochastic fluid dynamics that preserves all relevant symmetries. By considering an incompressible fluid, we demonstrate explicitly that the regularized theory is UV finite, and therefore admits a continuum limit. Strikingly, the regularized theory of stochastic fluid dynamics is not only amenable to direct numerical simulations of the lattice discretized theory, but also to functional methods in the continuum. We exploit this to perform renormalization group improved perturbative calculations of the renormalization of the shear viscosity of an incompressible fluid in two and three spatial dimensions, and compare our results to direct numerical simulations of the lattice discretized theory.

The physics-informed neural network (PINN) faces significant challenges when solving compressible multi-medium flows, including the inability to locate interface positions, poor approximation of discontinuities, and difficulty in handling high-pressure-ratio problems between media with large stiffness differences. To address these issues, we propose PINN with Learnable and Physically Consistent Domain Decomposition (PINN-LPCDD), a framework that incorporates the sharp interface method (SIM) into PINNs for solving compressible multi-medium flows. Firstly, we design separate sub-networks for each medium with learnable parameters to automatically learn interface positions, so that the domain decomposition is physically consistent, and the contact discontinuity at the interface is naturally sharp. Secondly, the Euler equations with artificial viscosity are solved to enhance robustness when handling problems involving shock waves. Lastly, the scaling invariance of the Euler equations is exploited to facilitate the solution of high pressure ratio problems. Numerical experiments on air-air, air-helium, air-water, and air-R22 problems demonstrate the acceptable accuracy of the proposed method in simulating multi-medium flows.

OpenAI reports a forced Navier-Stokes flow that becomes singular in finite time, raising the question of its physical consequences. Magnetic reconnection offers a test through the splitting and merging of flux structures. We use resistive magnetohydrodynamics to simulate a magnetic ring driven by an imposed, regularized flow that reproduces the geometry and scaling of the collapsing core. At the nominal singular time, we remove the imposed drive and allow the system to evolve freely. Reconnections before and after release split the ring into two or more daughter rings through bifurcations of the poloidal flux function, with Lorentz feedback selecting the bifurcation type. Unequal winding by the swirl above and below the midplane produces asymmetric toroidal magnetic stresses, unfolding the kinematic pitchfork-like transition into a fold. For single-island splits, the cusp normal form predicts the asymmetry of the daughter rings without adjustable parameters. Three-dimensional simulations retain the splits and merger, confirming that approach to hydrodynamic blow-up can trigger magnetic restructuring.

The Direct Simulation Monte Carlo (DSMC) method has long served as a reliable numerical approach for simulating rarefied and non-equilibrium gas flows. Its computational cost, however, increases rapidly as the flow approaches the near-continuum regime. This limitation has motivated the development of kinetic model equations that replace binary collisions with simplified relaxation processes. This paper presents a particle multi-relaxation unified BGK (UBGK) model for monatomic gas mixtures. The model retains pairwise species relaxation and determines the target velocity, temperature, shear stress, and heat flux by matching the corresponding production terms to those of the Boltzmann equation. A stochastic particle algorithm is developed. The model is implemented in SPARTA, and two validation problems are considered: homogeneous relaxation and a Mach 3 flow over a cylinder. In both cases, the UBGK solution reproduces the DSMC reference behavior, including species-dependent relaxation and non-equilibrium shock structure.

Conservation laws reveal invariant structure in dynamical systems and constrain their evolution to lower-dimensional level sets. Locally, however, per the flow-box theorem, every $d$-dimensional system generically admits $d-1$ functionally independent conservation laws near a regular point even though, generically, only a few such laws persist globally. Data-driven methods typically learn conservation laws on a prescribed region of phase space from which training samples are drawn, leaving their behavior beyond that region unresolved. We formulate this local-to-global continuation problem and develop an {expanding-domain neural deflation} framework that tracks the number of independent conservation laws over nested domains. The method recovers the expected $d-1$ local invariants and detects their successive breakdown as the domain expands, relaxing to the expected global conservation law limit. It distinguishes the local invariants (associated with Frobenius integrability) from persistent global structure and shows that the domain scale over which additional laws survive reflects proximity to Liouville integrability. Pointwise losses can localize isolated obstructions, whereas in more complicated dynamics the breakdown of our loss functions is gradual and spatially diffuse. The framework thus provides a data-driven approach for studying the persistence and breakdown of (so-far-learned) conservation laws across phase space.

We open the quantum baker map with a position window of width $w$ and center $q_c$. Classical pruning tiles the $(q_c,w)$ plane into diamonds where the $T$ leading resonances form root-of-unity multiplets. At $w=1/2$ one periodic orbit survives for almost every $q_c$, and the multiplets are quantized without free parameters: their modulus $2^{-1/2}$ saturates the pressure bound and their phase is the orbit action. They form cycling multicomponent cat states, and the opening becomes one mid-circuit measurement, enabling spectroscopy with $\sim10^2$ shots on quantum processors.

When communication consumes shared entanglement, a physical link does not guarantee that an interaction is available. We study synchronization of classical continuous-time systems whose interactions consume randomly replenished resources stored on edges. Under isotropic tangent coupling and state independent scheduling, the linearized evolution separates exactly into intrinsic node growth and an ordered product of communication matrices. This yields temporal contraction conditions and local nonlinear synchronization. Resource conservation bounds the contraction achievable by every schedule with acyclic event services. On a fixed acyclic orientation with a unique source, serving each ready edge immediately is optimal: the non-source node with the least total incoming supply determines the rate. Balanced incoming supplies attain the bound. For linear coupling on these orientations, a further condition guarantees synchronization throughout a convex invariant domain. In the specified Lorenz domain, this sufficient contraction requirement is about three percent above a necessary requirement for uniform exponential synchronization. Kuramoto simulations illustrate the effect of service direction, while Lorenz simulations compare resource policies and test local growth predictions against finite-time dynamics.

This work presents a systematic theoretical investigation of vector breathers and their nonlinear interactions in the coupled Hirota equation. This model describes the simultaneous propagation of ultrashort optical pulses in optical fibers and contains a key parameter that characterizes the strength of higher-order linear and nonlinear effects, such as third-order dispersion and self-steepening. For the model, we focus on the focusing-focusing case. On a nonzero plane-wave background, we derive explicit expressions for multi-breather solutions of the coupled Hirota equation by the dressing method. For the single-breather solution, by choosing special constant vectors, the vector breathers can be classified into three fundamental types: Type I, Type II, and Type III. We then analyze their characteristic parameters, including spatial localization and group velocity, as well as important special cases such as the Kuznetsov-Ma breathers, Peregrine soliton, and Akhmediev type breathers etc. Through the above analysis, we find that the higher-order effect parameter only modifies the propagation velocity and oscillation period of the breathers, while the resonance conditions remain satisfied: when the wave numbers and frequencies match, inelastic resonant interactions can occur between Type I and Type II breathers, manifesting either as a fusion process (I + II \rightarrow II) or the reverse decay process (III \rightarrow I + II). Furthermore, we present the explicit expression for the two breather solutions of the equation and analyze its rich interaction scenarios, including two breather resonances and elastic collisions, and we point out that the special case of resonance corresponds to the limiting case of merging eigenvalues. Finally, we carry out numerical simulations to verify the accuracy of the obtained solutions.

Reliable out-of-distribution generalization remains a central challenge in machine learning, particularly when models are deployed in data-scarce high-fidelity domains. Existing approaches often rely on statistical distribution alignment, or invariance assumptions that can fail when domain shifts reflect changes in underlying mechanisms. Inspired by a longstanding paradigm in physics that understands complex systems by starting from tractable idealizations and progressively incorporating additional mechanisms and levels of fidelity, we propose physics-transfer (PT) learning, a physics-constrained learning theory for zero-shot generalization along a ladder of complexity. PT constructs chains of anchor domains (CADs) that connect low-cost source domains to complex targets and introduces computable feasibility and reliability indicators for assessing transfer before target-domain labels are observed. Under physical-consistency and stable-representation assumptions, we derive an operational upper bound on target risk in terms of source empirical risk, the PT indicators, and finite-sample errors, and establish convergence as adjacent complexity gaps shrink and data coverage improves. We evaluate PT on excited-state energy prediction in quantum systems and dynamical-transition prediction in classical systems using neural networks trained without target-domain labels. Across substantial distribution shifts, PT yields accurate high-fidelity predictions, while the indicators identify incorrect physical mappings before target-domain prediction fails. These results provide a model-agnostic framework for designing, diagnosing, and controlling generalization in data-scarce learning problems.