We investigate the diffusion coefficients and mean-squared displacements in a polydisperse granular gas in a homogeneous cooling state by considering the roughness of the particles. We study their dependence on the normal and tangential restitution coefficients. We show that the motility of particles is strongly affected by their mechanical properties and surface characteristics.

This paper contends that counterion dehydration at the ion-exchange membrane/electrolyte solution interface is an instance of heterogeneous reaction whose kinetics is governed by a rate equation of the Butler-Volmer type. The finite rate of this reaction is hypothesized to constitute an important factor that affects counterion selectivity of the membrane. Simple theoretical examples show that this is what may lead to the relatively easier membrane transfer of the less mobile ions (e.g., ${\mathrm{Li}}^{+}$) compared to the more mobile ones (e.g., ${\mathrm{Na}}^{+}$).

Competition during range expansions is of great interest from both practical and theoretical viewpoints. Experimentally, range expansions are often studied in homogeneous Petri dishes, which lack spatial anisotropy that might be present in realistic populations. Here, we analyze a model of anisotropic growth, based on coupled Kardar-Parisi-Zhang and Fisher-Kolmogorov-Petrovsky-Piskunov equations that describe surface growth and lateral competition. The anisotropy is encoded in how strongly genetic boundaries between strains are moved as a result of the expansion front morphology. We completely characterize spatial patterns and invasion velocities in this generalized model. In particular, we find that strong anisotropy results in a distinct morphology of spatial invasion with a kink in the displaced strain ahead of the boundary between the strains. This morphology of the outcompeted strain is similar to a shock wave and serves as a signature of anisotropic growth. We confirm these predictions with a commonly employed reaction-diffusion model of anisotropic growth.

The Family-Vicsek scaling of island-size distributions is a well-known phenomenon in epitaxial growth of surface islands. Analytic scaling functions obtained from rate equations for surface growth at small critical size rarely fit the results of kinetic Monte Carlo (KMC) simulations, mainly due to uncertainty in the scaled capture number $C\left(x\right)$ in the Bartelt-Evans theory. We have recently presented a refinement of the theory that yields double-exponential scaling function. This function fits well the KMC results for compact islands, but fails to reproduce the data for point islands. Here we further develop this approach by showing that analytic Family-Vicsek scaling requires a certain form of $C\left(x\right)$ that eliminates discontinuities at large sizes. We present a family of empirical power-law, exponential, and double-exponential functions that describe a transition from the plateau-like behavior of $C\left(x\right)$ at small $x$ to linear increase at large $x$ and yield analytic scaling with the required normalizations. The scaling function obtained with double-exponential transition function fits well the KMC data on both scaled capture numbers and island-size distributions.

We study the fate of a forager who searches for food performing a random walk on lattices. The forager consumes the available food on the site it visits and leaves it depleted but can survive up to $S$ steps without food. We introduce the concept of intermittent rest in the dynamics which allows the forager to rest with probability $p$ upon consumption of food. The parameter $p$ significantly affects the lifetime of the forager, showing that the intermittent rest can be beneficial for the forager for chosen parameter values. The study of various other quantities reveals interesting scaling behavior with $p$ and also departure from usual diffusive behavior for $0.5<p<1$. In addition to numerical simulations, the problem has been studied with analytical approach in one dimension and the results up to $p<0.5$ agree with the numerical ones to a large extent.

The Caenorhabditis elegans (C.elegans) nematodes have long been a model organism for quantitative behavioral analysis due to their tractable nervous system and well-characterized genetics. In particular, dynamic diffraction has been a successful method of studying said microorganisms due to its low level of noise and the ability to simultaneously study multiple degrees of freedom of their neuromuscular system through their locomotion. In this study, we estimate the Lyapunov spectrum of C.elegans locomotion, which offers an insight into how volume elements evolve in the phase space of the underlying dynamical system. For that, we used the Sano-Sawada algorithm to estimate the spectra from the trajectories reconstructed using the Takens embedding procedure. In total, two positive and one negative exponents were calculated and verified to be nonspurious through investigations of their stability for different sets of parameters. Those exponents have values of $0.860\pm 0.028 {\text{s}}^{-1}, 0.389\pm 0.014 {\text{s}}^{-1}$, and $-3.451\pm 0.074 {\text{s}}^{-1}$, respectively. The presence of two positive exponents indicates that C.elegans locomotion is hyperchaotic, while the total sum being negative indicates that the system is dissipative. Those are key observations for the underlying system and will be significant for the potential formulation of future mathematical or computational models.

In stochastic processes with absorbing states, the quasi-stationary distribution provides valuable insights into the long-term behavior prior to absorption. In this work, we revisit two well-established numerical methods for its computation. The first is an iterative algorithm for solving the nonlinear equation that defines the quasi-stationary distribution. We generalize this technique to accommodate general Markov stochastic processes, either with discrete or continuous state space, and with multiple absorbing states. The second is a Monte Carlo method with resetting, for which we propose a single-trajectory approach that uses the trajectory's own history to perform resets after absorption. In addition to these methodological contributions, we provide a detailed analysis of implementation aspects for both methods. We also compare their accuracy and efficiency across a range of examples. The results indicate that the iterative algorithm is generally the preferred choice for problems with simple boundaries, while the Monte Carlo approach is more suitable for problems with complex boundaries, where the implementation of the iterative algorithm is a challenging task.

Understanding thermal fluctuations yields insights into a wide range of behaviors in many-body systems. In this work, we analyze the dynamical adaptation of the two-dimensional crystalline lattice system under harmonic interaction in response to the intricate interplay of thermal agitation and mechanical stress by developing the characteristic stress-absorbing quadrupole structures and stress-releasing fold structures. These thermally driven stress-regulator structures serve as a tangible embodiment of thermal fluctuations, offering a unique perspective on the characterization and manipulation of the elusive fluctuations. Specifically, we reveal the stretch-driven alignment and linear accumulation of quadrupoles, characterize the formation and proliferation of folds, and present the phase diagram of the dynamical states defined by these characteristic structures. This work demonstrates the promising avenue of re-examining classical mechanical systems subject to thermal agitation, which is of fundamental physical interest and has potential practical significance in the design of mechanical devices in thermal environments.

We present a novel extension of Hamiltonian mechanics to nonconservative systems built upon the Schwinger-Keldysh-Galley double-variable action principle. Departing from Galley’s initial-value action, we clarify important subtleties regarding boundary conditions, the emergence of the physical-limit trajectory, and the decomposition of the Lagrangian into conservative and dissipative sectors. Importantly, we demonstrate that the redundant doubled configuration space admits a gauge freedom at the level of the canonical momenta that leaves the physical dynamics unchanged. From a Legendre transform, we construct the corresponding family of gauge-related nonconservative Hamiltonians; we show that virtually any classical initial-value problem can be embedded on our enlarged symplectic manifold, supplying the associated Hamiltonian and Lagrangian functions explicitly. As a further contribution, we derive a completely equivalent linear “Lie” formulation of the double-variable action and Hamiltonian, which streamlines computations and renders transparent many structural properties of the formalism.

Motivated by the complexity of finite-resource transport systems in biological and physical contexts, we study a totally asymmetric simple exclusion process on a lattice coupled to two finite reservoirs: The left reservoir supplies particles to the first site depending on its occupancy, while the right reservoir collects particles leaving the last site. Particles hop unidirectionally from left to right along the lattice under hardcore exclusion, and, in addition, particles can transfer from the right reservoir back to the left, enabling closed-loop circulation. Using mean-field approach, we analytically derive all phase boundaries, density profiles, and shock positions, which are validated through extensive Monte Carlo simulations. The model exhibits a rich variety of phases, with five qualitatively distinct phase diagrams emerging as key parameters vary. Among these, three phase diagrams contain the same set of phases but differ in their topological structure. The shock position displays both monotonic and nonmonotonic dependence on the exit rate $\beta$, reflecting the intricate influence of finite resources and the coupling between entry and exit dynamics. A phenomenon, termed the back-and-forth transition, arises from the interplay between the interreservoir particle transfer and the total number of particles.

We present a compact dynamical mean-field theory (DMFT) for large networks of coupled phase oscillators whose phases live on the circle $S^1$ and interact with both coherent mean-field coupling and quenched randomness. Starting from wrapped Langevin dynamics, we build a path-integral representation that keeps the $2\pi$ periodicity of the phases explicit. After averaging over the disorder in the thermodynamic limit, this construction reduces to a single-oscillator stochastic equation driven by a deterministic mean field and a self-consistent colored Gaussian noise, whose covariance is fixed by a circular two-time correlator. In the limit of vanishing disorder, the formalism reproduces the Ott-Antonsen reduction and recovers standard Kuramoto and theta-neuron neural-mass equations. The same framework accommodates arbitrary $2\pi$-periodic coupling functions, including those obtained from infinitesimal phase response curves (IPRCs) of biophysical neuron models. As an example, we show that for adaptive exponential integrate-and-fire neurons, inserting an IPRC-fitted coupling into the compact DMFT yields quantitative predictions for synchronization thresholds, providing a direct route from single-neuron phase response data to network-level mean-field predictions for arbitrary phase-reducible oscillators.

We study the genetic interfaces between two species of an expanding colony that consists of individual microorganisms that reproduce and undergo diffusion, both at the frontier and in the interior. Within the bulk of the colony, the genetic interface is controlled in a simple way via interspecies interactions. However, at the frontier of the colony, the genetic interface width saturates at finite values for long times, for both neutral strains and interspecies interactions such as antagonism. This finite width arises from geometric effects: genetic interfaces drift toward local minima at an undulating colony frontier, where a focusing mechanism induced by curvature impedes diffusive mixing. Numerical simulations support a logarithmic dependence of the genetic interface width on the strength of the number fluctuations.

Topological entropy serves as a viable candidate for quantifying mixing and complexity of a highly chaotic system. Particularly in turbulence, this is determined as the exponential stretching rate of a fluid material line that typically necessitates a Lagrangian description. We extend our recent work [A. Manoharan, S. Subramanian, and A. Joy, Phys. Rev. E 112, 015106 (2025)] to three dimensions, and present an exact Eulerian framework to compute the topological entropy of stationary turbulent flows. The only prerequisite is a distribution of eigenvalues of the local strain-rate tensor and their decorrelation times. This can be easily obtained from a single wire probe at a fixed location, thereby eliminating the need for Lagrangian particle tracking which is formidable due to the chaotic nature of the flow. We believe that our results lend great utility in experiments targeting transport and mixing in many industrial and natural flows.

Neuromorphic or neurally inspired optimizers rely on local but parallel parameter updates to solve problems that range from quadratic programming to Ising machines. An ideal realization of such an optimizer not only uses a compute-in-memory paradigm to address the memory wall (i.e., energy dissipated due to repeated memory read access), but also uses a learning-in-memory paradigm to address the energy bottlenecks due to repeated memory writes at the precision required for optimization (the update wall), and to address the energy bottleneck due to the repeated transfer of information between short-term and long-term memories (the consolidation wall). In this paper, we derive theoretical estimates for the energy-to-solution metric that can be achieved by this ideal neuromorphic optimizer which is realized by modulating the energy barrier of the physical memories such that the dynamics of memory updates and memory consolidation matches the optimization or the annealing dynamics. The analysis presented in this paper captures the out-of-equilibrium thermodynamics of learning and the resulting energy-efficiency estimates are model agnostic and only depend on the number of model-update operations, the model size in terms of number of parameters, the speed of convergence, and the precision of the solution. To show the practical applicability of our results, we apply our analysis for estimating the lower bound on the energy-to-solution metrics for large-scale AI workloads.

We investigate the influence of an anonymous leader on a collective of self-propelled robots using Kilobot experiments and numerical simulations. Each robot possesses a binary internal state that determines the direction of its intrinsic rotational motion, leading to clockwise or counterclockwise circular trajectories. A single leader alternates deterministically between these two internal chiral states, while the other robots update their internal state through a stochastic majority rule based on local communication. The leader induces correlations with the collective response that peak at intermediate perturbation levels, resembling stochastic resonance. Numerical simulations confirm that this resonance arises when the leader's reversal period matches the mean residence time of the leaderless system. Our results contribute to understanding decision-making in active matter and suggest general principles for steering robotic swarms with minimal and anonymous leadership.

Plants often exhibit regular arrangements of seeds or leaves, known as phyllotaxis, and can famously exhibit Fibonacci spirals, as in sunflower heads or on pine cones. While there are many models which can reproduce a spiral formation, the actual mechanism of arrangement remains unclear. Here, we test a more general class of model, based on the Keller-Segel model, in which a diffusing chemical signal produces its own transport signal and can form local instabilities. By modeling the plant as a disk with a signal source at the center and radial growth, we show that we can reproduce both Fibonacci spirals and alternating patterns, depending on a balance between growth and source. Finally, using linear stability analysis, we show how the pattern arises due to a balance between the growth of instabilities and the growth of the plant. Overall, this work demonstrates how the Keller-Segel model can reproduce a wide range of observed patterns, and may act as a phenomenological description of a number of processes in plants.

For high-efficiency inertial confinement fusion implosions, it is predicted that a burning hot spot will successfully encompass all surrounding fuel and then transition into a thermal runaway where the internal energy increase from fusion occurs on a timescale faster than the expansion of the fuel is able to quench the fusion chain reaction after ignition occurs. Observation of this dynamic phase transition would indicate distinct burn properties and indicate an implosion's robustness. A technique for diagnosing the presence of thermal runaway from measurements of nuclear reaction history is presented. The technique is based on taking the logarithmic derivative of the nuclear reaction history, called the $\alpha$ curve, and allowing a mathematical decoupling of the mass, volume, and thermal reactivity in the fusion reaction rate equation. During thermal runaway, where the thermal temperature dominates the burn dynamics, a maximum in the $\alpha$ curve is found where there is a maximum in the first derivative of the thermal fusion reactivity, an effect to the deuterium-tritium (DT) fusion cross-section resonance. This provides a distinct signature related to the fundamental nature of the DT fusion nuclear resonance and signifies the transition into the fusion thermal instability. Impacts of charged particle transport on the effect are also assessed and the analytical formulas are compared and found to be in agreement with radiation hydrodynamic codes.

A consistent kinetic modeling and discretization strategy for compressible flows across all Prandtl numbers and specific heat ratios is developed using the quasiequilibrium approach within two of the most widely used double-distribution frameworks. The methodology ensures accurate recovery of the Navier-Stokes-Fourier equations, including all macroscopic moments and dissipation rates, through detailed hydrodynamic limit analysis and careful construction of equilibrium and quasiequilibrium attractors. Discretization is performed using high-order velocity lattices with a static reference frame in a discrete velocity Boltzmann context to isolate key modeling aspects such as the necessary requirements on expansion and quadrature orders. The proposed models demonstrate high accuracy, numerical stability, and Galilean invariance across a wide range of Mach numbers and temperature ratios. Separate tests for strict conservation and measurements of all dissipation rates confirm these insights for all Prandtl numbers and specific heat ratios. Simulations of a thermal Couette flow and a sensitive two-dimensional shock-vortex interaction excellently reproduce viscous Navier-Stokes-Fourier-level physics. The proposed models establish an accurate, efficient, and scalable framework for kinetic simulations of compressible flows with moderate supersonic speeds and discontinuities at arbitrary Prandtl numbers and specific heat ratios, offering a valuable tool for studying complex problems in fluid dynamics and paving the way for future extensions to the lattice Boltzmann context, by application of correction terms, as well as high-Mach and hypersonic regimes, employing target-designed reference frames.

We study two cross-linked polymer systems in the strong stretching regime. The first consists of two polymers sharing one endpoint, with the other two endpoints coupled by a harmonic potential. Within the weakly bending approximation, we analyze the tensile elastic response for freely jointed or wormlike chains; for the latter, the approximation applies either at large tension or at moderate tension with large persistence length (rodlike limit). We obtain analytic expressions for the force–extension relation and for the longitudinal and transverse mismatch of the cross-linked endpoints. In the thermodynamic limit, the cross-link does not affect the tensile elasticity, but it significantly suppresses transverse fluctuations, effectively forming a loop structure. The second system is a polymer necklace in the thermodynamic limit, composed of two strongly stretched polymers interconnected by a regular sequence of reversible cross-links. Using an analogy with a two-dimensional system of concatenated Gaussian loops (“Gaussian slinky”), we calculate the mean fraction of cross-linked sites as a function of the tensile force and find weak and strong binding regimes connected by a crossover. For shallow binding potential wells (compared with $k_{\mathrm{B}}T$), we employ a continuum description and exploit the mapping between directed polymers and a two-dimensional quantum particle to analytically determine the crossover behavior and the mean transverse separation between the two polymer chains. Overall, these results clarify that terminal cross-linking under strong tension primarily modifies transverse fluctuations while leaving longitudinal elasticity essentially unchanged, leading to an effectively additive stiffening of the composite tensile response. Moreover, the cross-link-induced modification of transverse fluctuations turns out to be independent of the microscopic polymer model (freely jointed versus wormlike).