We examine stationary regimes in granular materials from a dynamical systems theory perspective. The aim is to enrich the classical view of the critical state regime in granular materials, and more broadly, to improve the fundamental understanding of the underlying mesoscale mechanisms responsible for macroscopic stationary states in complex systems. This study is based on a series of discrete element method simulations, in which two-dimensional assemblies of nonuniformly sized circular particles are subjected to biaxial compression under constant lateral confining pressure. The lifespan and life expectancy of specific cluster conformations, comprising particles in force chains and grain loops, are tracked and quantified. Results suggest that these conformational clusters reorganize at similar rates in the critical state regime, depending on strain magnitudes and confining pressure levels. We quantified this rate of reorganization and found that the material memory rapidly fades, with an entirely new generation of force chains and grain loops replacing the old within a few percent strain.

In mechanical engineering Wöhler plots serve to measure the average number of load cycles before materials break, as a function of the maximal stress in each cycle. Although such plots have been prevalent in engineering for more than 150 years, their theoretical understanding is lacking. Recently a scaling theory of Wöhler plots in the context of cyclic bending was offered [Bhowmik, arXiv:2103.03040 (2021)]. Here we elaborate further on cyclic bending and extend the considerations to cyclic tensile loads on an amorphous strip of material; the scaling theory applies to both types of cyclic loading equally well. On the basis of atomistic simulations we conclude that the crucial quantities to focus on are the accumulated damage and the average damage per cycle. The dependence of these quantities on the loading determines the statistics of the number of cycles to failure. Finally, we consider the probability distribution functions of the number of cycles to failure and demonstrate that the scaling theory allows prediction of these distributions at one value of the forcing amplitude from measurements and another value.

We present numerical investigations on the clogging of adhesive particles carrying electric dipoles at pore scale using an adhesive discrete element method (DEM). Based on the simulation results, the long-range dipolar interaction is reported to promote the clogging process, which is quantified by the bulk permeability, the penetrating particle number, and the particle capture efficiency. A clogging phase diagram is constructed in terms of the Stokes number (St) and the adhesion parameter ($\mathrm{Ad}$) for both neutral and polarized particles. The influence of the dipolar interaction on the clogging-nonclogging transition is then described by the shifted boundary on the diagram. Also, the cake structure is characterized by different mathematical descriptions. A looser structure is formed with the increase of both the short-range adhesion and the long-range dipolar interaction. More ordered structures, such as particle chains, are observed in the presence of the stronger dipolar interaction. Furthermore, fluid stress is found to be essential in the compression and restructuring of the cake structure. Finally, a schematic representation of the cake structure is established, which provides a general physical picture showing the relationship between the cake structure and the particle-scale interactions.

We analyze the static response to perturbations of nonequilibrium steady states that can be modeled as one-dimensional diffusions on the circle. We demonstrate that an arbitrary perturbation can be broken up into a combination of three specific classes of perturbations that can be fruitfully addressed individually. For each class, we derive a simple formula that quantitatively characterizes the response in terms of the strength of nonequilibrium driving valid arbitrarily far from equilibrium.

We study the diffusion of $N$ particles in one dimension interacting via a drift proportional to their rank. In the attractive case (self-gravitating gas) a mapping to the Lieb-Liniger quantum model allows one to obtain stationary time correlations, return probabilities, and the decay rate to the stationary state. The rank field obeys a Burgers equation, which we analyze. It allows one to obtain the stationary density at large $N$ in an external potential $V\left(x\right)$ (in the repulsive case). In the attractive case the decay rate to the steady state is found to depend on the initial condition if its spatial decay is slow enough. Coulomb gas methods allow one to study the final equilibrium at large $N$.

We introduce a class of physically intriguing $\mathcal{P}T$-symmetric Dirac-$\delta$-Scarf-II optical potentials. We find the parameter region making the corresponding non-Hermitian Hamiltonian admit the fully real spectra, and present the stable parameter domains for these obtained peakons, smooth solitons, and double-hump solitons in the self-focusing nonlinear Kerr media with $\mathcal{P}T$-symmetric $\delta$-Scarf-II potentials. In particular, the stable wave propagations are exhibited for the peakon solutions and double-hump solitons from some given parameters even if the corresponding parameters belong to the linear $\mathcal{P}T$-phase broken region. Moreover, we also find the stable wave propagations of exact and numerical peakons and double-hump solitons in the interplay between the power-law nonlinearity and $\mathcal{P}T$-symmetric potentials. Finally, we examine the interactions of the nonlinear modes with exotic waves, and the stable adiabatic excitations of peakons and double-hump solitons in the $\mathcal{P}T$-symmetric Kerr nonlinear media. These results provide the theoretical basis for the design of related physical experiments and applications in $\mathcal{P}T$-symmetric nonlinear optics, Bose-Einstein condensates, and other relevant physical fields.

Gene expression in individual cells is inherently variable and sporadic, leading to cell-to-cell variability in mRNA and protein levels. Recent single-cell and single-molecule experiments indicate that promoter architecture and translational bursting play significant roles in controlling gene expression noise and generating the phenotypic diversity that life exhibits. To quantitatively understand the impact of these factors, it is essential to construct an accurate mathematical description of stochastic gene expression and find the exact analytical results, which is a formidable task. Here, we develop a stochastic model of bursty gene expression, which considers the complex promoter architecture governing the variability in mRNA expression and a general distribution characterizing translational burst. We derive the analytical expression for the corresponding protein steady-state distribution and all moment statistics of protein counts. We show that the total protein noise can be decomposed into three parts: the low-copy noise of protein due to probabilistic individual birth and death events, the noise due to stochastic switching between promoter states, and the noise resulting from translational busting. The theoretical results derived provide quantitative insights into the biochemical mechanisms of stochastic gene expression.

The calculation of the optical properties of hot dense plasmas with a model that has self-consistent plasma physics is a grand challenge for high energy density science. Here we exploit a recently developed electronic structure model that uses multiple scattering theory to solve the Kohn-Sham density functional theory equations for dense plasmas. We calculate opacities in this regime, validate the method, and apply it to recent experimental measurements of opacity for Cr, Ni, and Fe. Good agreement is found in the quasicontinuum region for Cr and Ni, while the self-consistent plasma physics of the approach cannot explain the observed difference between models and the experiment for Fe.

In order to predict the postcollision velocities in the binary collision, one needs the deflection angle given by the solution of the trajectory equation of classical mechanics. In the direct simulation Monte Carlo, it has been conventional to assume that the scattering is isotropic taking the hard sphere scattering law (the variable hard sphere model). Because the simulation carries out the ensemble average, and thus the collisional deflections should be averaged at the end, it is proposed to use the preaveraged deflection angle for each collision. This is a representative single deflection angle simulation. The present work postulates a method to estimate the mean deflection angles for arbitrary force models considering the differential cross section formula and the trajectory equation. For hard spheres, the representative single deflection simulation of normal shock waves recovers the conventional computations within $3\%$. For Maxwell molecules, the conventional simulation in which the isotropic scattering law is taken can exactly be reproduced by the single deflection when the representative angle is adjusted to the mean deflection angle together with the reference diameter obtained in the present method. It has been observed that the Maxwell-molecule-representative for the single angle simulation reproduces the conventional computations of any isotropic scattering models including hard spheres.

A Brownian yet non-Gaussian phenomenon has recently been observed in many biological and active matter systems. The main idea of explaining this phenomenon is to introduce a random diffusivity for particles moving in inhomogeneous environment. This paper considers a Langevin system containing a random diffusivity and an $\alpha$-stable subordinator with $\alpha <1$. This model describes the particle's motion in complex media where both the long trapping events and random diffusivity exist. We derive the general expressions of ensemble- and time-averaged mean-squared displacements which only contain the values of the inverse subordinator and diffusivity. Further taking specific time-dependent diffusivity, we obtain the analytic expressions of ergodicity breaking parameter and probability density function of the time-averaged mean-squared displacement. The results imply the nonergodicity of the random diffusivity model with any kind of diffusivity, including the critical case where the model presents normal diffusion.

Soundscape studies help us understand ecological processes, biodiversity distribution, anthropic influences, and even urban quality, across a wide variety of places and time periods. In this work, instead of looking for differences, we ask if there are common characteristics shared by all soundscapes. Based on our results, we propose a universal distribution of quiet-time (background noise) and sound-time (acoustic energy bursts) in audio recordings. We analyzed one continuous hour during daylight and one at night, from ten randomly selected days in each environment: urban, dry forest, savanna, rupestrian field, Atlantic forest, marine, and freshwater. We found that the histograms of the quiet-time followed a power law for all scenarios analyzed, they present fractal events or scale-free distributions. This distribution covers up to four orders of magnitude, with an exponent of $1.6\le \alpha \le 2.0$ for all soundscapes. By contrast, the sound-time distribution in all environments followed a log-normal or timescale dependence, with a typical time for the duration of sounds (0.06–0.12 s). Such time duration limitation can be related to the physiology of sound emission in animals.

This paper investigates evanescent waves in one-dimensional nonlinear monatomic chains using a first-order Lindstedt-Poincaré approach. Perturbation approaches applied to traveling waves in similar chains have predicted weakly nonlinear phenomena such as dispersion shifts and amplitude-dependent stability. However, nonlinear evanescent waves have received sparse attention, even though they are expected to serve a critical role in nonlinear interface problems. To aid in their analysis, the nonlinear evanescent waves are categorized herein as either complete or transitional evanescent waves. Complete evanescent waves, including linear evanescent waves, attenuate to zero amplitude in the far field. Transitional evanescent waves, only occurring in softening systems, attenuate to a nontrivial amplitude in the far field, regardless of the initial amplitude, resulting in a saturation effect. For both cases, the presented perturbation approach reveals that the imaginary wave number in the evanescent field is a function of space, rather than a constant value as in its linear counterpart. It also reveals that hardening and softening nonlinearity slow and accelerate the near-field decay, respectively. The predictions obtained from the perturbation approach are verified using numerical simulations with both initial-condition and boundary-continuous excitation, documenting strong agreement.

Spiral waves are found in many excitable systems and are thought to play a role in the incoherent electrical activation that underlies cardiac arrhythmias. It is well-known that spiral waves can be permanently trapped by local heterogeneities. In this paper, we demonstrate that spiral waves can also be intermittently trapped by such heterogeneities. Using simulations of a cardiac model in two dimensions, we show that a tissue heterogeneity of sufficient strength or size can result in a spiral wave that is trapped for a few rotations, after which it dislodges and meanders away from the heterogeneity. We also show that these results can be captured by a particle model in which the particle represents the spiral wave tip. For both models, we construct a phase diagram which quantifies which parameter combinations of heterogeneity size and strength result in permanent, intermittent, or no trapping. Our results are consistent with clinical observations in patients with atrial fibrillation that showed that spiral wave reentry can be intermittent.

Equilibrium shapes of magnetic rods and their stability under the action of an applied field are analyzed. The family of shapes is characterized by two magnetoelastic numbers due to the remanent magnetization and paramagnetic susceptibility of the rod. Since in experiments with flexible magnetic rods the ends are usually unfixed and unclamped, their stability is analyzed under these conditions. Solutions of the corresponding eigenvalue problems for particular cases show that under these conditions the equilibrium shapes are unstable.

Spontaneous pattern formation in living systems is driven by reaction-diffusion chemistry and active mechanics. The feedback between chemical and mechanical forces is often essential to robust pattern formation, yet it remains poorly understood in general. In this analytical and numerical paper, we study an experimentally motivated minimal model of coupling between reaction-diffusion and active matter: a propagating front of an autocatalytic and stress-generating species. In the absence of activity, the front is described by the well-studied Kolmogorov, Petrovsky, and Piskunov equation. We find that front propagation is maintained even in active systems, with crucial differences: an extensile stress increases the front speed beyond a critical magnitude of the stress, while a contractile stress has no effect on the front speed but can generate a periodic instability in the high-concentration region behind the front. We expect our results to be useful in interpreting pattern formation in active systems with mechanochemical coupling in vivo and in vitro.

We experimentally and computationally study the flow of a quasi-two-dimensional emulsion through a constricting hopper shape. Our area fractions are above jamming such that the droplets are always in contact with one another and are in many cases highly deformed. At the lowest flow rates, the droplets often clog and thus exit the hopper via intermittent avalanches. At the highest flow rates, the droplets exit continuously. The transition between these two types of behaviors is a fairly smooth function of the mean strain rate. The avalanches are characterized by a power-law distribution of the time interval between droplets exiting the hopper, with long intervals between the avalanches. Our computational studies reproduce the experimental observations by adding a flexible compliance to the system (in other words, a finite stiffness of the sample chamber). The compliance results in continuous flow at high flow rates, and allows the system to clog at low flow rates leading to avalanches. The computational results suggest that the interplay of the flow rate and compliance controls the presence or absence of the avalanches.

Friction at the endwalls of partially filled horizontal rotating tumblers induces curvature and axial drift of particle trajectories in the surface flowing layer. Here we describe the results of a detailed discrete element method study of the dry granular flow of monodisperse particles in three-dimensional cylindrical tumblers with endwalls and cylindrical wall that can be either smooth or rough. Endwall roughness induces more curved particle trajectories, while a smooth cylindrical wall enhances drift near the endwall. This drift induces recirculation cells near the endwall. The use of mixed roughness (cylindrical wall and endwalls having different roughness) shows the influence of each wall on the drift and curvature of particle trajectories as well as the modification of the free surface topography. The effects act in opposite directions and have variable magnitude along the length of the tumbler such that their sum determines both direction of net drift and the recirculation cells. Near the endwalls, the dominant effect is always the endwall effect, and the axial drift for surface particles is toward the endwalls. For long enough tumblers, a counter-rotating cell occurs adjacent to each of the endwall cells having a surface drift toward the center because the cylindrical wall effect is dominant there. These cells are not dynamically coupled with the two endwall cells. The competition between the drifts induced by the endwalls and the cylindrical wall determines the width and drift amplitude for both types of cells.

A classical wave-particle entity in the form of a millimetric walking droplet can emerge on the free surface of a vertically vibrating liquid bath. Such wave-particle entities have been shown to exhibit hydrodynamic analogs of quantum systems. Using an idealized theoretical model of this wave-particle entity in a tilted potential, we explore its transport behavior. The integro-differential equation of motion governing the dynamics of the wave-particle entity transforms to a Lorenz-like system of ordinary differential equations that drives the particle's velocity. Several anomalous transport regimes such as absolute negative mobility, differential negative mobility, and lock-in regions corresponding to force-independent mobility are observed. These observations motivate experiments in the hydrodynamic walking-droplet system for the experimental realizations of anomalous transport phenomena.

The Mpemba effect is a counterintuitive relaxation phenomenon whereby a system with a higher initial temperature may cool down to the thermal state faster than an identical system that was initially prepared at a lower temperature. Here, we investigate heat and work in a Markovian state transition system with cyclic switching hot-cold temperatures, which operates as an Otto heat engine working in long but finite time, either with or without the Mpemba effect. Under the condition of the periodic steady state having been reached, the time durations of the heating and cooling relaxation processes are determined by exploring a distance-from-equilibrium equivalent to the Kullback-Leibler divergence. We then numerically evaluate and compare the averages and variances of both the work and the power output of two scenarios with and without the Mpemba effect. The results show that the Markovian Mpemba effect can enhance the machine performance by significantly increasing the power output for a given efficiency without sacrificing the stability.

We present a framework for systems in which diffusion-advection transport of a tracer substance in a mobile zone is interrupted by trapping in an immobile zone. Our model unifies different model approaches based on distributed-order diffusion equations, exciton diffusion rate models, and random-walk models for multirate mobile-immobile mass transport. We study various forms for the trapping time dynamics and their effects on the tracer mass in the mobile zone. Moreover, we find the associated breakthrough curves, the tracer density at a fixed point in space as a function of time, and the mobile and immobile concentration profiles and the respective moments of the transport. Specifically, we derive explicit forms for the anomalous transport dynamics and an asymptotic power-law decay of the mobile mass for a Mittag-Leffler trapping time distribution. In our analysis we point out that even for exponential trapping time densities, transient anomalous transport is observed. Our results have direct applications in geophysical contexts, but also in biological, soft matter, and solid state systems.