The packing geometry of granular solids and other amorphous materials is important to understand their macroscopic behaviors. However, their particle-scale assembly mechanism and the underlying statistical mechanical laws remain unclear. In this work, we develop a model to generate the local packing structures of granular spheres by parking them sequentially and stochastically, and connect the fluctuating structures to the thermodynamic equations of state. The influences of entropy, friction, and mechanical action on local configurations are decomposed with the aid of an effective interparticle interaction, a parking sequence of neighboring particles, and an external potential. Quasiuniversal laws of granular sphere packings observed in previous experiments are replicated by our model and their empirical dependences on particle friction and packing protocol are rationalized. This model provides a general statistical mechanical approach to understanding the nonequilibrium assembly mechanism of amorphous particle packing systems.

We derive an equation capable of treating both electrostatic and nonelectrostatic interactions in charged liquids. The resulting equation is a complex version of the Poisson-Boltzmann equation, where nonelectrostatic interactions are represented as random fields through field theory. Consequently, the nonelectrostatic interactions of ions in charged liquids can be easily simulated by generating random numbers in accordance with these random fields. To solve the equation, we employ the finite element method. The nonelectrostatic interactions incorporated into the equation are general. In this study, we take the steric effect of ions as an example. The results show that the equation can capture the steric effect clearly. The steric effect excludes ions at the boundaries and alters the ion distribution within the bulk domain. In charged liquids with screening domains intersected, the steric effect in the bulk diminishes the steric effect at the boundaries.

Stress-strain relations for random packings of entangling chains under triaxial compression can exhibit strain stiffening and sustain stresses several orders-of-magnitude beyond typical granular materials. X-ray tomography reveals the transition to this strong strain stiffening occurs when chains are long enough to entangle an average of about one chain each, which results in system-filling clusters of entangled chains, similar to the Erdös-Rényi model for randomly connected graphs. The number of entanglements is nearly proportional to the area surrounded by entangling particles with an excluded volume effect, thus the existence of system-filling clusters of entanglements can be predicted assuming random particle positions and orientations with an excluded volume effect if the particle shapes in the packing are known. A tendency was found for chain links to stretch when the packing was strained. This suggests that the strength of these packings comes from stretching of the links of chains, but only when the system-filling network of entanglements provides constraints that prevents failure by shear banding, so that particles must be deformed to move further under strain. The slope of the stress-strain relation of a packing can be calculated from a mean-field model consisting of the product of the effective extensional modulus of the chain, packing fraction, probability of stretched links, and the ratio of strain of stretched links to packing strain. In this model, the increasing slope of the stress-strain curve is mainly due to the fraction of stretched links increasing with strain, and assuming the fraction of stretched links is proportional to strain results in a quadratic prediction for the stress-strain curve. The stress-strain model requires as input measurements of the ratio between local particle deformation and global average strain, and the probability of stretching for nonrigid particles, resulting in a quadratic curvature that agrees with experiments within the run-to-run variation ($30\%$). This model for the stress-strain relation is shown to be generalizable to different shapes of entangling particles by applying it to staples, where the packing strength comes from the bending of staples instead of stretching links. The permanent plastic deformation of staples allows measuring statistical quantities from inspection of a poured-out sample after a triaxial compression, without the need for in situ imaging. Both the probability of staples bending and the average bend angle of the arms were found to increase with strain, and these inputs into the model result in a quadratic curvature of the stress-strain that agrees with experiments within the model uncertainties ($37\%$).

The transition from individual to collective motion plays a significant role in many biological processes. While the implications of different types of particle-particle interactions for the emergence of particular modes of collective motion have been well studied, it is unclear how particular types of individual migration patterns influence collective motion. Here, motivated by swarming bacteria Myxococcus xanthus, we investigate the combined effects of the individual pattern of migration and particle-particle interactions on the emergence of collective migration. We analyze the effects of a feature of individual pattern migration, the persistence of motion, on the collective properties of the system that emerge from interactions among individuals, particularly when nematic velocity alignment interaction mediates collective dynamics. We find, through computer simulations and mathematical analysis, that an initially disordered migratory state can become globally ordered by increasing either the particle-particle alignment interaction strength or the persistence of individual migration. In contrast, we find that persistence prevents the emergence of global nematic order when both persistence and nematic alignment are comparatively high. We conclude that behavior at the population level not only depends on interactions between individuals but also on their own intrinsic behavior.

Avalanche phenomena characterized by power-law scaling are observed in amorphous solids and many other nonequilibrium systems during their deformation. Avalanches in these systems often exhibit scale invariance, a feature reminiscent of critical phenomena and universality classes, although their fundamental nature remains unclear. In this paper, we use in situ acoustic emission techniques to experimentally investigate the characteristics and evolution of avalanches during the deformation process of bulk metallic glass (BMG), a representative amorphous solid. We observed abundant avalanche events from the microplastic deformation region to the failure of the sample. We find that avalanches are power-law distributed with an exponent decreasing from 1.61 to 1.49 with increasing deformation throughout the tensile experiment. By quantitatively analyzing the strong strain dependence of various avalanche characteristics, we highlight the importance of additional coefficients that complete the widely studied finite size scaling description of avalanche dynamics and revealed a strain-mediated avalanche scaling mechanism. Through surface morphology analysis and spectral analysis of avalanche signals in BMG samples, we conclude that the underlying process of these avalanches are not macroscopic, such as cracks and large shear band propagation, but is instead related to nanoscale microstructural adjustments. Our results encourage further exploration into the microscopic origins of avalanches and suggest that theoretical frameworks beyond finite-size scaling merit more in-depth investigations.

The precooling strategy, which leads to exponentially faster heating, is a counterintuitive relaxation phenomenon wherein cooling the system before heating it dramatically shortens the relaxation time. We investigate the performance of a Markovian system functioning as an Otto refrigerator for a finite time, incorporating a precooling stage before the cyclic heating process. Our results demonstrate that precooling prior to the heating process in the Otto cycle optimizes the machine's performance by significantly enhancing the machine performance and the stability of the refrigerator.

Diffusion-based generative models are machine learning models that use diffusion processes to learn the probability distribution of high-dimensional data. In recent years they have become extremely successful in generating multimedia content. However, it is still unknown whether such models can be used to generate high-quality datasets of physical models. In this work we use a Landau-Ginzburg-like diffusion model to infer the distribution of a two-dimensional bond-diluted Ising model. Our approach is simple and effective, and we show that the generated samples correctly reproduce the statistical and critical properties of the physical model.

Nonreciprocal interactions are a generic feature of nonequilibrium systems. We define a nonreciprocal generalization of the kinetic Ising model in one spatial dimension. We solve the model exactly using two different approaches for infinite, semi-infinite, and finite systems with either periodic or open boundary conditions. The exact solution allows us to explore a range of novel phenomena tied to nonreciprocity like nonreciprocity induced frustration and wave phenomena with interesting parity-dependence for finite systems of size $N$. We study dynamical questions like the approach to equilibrium with various boundary conditions. We find different regimes, separated by $N\mathrm{th}$-order exceptional points, which can be classified as overdamped, underdamped, or critically damped phases. Despite these different regimes, long-time order is only present at zero temperature. Additionally, we explore the low-energy behavior of the system in various limits, including the aging and spatiotemporal Porod regimes, demonstrating that nonreciprocity induces unique scaling behavior at zero temperature. Lastly, we present general results for systems where spins interact with no more than two spins, outlining the conditions under which long-time order may exist.

The behavior of the kink in the sine-Gordon (sG) model in the presence of periodic inhomogeneity is studied. An ansatz is proposed that allows for the construction of a reliable effective model with two degrees of freedom. Effective models featuring very good agreement with the original field-theoretic partial differential equation are constructed, including in the nonperturbative region and for relativistic velocities. The numerical solutions of the sG model describing the evolution of the kink in the presence of a barrier as well as in the case of a periodic heterogeneity under the potential additional influence of a switched bias current and/or dissipation were obtained. The results of the field equation and the effective models were favorably compared. The effect of the choice of initial conditions in the field model on the agreement of the results with the effective model is also discussed.

Controlling the elastic response of materials to multiple stimuli is a key prerequisite for the design of adaptive soft matter, e.g., for applications in medicine or soft robotics. Here, we discuss a statistical mechanics model in which the nonlinear elastic response is governed by mechanically coupled bistable micromodules which can be switched by external stimuli. Exact analytical solutions show complex stimuli-mediated, nonlinear stiffening/softening responses tuneable by the microscopic switching parameters. Importantly, we report up to two maxima in the softness (compliance) originating from cooperative transitions and show how to control their existence and properties. We demonstrate the usefulness of the model by fitting it to experimental extension-force data on various scales. We further illustrate how to explore the entire nonlinear response map as a function of multiple stimuli, utilizing distinct pathways to either cancel/reset or amplify the elastic responses through a combination of these stimuli. Our analysis should be useful for the design of nonlinear elasticity, e.g., in bistable microgel networks or mechanical metamaterials.

We investigate the emergence of sustained spatiotemporal behaviors in reaction-phase separation systems. We focus on binary systems, in which either one or both species can phase separate, and we discuss the stability of the homogeneous state determining the conditions for the emergence of a Hopf-type bifurcation. We then examine the effects of a specific autocatalytic chemical reaction, and computationally determine the full solutions to the partial differential equations. We find that when both species phase separate, sustained pulsed dynamics arise in one dimension. When considered in two dimensions, the system generates persistent, complex dynamic droplets, which do not generally appear if only one of the species can phase separate. We finally discuss the emergence of dynamics with complex features, which can be understood using the framework of a cellular automata.

We study the kinetics of vapor-liquid phase separation in a quasi-one-dimensional confined active matter system using molecular dynamics simulations. Activity is invoked via the Vicsek rule, while passive interaction follows the Lennard-Jones potential. With the system density near the vapor branch, the evolution morphology features disconnected liquid clusters. In the passive limit, coarsening begins with nucleation, followed by an evaporation-condensation growth mechanism, leading to a metastable state without complete phase separation. We aim to understand the impact of Vicsek-like self-propulsion on the structure and growth of these clusters. Our key finding is that Vicsek activity results in a distinct growth mechanism, notably rapid cluster growth and the breakdown of the metastable state through ballistic aggregation. Relevant growth laws are analyzed and explained using appropriate theoretical models.

Electrokinetic ion transport under coupled external electric field and pressure drops has recently exhibited giant, but monotonous, mechanical amplifications of ionic current in some nanochannels. While such effects can be exploited to develop novel pressure-sensitive ionic circuits, they can also yield large undesirable current surges if the control parameter, i.e., the pressure drop, overshoots. To overcome this critical issue, we design a nanopore that displays a similar mechanical activation of ionic current, but up to a limited magnitude of pressure, after which current ceases to grow. We integrate a bipolar surface charge distribution with an asymmetric channel geometry in a nanopore to alter the effect of an applied pressure drop on the quasistatic distribution of ions in the pore, which directs how the ionic conductance varies with pressure, in a way that yields the desired current-pressure response. Via such steps, analyzed using numerical simulations, we devise a funnel-shaped nanopore with a negatively charged conical mouth and a positively charged elongated cylindrical stem, that acts as the intended “surge-protected” mechanical amplifier of ion transport. It yields a substantial pressure-driven growth in ionic current (by factors of $\sim 4$) up to a limited intensity of pressure drop exerted (along a constant external electric field) toward the stem, beyond which current begins to fall. Besides exhibiting this hitherto undetected electrokinetic behavior, our study implements and paves the way to an innovative “function to design” approach in the field of electrokinetics that can help build improved nanofluidic devices with desired advanced ion transport functionalities.

We revisit the number theoretic division model of self-organized criticality [B. Luque et al.Phys. Rev. Lett. 101, 158702 (2008)]. The model consists of a pool of $M-1$ ordered integers $\{2,3,\cdots ,M\}$, and the aim is to dynamically form a primitive set of integers, where no number can be divided or divisible by others. Using extensive simulation studies and finite-size scaling method, we find the primitive set size fluctuations in the division model to show power spectral density of the form $1/f^{\alpha }$ in the frequency regime $1/M\ll f\ll 1/2$ with $\alpha \approx 2$ (different from $\alpha \approx 1.80\left(1\right)$ as reported previously) along with an additional scaling in terms of the system size $\sim M^b$. We also show similar power spectra properties for a class of random walks with a power-law distributed jump size (Lévy flights).

The phase diagram of a two-dimensional frustrated Ising model with both anti-ferromagnetic and ferromagnetic couplings is studied using tensor network renormalization group techniques. This model can be seen as two antiferromagnetic Ising replicas coupled by nonlocal spin-spin interactions, designed in such a way that the continuum limit matches that of the still-debated $J_1-J_2$ model and induces a marginal critical behavior. Our model has the advantage of having more symmetries than the $J_1-J_2$ model and of allowing a more straightforward implementation of tensor network renormalization group algorithms. We demonstrate the existence of two transition lines, featuring both first- and second-order regimes. In the latter, the central charge and the critical exponents are shown to be compatible with the Ashkin-Teller universality class. This picture is consistent with that given by Monte Carlo simulations of the $J_1-J_2$ model but not with recent studies with tensor network techniques.

In recent studies, it has been established that higher-order interactions in coupled oscillators can induce a process from continuous to explosive phase transition. In this study, we identify a phase transition, termed the stepwise explosive phase transition, characterized by the emergence of multiple critical phase plateaus in a globally frequency-weighted coupled pendulum model. This transition bridges the continuous and explosive phase transitions, arising from a delicate balance between attractive higher-order interactions and repulsive pairwise interactions. Specifically, the stepwise explosive phase transition occurs when the higher-order coupling is moderate, neither large nor small, while the pairwise interactions remain repulsive. Our analysis shows that stronger attractive higher-order interactions necessitate weaker repulsive pairwise interactions, leading to partial frequency locking among oscillators and triggering the stepwise transition. We construct an analytical framework using self-consistent equations to provide an approximation of the steady-state behavior. This study uncovers an alternative pathway to the desynchronization, and it provides additional insights into the phase transitions in coupled dynamical networks.

The presence of excess free-ion impurities in ferroelectric liquid crystals (FLCs) results in several issues in electro-optical liquid-crystal displays (LCDs), such as slow electro-optical responses and image-sticking effects. This study experimentally demonstrated that two-dimensional (2D) hexagonal boron nitride ($h$-BN) nanosheets can function as both planar alignment and ion-capturing agents in an electro-optic FLC device. The 2D $h$-BN nanosheet was used as a planar alignment agent on one side of an LC cell, while a standard planar-aligning polyimide (PI) layer was used on the other side of the cell. The FLC exhibited uniform planar alignment in this $h$-BN-PI cell configuration. The results showed that free-ion impurities in the FLC were significantly suppressed in the $h$-BN-PI cell compared to a standard PI-PI LC cell. This reduction in free-ion density in the $h$-BN-PI cell was attributed to the ion-capturing capability of the 2D $h$-BN nanosheets. Consequently, the reduction of ionic impurities led to enhanced effective spontaneous polarization and accelerated electro-optic response of the FLC in the $h$-BN-based cell.

Already some years ago, Langdon [Phys. Rev. Lett. 44, 575 (1980)] proposed that inverse bremsstrahlung absorption in plasmas drives free electrons into non-Maxwellian distributions. Radiation-hydrodynamic simulations of plasma-based light sources, however, often (implicitly) assume Maxwellian-distributed electrons. In this paper, we quantify the effect of non-Maxwellian distributions on laser absorption and thermal conduction in laser-driven plasma light sources. For irradiation conditions $I_{\mathrm{las}}{\lambda }_{\mathrm{las}}^2\in [{10}^{11},{10}^{13}]\mathrm{W}{\mathrm{cm}}^{-2}\mu {\mathrm{m}}^2$ and plasma parameters $Z_{\mathrm{eff}}/T_e\in [0.2,0.6]{\mathrm{eV}}^{-1}$, the electron distributions are predicted to be super-Gaussian of order $m\simeq 2.2–2.4$. As a result, laser absorption is calculated to be $10–20\%$ lower than plasmas with Maxwellian-distributed electrons. A $\sim 10–30\%$ reduction of the Spitzer-Härm thermal conduction coefficient is also predicted.

Echo chamber effects in social networks are generally attributed to the prevalence of interactions among like-minded peers. However, recent evidence has emphasized the role of hostile interactions between opposite-minded groups. We investigate the role of polarization, identified with structural balance, in the formation of echo chambers in signed networks. To do so, we generalize the independent cascade model and the linear threshold model to describe information propagation in presence of negative edges. Antagonistic connections do not disrupt the flow of information, but instead, alter the way information is framed. Our results show that echo chambers spontaneously emerge in balanced networks, but also in antibalanced ones for specific parameters. This highlights that structural polarization and echo chambers do not necessarily display a one-to-one correspondence, showing instead a complex and often counterintuitive interplay. The robustness of our results is confirmed with a complex contagion model and through simulations in different network topologies, including real-world datasets.