We introduce branching annihilating attracting walk (BAAW) in one dimension. The attracting walk is implemented by a biased hopping in such a way that a particle prefers hopping to a nearest neighbor located on the side where the nearest particle is found within the range of attraction. We study the BAAW with four offspring by extensive Monte Carlo simulation. At first, we find the critical exponents of the BAAW with infinite range of attraction, which are different from those of the directed Ising (DI) universality class. Our results are consistent with the recent observation [Daga and Ray, Phys. Rev. E 99, 032104 (2019)]. Then, by studying crossover behaviors, we show that as far as the range of attraction is finite the BAAW belongs to the DI class. We conclude that the origin of non-DI critical behavior of the BAAW with infinite range of attraction is the long-range nature of the attraction.

We analyze the structure and stickiness in the chaotic components of generic Hamiltonian systems with divided phase space. Following the method proposed recently in Lozej and Robnik [Phys. Rev. E 98, 022220 (2018)], the sticky regions are identified using the statistics of recurrence times of a single chaotic orbit into cells dividing the phase space into a grid. We perform extensive numerical studies of three example systems: the Chirikov standard map, the family of Robnik billiards, and the family of lemon billiards. The filling of the cells is compared to the random model of chaotic diffusion, introduced in Robnik et al. [J. Phys. A: Math. Gen. 30, L803 (1997)] for the description of transport in the phase spaces of ergodic systems. The model is based on the assumption of completely uncorrelated cell visits because of the strongly chaotic dynamics of the orbit and the distribution of recurrence times is exponential. In generic systems the stickiness induces correlations in the cell visits. The distribution of recurrence times exhibits a separation of timescales because of the dynamical trapping. We model the recurrence time distributions to cells inside sticky areas as a mixture of exponential distributions with different decay times. We introduce the variable $S$, which is the ratio between the standard deviation and the mean of the recurrence times as a measure of stickiness. We use $S$ to globally assess the distributions of recurrence times. We find that in the bulk of the chaotic sea $S=1$, while $S>1$ in areas of stickiness. We present the results in the form of animated grayscale plots of the variable $S$ in the largest chaotic component for the three example systems, included as supplemental material to this paper.

The generalized Lotka-Volterra (gLV) equations are a mathematical proxy for ecological dynamics. We focus on a gLV model of the gut microbiome, in which the evolution of the gut microbial state is determined in part by pairwise interspecies interaction parameters that encode environmentally mediated resource competition between microbes. We develop an in silico method that controls the steady-state outcome of the system by adjusting these interaction parameters. This approach is confined to a bistable region of the gLV model. In this method, a dimensionality reduction technique called steady-state reduction (SSR) is first used to generate a two-dimensional (2D) gLV model that approximates the high-dimensional dynamics on the 2D subspace spanned by the two steady states. Then a bifurcation analysis of the 2D model analytically determines parameter modifications that drive an initial condition to a target steady state. This parameter modification of the reduced 2D model guides parameter modifications of the original high-dimensional model, resulting in a change of steady-state outcome in the high-dimensional model. This control method, called SSR-guided parameter change (SPARC), bypasses the computational challenge of directly determining parameter modifications in the original high-dimensional system. SPARC could guide the development of indirect bacteriotherapies, which seek to change microbial compositions by deliberately modifying gut environmental variables such as gut acidity or macronutrient availability.

Three-dimensional “particle in cell” simulations show that a quasistatic magnetic field can be generated in a plasma irradiated by a linearly polarized Laguerre-Gauss beam with a nonzero orbital angular momentum (OAM). Perturbative analysis of the electron dynamics in the low intensity limit and detailed numerical analysis predict a laser to electrons OAM transfer. Plasma electrons gain angular velocity thanks to the dephasing process induced by the combined action of the ponderomotive force and the laser induced–radial oscillation. Similar to the “direct laser acceleration,” where Gaussian laser beams transmit part of its axial momentum to electrons, Laguerre-Gaussian beams transfer a part of their orbital angular momentum to electrons through the dephasing process.

We present a theoretical study of the spatiotemporal antiresonance in a system of two diffusively coupled chemical reactions, one of which is driven by an external periodic forcing. Although antiresonance is well known in various physical systems, the phenomenon in coupled chemical reactions has largely been overlooked. Based on the linearized dynamics around the steady state of the two-component coupled reaction-diffusion systems we have derived the general analytical expressions for the amplitude-frequency response functions of the driven and undriven components of the system. Our theoretical analysis is well corroborated by detailed numerical simulations on coupled Gray-Scott reaction-diffusion systems exhibiting antiresonance dip in the amplitude-frequency response curve as a result of destructive interference between the coupling and the periodic external forcing imparting differential stability of the two subsystems. This leads to the emergence of spatiotemporal patterns in an undriven subsystem, while the driven one settles down to a homogeneously stable steady state.

A collection of self-propelled particles (SPPs) shows coherent motion and exhibits a true long-range-ordered state in two dimensions. Various studies show that the presence of spatial inhomogeneities can destroy the usual long-range ordering in the system. However, the effects of inhomogeneity due to the intrinsic properties of the particles are barely addressed. In this paper we consider a collection of polar SPPs moving at inhomogeneous speed (IS) on a two-dimensional substrate, which can arise due to varying physical strengths of the individual particles. To our surprise, the IS not only preserves the usual long-range ordering present in homogeneous speed models but also induces faster ordering in the system. Furthermore, the response of the flock to an external perturbation is also faster, compared to the Vicsek-like model systems, due to the frequent update of neighbors of each SPP in the presence of the IS. Therefore, our study shows that an IS can promote information transfer in a moving flock.

Electrostatic theory preserves charges, but allows dipolar excitations. Elasticity theory preserves dipoles, but allows quadrupolar (Eshelby-like) plastic events. Charged amorphous granular systems are interesting in their own right; here we focus on their plastic instabilities and examine their mechanical response to external strain and to an external electric field, to expose the competition between elasticity and electrostatics. In this paper a generic model is offered, its mechanical instabilities are examined, and a theoretical analysis is presented. Plastic instabilities are discussed as saddle-node bifurcations that can be fully understood in terms of eigenvalues and eigenfunctions of the relevant Hessian matrix. This system exhibits moduli that describe how electric polarization and stress are influenced by strain and the electric field. Theoretical expression for these moduli are offered and compared to the measurements in numerical simulations.

Neural-network quantum states have shown great potential for the study of many-body quantum systems. In statistical machine learning, transfer learning designates protocols reusing features of a machine learning model trained for a problem to solve a possibly related but different problem. We propose to evaluate the potential of transfer learning to improve the scalability of neural-network quantum states. We devise and present physics-inspired transfer learning protocols, reusing the features of neural-network quantum states learned for the computation of the ground state of a small system for systems of larger sizes. We implement different protocols for restricted Boltzmann machines on general-purpose graphics processing units. This implementation alone yields a speedup over existing implementations on multicore and distributed central processing units in comparable settings. We empirically and comparatively evaluate the efficiency (time) and effectiveness (accuracy) of different transfer learning protocols as we scale the system size in different models and different quantum phases. Namely, we consider both the transverse field Ising and Heisenberg $XXZ$ models in one dimension, as well as in two dimensions for the latter, with system sizes up to 128 and $8\times 8$ spins. We empirically demonstrate that some of the transfer learning protocols that we have devised can be far more effective and efficient than starting from neural-network quantum states with randomly initialized parameters.

This Rapid Communication highlights the physical processes at the origin of the constitutive law of dense granular flows. In simulated plane shear flows, we present a micro-mechanical expression for the phenomenological friction law $\mu \left(\mathcal{I}\right)$. The expression highlights two distinct pathways for momentum transport—through either balanced contact forces or grain micro-acceleration. We show that these two rate-dependent processes control and explain the friction law. This understanding may help advance rheological models for granular materials and other soft materials such as emulsions and suspensions.

Thermal fluctuations are not large enough to lead to state changes in granular materials. However, in many cases, such materials do achieve reproducible bulk properties, suggesting that they are controlled by an underlying statistical mechanics analogous to thermodynamics. While themodynamic descriptions of granular materials have been explored, they have not yet been concretely connected to their underlying statistical mechanics. We make this connection concrete by providing a first-principles derivation of the multiplicity and thus the entropy of the force networks in granular packings. We directly measure the multiplicity of force networks using a protocol based on the phase space volume of allowed force configurations. Analogous to Planck's constant, we find a scale factor, $h_f$, that discretizes this phase space volume into a multiplicity. To determine this scale factor, we measure angoricity over a wide range of pressures using the method of overlapping histograms and find that in the absence of a fundamental quantum scale it is set solely by the system size and dimensionality. This concretely links thermodynamic approaches of angoricity with the microscopic multiplicity of the force network ensemble.

We present a general framework to study the distribution of the flux through the origin up to time $t$, in a noninteracting one-dimensional system of particles with a step initial condition with a fixed density $\rho$ of particles to the left of the origin. We focus principally on two cases: (i) particles undergoing diffusive dynamics (passive case) and (ii) run-and-tumble dynamics for each particle (active case). In analogy with disordered systems, we consider the flux distribution for both the annealed and the quenched initial conditions, for passive and active particles. In the annealed case, we show that, for arbitrary particle dynamics, the flux distribution is a Poissonian with a mean $\mu \left(t\right)$ that we compute exactly in terms of the Green's function of the single-particle dynamics. For the quenched case, we show that, for the run-and-tumble dynamics, the quenched flux distribution takes an anomalous large-deviation form at large times, $P_{\mathrm{qu}}(Q,t)\sim exp\left[-\rho v_0\gamma t^2{\psi }_{\mathrm{RTP}}\left(\frac{Q}{\rho v_{0}t}\right)\right]$, where $\gamma$ is the rate of tumbling and $v_0$ is the ballistic speed between two successive tumblings. In this paper, we compute the rate function ${\psi }_{\mathrm{RTP}}\left(q\right)$ and show that it is nontrivial. Our method also gives access to the probability of the rare event that, at time $t$, there is no particle to the right of the origin. For diffusive and run-and-tumble dynamics, we find that this probability decays with time as a stretched exponential, $\sim exp(-c\sqrt{t})$, where the constant $c$ can be computed exactly. We verify our results for these large deviations by using an importance sampling Monte Carlo method.

We propose the Wishart planted ensemble, a class of zero-field Ising models with tunable algorithmic hardness and specifiable (or planted) ground state. The problem class arises from a simple procedure for generating a family of random integer programming problems with specific statistical symmetry properties but turns out to have intimate connections to a sign-inverted variant of the Hopfield model. The Hamiltonian contains only 2-spin interactions, with the coupler matrix following a type of Wishart distribution. The class exhibits a classical first-order phase transition in temperature. For some parameter settings the model has a locally stable paramagnetic state, a feature which correlates strongly with difficulty in finding the ground state and suggests an extremely rugged energy landscape. We analytically probe the ensemble thermodynamic properties by deriving the Thouless-Anderson-Palmer equations and free energy and corroborate the results with a replica and annealed approximation analysis; extensive Monte Carlo simulations confirm our predictions of the first-order transition temperature. The class exhibits a wide variation in algorithmic hardness as a generation parameter is varied, with a pronounced easy-hard-easy profile and peak in solution time towering many orders of magnitude over that of the easy regimes. By deriving the ensemble-averaged energy distribution and taking into account finite-precision representation, we propose an analytical expression for the location of the hardness peak and show that at fixed precision, the number of constraints in the integer program must increase with system size to yield truly hard problems. The Wishart planted ensemble is interesting for its peculiar physical properties and provides a useful and analytically transparent set of problems for benchmarking optimization algorithms.

Recent years have seen an increasing interest in quantum chaos and related aspects of spatially extended systems, such as spin chains. However, the results are strongly system dependent: generic approaches suggest the presence of many-body localization, while analytical calculations for certain system classes, here referred to as the “self-dual case,” prove adherence to universal (chaotic) spectral behavior. We address these issues studying the level statistics in the vicinity of the latter case, thereby revealing transitions to many-body localization as well as the appearance of several nonstandard random-matrix universality classes.

We present experiments on multiple pinned self-propelled camphor ribbons, which is a rectangular piece of paper with camphor infused in its matrix. Experiments were performed on three, four, and five ribbons placed in linear and polygonal geometries. The pinned ribbons rotate on the surface of water, due to the surface tension gradient introduced by the camphor layer in the neighborhood of the ribbon. This camphor layer leads to a chemical coupling between the ribbons. In different geometries, the ribbons have been observed to rotationally synchronize in all the possible configurations. A numerical model, emulating the interactions between the ribbons as Yukawa interaction was studied, which was qualitatively able to reproduce the experimental findings.

In the classical susceptible-infected-susceptible (SIS) model, a disease or infection spreads over a given, mostly fixed graph. However, in many real complex networks, the topology of the underlying graph can change due to the influence of the dynamical process. In this paper, besides the spreading process, the network adaptively changes its topology based on the states of the nodes in the network. An entire class of link-breaking and link-creation mechanisms, which we name Generalized Adaptive SIS (G-ASIS), is presented and analyzed. For each instance of G-ASIS using the complete graph as initial network, the relation between the epidemic threshold and the effective link-breaking rate is determined to be linear, constant, or unknown. Additionally, we show that there exist link-breaking and link-creation mechanisms for which the metastable state does not exist. We confirm our theoretical results with several numerical simulations.

The equations governing lipid membrane dynamics in planar, spherical, and cylindrical geometries are presented here. Unperturbed and first-order perturbed equations are determined and nondimensionalized. In membrane systems with a nonzero base flow, perturbed in-plane and out-of-plane quantities are found to vary over different length scales. A new dimensionless number, named the Scriven-Love number, and the well-known Föppl–von Kármán number result from a scaling analysis. The Scriven-Love number compares out-of-plane forces arising from the in-plane, intramembrane viscous stresses to the familiar elastic bending forces, while the Föppl–von Kármán number compares tension to bending forces. Both numbers are calculated in past experimental works, and span a wide range of values in various biological processes across different geometries. In situations with large Scriven-Love and Föppl–von Kármán numbers, the dynamical response of a perturbed membrane is dominated by out-of-plane viscous and surface tension forces—with bending forces playing a negligible role. Calculations of non-negligible Scriven-Love numbers in various biological processes and in vitro experiments show in-plane intramembrane viscous flows cannot generally be ignored when analyzing lipid membrane behavior.

We investigate in free-standing smectic films coalescence of holes (circular regions with thickness smaller than the surrounding film). This process can be considered as a two-dimensional analog of coalescence of bubbles in a three-dimensional fluid. A high speed video camera was used to study the evolution of domains at different stages of coalescence. Special attention was given to investigations of the dependence of the size of the bridge between two holes at the initial stage of coalescence, which was considered in numerous theoretical works and bears information on the coalescence mechanism. It is established that the scaling law is applicable for the description of the transformation of bridges for holes of different radius $R$. We found that in the regime corresponding to the experimental situation the length of the bridge $H$ increases with the scaling law $H/R={\left(t/{\tau }_R\right)}^{1/2}$. The characteristic time ${\tau }_R$ determined from the scaling law is larger than the theoretical time, which can be connected with dissipation of energy both in the film and inside the holes.

We analyze stress distributions in a two-dimensional bidisperse cemented granular packing for a broad range of the values of particle-size ratio, the volumes of large and small particles, and the amount of cementing matrix. In such textured porous materials, the stress concentration, which controls the fracture and fragmentation of the material under tensile loading or in grinding processes, reflects not only the porosity but also the contact network of the particle phase and the resulting stress chains. By means of peridynamic simulations under tensile loading, we show how both the texture and stress distribution depend on size ratio, volume ratio, and the amount of the cementing matrix. In particular, the volume fraction of the class of small particles plays a key role in homogenizing stresses across the system by reducing porosity. Interestingly, the texture controls not only the porosity but also the distribution of pores inside the system with its statistical variability, found to be strongly correlated with the homogeneity of stresses inside the large particles. The most homogeneous stress distribution occurs for the largest size ratio and largest volume fraction of small particles, corresponding to the lowest pore size dispersion and the cushioning effect of small particles and its similar role to the binding matrix for stress redistribution across the packing. At higher porosity, the tensile stresses above the mean stress fall off exponentially in all phases with an exponent that strongly depends on the texture. The exponential part broadens with decreasing matrix volume fraction and particle-size ratio. These correlations reveal the strong interplay between size polydispersity and the cohesive action of the binding matrix for stress distribution, which is significant for the behavior of textured materials in grinding operations.

The dynamics of amorphous granular matter with frictional interactions cannot be derived in general from a Hamiltonian and therefore displays oscillatory instabilities stemming from the onset of complex eigenvalues in the stability matrix. These instabilities were discovered in the context of one- and two-dimensional systems, while the three-dimensional case was never studied in detail. Here we fill this gap by deriving and demonstrating the presence of oscillatory instabilities in a three-dimensional granular packing. We study binary assemblies of spheres of two sizes interacting via classical Hertz and Mindlin force laws for the longitudinal and tangent interactions, respectively. We formulate analytically the stability matrix in three dimensions and observe that a couple of complex eigenvalues emerge at the onset of the instability as in the case of frictional disks in two dimensions. The dynamics then shows oscillatory exponential growth in the mean-square displacement, followed by a catastrophic event in which macroscopic portions of mechanical stress and energy are lost. The generality of these results for any choice of forces that break the symplectic Hamiltonian symmetry is discussed.

Atom-in-jellium calculations of the Einstein frequency were used to calculate the mean displacement of an ion over a wide range of compression and temperature. Expressed as a fraction of the Wigner-Seitz radius, the displacement is a measure of the asymptotic freedom of the ion at high temperature, and thus of the change in heat capacity from six to three quadratic degrees of freedom per atom. A functional form for free energy was proposed based on the Maxwell-Boltzmann distribution as a correction to the Debye free energy, with a single free parameter representing the effective density of potential modes to be saturated. This parameter was investigated using molecular dynamics simulations, and found to be $\sim 0.2$ per atom. In this way, the ion-thermal contribution can be calculated for a wide-range equation of state (EOS) without requiring a large number of molecular dynamics simulations. Example calculations were performed for carbon, including the sensitivity of key EOS loci to ionic freedom.