We conducted avalanching experiments with an external magnetic field and granular samples of different grain sizes (3.18 mm, 6.35 mm, and 8.73 mm) and different materials (low-carbon steel, alloy steel, stainless steel, and brass). The magnetic field was varied to control the magnetic Bond number (the ratio between the magnetic and the gravitational forces in the system). For each test, we compared the angle of repose and the surface roughness of the material in its postavalanche state. The samples containing only steel beads transitioned through three flow regimes as the magnetic field increased. Initially, the grains flowed freely. Above a threshold magnetic field, the material began to move in clumps, and above a second threshold, it solidified completely. The steel-brass mixtures with low magnetic susceptibilities only transitioned through the first two states. We find that the angle of repose and surface roughness increase linearly with magnetic cohesion in the first regime, but that the trends in the second regime depend on the composition and magnetic susceptibility of the mixture. When the angle of repose and surface roughness are expressed in terms of the magnetic Bond number, the homogeneous samples that vary in grain size and magnetic susceptibility collapse onto a single curve, but the mixtures (i.e., the samples that contain more than one type of material) do not.

This article addresses the stability of a nonlinear electron plasma wave (EPW) against the growth of longitudinal sidebands. The electron distribution function consistent with the EPW is assumed to only depend on the dynamical action. Consequently, the EPW is either stationary (a so-called Berstein-Greene-Kruskal mode) or varies very slowly in space and time (a so-called adiabatic wave). The sideband growth rates and the unstable spectrum are calculated theoretically by accounting for the exact nonlinear electron orbits in the EPW. Our theoretical results are compared against those from previous theories, and also against those from Vlasov simulations when the distribution function is differentiable. The latter comparisons show that our theory may also apply when the electron distribution function depends on, both the action and the angle. Moreover, our theory allows for discontinuous distributions, which are consistent with important classes of EPWs, e.g., those resulting from stimulated Raman scattering. Addressing such distributions using kinetic codes remains a challenge. Nevertheless, using our theoretical results, in this article we discuss the impact of discontinuities on the unstable spectrum in the linear regime, and on the range of validity of the linear approximation.

Physics-based Ising machines (IM) have been developed as dedicated processors for solving hard combinatorial optimization problems with higher speed and better energy efficiency. Generally, such systems employ local search heuristics to traverse energy landscapes in searching for optimal solutions. Here, we quantify and address some of the major challenges met by IMs by extending energy-landscape geometry visualization tools known as disconnectivity graphs. Using efficient sampling methods, we visually capture landscapes of problems having diverse structure and hardness manifesting as energetic and entropic barriers for IMs. We investigate energy barriers, local minima, and configuration space clustering effects caused by locality reduction methods when embedding combinatorial problems to the Ising hardware. To this end, we sample disconnectivity graphs of PUBO energy landscapes and their different QUBO mappings accounting for both local minima and saddle regions. We demonstrate that QUBO energy-landscape properties lead to the subpar performance for quadratic IMs and suggest directions for their improvement.

We propose an efficient sensitivity analysis method for a wide class of colored-noise-driven interacting particle systems (IPSs). Our method is based on unperturbed simulations and significantly extends the Malliavin weight sampling method proposed by Szamel [Europhys. Lett. 117, 50010 (2017)] for evaluating sensitivities such as linear response functions of IPSs driven by simple Ornstein-Uhlenbeck processes. We show that the sensitivity index depends not only on two effective parameters that characterize the variance and correlation time of the noise, but also on the noise spectrum. In the case of a single particle in a harmonic potential, we obtain exact analytical formulas for two types of linear response functions. By applying our method to a system of many particles interacting via a repulsive screened Coulomb potential, we compute the mobility and effective temperature of the system. Our results show that the system dynamics depend, in a nontrivial way, on the noise spectrum.

We consider a model of heat engine operating in the microscopic regime: the two-stroke engine. It produces work and exchanges heat in two discrete strokes that are separated in time. The working body of the engine consists of two $d$-level systems initialized in thermal states at two distinct temperatures. Additionally, an auxiliary nonequilibrium system called catalyst may be incorporated with the working body of the engine, provided the state of the catalyst remains unchanged after the completion of a thermodynamic cycle. This ensures that the work produced by the engine arises solely from the temperature difference. Upon establishing the rigorous thermodynamic framework, we characterize twofold improvement stemming from the inclusion of a catalyst. Firstly, we prove that in the noncatalytic scenario, the optimal efficiency of the two-stroke heat engine with a working body composed of two-level systems is given by the Otto efficiency, which can be surpassed by incorporating a catalyst with the working body. Secondly, we show that incorporating a catalyst allows the engine to operate in frequency and temperature regimes that are not accessible for noncatalytic two-stroke engines. We conclude with a general conjecture about the advantage brought by a catalyst: including the catalyst with the working body always allows to improve efficiency over the noncatalytic scenario for any microscopic two-stroke heat engines. We prove this conjecture for two-stroke engines where the working body is composed of two $d$-level systems initialized in thermal states at two distinct temperatures, as long as the final joint state leading to optimal efficiency in the noncatalytic scenario is not a product state, or at least one of the $d$-level system is not thermal.

Dimensional correspondences have a long history in critical phenomena. Here, we review the effective dimension approach, which relates the scaling exponents of a critical system in $d$ spatial dimensions with power-law decaying interactions $r^{d+\sigma }$ to a local system, i.e., with finite-range interactions, in an effective fractal dimension $d_{\mathrm{eff}}$. This method simplifies the study of long-range models by leveraging known results from their local counterparts. While the validity of this approximation beyond the mean-field level has been long debated, we demonstrate that the effective dimension approach, while approximate for non-Gaussian fixed points, accurately estimates the critical exponents of long-range models with an accuracy typically larger than $97\%$. To do so, we review perturbative renormalization-group (RG) results, extend the approximation's validity using functional RG techniques, and compare our findings with precise numerical data from conformal bootstrap for the two-dimensional Ising model with long-range interactions.

We investigated the dynamical behavior of the Ziff, Gulari, and Barshad model considering the adsorption rates of the carbon monoxide and oxygen molecules on a catalytic surface as a periodic function of time. For a two-dimensional square lattice and using the Monte Carlo simulation method, we found the stationary states of the model for various values of the amplitude and period of oscillation, taking into account different periodic expressions for the adsorption rates. Depending on the values of the parameters of the model, as well as of the form of the periodic adsorption rates, the stationary states can be active or inactive. For each periodic adsorption rate used in this work we determined a phase diagram in the plane amplitude versus period of oscillation. These phase diagrams can exhibit continuous and/or discontinuous lines separating the active phase from the inactive ones, and a nonexpected new discontinuous transition line separating the two absorbing states. Moreover, we also observed that the area of the active phase shows a strong dependence on the way how the periodic adsorption rates are applied on the system, and in specific situations the phase poisoned by oxygen atoms can even disappear.

We discuss the effective diffusion constant $D_{\mathrm{eff}}$ for stochastic processes with spatially dependent noise. Starting from a stochastic process given by a Langevin equation, different drift-diffusion equations can be derived depending on the choice of the discretization rule $0\le \alpha \le 1$. We initially study the case of periodic heterogeneous diffusion without drift, and we determine a general result for the effective diffusion coefficient $D_{\mathrm{eff}}$, which is valid for any value of $\alpha$. We study the case of periodic sinusoidal diffusion in detail, and we find a relationship with Legendre functions. Then we derive $D_{\mathrm{eff}}$ for general $\alpha$ in the case of diffusion with periodic spatial noise and in the presence of a drift term, generalizing the Lifson-Jackson theorem. Our results are illustrated by analytical and numerical calculations on generic periodic choices for drift and diffusion terms.

Here we introduce the non-Hermitian diluted banded random matrix (nHdBRM) ensemble as the set of $N\times N$ real nonsymmetric matrices whose entries are independent Gaussian random variables with zero mean and variance one if $|i-j|<b$ and zero otherwise, moreover off-diagonal matrix elements within the bandwidth $b$ are randomly set to zero such that the sparsity $\alpha$ is defined as the fraction of the $N(b-1)/2$ independent nonvanishing off-diagonal matrix elements. By means of a detailed numerical study we demonstrate that the eigenfunction and spectral properties of the nHdBRM ensemble scale with the parameter $x=\gamma {[{\left(b\alpha \right)}^2/N]}^{\delta }$, where $\gamma ,\delta \sim 1$. Moreover, the normalized localization length $\beta$ of the eigenfunctions follows a simple scaling law: $\beta =x/(1+x)$. For comparison purposes, we also report eigenfunction and spectral properties of the Hermitian diluted banded random matrix ensemble.

Here we introduce simple structures for the analysis of complex hypergraphs, hypergraph animals. These structures are designed to describe the local node neighborhoods of nodes in hypergraphs. We establish their relationships to lattice animals and network motifs, and we develop their combinatorial properties for sparse and uncorrelated hypergraphs. We make use of the tight link of hypergraph animals to partition numbers, which opens up a vast mathematical framework for the analysis of hypergraph animals. We then study their abundances in random hypergraphs. Two transferable insights result from this analysis: (i) it establishes the importance of high-cardinality edges in ensembles of random hypergraphs that are inspired by the classical Erdös-Renyí random graphs; and (ii) there is a close connection between degree and hyperedge cardinality in random hypergraphs that shapes animal abundances and spectra profoundly. Both findings imply that hypergraph animals can have the potential to affect information flow and processing in complex systems. Our analysis also suggests that we need to spend more effort on investigating and developing suitable conditional ensembles of random hypergraphs that can capture real-world structures and their complex dependency structures.

Insight into the blockage vulnerability of evolving spatial networks is important for understanding transport resilience, robustness, and failure of a broad class of real-world structures such as porous media and utility, urban traffic, and infrastructure networks. By exhaustive search for central transport hubs on porous lattice structures, we recursively determine and block the emerging main hub until the evolving network reaches the impenetrability limit. We find that the blockage backbone is a self-similar path with a fractal dimension which is distinctly smaller than that of the universality class of optimal path crack models. The number of blocking steps versus the rescaled initial occupation fraction collapses onto a master curve for different network sizes, allowing for the prediction of the onset of impenetrability. The shortest-path length distribution broadens during the blocking process reflecting an increase of spatial correlations. We address the reliability of our predictions upon increasing the disorder or decreasing the fraction of processed structural information.

We discuss the short-time behavior of the majority vote dynamics on scale-free networks at the critical threshold. A heterogeneous mean-field theory on the critical short-time behavior of the majority-vote model on scale-free networks is introduced. In addition, the heterogeneous mean-field predictions are compared with extensive Monte Carlo simulations of the short-time dependencies of the order parameter and the susceptibility. Closed expressions of the dynamical exponent $z$ and the time correlation exponent ${\nu }_{\parallel }$ are obtained. The short-time scaling is compatible with a nonuniversal critical behavior for $5/2<\gamma <7/2$. However, for $\gamma \ge 7/2$, we have the mean-field Ising criticality with additional logarithmic corrections for $\gamma =7/2$, the same as the stationary scaling.

The ability to actually implement epidemic models is a crucial stake for public institutions, as they may be overtaken by the increasing complexity of current models and sometimes tend to revert to less elaborate models such as the susceptible-infected-recovered (SIR) model. In our work, we study a simple epidemic propagation model, called $\mathrm{SIR}\text{−}k$, which is based on a homogeneous network of degree $k$, where each individual has the same number $k$ of neighbors. This model represents a refined version of the basic SIR which assumes a completely homogeneous population. We show that nevertheless, analytical expressions, simpler and richer than the ones existing for the SIR model, can be derived for this $\mathrm{SIR}\text{−}k$ model. In particular, we obtain an exact implicit analytical solution for any $k$, from which quantities such as the epidemic threshold or the total number of agents infected during the epidemic can be obtained. We furthermore obtain simple exact explicit solutions for small $k\mathrm{s}$, and in the large $k$ limit we find a new formulation of the analytical solution of the basic SIR model, which comes with new insights.

Multiphase field models have emerged as an important computational tool for understanding biological tissue while resolving single-cell properties. While they have successfully reproduced many experimentally observed behaviors of living tissue, the theoretical underpinnings have not been fully explored. We show that a two-dimensional version of the model, which is commonly employed to study tissue monolayers, can be derived from a three-dimensional version in the presence of a substrate. We also show how viscous forces, which arise from friction between different cells, can be included in the model. Finally, we numerically simulate a tissue monolayer and find that intercellular friction tends to solidify the tissue.

We discuss and compare the statistical properties of two stochastic three-sphere micromachines, i.e., odd micromachine and thermal micromachine. We calculate the steady state time-correlation functions for these micromachines and decompose them into symmetric and antisymmetric parts. In both models, the cross-correlation between the two spring extensions has an antisymmetric part, which is a direct consequence of the broken time-reversal symmetry. For the odd micromachine, the antisymmetric part of the correlation function is proportional to the odd elasticity, whereas it is proportional to the temperature difference between the two edge spheres for the thermal micromachine. The entropy production rate and the Green-Kubo relations for the two micromachines are also obtained. Comparing the results of the two models, we argue an effective odd elastic constant of the thermal micromachine. We find that it is proportional to the temperature difference among the spheres, which causes an internal heat flow and leads to directional locomotion in the presence of hydrodynamic interactions.

Generalizing recent work on isotropic tensor fields in isotropic and achiral condensed matter systems from two to arbitrary dimensions we address both mathematical aspects assuming perfectly isotropic systems and applications focusing on correlation functions of displacement and strain field components in amorphous solids where isotropy may not hold. Various general points are exemplified using simulated polydisperse Lennard-Jones particles. It is shown that the strain components in reciprocal space have essentially a complex circularly symmetric Gaussian distribution albeit weak non-Gaussianity effects become visible for large wave numbers $q$ where also anisotropy effects become relevant. The dynamical strain correlation functions are strongly nonmonotonic with respect to $q$ with a minimum roughly at the breakdown of the continuum limit.

The relaxation of a weakly collisional plasma, which is of fundamental interest to laboratory astrophysical plasmas, can be described by the self-consistent Boltzmann-Poisson equations with the Lenard-Bernstein collision operator. We perform a perturbative (linear and second-order) analysis of the Boltzmann-Poisson equations and obtain exact analytic solutions which resolve some longstanding controversies regarding the impact of weak collisions on the continuous spectra, the discrete Landau eigenmodes, and the decay of plasma echoes. We retain both damping and diffusion terms in the collision operator throughout our treatment. We find that the linear response is a temporal convolution of two types of contribution: a continuum that depends on the continuous velocities of particles (crucial for the plasma echo), and another, consisting of discrete modes that are coherent modes of oscillation of the entire system. The discrete modes are exponentially damped over time due to collective effects or wave-particle interactions (Landau damping), as well as collisional dissipation. The continuum is also damped by collisions but somewhat differently than the discrete modes. Up to a collision time, which is the inverse of the collision frequency ${\nu }_{\mathrm{c}}$, the continuum decay is driven by the diffusion of particle velocities and is cubic exponential, occurring over a timescale $\sim {\nu }_{\mathrm{c}}^{-1/3}$. After a collision time, however, the continuum decay is driven by the collisional damping of particle velocities and diffusion of their positions and occurs exponentially over a timescale $\sim {\nu }_{\mathrm{c}}$. This slow exponential decay causes perturbations to damp the most on scales comparable to the mean free path but very slowly on larger scales. This establishes the local thermal equilibrium, which is the essence of the fluid limit. The long-term decay of the linear response is driven by the discrete modes on scales smaller than the mean free path but, on larger scales, is governed by a combination of the slowly decaying continuum and the least damped discrete mode. This slow exponential decay implies that the echo, which results from the interference of the continuum response to two subsequent pulses, is detectable even on scales comparable to the mean free path, as long as the second pulse is introduced within a few phase-mixing timescales after the first.

In this work, we aim to unveil the general correlations between the performance of a physical reservoir computing (RC) system and the inherent nonlinear dynamics of the adopted device. Taking the metal-ferroelectric-metal (MFM) capacitor, one of the most popular candidate devices for compute-in-memory (CIM) technology, as the computational platform, we construct a nonlinear dynamical model of polarization in the ferroelectric layer. We then design the physical RC utilizing a single and/or an array of MFM capacitors by analyzing the model's stability and feasible dynamical cases. Subsequently, both the initial task and benchmark are numerically conducted to verify the designed RC's superiority. It is proven that by selecting an appropriate dynamical case, the RC can achieve a recognition rate as high as 96.13%, surpassing the results reported in previous work. Finally, we discuss how these key parameters play their role in the RC's performance from the perspective of affecting the system's transient responses, nonlinearity, and short-fading memory. This work paves the foundation for designing highly efficient reservoir computing based on MFM capacitors as well as other memristive devices such as memristors, tunneling diodes, etc.

This study provides a comprehensive analysis of the ground state and thermodynamic properties of a spin-pseudospin chain representing a model of a one-dimensional dilute magnet with two types of nonmagnetic charged impurities. For this purpose, a method utilizing the transfer-matrix properties is employed. Despite the wide variety of intriguing frustrated phase states, we show that the model showcases pseudotransitions solely between simple charge and magnetic quasiorders. These pseudotransitions are characterized by distinct features in the thermodynamic and magnetic quantities, resembling first- and second-order phase transitions. In addition to pseudotransitions for the “pure” system, similar to those observed in other one-dimensional spin models, this study also reveals the presence of “second-order” pseudotransitions for the dilute case. We show that the nature of these discovered pseudotransitions is associated with the phase separation in the chain into regions of (anti)ferromagnetic and charge-ordered phases. The ability to compare the results of an exact transfer-matrix calculation with a simple phenomenological description within the framework of Maxwell construction contributes to a deeper understanding of both the physical mechanisms underlying this phenomenon and the analytical methods used.

It is well established that neural mass models (NMMs) can effectively simulate the mesoscopic and macroscopic dynamics of electroencephalography (EEG), including epileptic EEG. However, the use of NMMs to gain insight on the neuronal system by parameter estimation is hampered by their high dimensionality and the lack of knowledge on what NMM parameters can be reliably estimated. In this article, we analyze the parameter sensitivity of the Jansen and Rit NMM (JR NMM) in order to identify the most sensitive JR-NMM parameters for reliable parameter estimation from EEG data. We then propose a Bayesian approach for estimating the JR-NMM states and parameters based on an expectation-maximization algorithm combined with the unscented Kalman smoother (UKS EM). Global sensitivity analysis methods including the Morris method and the Sobol method are used to perform sensitivity analysis. Results from both the Morris and the Sobol method show that the average inhibitory synaptic gain, $B$, and the reciprocal of the time constant of the average inhibitory postsynaptic potentials, $b$, have a significant impact on the JR-NMM output along with having the least interaction with other model parameters. The UKS-EM method for estimating the parameters $B$ and $b$ is validated using simulations under varying levels of measurement noise. Finally we apply the UKS-EM algorithm to intracranial EEG data from 16 epileptic patients. Our results, both at individual and group level show that the parameters $B$ and $b$ change significantly between the preseizure and seizure period, and between the seizure and postseizure period, with the transition to seizure characterized by a decrease in the average $B$, and the high frequency activity in seizure characterized by an increase in $b$. These results establish a sensitivity analysis guided Bayesian parameter estimation as a powerful tool for reducing the parameter space of high-dimensional NMMs enabling reliable and efficient estimation of the most sensitive NMM parameters, with the potential for online and fast tracking of NMM parameters in applications such as seizure tracking and control.