Based on the measured data, in this paper, we find that there are significant differences in the ideal speed of drivers with different attributes during their driving process. Through wavelet analysis, it is proved that the regularity of the car-following behavior of the driver is poor in a short time, and it cannot be predicted and analyzed at a small time scale. As one of the important participants in the traffic system, it is necessary to consider the driving behavior factors in the traffic flow model. Therefore, in this paper, we propose a nonuniform continuous traffic flow model. Based on the difference in the expected headway of the driver, the model considers the self-stabilization effect of the prediction time of the driver on the optimal speed difference and considers control theory to further improve the model. Through this model, the bifurcation theory can be applied to the stability analysis of the traffic system to study the stability mutation behavior of the traffic system at the bifurcation point. Through linear and nonlinear analysis methods, the stability conditions of the model can be derived, and the type of equilibrium point of the model can be judged. In addition, the random function is applied to the traffic model, and the bifurcation control is carried out for the bifurcation behavior in the traffic; that is, the bifurcation characteristics of the traffic system are changed by designing linear and nonlinear random feedback controllers. In this paper, we theoretically prove the existence conditions and types of Hopf bifurcation at the equilibrium point of the model and analyze the internal causes of the stability mutation of the traffic flow through the Hopf bifurcation point. Then a feedback controller is designed to control the amplitude of the Hopf bifurcation and the limit cycle formed by the Hopf bifurcation. Finally, the theoretical derivation results are verified by experimental numerical simulation. In this paper, we show that, by adjusting the control parameters of the feedback controller, the Hopf bifurcation of the stochastic system can be delayed or even eliminated, and the amplitude of the limit cycle formed by the Hopf bifurcation can be adjusted to achieve the purpose of controlling the stability of the traffic system and prevent or alleviate traffic congestion.

Community detection is a classic network problem with extensive applications in various fields. Its most common method is using modularity maximization heuristics which rarely return an optimal partition or anything similar. Partitions with globally optimal modularity are difficult to compute, and therefore have been underexplored. Using structurally diverse networks, we compare 30 community detection methods including our proposed algorithm that offers optimality and approximation guarantees: the Bayan algorithm. Unlike existing methods, Bayan globally maximizes modularity or approximates it within a factor. Our results show the distinctive accuracy and stability of maximum-modularity partitions in retrieving planted partitions at rates higher than most alternatives for a wide range of parameter settings in two standard benchmarks. Compared to the partitions from 29 other algorithms, maximum-modularity partitions have the best medians for description length, coverage, performance, average conductance, and well clusteredness. These advantages come at the cost of additional computations which Bayan makes possible for small networks (networks that have up to 3000 edges in their largest connected component). Bayan is several times faster than using open-source and commercial solvers for modularity maximization, making it capable of finding optimal partitions for instances that cannot be optimized by any other existing method. Our results point to a few well-performing algorithms, among which Bayan stands out as the most reliable method for small networks. A python implementation of the Bayan algorithm (bayanpy) is publicly available through the package installer for python.

The low-to-high confinement (L-H) transition signifies one of the important plasma bifurcations occurring in magnetic confinement plasmas, with vital implications for exploring high-performance regimes in future fusion reactors. In particular, the accurate turbulence statistical description of self-regulation and causal relation among turbulence and shear flows is essential for accessing enhanced plasma performance and advanced operation scenarios. To address this, we provide a nonperturbative theory of the L-H transition by stochastic simulations of a reduced L-H transition model and detailed statistical analysis. By calculating time-dependent probability density functions (PDFs) of turbulence, zonal flows, and the mean pressure gradient, we elucidate how statistical properties change over time with the help of the information geometry theory (information rate, causal information rate), highlighting its utility in capturing self-regulation and causal relation among turbulence, zonal flow shears, and the mean flow shears. Furthermore, stochastic noises in turbulence, zonal flows, and/or input power are shown to induce uncertainty in the power threshold $Q_c$ above which the L-H transition occurs while leading to a rather gradual L-H transition. A time-dependent PDF of power loss over the L-H transition is presented.

Pipelining is a design technique for logical circuits that allows for higher throughput than circuits in which multiple computations are fed through the system one after the other. It allows for much faster computation than architectures in which inputs must pass through every layer of the circuit before the next computation can begin (phased chaining). We explore the hypothesis that these advantages may be offset by a higher error rate, logical irreversibility, and greater thermodynamic costs by simulating pipelined molecular mechanical circuits using an explicit physical model. We observe the emergent logical irreversibility, and see that the simultaneous action of multiple components indeed leads to a higher error rate than in phase-chained circuits. The thermodynamic costs of operating the gates are much larger than in equivalent phase-chained circuits, and these costs do not appear to tend to zero in the limit of slowgate operation. Redesigning the gates to eliminate errors and artificially enforcing logical reversibility reduces the thermodynamic costs and recovers thermodynamically reversible behavior in the limit of slow gate operation. The breakdown of logical reversibility and accuracy are both associated with a breakdown of the digital behavior of the device, likely contributing to thermodynamic costs that are large relative to the scale of the information being processed.

A central unsolved problem in percolation theory over the past five decades has been whether there is a direct relationship between the critical exponents that characterize the power-law behavior of the transport properties near the percolation threshold, particularly the effective electrical conductivity ${\sigma }_e$, and the exponents that describe the morphology of percolation clusters. The problem is also relevant to the relation between the static exponents of percolation clusters and the critical dynamics of spin waves in dilute ferromagnets, the elasticity of gels and composite solids, hopping conductivity in semiconductors, solute transport in porous media, and many others. We propose an approach to address the problem by showing that the contributions to ${\sigma }_e$ can be decomposed into several groups representing the structure of percolation networks, including their mass and tortuosity, as well as constrictivity that describes the fluctuations in the driving potential gradient along the transport paths. The decomposition leads to a relationship between the critical exponent $t$ of ${\sigma }_e$ and other percolation exponents in $d$ dimensions, $t/\nu =(d-D_{\mathrm{bb}})+2(D_{\mathrm{op}}-1)+d_C$, where $\nu$, $D_{\mathrm{bb}}$, $D_{\mathrm{op}}$, and $d_C$ are, respectively, the correlation length exponent, the fractal dimensions of the backbones and the optimal paths, and the exponent that characterizes the constrictivity. Numerical simulations in two and three dimensions, as well as analytical results in $d=1$ and $d=6$, the upper critical dimension of percolation, validate the relationship. We, therefore, believe that the solution to the 50-year-old problem has been derived.

This study investigates the anisotropic effects on a system of three qubits with chain and ring topology, described by the antiferromagnetic Heisenberg $XXX$ model subjected to a homogeneous magnetic field. We explore the Stirling and Otto cycles and find that easy-axis anisotropy significantly enhances engine efficiency across all cases. At low temperatures, the ring configuration outperforms the chain on both work and efficiency during the Stirling cycle. Additionally, in both topologies, the Stirling cycle achieves Carnot efficiency with finite work at quantum critical points. In contrast, the quasistatic Otto engine also reaches Carnot efficiency at these points but yields no useful work. Notably, the Stirling cycle exhibits all thermal operational regimes—engine, refrigerator, heater, and accelerator—unlike the quasistatic Otto cycle, which functions only as an engine or refrigerator.

We derive generalized Langevin equations (GLEs) for single beads in linear elastic networks. In particular, the derivations of the GLEs are conducted without employing normal modes, resulting in two distinct representations in terms of resistance and mobility kernels. The fluctuation-dissipation relations are also confirmed for both GLEs. Subsequently, we demonstrate that these two representations are interconnected via Laplace transforms. Furthermore, another GLE is derived by utilizing a projection operator method, and it is shown that the equation obtained through the projection scheme is consistent with the GLE with the resistance kernel. As simple examples, the general theory is applied to the Rouse model and the ring polymer, where the GLEs with the resistance and mobility kernels are explicitly derived for arbitrary positions of the tagged bead in these models. Finally, the GLE with the mobility kernel is also derived for the elastic network with hydrodynamic interactions under the pre-averaging approximation.

Correlation functions are a standard tool for analyzing statistical particle trajectories. Recently, a so-called mean back relaxation (MBR) has been introduced, which correlates positions at three time points. The deviation of its long-time value from $\frac{1}{2}$ has been shown to be a marker for breakage of time-reversal symmetry for confined particles. Here, we extend the analysis of MBR in several ways, including discussion of a cutoff length used when evaluating MBR from trajectory data. Using a path integral approach, we provide a general expression for MBR in terms of multipoint density correlations. For Gaussian systems, this expression yields a relation between MBR and mean-squared displacement. We finally demonstrate that MBR can be applied to other stochastic observables besides particle position. Using it for microscopic densities, its deviation from $\frac{1}{2}$ is a marker for broken detailed balance in confinement or in bulk systems.

This paper investigates the stochastic response of a classical model of the birhythmic Van der Pol oscillator under Poisson white noise excitation. The improved path integration (PI) method is comprehensively derived in this paper and the probability density of the system is calculated using this method. Monte Carlo simulations are employed to validate the accuracy of the improved PI method. The findings reveal that the nonlinear parameters of the system significantly influence the mechanism by which Poisson white noise impacts the birhythmic oscillator. For the stationary response, we compare the effects of Gaussian white noise and Poisson white noise at equivalent intensities, and specifically analyze the mechanisms of two key parameters of Poisson white noise. This analysis offers general insights into the mechanisms by which Poisson noise impacts the birhythmic oscillator. For transient response, the occurrence time of birhythmicity, along with the system's probability distribution at different moments, are influenced by random perturbations, yet the nonlinear parameters of the system remain pivotal factors. This study provides a perspective for investigating the dynamic behavior of birhythmic oscillators under discontinuous stochastic disturbances.

Researchers are drawn to exploring wave dispersion in nonlinear systems because of the amplitude-dependent tunability of the band gap. This paper investigates the amplitude-dependent wave dispersion in continuous beam structures supported periodically by nonlinear springs. Additionally, it examines the influence of inherent beam damping on wave dispersion. The analytical framework consists of homogenization of the unit cell and the method of multiple scales with two distinct time scales to derive the wave dispersion equation. The proposed analytical approach for nonlinear wave propagation is validated through numerical finite element simulations. It is observed that the frequency shift is positive for hardening and negative for softening supports. Following this, the dispersion shift over time in the damped systems is examined by considering viscous and strain rate–dependent damping. The sensitivity of strain rate damping to propagation constant and the independence of viscous damping from propagation constant are thoroughly investigated. In a damped system, the frequency shift diminishes over time as the amplitude decreases reducing the effect of nonlinearity. This study opens up avenues for controlling or filtering vibrations through the tunable band gap of continuous nonlinear metamaterials.

Individual participants in human society collectively exhibit aggregation behavior. In this study, we present a simple microscopic model of labor force migration based on the active Brownian particles framework. In particular, agent-based simulations show that the model produces clusters of agents from a random initial distribution. Furthermore, two empirical regularities called Zipf's and Okun's laws were observed. To reveal the mechanism underlying the reproduced aggregation phenomena, we use our microscopic model to derive an extended Keller-Segel system, which is a classic model describing the aggregation behavior of biological organisms called taxis. The obtained macroscopic system indicates that the concentration of the workforce in the real world can be explained through a new type of taxis central to human behavior, highlighting the relevance of urbanization to blow-up phenomena in the derived PDE system. We then characterize the transition between the aggregation and diffusion regimes both analytically and computationally. The predicted long-term dynamics of urbanization—originating in the asymmetric natures of employed and unemployed agents—are compared with global empirical data, particularly in the realms of labor statistics and urban indicators.

In vitro cell biology experiments are routinely used to characterize cell migration properties under various experimental conditions. These experiments can be interpreted using lattice-based random walk models to provide insight into underlying biological mechanisms, and continuum limit partial differential equation (PDE) descriptions of the stochastic models can be used to efficiently explore model properties instead of relying on repeated stochastic simulations. Working with efficient PDE models is of high interest for parameter estimation algorithms that typically require a large number of forward model simulations. Quantitative data from cell biology experiments usually involve non-negative cell counts in different regions of the experimental images, and it is not obvious how to relate finite, noisy count data to the solutions of continuous PDE models that correspond to noise-free density profiles. In this work, we illustrate how to develop and implement likelihood-based methods for parameter estimation, parameter identifiability, and model prediction for lattice-based models describing collective migration with an arbitrary number of interacting subpopulations. We implement a standard additive Gaussian measurement error model as well as a new physically motivated multinomial measurement error model that relates noisy count data with the solution of continuous PDE models. Both measurement error models lead to similar outcomes for parameter estimation and parameter identifiability, whereas the standard additive Gaussian measurement error model leads to nonphysical prediction outcomes. In contrast, the new multinomial measurement error model involves a lower computational overhead for parameter estimation and identifiability analysis, as well as leading to physically meaningful model predictions.

We present a two-phase field model and a hybrid particle-phase field model to simulate dilute colloidal sedimentation and flotation near a liquid-gas interface (or fluid-fluid interface in general). Both models are coupled to the incompressible Stokes equation, which is solved numerically using a combination of sine and regular Fourier transforms to account for the no-slip boundary conditions at the boundaries. The continuum two-phase field model allows us to analytically solve the equilibrium interfacial profile using a perturbative approach, demonstrating excellent agreement with numerical simulations. Notably, we show that strong coupling to particle dynamics can significantly alter the liquid-gas interface, thereby modifying the liquid-gas interfacial tension. In particular, we show that the renormalized surface tension is monotonically decreasing with increasing colloidal particle concentration and decreasing buoyant mass.

Considering the significant influence of interparticle potentials on traditional depletion forces, we here employ computer simulations to investigate how varying potentials between particles affect the effective interaction of probes diffusing freely in a 2D colloidal crystal. Our results reveal that attractive potentials between the background particles and probes significantly modify the interprobe effective interactions, whereas long-range repulsive tails among the background particles have minimal impact. Furthermore, we observe contrary temperature dependencies of the effective force for soft and stiff repulsions between the background particles. These findings provide deeper insights into how direct interparticle potentials shape entropic-dominated effective forces mediated by colloidal crystals.

Granular materials in nature are nearly always nonspherical, but particle shape effects in granular flow remain largely elusive. This study uses discrete element method simulations to investigate how elongated particle shapes affect the mobility of dense granular flows down a rough incline. For a range of systematically varied particle length-to-diameter aspect ratios (AR), we run simulations with various flow thicknesses $h$ and slope angles $\theta$ to extract the well-known $h_{\text{stop}}\left(\theta \right)$ curves (below which the flow ceases) and the $Fr\text{−}h/h_{\text{stop}}$ relations following Pouliquen's approach, where $Fr=u/\sqrt{gh}$ is the Froude number, $u$ is the mean flow velocity, and $g$ is the gravitational acceleration. The slope $\beta$ of the $Fr\text{−}h/h_{\text{stop}}$ relations shows an intriguing S-shaped dependence on AR, with two plateaus at small and large AR, respectively, transitioning with a sharp increase. We understand this S-shaped dependence by examining statistics of particle orientation, alignment, and hindered rotation. We find that the rotation ability of weakly elongated particles ($\text{AR}\lesssim 1.3$) remains similar to spheres, leading to the first plateau in the $\beta$-AR relation, whereas the effects of particle orientation saturate beyond $\text{AR}\approx 2.0$, explaining the second plateau. An empirical sigmoidal function is proposed to capture this nonlinear dependence. The findings are expected to enhance our understanding of how particle shape affects the flow of granular materials from both the flow- and particle-scale perspectives.

In the domain growth process, small structures gradually vanish, leaving behind larger ones. We investigate spectral energy transfers in two standard models for domain growth: (a) the Cahn-Hilliard (CH) equation with conserved dynamics and (b) the time-dependent Ginzburg-Landau (TDGL) equation with nonconserved dynamics. The nonlinear terms in these equations dissipate fluctuations and facilitate energy transfers among Fourier modes. In the TDGL equation, only the $\varphi (\mathbf{k}=0,t)$ mode survives, and the order parameter $\varphi (\mathbf{r},t)$ approaches a uniform state with $\varphi =+1$ or $-1$. On the other hand, there is no dynamics of the $\varphi (\mathbf{k}=0,t)$ mode in the CH equation due to the conservation law, highlighting the different dynamics of these equations.

Recent years have witnessed a surge of discoveries in the studies of thermodynamic inequalities: the thermodynamic uncertainty relation (TUR) and the entropic bound (EB) provide a lower bound on the entropy production (EP) in terms of nonequilibrium currents; the classical speed limit (CSL) expresses the lower bound on the EP using the geometry of probability distributions; the power-efficiency (PE) tradeoff dictates the maximum power achievable for a heat engine given the level of its thermal efficiency. In this study, we show that there exists a unified hierarchical structure encompassing all of these bounds, with the fundamental inequality given by an extension of the TUR (XTUR) that incorporates the most general range of currentlike and state-dependent observables. By selecting more specific observables, the TUR and the EB follow from the XTUR, and the CSL and the PE tradeoff follow from the EB. Our derivations cover both Langevin and Markov jump systems, with the first proof of the EB for the Markov jump systems and a more generalized form of the CSL. We also present concrete examples of the EB for the Markov jump systems and the generalized CSL.

We study the long-time dynamics in non-Markovian single-population stochastic models, where one or more reactions are modeled as a stochastic process with a fat-tailed nonexponential distribution of waiting times, mimicking long-term memory. We focus on three prototypical examples: genetic switching, population establishment, and population extinction, all with nonexponential production rates. The system is studied in two regimes. In the first, the distribution of waiting times has a finite mean. Here, the system approaches a (quasi)stationary steady state at long times, and we develop a general Wentzel-Kramers-Brillouin approach for these non-Markovian systems. We derive explicit results for the mean population size and mean escape time from the metastable state of the stochastic dynamics. In this realm, we reveal that for sufficiently strong memory, a memory-induced (meta)stable state can emerge in the system. In the second regime, the waiting time distribution is assumed to have an infinite mean. Here, for bistable systems we find two distinct scaling regimes, separated by an exponentially long time which may strongly depend on the initial conditions of the system.

We perform a numerical study of the kinetic Blume-Capel (BC) model to find if it exhibits the metamagnetic anomalies previously observed in the kinetic Ising model for supercritical periods [P. Riego et al., Phys. Rev. Lett. 118, 117202 (2017); G. M. Buendía et al., Phys. Rev. B 96, 134306 (2017)]. We employ a heat-bath Monte Carlo (MC) algorithm on a square lattice in which spins can take values of $\pm 1,0$, with a nonzero crystal field, subjected to a sinusoidal oscillating field in conjunction with a constant bias. In the ordered region, we find an equivalent hysteretic response of the order parameters with its respective conjugate fields between the kinetic and the equilibrium model. In the disordered region (supercritical periods), we observed two peaks, symmetrical with respect to zero bias, in the susceptibility and scaled variance curves, consistent with the numerical and experimental findings on the kinetic Ising model. This behavior does not have a counterpart in the equilibrium model. Furthermore, we find that the peaks occur at higher values of the bias field and become progressively smaller as the density of zeros, or the amplitude of the oscillating field, increases. Using nucleation theory, we demonstrate that these fluctuations, as in the Ising model, are not a critical phenomenon, but that they are associated with a crossover between a single-droplet (SD) and a multidroplet (MD) magnetization switching mechanism. For strong (weak) bias, the SD (MD) mechanism dominates. We also found that the zeros concentrate on the droplets' surfaces, which may cause a reduced interface tension in comparison with the Ising model [M. Schick et al., Phys. Rev. B 34, 1797 (1986)]. Our results suggest that metamagnetic anomalies are not particular to the kinetic Ising model, but rather are a general characteristic of spin kinetic models, and provide further evidence that the equivalence between dynamical phase transitions and equilibrium ones is only valid near the critical point.

There are conflicting reports in the literature regarding the finite-size scaling of the Liouvillian gap and dynamical fluctuations at discontinuous phase transitions, with various studies reporting either exponential or power-law behavior. We clarify this issue by employing large deviation theory. We distinguish two distinct classes of discontinuous phase transitions that have different dynamical properties. The first class is associated with phase coexistence, i.e., the presence of multiple stable attractors of the system dynamics (e.g., local minima of the free-energy functional) in a finite phase diagram region around the phase transition point. In that case, one observes asymptotic exponential scaling related to stochastic switching between attractors (though the onset of exponential scaling may sometimes occur for very large system sizes). In the second class, there is no phase coexistence away from the phase transition point, while at the phase transition point itself there are infinitely many attractors. In that case, one observes power-law scaling related to the diffusive nature of the system relaxation to the stationary state.