Physical review. E最新文献

Higher-order dynamics are essential for maintaining species diversity in ecological systems. In this paper, we examine how intraspecific competition affects interspecific interactions within spatially embedded hyperlattice frameworks. We thoroughly analyze their impact on conserving biodiversity by including higher-order competitive processes. Extensive numerical simulations show that increased higher-order competition significantly boosts biodiversity, even with higher mobility. The snapshot analyses further identify four distinct spatial patterns resulting from species interactions: regular pattern formation, two-species dominance, spiral wave structures, and single-species dominance. These results emphasize the key role of higher-order competitive interactions in shaping and stabilizing ecological diversity.

We study single-variable approaches for describing stochastic dynamics with small inertia. The basic models we deal with describe passive Brownian particles and phase elements (phase oscillators, rotators, superconducting Josephson junctions) with an effective inertia in the case of a linear dissipation term and active Brownian particles in the case of a nonlinear dissipation. Elimination of a fast variable (velocity) reduces the characterization of the system state to a single variable and is formulated in four representations: moments, cumulants, the basis of Hermite functions, and the formal cumulant variant of the last. This elimination provides rigorous mathematical description for the overdamped limit in the case of linear dissipation and the overactive limit of active Brownian particles. For the former, we derive a low-dimensional equation system which generalizes the Ott-Antonsen Ansatz to systems with small effective inertia. In the latter case, we derive a Fokker-Planck-type equation with a forced drift term and an effective diffusion in one dimension, where the standard two- and three-dimensional mechanism is impossible. In the four considered representations, truncated equation chains are demonstrated to be utilitary for numerical simulation for a small finite inertia.

Growing evidence suggests that the macroscopic functional states of urban road networks exhibit multistability and hysteresis, but microscopic mechanisms underlying these phenomena remain elusive. Here, we demonstrate that in real-world road networks, the recovery process of congested roads is not spontaneous, as assumed in existing models, but is hindered by connected congested roads, and such hindered recovery can lead to the emergence of multistability and hysteresis in urban congestion dynamics. By analyzing real-world urban traffic data, we observed that congestion propagation between individual roads is well described by a simple contagion process as an epidemic, but the recovery rate of a congested road decreases drastically by the congestion of the adjacent roads unlike an epidemic. Based on this microscopic observation, we proposed a simple model of congestion propagation and dissipation, and found that our model shows a discontinuous phase transition between macroscopic functional states of road networks when the recovery hindrance is strong enough through a mean-field approach and numerical simulations. Our findings shed light on an overlooked role of recovery processes in the collective dynamics of failures in networked systems.

We present a machine-learning method for data-driven synchronization of rhythmic spatiotemporal patterns in reaction-diffusion systems. Extending the phase autoencoder [Yawata et al., Chaos 34, 063111 (2024)1054-150010.1063/5.0205718] for low-dimensional oscillators, we develop a framework to map high-dimensional field variables of the reaction-diffusion system to low-dimensional latent variables characterizing the asymptotic phase and amplitudes of the field variables. This yields a reduced phase description of the limit cycle underlying the rhythmic spatiotemporal dynamics in a data-driven manner. We propose a method to drive the system along the tangential direction of the limit cycle, enabling phase control without inducing amplitude deviations. With examples of 1D oscillating spots and 2D spiral waves in the FitzHugh-Nagumo reaction-diffusion system, we show that the method achieves rapid synchronization in both reference-based and coupling-based settings. These results demonstrate the potential of data-driven phase description based on the phase autoencoder for synchronization of high-dimensional spatiotemporal dynamics.

We present a demonstration of finite-time gradient blow-ups in Israel-Stewart (IS) theories with 1+1D plane symmetry, mathematically showing the existence of smooth initial data that can evolve into shocks across three regimes: pure bulk viscosity, shear viscosity, and diffusion. Through numerical simulations of bulk-viscous fluids, we verify that these shocks satisfy Rankine-Hugoniot conditions, exhibit characteristic velocity crossing (the Mach number obeys M_{u}>1>M_{d}), and maintain thermodynamic consistency, required for physical shocks. Our results reveal a crucial early-time dynamical phase where nonlinear effects dominate viscous damping, resolving the apparent impossibility of IS-type theories predicting shock formation. While restricted to simplified 1+1D systems with separate viscous effects, this work establishes foundational insights for shock formation in relativistic viscous hydrodynamics, highlighting critical challenges for extending to 3+1D systems or to a full IS theory where multiple nonlinear modes interact. The findings emphasize that both initial data structure and numerical methodology require careful consideration when studying shocks in relativistic viscous fluids.

In this work, we investigate the relationship between the Seebeck coefficient (S), and the differential entropy per particle (DEP, s), as a tool for characterizing charge carriers in two-dimensional systems. Using armchair silicene nanoribbons as a model platform, we analyze how both quantities and their ratio depend on chemical potential at room temperature. While the Seebeck coefficient captures transport properties through the energy dependence of the electronic transmission, the DEP is directly connected to the system's electronic entropy, offering a direct thermodynamic alternative for estimating S. We evaluate these transport-thermodynamic properties considering diverse ribbon widths, defining metallic and semiconducting regimes. We find both quantities S and s, are highly interconnected within the ribbon's band gap energy region, and their ratio s/S converges to the elementary charge e across that energy window, fulfilling the Kelvin formula S=s/e. On the contrary, s/S is undefined for gapless ribbons in the energy window of the first transmission channel. These results establish the ratio between the DEP and the Seebeck coefficient as a reliable and complementary probe for the determination of the elementary charge, and to identify the cleanness of electronic band gaps as s/S matches with e.

Rotating equilibrated systems are widespread, but relatively little attention has been devoted to studying them from the first principles of statistical mechanics. We fill this gap by studying a Brownian particle coupled with a thermal bath made of rotating harmonic oscillators. We show that the Langevin equation that describes the dynamics of the Brownian particle contains (due to rotation) long-range correlated noise. In contrast to the usual situation of (nonrotating) equilibration, the rotating Gibbs distribution is recovered only for a weak coupling with the bath. In the presence of a uniform magnetic field, the stationary state is not Gibbsian, even under weak coupling. In this context, we clarify the applicability of the Bohr-van Leeuwen theorem to classical systems in rotating equilibrium, as well as the concept of work done by a changing magnetic field. We show that the Brownian particle under a rotationally symmetric potential reaches a stationary state that behaves as an effective equilibrium, characterized by a free energy. As a result, no work can be extracted via cyclic processes that respect the rotation symmetry. However, if the external potential exhibits asymmetry, then work extraction via slow cyclic processes is possible. This is illustrated by a general scenario involving a slow rotation of a non-rotation-symmetric potential. We study sedimentation equilibrium and show that centrifugal instability is prevented by a finite friction.

This study combines broadband dielectric spectroscopy experiments with molecular dynamics (MD) simulations to investigate the impact of nanoparticle (NP) inclusions on pretransitional phenomena in liquid-crystal (LC) systems, specifically focusing on the relationship between nanoparticles, topological defects, and prenematic behavior. Our experimental results, using SiO_{2}-doped 4-Cyano-4'-pentylbiphenyl composites, demonstrate that while NP additions do not significantly alter the isotropic-nematic transition temperature (T_{c}), prenematic effects exhibit universal behavior, confirmed by identical critical exponents across all samples. This indicates that the fundamental character of prenematic fluctuations remains unperturbed by the nanoparticles at these concentrations. Crucially, the observed systematic decrease in dielectric permittivity with increasing NP concentration is elucidated by MD simulations. These simulations reveal that nanoparticles act as "seeds" for topological defects, specifically forcing the surrounding LC molecules into a "hedgehog" configuration. This static, defect-induced structure leads to a local antiparallel alignment and cancellation of molecular dipoles. This provides a direct microscopic mechanism for the macroscopic dielectric response, successfully bridging the micro-macro scales and highlighting the nanoparticle-induced local ordering as a key factor in modifying the dielectric properties of the composite system.

Stressed under a constant load, materials creep with a final acceleration of deformation and for any given applied stress and material, the creep failure time can strongly vary. We investigate creep on sheets of paper and confront the statistics with a simple fiber bundle model of creep failure in a disordered landscape. In the experiments, acoustic emission event times t_{j} were recorded, and both this data and simulation event series reveal sample-dependent history effects with log-normal statistics and non-Markovian behavior. This leads to a relationship between t_{j} and the failure time t_{f} with a power law relationship, evolving with time. These effects and the predictability result from how the energy gap distribution develops during creep.

In eukaryotic cells, the nucleolus is a pivotal subnuclear organelle, instrumental in ribosomal RNA synthesis and nuclear organization. Although the unique viscoelastic properties of the nucleolus are associated with transient interactions between chromatin and regulatory proteins, the specific mechanistic details driving nucleolar phase separation and mechanical responses have remained largely undefined. In this study, we employ a computational approach to elucidate chromatin-protein interactions within the nucleolus of budding yeast, using a sophisticated bead-spring polymer model. This model integrates DNA and nucleolar architectures with dynamic simulations of interactions involving chromosomal structural maintenance proteins and rDNA transcriptional regulators through systematically varied cross-linking kinetics. Our findings reveal that modulations in protein-DNA interactions critically dictate the phase behavior, relaxation dynamics, and viscoelastic properties of the nucleolus, underscoring a complex but precise regulatory mechanism at play. Notably, protein-mediated bridging emerges as a critical factor enhancing nucleolar condensation and modulating stress relaxation, highlighting the transformative role of transient cross-linking in nuclear mechanics regulation. These insights not only deepen our understanding of nucleolar function but also open avenues for interventions in genetic engineering and disease therapeutics.