Physical Review E最新文献

In this work, we propose a comprehensive theoretical framework combining percolation theory with nonlinear dynamics to study hypergraphs with a time-varying giant component. We consider in particular hypergraphs with higher-order triadic interactions. Higher-order triadic interactions occur when one or more nodes up-regulate or down-regulate a hyperedge. For instance, enzymes regulate chemical reactions involving multiple reactants. Here we propose and investigate higher-order triadic percolation on hypergraphs showing that the giant component can have a nontrivial dynamics. Specifically, we show that the fraction of nodes in the giant component undergoes a route to chaos in the universality class of the logistic map. In hierarchical higher-order triadic percolation, we extend this paradigm in order to treat hierarchically nested higher-order triadic interactions. We demonstrate the nontrivial effects of their increased combinatorial complexity on the critical phenomena and the dynamical properties of the process. Finally, we consider other generalizations of the model studying the effect of adopting interdependencies and node regulation instead of hyperedge regulation. The comprehensive theoretical framework presented here sheds light on possible scenarios for climate networks, biological networks, and brain networks, where the hypergraph connectivity changes over time.

For self-propelled particles in a corrugated potential landscape, we describe a discontinuous change of the classical depinning transition and a host of unique behaviors sensitive to the persistence of the propulsion direction. Exact and semianalytic results for active Brownian particles corroborate a creep regime with a superexponentially suppressed drift velocity upon lowering the force towards the threshold value. This unusual nonlinear response emerges from the competition of two critical scaling laws with exponents of 1/2 for rapidly reorienting particles and d/2 for particles with a persistent orientation; the latter case depends on the dimensionality d of rotational motion and also includes run-and-tumble particles. Additionally, different giant diffusion phenomena occur in the two regimes. Our findings extend to random dynamics with bounded noise near a saddle-node bifurcation and have potential applications in various nonequilibrium problems, including arrested active matter and cell migration.

Focusing on the standard map of the kicked rotor, we investigate the effects of classical stickiness (orbits temporarily confined to a region of a chaotic phase space) on an open quantum system. The regions of stickiness that we identify emerge in the strongly chaotic map. By scanning the system's phase space with a leak, we show that stickiness reduces the degree of delocalization of the quantum states and the decay rate of generic initial states. We find an excellent correspondence between the classical dwell time and finite-time Lyapunov exponents with the quantum dwell time and Wehrl entropies of the quantum states. Knowledge of the structure of the classically chaotic trajectories can thus be used to determine the best placement of leaks to enhance or decrease the degree of delocalization of quantum states and to modify the quantum dynamics of open systems.

The growing self-avoiding walk has been extensively studied, particularly in relation to whether it shares universality classes with equally weighted self-avoiding walks. This study expands the understanding of growing self-interacting self-avoiding walks and presents perspective on how lattice geometry and interaction strength interplay. We compare these walks on square and honeycomb lattices, and enhance the analysis of their decision points to deepen insights into the trapping effect in these models. The main numerical results uncover a minimum in the mean trapping length as the interaction strength varies for the honeycomb lattice, similar to what is known for the square lattice, and saturation effects in mean trapping lengths, as well as insights originating from the trap size.

In this work, we present an analytical study of a linear kinetic energy harvester driven by Gaussian noise through a nonequilibrium potential (NEP) approach. Taking advantage of the NEP, we conduct a statistical and thermodynamic analysis that reveals the stationary probability distribution function and its moments, offering insight into the harvester's stochastic behavior. Additionally, we make use of the energy landscape approach to visualize the implications of connecting a high load resistor, highlighting its impact on performance. Our findings also include generalized formulations of the Clausius inequality and Jarzynski equation, which we verify numerically.

We derive mean-field equations for a large population of globally coupled quadratic integrate-and-fire neurons subject to weak Gaussian noise and heterogeneous time-independent non-Cauchy distributed currents. We employ a circular cumulant approach that has previously been used only in the context of Cauchy heterogeneity, to the best of our knowledge. We extend this approach to rational distribution functions, which, unlike the Cauchy function, can have many poles in the complex plane. Population dynamics are analyzed for two families of rational functions that are approximations of the uniform and normal distributions. It is found that Gaussian noise and all considered types of heterogeneities have qualitatively the same effect on the population dynamics. This differs from the case of Cauchy noise, which has been shown to have the same effect on population dynamics only in the case of Cauchy heterogeneity, while Cauchy noise and non-Cauchy heterogeneity can have qualitatively different effects. The mean-field equations for both families of distribution functions are validated through a comparison of their solutions with the "exact" solutions of the Fokker-Planck equation, as well as with the results of modeling the stochastic microscopic dynamics of finite-size populations.

We perform molecular dynamics simulations of liquid water at different temperatures and calculate the water viscosity, the translational and rotational water diffusivities in the laboratory frame as well as in the comoving molecular frame. Instead of interpreting the results as deviations from the Stokes-Einstein and Stokes-Einstein-Debye relations, we describe the translational and rotational diffusivities of water molecules by three models of increasing complexity that take the structural anisotropy of water into account on different levels. We first compare simulation results to analytical predictions for a no-slip sphere and a no-slip ellipsoid. We show that the no-slip sphere can approximate laboratory-frame isotropic translational and rotational diffusivities but fails to describe the anisotropic molecular-frame diffusivities. The no-slip ellipsoid can describe the translational anisotropic molecular-frame diffusivities exactly but fails to describe the translational and rotational anisotropic molecular-frame diffusivities simultaneously. Since an ellipsoidal model with slip boundary conditions is not analytically tractable, we define a heuristic spherical model with tensorial slip lengths and tensorial hydrodynamic radii. We show that this model simultaneously describes the laboratory-frame isotropic translational and rotational diffusivities, as well as, in a restricted viscosity range, the anisotropic molecular-frame diffusivities.

Mutual information is commonly used as a measure of similarity between competing labelings of a given set of objects, for example to quantify performance in classification and community detection tasks. As argued recently, however, the mutual information as conventionally defined can return biased results because it neglects the information cost of the so-called contingency table, a crucial component of the similarity calculation. In principle the bias can be rectified by subtracting the appropriate information cost, leading to the modified measure known as the reduced mutual information, but in practice one can only ever compute an upper bound on this information cost, and the value of the reduced mutual information depends crucially on how good a bound is established. In this paper we describe an improved method for encoding contingency tables that gives a substantially better bound in typical use cases and approaches the ideal value in the common case where the labelings are closely similar, as we demonstrate with extensive numerical results.

Thermally bistable fluid tends to self-organize into clouds of hot and cold material, which are internally uniform and separated by thin conduction fronts. The evolution of these clouds has been studied for isobaric systems, but when pressure is instead treated as a dynamical quantity and allowed to evolve self-consistently, fundamentally different dynamics appear. Such a treatment is necessary in some laboratory plasmas, whose volume is constrained but whose pressure can vary. Solutions are derived for the evolution of clouds, accounting for pressure variation and interactions between conduction fronts. Additional stable configurations and secondary instabilities are derived, which may be relevant to fusion plasmas and to the study of photoionized plasma in the laboratory.

The effect of correlations in disorder variables is a largely unexplored topic in spin glass theory. We study this problem through a specific example of correlated disorder introduced in the Ising spin glass model. We prove that the distribution function of the magnetization along the Nishimori line in the present model is identical to the distribution function of the spin glass order parameter in the standard Edwards-Anderson model with symmetrically distributed independent disorder. This result means that if the Edwards-Anderson model exhibits replica symmetry breaking, the magnetization distribution in the correlated model has support on a finite interval, in sharp contrast to the conventional understanding that the magnetization distribution has, at most, two delta peaks. This unusual behavior challenges the traditional argument against replica symmetry breaking on the Nishimori line in the Edwards-Anderson model. In addition, we show that when temperature chaos is present in the Edwards-Anderson model, the ferromagnetic phase is strictly confined to the Nishimori line in the present model. These findings are valid not only for finite-dimensional systems but also for the infinite-range model, and highlight the need for a deeper understanding of disorder correlations in spin glass systems.