Physical Review E最新文献

We consider two globally coupled populations of phase oscillators featuring as conformists and contrarians, respectively. By employing an asymmetric parameter for contrarians, we unravel the emergence of various collective dynamical states, including incoherent, chimera, phase clusters, quasiperiodic chimera, and frequency clusters states. Specifically, chimera, quasiperiodic chimera, and frequency clusters states emerge only for appropriate fractions of both conformists and contrarians, and for a large enough asymmetric parameter. We also show that the asymmetric parameter diminishes the spread of the bistable region and eventually leads to a second-order transition for larger coupling strengths of the contrarians. Further, the spread of the incoherent state decreases in the phase diagrams as the asymmetry between the contrarians is increased. Furthermore, libration of the collective phases onsets for the quasiperiodic chimera state and in the frequency clusters state. We deduce the evolution equations corresponding to the macroscopic order parameters using the finite-dimensional reduction by Watanabe and Strogatz. The analytical stability conditions obtained from the evolution equations for the macroscopic order parameters agree very well with the simulation boundaries of the dynamical states.

The author, in a previous work, solved the generalized Langevin equation of a Brownian particle in a thermal bath whose constituents were composed of noninteracting harmonic oscillators interacting with a parabolic potential. This approach acceptably describes the memory kernel and the frequency-dependent friction coefficient when compared with the molecular dynamic simulation at a constant temperature of methane immersed in water modeled as a Lennard-Jones fluid. In this work, we determine properties, for a field frequency greater than that of the simulation, such as the susceptibility, the timescales of the colored noise correlation function, the average position of the tagged particle, the standard deviation of the position probability density, the time-dependent diffusion coefficient, the system's entropy and production, and the mechanical work generated by an optimum external protocol. The calculations show the system would undergo an atypical-anomalous diffusion because a solvent aggregation process around the particle occurs before it reaches the steady state. This leads to momentary negative entropy production, which vanishes at longer times and is explained in terms of Maxwell's demons and the fulfillment of the second law. Likewise, the optimum driving is no longer linear, and work can be extracted. Furthermore, an alternate method to determine the fluctuation-dissipation theorem is derived. The procedure hasn't appeared in the literature and doesn't appeal to its probability distribution but to simple rules.

Individual species may experience diverse outcomes, from prosperity to extinction, in an ecological community subject to external and internal variations. Despite the wealth of theoretical results derived from random matrix ensembles, a theoretical framework still remains to be developed to understand species-level dynamical heterogeneity within a given community, hampering real-world ecosystems' theoretical assessment and management. Here, we consider empirical plant-pollinator mutualistic networks, additionally including all-to-all intragroup competition, where species abundance evolves under a Lotka-Volterra-type equation. Setting the strengths of competition and mutualism to be uniform, we investigate how individual species persist or go extinct under varying these interaction strengths. By taking a dynamical systems approach, we meticulously study how increments in these interactions create particular sequences of extinctions and find the interaction strengths threshold values in which multistability arises. Hence, we are able to elucidate interaction strength regimes where, depending on the initial abundances of the species, different extinction scenarios arise within an ecological network.

While linear stochastic differential equations are exactly solvable, the solutions for nonlinear equations are traditionally sought from the corresponding Fokker-Planck description. Based on the separation of deterministic and stochastic time scales in the dynamics, a method for direct calculation of the mean and variance of the distribution for nonlinear stochastic differential equations is proposed using the renormalization group (RG) technique. We have shown how nonlinearity and its interplay with noise brings corrections to the frequency of the dynamical system, as reflected in the RG flow equations for amplitude and phase. Two broad classes of nonlinear systems were explored, one with linear dissipation, nonlinear potential, and internal noise obeying fluctuation-dissipation relation, and the other with nonlinear dissipation and linear potential, allowing a limit cycle solution subjected to external noise. We analyzed the mean-square displacement as a measure of diffusive behavior and determined the stability threshold of the limit cycle against the external noise. Our theory is compared with full numerical simulations.

A systematic comparative study of two-disk dynamo models without friction (the Rikitake model) and with friction has been carried out. It is shown that the sets of chaotic and periodic modes realized in both models are qualitatively similar. We introduce a simple measure of the complexity of a solution, which allows finding the chaotic mode characterized by long-lived quasistationary states with very weak oscillations of variables, ending with a sharp burst of oscillations with a possible transition to the attraction area of the other stationary solution. This transition corresponds to the change in the magnetic field sign. Such a behavior of the field is somewhat similar to the dynamics of the Earth's large-scale field in terms of the chaotic change of zones from one polarity to another. This rare reversal chaos was found in both two-disk dynamo models (without friction and with friction), but in the viscous case, it appears only at weak friction.

Ant colony optimization leverages the parameter α to modulate the decision function's sensitivity to pheromone levels, balancing the exploration of diverse solutions with the exploitation of promising areas. Identifying the optimal value for α and establishing an effective annealing schedule remain significant challenges, particularly in complex optimization scenarios. This study investigates the α-annealing process of the linear ant system within the infinite-range Ising model to address these challenges. Here, "linear" refers to the decision function employed by the ants. By systematically increasing α, we explore its impact on enhancing the search for the ground state. We derive the Fokker-Planck equation for the pheromone ratios and obtain the joint probability density function (PDF) in stationary states. As α increases, the joint PDF transitions from a monomodal to a multimodal state. In the homogeneous fully connected Ising model, α-annealing facilitates the transition from a trivial solution at α=0 to the ground state. The parameter α in the annealing process plays a role analogous to the transverse field in quantum annealing. Our findings demonstrate the potential of α-annealing in navigating complex optimization problems, suggesting its broader application beyond the infinite-range Ising model.

Systems of oscillators whose internal phases and spatial dynamics are coupled, swarmalators, present diverse collective behaviors which in some cases lead to explosive synchronization in a finite population as a function of the coupling parameter between internal phases. Near the synchronization transition, the phase energy of the particles is represented by the XY model, and they undergo a transition which can be of the first order or the second depending on the distribution of natural frequencies of their internal dynamics. The first-order transition is obtained after an intermediate state (static wings phase wave state) from which the nodes, in cascade over time, achieve complete phase synchronization at a precise value of the coupling constant. For a particular case of natural frequencies distribution, a new phenomenon, the rotational splintered phase wave state, is observed and leads progressively to synchronization through clusters switching alternatively from one to two and for which the frequency decreases as the phase coupling increases.

We develop a hypothesis that the dynamics of equilibrium systems at criticality have their dynamics constricted to a fractal subspace. We relate the correlation fractal dimension associated with this subspace to the Fisher critical exponent controlling the singularity associated with the correlation function. This fractal subspace is different from that associated with the order parameter. We propose a relation between the correlation fractal dimension and the order parameter fractal dimension. The fractal subspace we identify has as a defining property that the correlation function is restored at the critical point by restricting the dynamics this way. We determine the correlation fractal dimension of the two-dimensional Ising model and validate it by computer simulations. We discuss growth models briefly in this context.

We study negative large deviations of the long-time empirical front velocity of the center of mass of the one-sided N-BBM (N-particle branching Brownian motion) system in one dimension. Employing the macroscopic fluctuation theory, we study the probability that c is smaller than the limiting front velocity c_{0}, predicted by the deterministic theory, or even becomes negative. To this end, we determine the optimal path of the system, conditioned on the specified c. We show that for c_{0}-c≪c_{0} the properly defined rate function s(c), coincides, up to a nonuniversal numerical factor, with the universal rate functions for front models belonging to the Fisher-Kolmogorov-Petrovsky-Piscounov universality class. For sufficiently large negative values of c, s(c) approaches a simple bound, obtained under the assumption that the branching is completely suppressed during the whole time. Remarkably, for all c≤c_{*}, where c_{*}<0 is a critical value that we find numerically, the rate function s(c) is equal to the simple bound. At the critical point c=c_{*} the character of the optimal path changes, and the rate function exhibits a dynamical phase transition of second order.

We propose an upwind hybrid discontinuous Galerkin (HDG) method for the first-order hyperbolic linear Boltzmann transport equation, featuring a flexible expansion suitable for multiscale scenarios. Within the HDG scheme, primal variables and numerical traces are introduced within and along faces of elements, respectively, interconnected through projection matrices. Given the variables in two stages, the HDG method offers significant flexibility in the selection of spatial orders. The global matrix system in this framework is exclusively constructed from numerical traces, thereby effectively reducing the degrees of freedom (DoFs). Additionally, the matrix system in each discrete direction features a blocked-lower-triangular stencil, enhancing the efficiency of solving hyperbolic equations through an upwind sweep sequence. Based on the proposed method, we perform an asymptotic analysis of the upwind-HDG method in the thick diffusion limit. The result reveals that the correct convergence of the upwind-HDG is closely associated with the properties of the response matrix L. A series of numerical experiments, including comparisons with the even-parity HDG, confirms the accuracy and stability of the upwind-HDG method in managing thick diffusive regimes and multiscale heterogeneous problems.