Physical Review E最新文献

We present a continuous-space realization of the coupled memory graph process, a minimal non-Markovian framework in which coherence emerges through internal feedback. A single Brownian particle evolves on a viscoelastic substrate that records its trajectory as a scalar memory field and exerts local forces via the gradient of accumulated imprints. This autonomous, closed-loop dynamics generates structured, phase-locked motion without external forcing. The system is governed by coupled integro-differential equations: the memory field evolves as a spatiotemporal convolution of the particle's path, while its velocity responds to the gradient of this evolving field. Simulations reveal a sharp transition from unstructured diffusion to coherent burst-trap cycles, controlled by substrate stiffness and marked by multimodal speed distributions, directional locking, and spectral entrainment. This coherence point aligns across three axes: (i) saturation of memory energy, (ii) peak transfer entropy, and (iii) a bifurcation in transverse stability. We interpret this as the emergence of a memory engine-a self-organizing mechanism converting stored memory into predictive motion-illustrating that coherence arises not from tuning, but from coupling.

In this paper, we consider a class of interacting particle systems on dynamic random networks, in which the joint dynamics of vertices and edges acts as one-way feedback, i.e., edges appear and disappear over time depending on the state of the two connected vertices, while the vertex dynamics does not depend on the edge process. Our goal is to estimate the underlying dynamics from partial information of the process, specifically from snapshots of the total number of edges present. We showcase the effectiveness of our inference method through various numerical results.

We study the large-order behavior of the functional renormalization group (FRG). For a model in dimension zero, we establish Borel summability for a large class of microscopic couplings. Writing the derivatives of FRG as contour integrals, we express the Borel transform as well as the original series as integrals. Taking the strong-coupling limit in this representation, we show that all short-ranged microscopic disorders flow to the same universal fixed point. Our results are relevant for FRG in disordered elastic systems.

Reservoir computing has emerged as a powerful framework for predicting critical transitions in dynamical systems. In this work, we employ parallel parameter-aware reservoir computing to predict the dynamics of multilayer networks with distinct coupling mechanisms. We consider a two-layer multiplex network in which the first layer oscillators are coupled with attractive coupling, which promotes in-phase synchronization, while the second layer oscillators are coupled with repulsive coupling, encouraging anti-phase synchronization and oscillation death. With sufficiently strong interlayer coupling, collective emergent phenomena can be transferred from one layer to another. Notably, we also observe that interlayer coupling can induce oscillation death simultaneously in both layers. Using a parallel parameter-aware reservoir computing scheme, we accurately predict the critical parameter values at which the transfer of dynamical phenomenon occurs. We use two reservoirs designated to learn the dynamics of each layer in a two-layer multiplex network. Our findings provide valuable insight into the role of reservoir computing in forecasting transitions in multilayer networks.

Several important dynamical systems are in R^{2}, defined by the pair of differential equations (x^{'},y^{'})=(f(x,y),g(x,y)). A question of fundamental importance is how such systems might behave quantum mechanically. In developing quantum theory, Dirac and others realized that classical Hamiltonian systems can be mapped to their quantum counterparts via canonical quantization. The resulting quantum dynamics is always physical, characterized by completely positive and trace-preserving evolutions in the Schrödinger picture. However, whether non-Hamiltonian systems can be quantized systematically while respecting the same physical requirements has remained a long-standing problem. Here, we resolve this question when f(x,y) and g(x,y) are arbitrary polynomials. By leveraging open-systems theory, we prove constructively that every polynomial system admits a physical generator of time evolution in the form of a Lindbladian. We call our method cascade quantization, and demonstrate its power by analyzing several paradigmatic examples of nonlinear dynamics such as bifurcations, noise-activated spiking, and Liénard systems. In effect, our method can quantize any classical system whose f(x,y) and g(x,y) are analytic with arbitrary precision. More importantly, cascade quantization is exact. This means restrictive system properties usually assumed in the literature to facilitate quantization, such as weak nonlinearity, rotational symmetry, or semiclassical dynamics, can all be dispensed with by cascade quantization. We also highlight the advantages of cascade quantization over existing proposals, by weighing it against examples from the variational paradigm using Lagrangians, as well as nonvariational approaches.

We propose a new framework for analyzing vehicular traffic jams based on the space-time geometry of congestion. Using the simple but instructive model elementary cellular automaton rule 184 (ECA 184), we identify jammed regions as connected clusters in space-time and show that their statistical properties follow scaling laws characteristic of a percolation transition. Key traffic observables-including total delay, relaxation time, and jam lifetimes-exhibit consistent scaling behavior. We introduce an auxiliary quantity, termed "elementary jams," that serves as the basis for computing these observables and interpreting jam propagation. The simplicity of ECA 184 allows for efficient analysis and reveals structure that we believe generalizes to more complex traffic models. We outline how this percolation-based approach can be applied to models such as the Nagel-Schreckenberg model.

Using a delay differential equation model for a two-section semiconductor laser, we have found a new bifurcation scenario leading to stable mode-locked operation with normal dispersion properties of the light travel. The pulse profile is asymmetric, with a slower leading edge and a negative chirp. We classify the parameter space in which this regime exists as a Busse balloon and describe its boundaries.

While traditional thermodynamic equilibrium requires uniform temperature across coexisting phases, underdamped active matter systems can sustain nonequilibrium hot-cold coexistence through motility-induced phase separation. We investigate particle demixing and emergent temperature gradients in binary mixtures of inertial active and passive particles. Remarkably, within specific parameter ranges of intermediate particle inertia and self-propulsion strength, the system simultaneously achieves pronounced particle demixing and sustains significant hot-cold coexistence. Activity differences drive rapid species separation, which is further enhanced over time by persistent rotational diffusion. The synergy between inertia and activity significantly amplifies temperature differences both between particle species and across coexisting gas-liquid phases. These temperature disparities originate from inertia-enabled energy storage, collision-mediated energy transfer, propulsion-driven acceleration, and weakened liquid-phase cohesion. Unlike equilibrium systems, active-passive mixtures circumvent thermal homogenization by maintaining kinetic temperature gradients through continuous energy injection and dissipation. These findings elucidate fundamental principles of nonequilibrium self-organization in hybrid systems, with implications for bio-inspired materials, microbial ecology, and energy transport in active composites.

We study the zero-temperature Glauber dynamics of homogeneous Ising ferromagnets on hypercubes, as their dimension d varies. By hypercube, we mean the d-dimensional hypercubic graph with 2^{d} vertices, where each vertex is connected to d neighbors. We investigate the asymptotic (d→∞ and time t→∞) behavior of various quantities on hypercubes, such as the final magnetization, the probability for the system to enter a ground state, etc. Our numerical studies are carried out using a uniformly random initial state but with the constraint that the initial magnetization is zero. The final states can be divided into three categories: ground states, frozen states, and blinker states. We use the notion of a k-core to describe the geometry of the frozen states and give an exponential lower bound for the number of frozen states in terms of d. Blinker states-which exist only in even d-are final states containing at least one blinker (a permanently flipping spin). Blinkers states can have rich local structures; we give explicit constructions for configurations that contain blinkers and prove that the lowest possible dimension for blinker configurations is d=8. We also study the "nature versus nurture" problem on hypercubes, asking how much the final state depends on the information contained in the initial configuration, and how much depends on the realization of the dynamical evolution. Finally, we provide several conjectures and suggest some open problems based on the numerical results.

Characterizing the degeneracy of local stress states is a central challenge in obtaining the complete statistical mechanics of disordered media. Here, we introduce a minimal force-balance model for isolated granular clusters to probe the structure of the stress space through principal stress orientation and stress anisotropy. We further show that when complemented by physically motivated pairwise constraints, the model produces predictions for the stress alignment in packings of repulsive hard spheres. We compare these predictions against simulation data for grains in hopper and simple shear flows, finding qualitative agreement. This demonstrates the promise of modeling bulk athermal disordered systems through the combinatorics of few primitive geometric motifs.