Physical review. E最新文献

Tipping points (TP) are abrupt transitions between metastable states in complex systems, most often described by a bifurcation or crisis of a multistable system induced by a slowly changing control parameter. An avenue for predicting TPs in real-world systems is critical slowing down (CSD), which is a decrease in the relaxation rate after perturbations prior to a TP that can be measured by statistical early warning signals (EWS) in the autocovariance of observational time series. In high-dimensional systems, we cannot expect a priori chosen scalar observables to show significant EWS, and some may even show an opposite signal. Thus, to avoid false negative or positive early warnings, it is desirable to monitor fluctuations only in observables that are designed to capture CSD. Here we propose that a natural observable for this purpose can be obtained by a data-driven approximation of the first nontrivial eigenfunction of the backward Fokker-Planck (or Kolmogorov) operator, using the diffusion map algorithm.

Over the past seven decades, the classical Monte Carlo method has played a huge role in the fields of rarefied gas flow and micro/nanoscale heat transfer, but it also has shortcomings: the time step and cell size are limited by the relaxation time and mean free path, making it difficult to efficiently simulate multiscale heat and mass transfer problems from the ballistic to diffusion limit. To overcome this drawback, a unified gas-kinetic wave-particle (UGKWP) method is developed for solving the phonon Boltzmann transport equation (BTE) in all regimes covering both ballistic and diffusive limits. This method is built upon the space-time coupled evolution model of the phonon BTE, which provides the framework for constructing a multiscale flux at the cell interfaces. At the same time, in order to capture nonequilibrium transport efficiently, the multiscale flux comprises two distinct components: a deterministic part for capturing the near-equilibrium or diffusive transport, and a statistical particle part for recovering nonequilibrium or ballistic transport phenomena. The UGKWP method exhibits remarkable multiscale adaptability and versatility, seamlessly bridging the gap between the diffusive and ballistic transport phenomena. In the diffusive limit, the present method naturally converges to Fourier's law, with the diminishing particle contribution, whereas in the ballistic limit, the nonequilibrium flux is fully described by the free-streaming particles. This inherent adaptability not only allows for precise capturing of both equilibrium and nonequilibrium heat transfer processes, but it also guarantees that the model adheres strictly to the underlying physical laws in each phonon transport regime. A series of numerical tests fully demonstrate the excellent performance of the UGKWP method in all Knudsen regimes, where the time step and cell size are not constrained by the relaxation time and mean free path in the diffusive regime. The present method is an efficient and accurate computational tool for simulating multiscale nonequilibrium heat transfer, and offering significant advantages over traditional methods in terms of numerical performance and physical applicability.

We focus on the Feigenbaum-Coullet-Tresser point of the dissipative one-dimensional z-logistic map x_{t+1}=1-a|x_{t}|^{z}(z≥1). We show that sums of iterates converge to q-Gaussian distributions P_{q}(y)=P_{q}(0)exp_{q}(-β_{q}y^{2})=P_{q}(0)[1+(q-1)β_{q}y^{2}]^{1/(1-q)}(q≥1;β_{q}>0), which optimize the nonadditive entropic functional S_{q} under simple constraints. We propose and justify heuristically a closed-form prediction for the entropic index, q(z)=1+2/(z+1), and validate it numerically via data collapse for typical z values. The formula captures how the limiting law depends on the nonlinearity order and implies finite variance for z>2 and divergent variance for 1≤z≤2. These results extend edge-of-chaos central limit behavior beyond the standard (z=2) case and provide a simple predictive law for unimodal maps with varying maximum order.

Experiments using a rotational rheometer have demonstrated that the apparent viscosity becomes negative under the electric-field-induced turbulent state of conductive nematic liquid crystals [Orihara et al., Phys. Rev. E 99, 012701 (2019)10.1103/PhysRevE.99.012701; F. Kobayashi et al., Phys. Rev. E 101, 022702 (2020)10.1103/PhysRevE.101.022702]. When the upper rotating plate of the rheometer is left free, spontaneous rotation-that is, spontaneous shear flow-has also been observed. In this study, we reproduce these phenomena through three-dimensional simulations based on continuum theory. The simulations reveal characteristic velocity, director, and stress fields in the negative-viscosity state. Furthermore, they clarify the interplay between topological defects (disclinations) and space charges which drive the turbulence.

Modeling how information or disease spreads on a network is a major problem in network science. The problem of determining seed nodes that maximize influence is called the influence maximization problem and has been well studied for various models of influence dissemination. The influence computation problem has an even more ambitious goal as it seeks to determine the exact probability of particular nodes getting influenced. H. Z. Brooks et al. [arXiv:2403.01066] introduced a model for the spreading of content on networks inspired by bounded confidence models. We show that this content-spreading model generalizes the independent cascade model and propose various influence computation and influence maximization problems. We discuss centrality measures for identifying influential nodes in the case of trees, which is analytically and computationally tractable. Finally, we train graph neural networks to predict the influence probabilities and propose this as a benchmark task to evaluate the oversquashing problem in graph neural networks.

In contrast to the central pattern generator hypothesis, which posits that neural networks generate rhythmic motor patterns without sensory feedback, recent robotics studies have demonstrated that independent oscillating agents with load-dependent feedback can organize coordinated gaits in quadrupedal robots. In this study, we develop minimal mathematical models to describe how such coordination emerges from physical interactions through the trunk and environment. By employing active rotators as limb controllers, we demonstrate their capacity to generate distinct gait patterns, including the trot, pace, and bound. We can also predict gait transitions with walking speed. These models provide insight into why different animals with specific physiques have limited gait patterns and offer suggestions for designing quadrupedal robots.

Many real-world networks, ranging from subway systems to polymer structures and fungal mycelia, do not form by the incremental addition of individual nodes but instead grow through the successive extension and intersection of lines or filaments. Yet most existing models for spatial network formation focus on node-based growth, leaving a significant gap in our understanding of systems built from spatially extended components. Here we introduce a minimal model for spatial networks, rooted in the iterative growth and intersection of lines, a mechanism inspired by diverse systems including transportation networks, fungal hyphae, and vascular structures. Unlike classical approaches, our model constructs networks by sequentially adding lines across a domain populated with randomly distributed points. Each line grows greedily to maximize local coverage, while subject to angular continuity and the requirement to intersect existing structures. This emphasis on extended, interacting elements governed by local optimization and geometric constraints leads to the spontaneous emergence of a core-and-branches architecture. The resulting networks display a range of nontrivial scaling behaviors: the number of intersections grows subquadratically; Flory exponents and fractal dimensions emerge consistent with empirical observations; and spatial scaling exponents depend on the heterogeneity of the underlying point distribution, aligning with measurements from subway systems. Our model thus captures the key organizational features observed across diverse real-world networks, establishing a universal paradigm that goes beyond node-based approaches and demonstrates how the growth of spatially extended elements can shape the large-scale architecture of complex systems.

Coherently coupled nonlinear Schrödinger equations arise for wave interactions in media where the relative phase of the components is critical. An example is the propagation of electric fields in an optical waveguide in the weak birefringence limit. The competing factors are second-order dispersion and four-wave mixing. Doubly periodic structures of the nonlinear Schrödinger equation returning to their initial states after complex evolution have been previously studied. Recurrence for a coherently coupled system is studied here via approaches of spectral and linear instabilities. A doubly periodic solution for coherently coupled systems is established in terms of Jacobi elliptic functions, and its robustness is investigated. For spectral instability, the eigenvalues of the associated matrix are computed. For linear instability, direct numerical simulations are performed for slightly perturbed doubly periodic patterns. These patterns generally display various degrees of instability. Special disturbances favorable for recurrence phenomena arising from a continuous wave background and singly periodic solutions are identified. The agreement between spectral and linear instabilities on the trends of growth of disturbances is excellent. Knowledge gained here will be useful for studying wave evolution and instabilities in fluids and optics.

In recent years, unconventional computing architectures that transcend traditional semiconductor-based systems have witnessed far-ranging research interest. Here we propose an approach to the construction of logic gates, using active particles, specifically 1-pentanol-infused disks, exploiting the principle of the Marangoni effect. In our experimental setup, we design a channel with arms designated for inputs and an arm to observe the output. The inputs are provided by disks, where active disks infused with pentanol are considered to have a truth value of 1, while passive disks are considered to have a truth value of 0. The movement of a controller disk placed in a decision-making region determines the output. We demonstrate that the complex interplay of surface tension, drag, and repulsive and attractive forces yields the fundamental AND and OR logic responses. Interestingly, the logic function can be switched by solely changing the activity of the controller by decreasing the pentanol concentration, thus giving the same channels the capacity to morph the logic functionality. Additionally, the complementary NAND and NOR logic can be obtained with a simple change in the output encoding. Such active-matter-based logic gates have the potential to perform in fluid conditions, making them ideal for biomedical applications, bio sensing, molecular computing, and targeted drug delivery by responding to biological signals without external power sources.

A universal and rigorous ensemble framework for nonequilibrium systems remains lacking. Here, we provide a concise framework for the generalized ensemble theory of nonequilibrium discrete systems using a matrix-based approach. By introducing an observation matrix, we show that any discrete probability distribution can be formulated as a generalized Boltzmann distribution, with observables and their conjugate variables serving as basis vectors and coordinates in a vector space. Within this framework, we identify the minimal sufficient statistics required to infer the Boltzmann distribution. The nonequilibrium thermodynamic relations and fluctuation-dissipation relations naturally emerge from this framework. Our findings provide a new approach to developing generalized ensemble theory for nonequilibrium discrete systems.