We report a phenomenon of collective dynamics on discrete-time complex networks: a random temporal interaction matrix even of zero or/and small average is able to significantly enhance synchronization with probability one. According to current knowledge, there is no verifiably sufficient criterion for the phenomenon. We use the standard method of synchronization analytics and the theory of stochastic processes to establish a criterion, by which we rigorously and accurately depict how synchronization occurring with probability one is affected by the statistical characteristics of the random temporal connections such as the strength and topology of the connections as well as their probability distributions. We also illustrate the enhancement phenomenon using physical and biological complex dynamical networks.

Deep-learning techniques have recently demonstrated broad success in predicting complex dynamical systems ranging from turbulence to human speech, motivating broader questions about how neural networks encode and represent dynamical rules. We explore this problem in the context of cellular automata (CA), simple dynamical systems that are intrinsically discrete and thus difficult to analyze using standard tools from dynamical systems theory. We show that any CA may readily be represented using a convolutional neural network with a network-in-network architecture. This motivates the development of a general convolutional multilayer perceptron architecture, which we find can learn the dynamical rules for arbitrary CA when given videos of the CA as training data. In the limit of large network widths, we find that training dynamics are nearly identical across replicates, and that common patterns emerge in the structure of networks trained on different CA rulesets. We train ensembles of networks on randomly sampled CA, and we probe how the trained networks internally represent the CA rules using an information-theoretic technique based on distributions of layer activation patterns. We find that CA with simpler rule tables produce trained networks with hierarchical structure and layer specialization, while more complex CA produce shallower representations—illustrating how the underlying complexity of the CA's rules influences the specificity of these internal representations. Our results suggest how the entropy of a physical process can affect its representation when learned by neural networks.

We report an experiment on the unclogging dynamics in a two-dimensional silo submitted to a sustained gentle vibration. We find that arches present a jerking motion where rearrangements in the positions of their beads are interspersed with quiescent periods. This behavior occurs for both arches that break down and those that withstand the external perturbation: Arches evolve until they either collapse or get trapped in a stable configuration. This evolution is described in terms of a scalar variable characterizing the arch shape that can be modeled as a continuous-time random walk. By studying the diffusivity of this variable, we show that the unclogging is a weakly nonergodic process. Remarkably, arches that do not collapse explore different configurations before settling in one of them and break ergodicity much in the same way than arches that break down.

We present calculations of electrical resistivity in dense plasmas using the average-atom model. The Born approximation is proposed to improve the computations especially in the hot domain of the density and temperature plane. Both the nonrelativistic and relativistic regimes are considered. Numerical examples are given.

This work addresses the superdiffusive motion of a random walker on a discrete finite-size substrate. It is shown that, with the inclusion of suitably tuned time-dependent probability of large distance jumps over the substrate, the mean square displacement (MSD) of the walker has a power-law dependence on time with a previously chosen exponent $\gamma >1$. The developed framework provides an exact solution to the inverse problem, i.e., an adequate jump probability function leading to a preestablished solution is evaluated. Using the Markov Chain (MC) formalism, an exact map for the time dependence of the probability function is derived, which depends on the topology of the substrate and on the chosen value of $\gamma$. While the formalism imposes no restriction on the substrate, being applicable from ordered Euclidean lattices to complex networks, results for the cycle graph and two-dimensional torus are highlighted. It is also shown that, based on the previously derived probability function, MSD values resulting from direct numerical simulations agree quite well with those solely obtained within the MC framework.

We introduce a way to stabilize steady micro/nanoliquid jets issuing from Taylor cones together with coflowing gas streams. We study the dripping-jetting transition of this configuration theoretically through a global stability analysis as a function of the governing parameters involved. A balance between the local radial acceleration to the surface tension gradient, the mass conservation, and the energy balance equations enable us to derive two coupled scaling laws that predict both the minimum jet diameter and its maximum velocity. The theoretical prediction provides a single curve that describes not only the numerical computations but also experimental data from the literature for cone jets assisted with gas coflow. Additionally, we performed a set of experiments to verify what parameters influence the jet length. We adopt a very recent model for capillary jet length to our configuration by combining electrohydrodynamic effects with the gas flow through an equivalent liquid pressure. Due to diameters below 1 $\mu \text{m}$ and high speeds attainable in excess of 100 m/s, this concept has the potential to be utilized for structural biology analyses with x-ray free-electron lasers at megahertz repetition rates as well as other applications.

Rayleigh and Onsager showed that in the regime where the flows are small and the thermodynamic forces vary slowly, the entropy generation rate is linearly related to the flows, and the flows are related to the gradient of the forces. Hence, the Rayleigh-Onsager dissipation is only applicable to linear irreversible thermodynamics. We introduce the extension of Rayleigh-Onsager dissipation to highly nonlinear dissipation to treat nonlinear irreversible thermodynamics. This extension fulfills the positive entropy generation criterion. To demonstrate this nonlinear dissipation, we apply it to obtain the generalized hydrodynamics from the kinetic theory according to Eu theory. Specifically, it provides an alternative evolution for a stress tensor and heat flux. The challenging problems of nonlinear irreversible thermodynamics, as represented by nonequilibrium flows, are investigated. The result implies that this study provides a promising alternative to obtain a unified framework for modeling both equilibrium and nonequilibrium gas flows.

Using the replica approach and the cavity method, we study the fluctuations of the optimal cost in the random-link matching problem. By means of replica arguments, we derive the exact expression of its variance. Moreover, we study the large deviation function, deriving its expression in two different ways, namely using both the replica method and the cavity method.

We consider the problem of how a condensed molecular system approaches equilibrium, focusing on the particular case of water. We show, by means of extensive molecular dynamics simulations, that the existence of different types of degrees of freedom affects the dynamics of equilibration, and this influence is made most obvious in the system's temperature. When equipartition of energy does not hold in the initial, nonequilibrium state, the instantaneous temperature can be up to a few degrees lower than that observed under equipartition conditions, resulting in a Mpemba-like effect. Though our study considers water in particular, our findings apply more generally to condensed molecular systems.

An equivalence between nonequilibrium steady states (NESS) driven by a time-independent force and stochastic pumps (SP) stirred by a time-varying conservative force is studied for general many-body diffusive systems. When the particle density and current of NESS are imitated by SP time-averaged counterparts, we prove that the entropy production rate in the SP is always greater than that of the NESS, provided that the conductivity of the particle current is concave as a function of the particle density. Searching for a SP protocol that saturates the entropy production bound reveals an unexpected connection with traffic waves, where a high density region propagates against the direction of the particle current.

We present a wave-memory-driven system that exhibits intermittent switching between two propulsion modes in free space. The model is based on a pointlike particle emitting periodically cylindrical standing waves. Submitted to a force related to the local wave-field gradient, the particle is propelled, while the wave field stores positional information on the particle trajectory. For long memory, the linear motion is unstable and we observe erratic switches between two propulsive modes: linear motion and diffusive motion. We show that the bimodal propulsion and the stochastic aspect of the dynamics at long time are generated by a Shil'nikov chaos. The memory of the system controls the fraction of time spent in each phase. The resulting bimodal dynamics shows analogies with intermittent search strategies usually observed in living systems of much higher complexity.

We study a fully on-fiber optomechanical cavity and characterize its performance as a sensor. The cavity is formed by patterning a suspended metallic mirror near the tip of an optical fiber and by introducing a static reflector inside the fiber. Optically induced self-excited oscillation (SEO) is observed above a threshold value of the injected laser power. The SEO phase can be synchronized by periodically modulating the optical power that is injected into the cavity. Noise properties of the system in the region of synchronization are investigated. Moreover, the spectrum is measured near different values of the modulation frequency, at which phase locking occurs. A universal behavior is revealed in the transition between the regions of phase locked and free running SEO.

Many biological and chemical systems exhibit collective behavior in response to the change in their population density. These elements or cells communicate with each other via dynamical agents or signaling molecules. In this work, we explore the dynamics of nonlinear oscillators, specifically Stuart-Landau oscillators and Rayleigh oscillators, interacting globally through dynamical agents in the surrounding environment modeled as a quorum sensing interaction. The system exhibits the typical continuous second-order transition from oscillatory state to death state, when the oscillation amplitude is small. However, interestingly, when the amplitude of oscillations is large we find that the system shows an abrupt transition from oscillatory to death state, a transition termed “explosive death.” So the quorum-sensing form of interaction can induce the usual second-order transition, as well as sudden first-order transitions. Further, in the case of the explosive death transitions, the oscillatory state and the death state coexist over a range of coupling strengths near the transition point. This emergent regime of hysteresis widens with increasing strength of the mean-field feedback, and is relevant to hysteresis that is widely observed in biological, chemical, and physical processes.

We consider the reflectionless transport of solitons in networks. The system is modeled in terms of the nonlinear Schrödinger equation on metric graphs, for which transparent boundary conditions at the branching points are imposed. This approach allows to derive simple constraints, which link the equivalent usual Kirchhoff-type vertex conditions to the transparent ones. Our method is applied to a metric star graph. An extension to more complicated graph topologies is straightforward.

The mathematical framework of matrix decomposition implies the possibility to perform statistical analyses of directed graphs focused on the distributions of the independent cyclic and starlike hierarchical components. In this approach the weighted directed graphs with $n$ nodes are built up as a linear combination of starlike graphs with $n$ outgoing edges and a suitable set of three-edge cyclic subgraphs. The applicability of this approach is illustrated by quantifying several general features: e.g., ratio of the cyclic and hierarchical components and asymmetry in the hierarchical components. The applicability of these methods is illustrated by considering the averages over random directed graphs and comparing these values with those characterizing simple directed graphs of tournaments.

Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric payoffs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic (fine-grained) environment, the time-averaged population frequencies are shown to obey a replicator dynamics with a nonlinear fitness that is induced by environmental changes. The nonlinear terms in the fitness emerge due to populations tracking their time-dependent environment. These terms can induce a stable polymorphism, though they do not spoil the polymorphism that exists already without them. In this sense polymorphic populations are more robust with respect to their time-dependent environments. The overall fitness of the problem is still given by its time-averaged value, but the emergence of polymorphism during genetic selection can be accompanied by decreasing mean fitness of the population. The impact of the uncovered polymorphism scenario on the models of diversity is exemplified via the rock-paper-scissors dynamics, and also via the prisoner's dilemma in a time-periodic environment.

Many previous studies of unbinding kinetics have focused on a two-state model, with fully bonded and free states, which may not extend to more complicated biopolymer dynamics involving other reactions. Here we address the kinetic rate of this process at the segment level, as it is influenced by a growing dangling end of the chain. We use the mean first-passage time approach and treat the polymer as a chain attached to a wall through a succession of spring potentials, with two distinct regions of bonded and free segments. The interaction between the wall and free-moving chain end adds an entropic repulsion to this process. We estimate the average monomer detachment rate $K$ as a function of the free dangling length $L$. For a flexible polymer, we find an acceleration factor in the average detachment rate depending on $L$ and the details of the spring bond; when $L$ is long, this factor is a simple ratio of its breaking distance to the natural bond length. For a semiflexible filament, we examine the regime where $L$ is shorter than persistence length $L_p$, as the limit opposite to that of the flexible chain. An enhancing factor also appears, speeding up the filament unbinding when the free length grows; for a long rigid rod, this factor becomes two, independently of the bond details. We also examine the total unbinding time of an irreversible detaching process by integrating $(1/K)$ over polymer length and discover that its power-law scaling with chain length is smaller than one, over the commonly seen range of polymer size.

Many systems in chemical and biological physics involve diffusing particles being trapped by absorbing patches on otherwise reflecting surfaces. Such systems are commonly studied by boundary homogenization, in which the heterogenous boundary condition on the patchy surface is replaced by a uniform boundary condition involving a single parameter which encapsulates the effective trapping properties of the surface. In prior works on boundary homogenization, the surface is patchy and the diffusing particles are homogeneous. In this paper, we consider the opposite scenario in which a homogenous surface traps patchy particles, which could model proteins with localized binding sites, cells with membrane receptors, or patchy colloids or nanoparticles. We derive an explicit formula for the effective trapping rate which reveals a fundamental interplay between the translational and rotational diffusivities of the patchy particle, a phenomenon not typically seen in boundary homogenization. Motivated by receptors on the cell membrane, our analysis also allows for the possibility that the patches diffuse on the surface of the particle. We formulate the system in terms of a high-dimensional, time-dependent, anisotropic diffusion equation and employ matched asymptotic analysis to derive the effective trapping rate. We confirm our results by detailed numerical simulations.

We introduce a theoretical approach to describe structural correlations among charged permeable spheres at finite particle concentrations. This theory explicitly accounts for correlations among microions and between microions and macroions and allows for the proposal of an effective interaction among macroions that successfully captures structural correlations observed in poly-$N$-isopropyl acrylamide microgel systems. In our description the bare charge is fixed and independent of the microgel size, the microgel concentration, and the ionic strength, which contrasts with results obtained using linear response approximations, where the bare charge needs to be adapted to properly account for microgel correlations obtained at different conditions.

We investigate the statistical properties of adjacency relationships in a two-dimensional Vicsek model. We define adjacent edges for all particles at every time step by (a) Delaunay triangulation and (b) Euclidean distance, and obtain cumulative distributions $P\left(\tau \right)$ of lifetime $\tau$ of the edges. We find that the shape of $P\left(\tau \right)$ changes from an exponential to a power law depending on the interaction radius, which is a parameter of the Vicsek model. We discuss the emergence of the power-law distribution from the viewpoint of first passage time problem for a fractional Brownian motion.