A new behavior type of reservoir computing model for predicting dynamics of stochastic systems has been observed. It has been shown that when the control parameters of the predicted stochastic system and the reservoir computing model are turned, we observe intermittent behavior, i.e., close to the threshold parameter value the reservoir computing model demonstrates the accurate prediction most of the time, but there are time intervals during which the accurate prediction is interrupted by intervals characterized by the lack of prediction. The characteristics of the intermittency in predicting the behavior of the stochastic system correspond to the well-known on–off intermittency. The concept of the effective noise to describe the quality of prediction is proposed, and the technique of its amplitude value estimation is developed.

Understanding of the effect of coupling interaction is at the heart of nonlinear science since some nonequilibrium systems are composed of different layers or units. In this paper, we demonstrate various spatio-temporal patterns in a nonlinearly coupled two-layer Turing system with nonidentical reaction kinetics. Both the type of Turing mode and coupling form play an important role in the pattern formation and pattern selection. Two kinds of Turing mode interactions, namely supercritical-subcritical and supercritical-supercritical Turing mode interaction, have been investigated. Stationary resonant superlattice patterns arise spontaneously in both cases, while dynamic patterns can also be formed in the latter case. The destabilization of spike solutions induced by spatial heterogeneity may be responsible for these dynamic patterns. In contrast to linear coupling, the nonlinear coupling not only increases the complexity of spatio-temporal patterns, but also reduces the requirements of spatial resonance conditions. The simulation results are in good agreement with the experimental observations in dielectric barrier discharge systems.

Most of the analyses concerning signed networks have focused on balance theory, hence identifying frustration with undirected, triadic motifs having an odd number of negative edges; much less attention has been paid to their directed counterparts. To fill this gap, we focus on signed, directed connections, with the aim of exploring the notion of frustration in such a context. When dealing with signed, directed edges, frustration is a multifaceted concept, admitting different definitions at different scales: if we limit ourselves to consider cycles of length 2, frustration is related to reciprocity, i.e., the tendency of edges to admit the presence of partners pointing in the opposite direction. As the reciprocity of signed networks is still poorly understood, we adopt a principled approach for its study, defining quantities and introducing models to consistently capture empirical patterns of the kind. In order to quantify the tendency of empirical networks to form either mutualistic or antagonistic cycles of length 2, we extend the exponential random graph framework to binary, directed, signed networks with global and local constraints and then compare the empirical abundance of the aforementioned patterns with the one expected under each model. We find that the (directed extension of the) balance theory is not capable of providing a consistent explanation of the patterns characterizing the directed, signed networks considered in this work. Although part of the ambiguities can be solved by adopting a coarser definition of balance, our results call for a different theory, accounting for the directionality of edges in a coherent manner. In any case, the evidence that the empirical, signed networks can be highly reciprocated leads us to recommend to explicitly account for the role played by bidirectional dyads in determining frustration at higher levels (e.g., the triadic one).

Nucleation in the supercooled Yukawa system is relevant for addressing current challenges in understanding a range of crystallizing systems including white dwarf (WD) stars. We use both brute force and seeded molecular dynamics simulations to study homogeneous nucleation of crystals from supercooled Yukawa liquids. With our improved approach to seeded simulations, we obtain quantitative predictions of the crystal nucleation rate and cluster size distributions as a function of temperature and screening length. These quantitative results show trends towards fast nucleation with short-ranged potentials. They also indicate that for temperatures $T>0.9T_m$, where $T_m$ is the melt temperature, classical homogeneous nucleation is too slow to initiate crystallization but transient clusters of $\sim 100$ particles should be common. We apply these general results to a typical WD model and obtain a delay of $\sim 0.6$ Gyr in the onset of crystallization that may be observable.

The modeling of a spatially incoherent laser beam remains a central problem of the parametric instabilities in the context of inertial confinement fusion. This paper gives a simplified and comprehensive overview of the recent analytical developments regarding the modeling of these laser beams and a comparison with a dedicated experiment. Our model accounts for the statistical standard deviation of the gain and accurately captures the entanglement between wave mixing processes and the speckle correlations thus resolving the longstanding contradictions between the random phase approximation and the model of independent speckles. It is successfully compared to a recent laser beam spray experiment and the associated paraxial simulations, demonstrating that backscattering predictions require accounting for the beam spray. Our framework thus provides a way to evaluate and guide the analysis of parametric instabilities in high laser energy experiments.

We observe a flocking mechanism, the emergence of a state with global polar order, in mixed systems of self-propelled particles with purely antialigning interactions, i.e., the ground state for any pair of particles is to be opposedly oriented. In binary mixtures, we find that flocking can be realized by cross-species antialigning that is dominant compared to intraspecies antialignment. While the key mechanism can be understood within a mean-field description, beyond mean-field we develop an asymptotically exact Boltzmann-scattering theory from first principles. This theory yields analytical predictions for the flocking transition and shows excellent quantitative agreement with simulations of dilute systems. For large systems, we find either microphase separation or static patterns with patches or stripes that carry different polarization orientations.

In the last twenty years neuronal avalanches have been deeply investigated, both experimentally and numerically, also framing the results in the context of the avalanche scaling theory. In particular the avalanche shape has recently received a wide attention, also because the existence of a universal shape is an indication of the brain acting at a critical point. Within this scope, the detection of the shape asymmetry and the understanding of the mechanisms leading to it can provide useful insights into brain activity. Experimental data evidence, either symmetric or leftward asymmetry in the shape, results are not confirmed by numerical studies. Here we analyze the role of inhibition, connectivity range, and short term plasticity in determining the avalanche shape in an integrate and fire model. Results indicate that, not only the physiological fraction of inhibitory neurons is crucial to observe leftward asymmetry, but also the different synaptic recovery rates between excitatory and inhibitory neurons, confirming the importance of a dynamic balance between excitation and inhibition in brain activity.

We introduce and study the planted directed polymer, in which the path of a random walker is inferred from noisy "images" accumulated at each time step. Formulated as a nonlinear problem of Bayesian inference for a hidden Markov model, this problem is a generalization of the directed polymer problem of statistical physics, coinciding with it in the limit of zero signal to noise. For a one-dimensional walker we present numerical investigations and analytical arguments that no phase transition is present. When formulated on a Cayley tree, methods developed for the directed polymer are used to show that there is a transition with decreasing signal to noise where effective inference becomes impossible, meaning that the average fractional overlap between the inferred and true paths falls from one to zero.

We formulate a compounded random walk that is physically well defined on both finite and infinite domains, and samples space-dependent forces throughout jumps. The governing evolution equation for the walk limits to a space-fractional Fokker-Planck equation valid on bounded domains, and recovers the well known superdiffusive space-fractional diffusion equation on infinite domains. We describe methods for numerical approximation and Monte Carlo simulations and demonstrate excellent correspondence with analytical solutions. This compounded random walk, and its associated fractional Fokker-Planck equation, provides a major advance for modeling space-fractional diffusion through potential fields and on finite domains.

Polycarbonate is commonly used in extreme environments, particularly in applications involving high-velocity impact. A critical failure mode in high-velocity impact is that of spallation, where intersecting release waves result in the dynamic fracture of the material under high-rate tension. Despite the ubiquity of polycarbonate, major gaps exist in our understanding of its behavior at high rates over very short timescales. Here we investigate the spallation of polycarbonate on nanosecond timescales at strain rates of $\sim {10}^6{\mathrm{s}}^{-1}$ through a data set of 117 spall experiments. The size and fidelity of our dataset allow us to calculate fundamental uncertainties associated with the spallation of polycarbonate. Compared to lower rate experiments, we observe higher spall strengths, a higher spall initiation threshold, and a more gradual decrease in spall strength with increasing prior shock stress. This paper provides a strong basis for future computational model development and brings up questions on the underlying mechanisms that control spallation in polymers at extreme strain rates.

Chemical gradients can be used by a particle to determine its position. This positional information is of crucial importance, for example, in developmental biology in the formation of patterns in an embryo. The central goal of this paper is to study the fundamental physical limits on how much positional information can be stored inside a system. To achieve this, we study positional information for boundary-driven systems, and derive, in the near-equilibrium regime, a universal expression involving only the chemical potential and density gradients of the system. We also conjecture that this expression serves as an upper bound on the positional information of boundary-driven systems beyond linear response. To support this claim, we test it on a broad range of solvable boundary-driven systems.

For nonequilibrium systems in which fluctuations are important, it is well established that there can be events that violate the second law of thermodynamics on the trajectory level. For nonequilibrium steady-states, these second-law violating events are rare, but this may not be true for far-from-equilibrium nonsteady processes. In the paradigm system of a Brownian particle trapped under a time-dependent compressing potential, we demonstrate that second-law violating trajectories can outnumber the second-law obeying ones. In particular, for abrupt compressing harmonic and anharmonic potentials, analytic expressions for the total entropy production distribution and the fraction of second-law violating events are derived to show explicitly that second-law violating events can be of significant majority. These results are further confirmed in experiments.

We present the emergence of topological phase transition in the minimal model of two-dimensional rock-paper-scissors cycle in the form of a doublet chain. The evolutionary dynamics of the doublet chain is obtained by solving the anti-symmetric Lotka-Volterra equation. We show that the mass decays exponentially towards edges and robust against small perturbation in the rate of change of mass transfer, a signature of a topological phase. For one of the configuration of our doublet chain, the mass is transferred towards both edges and the bulk is gaped. Further, we confirm this phase transition within the framework of topological band theory. For this, we calculate the winding number, which change from zero to one for trivial and nontrivial topological phases, respectively.

Recent advances in machine learning have introduced physics-informed neural networks (PINN) as a valuable tool for addressing dynamics through governing equations and experimental observations. Outliers can be present in measurements and significantly affect the accuracy of the solutions provided by PINN. To overcome this limitation, we construct an outlier-resistant PINN (OrPINN) based on Tsallis statistics. We investigate the robustness of OrPINN in describing the acoustic and linear elastic wave dynamics under various outlier-level scenarios. We find that the OrPINN can improve the accuracy of the solutions even when the data is highly corrupted.

We study spin-$S$ Ising models with $p$-spin interactions on the one-dimensional chain and the two-dimensional square lattice. Here, $S$ denotes the magnitude of the spin and $p$ represents the number of spins involved in each interaction. The analysis is performed for $S=1/2,1,3/2,2$, and $p=3,4,5$. For the one-dimensional model, we formulate transfer matrices and numerically diagonalize them to analyze the temperature dependence of the free energy and spin-spin correlations. In the case of $S=1/2$, the free energy does not depend on $p$, and the spin-spin correlations are uniformly enhanced across all temperature scales as $p$ increases. In contrast, for $S\ge 1$, the free energy varies with $p$, and the spin-spin correlations are significantly enhanced at lower temperatures as $p$ increases. For the two-dimensional model, by using multicanonical simulations, we analyze physical quantities such as an order parameter, internal energy, and specific heat. In addition, we define and examine an order parameter to distinguish ordered and disordered phases. It is found that a first-order phase transition occurs at finite temperatures for all $S$ and $p\ge 3$, and increasing $p$ strengthens its nature. We present $S$ and $p$ dependence of the transition temperature and latent heat, and discuss effects of higher-order interactions on the nature of phase transitions.

Structural balance has been posited as one of the factors influencing how friendly and hostile relations of social actors evolve over time. This study investigates the behavior of the Heider balance model in Erdös-Rényi random graphs in the presence of a noisy environment, particularly the transition from an initially entirely positively polarized paradise state to a disordered phase. We examine both single-layer and bilayer network configurations and provide a mean-field solution for the average link polarization that predicts a first-order transition where the critical temperature scales with the connection probability $p$ as $p^2$ for a monolayer system and in a more complex way for a bilayer. We show that, to mimic the dynamics observed in complete graphs, the intralayer Heider interaction strengths should be scaled as $p^{-2}$, while the interlayer interaction strengths should be scaled as $p^{-1}$ for random graphs. Numerical simulations have been performed, and their results confirm our analytical predictions, provided that graphs are dense enough.

Social networks are often permeated by agents who promote their opinions without allowing for their own mind to be changed. Understanding how these so-called "zealots" act to increase the prevalence of their promoted opinion over the network is important for understanding opinion dynamics. In this work, we consider these promoted opinions to be "weak" and therefore less likely to be accepted relative to the default opinion in the network. We show how the proportion of zealots in the network, the relative strength of the weak opinion, and the structure of the network impact the long-term proportion of those in the network who subscribe to the weak opinion.

Ion acoustic solitons can be generated by a charged object immersed in an electrostatic quasineutral two-temperature plasma flow. These are often described by the forced Korteweg–de Vries equation. Two-fluid simulations of this scenario are conducted and compared to numerical solutions of the forced Korteweg–de Vries equation and theoretical predictions. As in forced Korteweg–de Vries theory, flow regimes are observed where either precursor or pinned solitons are generated depending on the background bulk velocity and debris size. However, the critical velocities that govern phase transitions from wakes to precursor and precursor to pinned solitons are found to differ substantially with precursor solitons being much more likely to be produced than previously thought. A theory is derived for the supercritical transition speed. These disagreements, in theory, have ramifications on the use of ion acoustic solitons to detect space debris.

Phase space engineering by rf waves plays important roles in both thermal D-T fusion and nonthermal advanced fuel fusion, but not all phase space manipulation is allowed; certain fundamental limits exist. In addition to Liouville's theorem, which requires the manipulation to be volume preserving, Gromov's nonsqueezing theorem imposes another constraint. The Gardner ground state is defined as the ground state accessible by smooth volume-preserving maps. However, the extra Gromov constraint should produce a higher-energy ground state. An example of a Gardner ground state forbidden by Gromov's nonsqueezing theorem is given. The challenge question is “What is the Gromov ground state, i.e., the lowest energy state accessible by smooth symplectic maps?” This is a difficult problem. As a simplification, we conjecture that the linear Gromov ground state problem is solvable.