Accumulating evidence shows that the cerebral cortex is operating near a critical state featured by power-law size distribution of neural avalanche activities, yet evidence of this critical state in artificial neural networks mimicking the cerebral cortex is still lacking. Here we design an artificial neural network of coupled phase oscillators and, by the technique of reservoir computing in machine learning, train it for predicting chaos. It is found that when the machine is properly trained, oscillators in the reservoir are synchronized into clusters whose sizes follow a power-law distribution. This feature, however, is absent when the machine is poorly trained. Additionally, it is found that despite the synchronization degree of the original network, once properly trained, the reservoir network is always developed to the same critical state, exemplifying the “attractor” nature of this state in machine learning. The generality of the results is verified in different reservoir models and by different target systems, and it is found that the scaling exponent of the distribution is independent of the reservoir details and the bifurcation parameters of the target system, but is modified when the dynamics of the target system is changed to a different type. The findings shed light on the nature of machine learning, and are helpful to the design of high-performance machines in physical systems.

We investigate the phase behavior of a two-dimensional athermal lattice gas in which every hard-core particle can have two or fewer nearest neighboring occupied sites on the square lattice. The ground state and close packing density are determined and it is found that at large chemical potential the model undergoes an ordering phase transition with preferential sublattice occupation. Although near the transition point the particle density and entropy exhibit an apparent discontinuity, we find that the order parameter and fluctuations of thermodynamic quantities do not scale with the system volume. These paradoxical results are reconciled by analyzing the size-dependent flow of the thermal exponent by phenomenological renormalization and the curve-crossing method, which lead to a weakly first-order phase transition scenario.

Social physics is the mathematical study of how the flow of ideas can change the behavior of individuals. Models in social physics include processes for searching after new ideas and dispersing them inside the population. The present paper makes use of exploration and imitation processes for the mentioned purpose. A new type of imitation is employed here, in which the imitant strategy is not simply replaced by role model strategy, but rather moves toward it. Our exploration process is additive Gaussian noise. To study these processes, we both analyze and simulate the strategy distribution function. By combining exploration and soft imitation, the width of the strategy distribution function becomes stationary. In this model, regular imitation is a particular limit of soft imitation, where an imitant copies the role model, through which the stationary width of the distribution function disappears. As the network causes complex behavior, soft imitation and exploration have been studied in some complex networks as well. Simulation results show that for a small world, scale-free, random regular, and random network, and by selected parameters in this research, distribution function width reaches stationary states.

In this paper we study a conserved system comprised of two directed lanes having identical dynamics and two reservoirs with scaled resources that are strategically connected to the boundaries of the lanes, forming a ringlike structure. The steady-state properties of the system have been analyzed in the framework of mean-field theory. Our findings display a rich behavior, emphasizing the nontrivial effects of incorporating two reservoirs. As a consequence, two distinct phases that admit delocalized shocks emerge and occupy a significant region in the phase diagram. Moreover in one of theses phases, each lane admits a delocalized shock whose movements are perfectly synchronized. In another phase, the single shock in the system may traverse both lanes or remain restricted to a single lane, depending upon the size of the system. All the findings are validated by Monte Carlo simulations.

Localization and delocalization of quantum diffusion in a time-continuous one-dimensional Anderson model perturbed by the quasiperiodic harmonic oscillations of $M$ colors is investigated systematically, which has been partly reported by a preliminary Letter [H. S. Yamada and K. S. Ikeda, Phys. Rev. E 103, L040202 (2021)]. We investigate in detail the localization-delocalization characteristics of the model with respect to three parameters: the disorder strength $W$, the perturbation strength $\epsilon$, and the number of colors, $M$, which plays the similar role of spatial dimension. In particular, attention is focused on the presence of localization-delocalization transition (LDT) and its critical properties. For $M\ge 3$ the LDT exists and a normal diffusion is recovered above a critical strength $\epsilon$, and the characteristics of diffusion dynamics mimic the diffusion process predicted for the stochastically perturbed Anderson model even though $M$ is not large. These results are compared with the results of discrete-time quantum maps, i.e., the Anderson map and the standard map. Further, the features of delocalized dynamics are discussed in comparison with a limit model which has no static disordered part.

Weak Gaussian perturbations on a plane wave background could trigger lots of rogue waves (RWs), due to modulational instability. Numerical simulations showed that these RWs seemed to have similar unit structure. However, to the best of our knowledge, there are no relative results to prove that these RWs have the similar patterns for different perturbations, partly due to that it is hard to measure the RW pattern automatically. In this work, we address these problems from the perspective of computer vision via using deep neural networks. We propose a rogue wave detection network (RWD-Net) model to automatically and accurately detect RWs in the images, which directly indicates they have the similar computer vision patterns. For this purpose, we herein meanwhile have designed and release the corresponding dataset, termed as rogue wave dataset-$10\mathrm{K}$ (RWD-$10\mathrm{K}$), which has $10191$ RW images with bounding box annotations for each RW unit. In our detection experiments, we get $99.29\%$ average precision on the test splits of the proposed dataset. Finally, we derive our metric, termed as the density of RW units, to characterize the evolution of Gaussian perturbations and obtain the statistical results on them.

Reservoir computing offers a great computational framework where a physical system can directly be used as computational substrate. Typically a “reservoir” is comprised of a large number of dynamical systems, and is consequently high dimensional. In this work, we use just a single simple low-dimensional dynamical system, namely, a driven pendulum, as a potential reservoir to implement reservoir computing. Remarkably we demonstrate, through numerical simulations as well as a proof-of-principle experimental realization, that one can successfully perform learning tasks using this single system. The underlying idea is to utilize the rich intrinsic dynamical patterns of the driven pendulum, especially the transient dynamics which has so far been an untapped resource. This allows even a single system to serve as a suitable candidate for a reservoir. Specifically, we analyze the performance of the single pendulum reservoir for two classes of tasks: temporal and nontemporal data processing. The accuracy and robustness of the performance exhibited by this minimal one-node reservoir in implementing these tasks strongly suggest an alternative direction in designing the reservoir layer from the point of view of efficient applications. Further, the simplicity of our learning system offers an opportunity to better understand the framework of reservoir computing in general and indicates the remarkable machine-learning potential of even a single simple nonlinear system.

Three-species cyclic predator-prey systems are known to establish spiral waves that allow species to coexist. In this study, we analyze a structured heterogeneous system which gives one species an advantage to escape predation in an area that we refer to as a habitat and study the effect on species coexistence and emerging spatiotemporal patterns. Counterintuitively, the predator of the advantaged species emerges as dominant species with the highest average density inside the habitat. The species given the advantage in the form of an escape rate has the lowest average density until some threshold value for the escape rate is exceeded, after which the density of the species with the advantage overtakes that of its prey. Numerical analysis of the spatial density of each species as well as of the spatial two-point correlation function for both inside and outside the habitats allow a detailed quantitative discussion. Our analysis is extended to a six-species game that exhibits spontaneous spiral waves, which displays similar but more complicated results.

The dynamics of a unique type of clock mechanism known as grasshopper escapement is investigated with the aim of evaluating its accuracy in a noisy environment. It is demonstrated that the clock's precision scales linearly with the rate of its entropy production, consistently with recently reported results regarding nanoscale and quantum clocks. Moreover, it is shown that the inevitable force variations present in the mechanism can be modeled with a Maxwell-Boltzmann statistic. Finally, the function of clock error is compared with Brownian motion and its fractal-like properties are discussed. The numerical results are confirmed with experimental data.

For a laboratory discharge initiated in a long air gap by a microsecond megavolt pulse, we simultaneously register wideband high-frequency microwave and hard-x-ray emissions and thoroughly analyze the temporal relationship of the emissions depending on the discharge evolution. The temporal structure of microwave radiation is found to consist of numerous short intense bursts with high-frequency components. We directly show that x-ray and microwave emissions can appear almost synchronously in the discharge but only when a complex net of countless plasma channels forms and spans the entire discharge gap. The channel formation is closely related to the intense development of multiple streamers.

A bit reset is a basic operation in irreversible computing. This costs work and dissipates energy in the computer, creating a limit on speeds and energy efficiency of future irreversible computers. It was recently shown by Zhen et al. [Phys. Rev. Lett. 127, 190602 (2021)] that for a finite-time reset protocol, the additional work on top of the quasistatic protocol can always be minimized by considering a two-level system, and then be lower bounded through a thermodynamical speed limit. An important question is to understand under what protocol parameters, including a bit reset error and maximum energy shift, this penalty decreases exponentially vs inverse linearly in the protocol time. Here we provide several analytical results to address this question, as well as numerical simulations of specific examples of protocols.

The $M$-dimensional scattering matrix $S\left(E\right)$ which connects incoming to outgoing waves in a chaotic systyem is always unitary, but shows complicated dependence on the energy. This is partly encoded in correlators constructed from traces of powers of $S(E+\epsilon )S^{†}(E-\epsilon )$, averaged over $E$, and by the statistical properties of the time delay operator, $Q\left(E\right)=-i\hslash S^{†}dS/dE$. Using a semiclassical approach for systems with broken time-reversal symmetry, we derive two kinds of expressions for the energy correlators: one as a power series in $1/M$ whose coefficients are rational functions of $\epsilon$, and another as a power series in $\epsilon$ whose coefficients are rational functions of $M$. From the latter we extract an explicit formula for $\mathrm{Tr}\left(Q^m\right)$ which is valid for all $m$ and is in agreement with random matrix theory predictions.

The area-preserving rule for botanical trees by Leonardo da Vinci is discussed in terms of a very specific fractal structure, a logarithmic fractal. We use a method of the numerical Fourier analysis to distinguish the logarithmic fractal properties of the two-dimensional objects and apply it to study the branching system of real trees through its projection on the two-dimensional space, i.e., using their photographs. For different species of trees (birch and oak) we observe the $Q^{-2}$ decay of the spectral intensity characterizing the branching structure that is associated with the logarithmic fractal structure in two-dimensional space. The experiments dealing with the side view of the tree should complement the area preserving Leonardo's rule with one applying to the product of diameter $d$ and length $l$ of the $k$ branches: $d_i{l}_i=k{d}_{i+1}{l}_{i+1}$. If both rules are valid, then the branch's length of the next generation is $\sqrt{k}$ times shorter than previous one: $l_i=\sqrt{k}{l}_{i+1}$. Moreover, the volume (mass) of all branches of the next generation is a factor of $d_i/d_{i+1}$ smaller than previous one. We conclude that a tree as a three-dimensional object is not a logarithmic fractal, although its projection onto a two-dimensional plane is. Consequently, the life of a tree flows according to the laws of conservation of area in two-dimensional space, as if the tree were a two-dimensional object.

We present experimental results of cooper surface temperature measured nanosecond by nanosecond at the very beginning of the laser-induced breakdown experiment. The experiment is conducted by Nd:YAG laser for three irradiances: $1.4\times {10}^9$, $3.2\times {10}^{11}$, and $3.7\times {10}^{12}$ $\mathrm{W}/{\mathrm{cm}}^2$. The temperatures of the metal surface, before plasma is created, are in the interval 7 400–11 200 K. These values are close to most estimates for the critical temperature of copper. The moment when plasma was created is recognized applying a bifurcated optical cable. After creation, temperature of the plasma increases attaining values over 50 000 K. All temperatures are derived relying on continuous spectra emitted from the bright spot illuminated by the laser.

In this paper, two discrete unified gas-kinetic scheme (DUGKS) methods with piecewise-parabolic flux reconstruction are presented for the conservative Allen-Cahn equation (CACE). One includes a temporal derivative of the order parameter in the force term while the other does not include temporal derivative in the force term but results in a modified CACE with additional terms. In the context of DUGKS, the continuum equations recovered from the piecewise-linear and piecewise-parabolic reconstructions for the fluxes at cell faces are subsequently derived. It is proved that the resulting equation with the piecewise-linear reconstruction is a first-order approximation to the discrete velocity kinetic equation due to the presence of the force term and the nonconservation property of the momentum of the collision model. To guarantee second-order accuracy of DUGKS, the piecewise-parabolic reconstruction for numerical flux is proposed. To validate the accuracy of the present DUGKS with the proposed flux evaluation, several benchmark problems, including the diagonal translation of a circular interface, the rotation of a Zalesak disk and the deformation of a circular interface, have been simulated. Numerical results show that the accuracy of both proposed DUGKS methods is almost comparable and improved compared with the DUGKS with linear flux reconstruction scheme.

We show that coupled autonomous thermal machines, in the presence of three heat reservoirs and following a global linear-irreversible description, can have efficiency at maximum power (EMP) which is analogous in form to the EMP of models with two (hot and cold) reservoirs. In particular, the temperature dependence of EMP in the coupled model is via only the ratio of hot and cold temperatures if the intermediate reservoir temperature is expressed as an algebraic mean of these temperatures. Many popular expressions of EMP in the literature can be recovered by making a choice of some standard mean. Further, the universal properties of EMP near equilibrium can be explained in terms of the properties of symmetric means. For the case of broken time-reversal symmetry, a universal second-order coefficient of 6/49 is predicted in the series expansion of EMP, analogous to the 1/8 coefficient in the time-reversal symmetric case.

Progressive quenching (PQ) is a stochastic process during which one fixes, one after another, the degrees of freedom of a globally coupled Ising spin system while letting it thermalize through a heat bath. It has previously been shown that during PQ, the mean equilibrium spin value follows a martingale process and this process can characterize the memory of the system. In the present study, we find that the aforementioned martingale implies a local invariance of the path weight for the total quenched magnetization, the Markovian process whose increment is the spin that is fixed last. Consequently, PQ lets the probability distribution for the total quenched magnetization evolve while keeping the Boltzmann-like factor, or a canonical structure, under constraint, which consists of a path-independent potential and a path-counting entropy. Moreover, when the PQ starts from full equilibrium, the probability distribution at each stage of PQ is found to be the limit distribution of what we call recycled quenching, the process in which a randomly chosen quenched spin is unquenched after a single step of PQ. The local invariance is directly derived from the martingale property, and not from other known theorems on martingale processes.

By now active Brownian motion is a well-established model to describe the motion of mesoscopic self-propelled particles in a Newtonian fluid. On the basis of the generalized Langevin equation, we present an analytic framework for active Brownian motion with memory delay assuming time-dependent friction kernels for both translational and orientational degrees of freedom to account for the time-delayed response of a viscoelastic medium. Analytical results are obtained for the orientational correlation function, mean displacement, and mean-square displacement which we evaluate in particular for a Maxwell fluid characterized by a kernel which decays exponentially in time. Further, we identify a memory-induced delay between the effective self-propulsion force and the particle orientation which we quantify in terms of a special dynamical correlation function. In principle, our predictions can be verified for an active colloidal particle in various viscoelastic environments such as a polymer solution.

We demonstrate the sensitivity of the plasma composition in the filament wake channel in a dense gas to the temporal shape of the driving femtosecond laser pulse. During the pulse, the electrons released via strong-field ionization and driven by oscillating laser field are actively engaged in collisional processes with neutral neighbor atoms, including inverse Bremsstrahlung, impact ionization, and collisional excitation. By the end of the pulse, these collisional processes produce considerable numbers of additional free electrons (or ionized atoms) and excited atoms, and these contents of the filament wake channel determine its subsequent evolution dynamics. Addressing the case of high-pressure argon gas and using a kinetic model of these competing collisional processes, we explore the sensitivity of the resulting excited-to-ionized atoms number density ratio to the envelope shape of the driving laser pulse. By considering several families of pulses, we show that asymmetric pulse envelopes skewed toward the earlier time allow for efficient control of the ratio of excited atoms to ionized atoms. The pulse-shape control of the plasma composition in the immediate wake of the laser pulse projects into control of the wake channel evolution and of the associated transient electronic and optical nonlinearities.