We investigate nonequilibrium relaxations of Ising models at the critical point by using a cluster update. While preceding studies imply that nonequilibrium cluster-flip dynamics at the critical point are universally described by the stretched-exponential function, we find that the dynamics changes from the stretched exponential to the power function as the dimensionality is increased: The two-, three-, four-, and infinite-dimensional Ising models are numerically studied, and the four- and infinite-dimensional Ising models exhibit the power-law relaxation. We also show that the finite-size scaling analysis using the normalized correlation length is markedly effective for the analysis of relaxational processes rather than the direct use of the Monte Carlo step.

In exchange processes clusters composed of elementary building blocks, monomers, undergo binary exchange in which a monomer is transferred from one cluster to another. In assortative exchange only clusters with comparable masses participate in exchange events. We study maximally assortative exchange processes in which only clusters of equal masses can exchange monomers. A mean-field framework based on rate equations is appropriate for spatially homogeneous systems in sufficiently high spatial dimension. For diffusion-controlled exchange processes, the mean-field approach is erroneous when the spatial dimension is smaller than critical; we analyze such systems using scaling and heuristic arguments. Apart from infinite-cluster systems we explore the fate of finite systems and study maximally assortative exchange processes driven by a localized input.

We study the collective dynamics of strongly diffusively coupled excitable elements on small random tree networks. Stochastic external inputs are applied to the leaves causing large spiking events. Those events propagate along the tree branches and, eventually, excite the root node. Using Hodgkin-Huxley type nodal elements, such a setup serves as a model of sensory neurons with branched myelinated distal terminals. We focus on the influence of the variability of tree structures on the spike train statistics of the root node. We present a statistical description of random tree networks and show how the structural variability translates into the collective network dynamics. In particular, we show that in the physiologically relevant case of strong coupling the variability of collective response is determined by the joint probability distribution of the total number of leaves and nodes. We further present analytical results for the strong-coupling limit in which the entire tree network can be represented by an effective single element.

The elastic bending constants $\kappa$ (elastic bending modulus) and $\overline{\kappa }$ (saddle-splay modulus) are key parameters for understanding the properties of microemulsions (MEs), vesicles, biological membranes, and other self-assembled amphiphilic molecular structures. The determination of $\kappa$ is rather straight forward, whereas $\overline{\kappa }$ is quiet difficult to access experimentally. Nonetheless, the estimation of $\overline{\kappa }$ is crucial, owing to its importance in governing the intricate phase behavior, topology, and stability of these self-assembled structures. Here, we present an elegant protocol to determine the saddle-splay modulus of the spherical droplet phase of microemulsions using small-angle neutron scattering (SANS) and dielectric relaxation spectroscopy (DRS) techniques. The $\kappa$ of AOT [sodium 1,4-bis(2-ethylhexoxy)-1,4-dioxobutane-2-sulfonate)]stabilized reverse MEs is estimated by probing their percolation transitions. Further, the effective elastic bending constant $K$ is determined from the polydispersity of ME droplets measured using SANS, where the droplet deformations due to thermal fluctuations are described in terms of spherical harmonics. Strikingly, the ratio $\overline{\kappa }/\kappa$ lies in the acceptable range, $-2<\overline{\kappa }/\kappa <0$, for the spherical droplet phase of MEs [R. H. Templer, B. J. Khoo, and J. M. Seddon, Langmuir 14, 7427 (1998)], which further validates the proposed strategy to estimate the saddle-splay modulus.

The self-consistency of the distributional fixed-point equation (DFPE) approach to understanding the statistical properties of island nucleation and growth during submonolayer deposition is explored. We perform kinetic Monte Carlo simulations, in which point islands nucleate on a one-dimensional lattice during submonolyer deposition with critical island size $i$, and we examine the evolution of the inter-island gaps as they are fragmented by new island nucleation. The DFPE couples the fragmentation probability distribution within the gaps to the consequent gap size distribution (GSD), and we find a good fit between the DFPE solutions and the observed GSDs for $i=0$, 1, 2, and 3. Furthermore, we develop numerical methods to address the inverse problem, namely the problem of obtaining the gap fragmentation probability from the observed GSD, and again find good self-consistency in the approach. This has consequences for its application to experimental situations where only the GSD is observed and where the growth rules embodied in the fragmentation process must be deduced.

We first argue that negative muons in the MeV energy range can be fully stopped in warm-dense-matter and fast ignition scenario ultradense plasmas on a picosecond time scale by taking into account the slowing down of partially degenerate electrons and charged hydrogen isotope ions taken as classical. Atomic and molecular recombinations within these plasmas on the lowest available exoatom bound states are then demonstrated. The very existence of in situ produced exoatoms can be proved with x-ray line Stark broadening. Finally, a former conjecture about the negligibility of meson sticking on fusion-produced particles is reinforced. Mesonic catalysis of deuterium-tritium fusion reactions is then shown to be possible in short-lived plasma targets with rates that are orders of magnitude above cold deuterium reactions. The dipole exoatom orientations clearly favor the cold and long-lived warm-dense-matter option.

A central concept in the connection between physics and information theory is entropy, which represents the amount of information extracted from the system by the observer performing measurements in an experiment. Indeed, Jaynes' principle of maximum entropy allows to establish the connection between entropy in statistical mechanics and information entropy. In this sense, the dissipated energy in a classical Hamiltonian process, known as the thermodynamic entropy production, is connected to the relative entropy between the forward and backward probability densities. Recently, it was revealed that energetic inefficiency and model inefficiency, defined as the difference in mutual information that the system state shares with the future and past environmental variables, are equivalent concepts in Markovian processes. As a consequence, the question about a possible connection between model unpredictability and energetic inefficiency in the framework of classical physics emerges. Here, we address this question by connecting the concepts of random behavior of a classical Hamiltonian system, the Kolmogorov-Sinai entropy, with its energetic inefficiency, the dissipated work. This approach allows us to provide meaningful interpretations of information concepts in terms of thermodynamic quantities.

Biological systems are often composed of various heterogeneous excitable units. It is a fascinating problem to investigate how this heterogeneity affects collective behavior of biological systems. In this paper, to understand the effect of the unit heterogeneity on the dynamical mechanism for the onset of collective oscillatory behavior, we analyze coupled heterogeneous excitable units. We clarify how spontaneous oscillations emerge depending on the degree of heterogeneity of the units. With an increase in the coupling strength, the system undergoes a saddle-node on invariant circle bifurcation and a heteroclinic bifurcation. Based on bifurcation theory, we reveal that the order of the two bifurcations plays key roles in the mechanism of the emergence of spontaneous oscillations. In addition, we analytically show that when the system has a symmetric property, a 5th-order pitchfork bifurcation occurs instead of the two bifurcations. We also find that spontaneous oscillations are more likely to occur when the sizes of subpopulations of excitable units with different parameters are more balanced.

A periodically forced Liénard system is capable of generating frequent large-amplitude chaotic bursts for a range of system and external forcing parameter values which are known as mixed mode oscillations. Particularly, if these large chaotic bursts occur infrequently and randomly, then they are characterized as extreme events. We present a numerical study of the effect of self-time-delay feedback on these extreme events in this system and interestingly find that extreme events can be completely eliminated from the system dynamics, even for smaller values of delay feedback strength. We show here that the number of extreme events is reduced, and the probability of the occurrence of high-amplitude events is transformed from a long-tailed statistics to the localized structure, as a function of the feedback strength corroborates our results. Further, we show that the autonomous Liénard system loses its conservative nature when delay feedback is added and only a dissipative nature remains in the entire phase space, which is the underlying mechanism behind the elimination of such large events. Further, we have revealed a type of delay-induced damping behavior, named anomalous damping, in which the amplitude of the oscillations suddenly vanishes when the total energy of the system becomes zero.

Settling dynamics of non-Brownian particles is investigated using particle-resolved direct numerical simulations. There are two aims of this paper: first is to study the variation of particle velocity fluctuations with solid volume for a wide range of settling Reynolds number; second is to investigate the effects of solid volume fraction and settling Reynolds number on the distribution of particle velocity fluctuations after reaching the steady state. Simulations are performed in the periodic domain and the settling Reynolds number and solid volume fraction are varied from 0.5 to 400 and 0.01 to 0.2, respectively. It is observed that particle velocity fluctuations increase with increase in solid volume fraction for settling Reynolds number less than 100. Further increase in the settling Reynolds number alters the behavior of settling particles, making the particle velocity fluctuations either remain nearly constant or even decrease with the increase in solid volume fraction. For dense suspensions, it is observed by simulations that the distribution of particle velocities has Gaussian form during settling. However, for dilute and moderately dense suspensions, particle velocity distribution becomes non-Gaussian for the studied range of settling Reynolds number. At the end of paper, the physics behind the scaling of particle velocity fluctuations with solid volume fraction and the distribution of particle velocity fluctuations during settling is explained.

We study active restoration of noise-corrupted images generated via the Gibbs probability of an Ising ferromagnet in external magnetic field. Ferromagnetism accounts for the prior expectation of data smoothness, i.e., a positive correlation between neighboring pixels (Ising spins), while the magnetic field refers to the bias. The restoration is actively supervised by requesting the true values of certain pixels after a noisy observation. This additional information improves restoration of other pixels. The optimal strategy of active inference is not known for realistic (two-dimensional) images. We determine this strategy for the mean-field version of the model and show that it amounts to supervising the values of spins (pixels) that do not agree with the sign of the average magnetization. The strategy leads to a transparent analytical expression for the minimal Bayesian risk, and shows that there is a maximal number of pixels beyond of which the supervision is useless. We show numerically that this strategy applies for two-dimensional images away from the critical regime. Within this regime the strategy is outperformed by its local (adaptive) version, which supervises pixels that do not agree with their Bayesian estimate. We show on transparent examples how active supervising can be essential in recovering noise-corrupted images and advocate for a wider usage of active methods in image restoration.

We present a semiclassical approach to $n$-point spectral correlation functions of quantum systems whose classical dynamics is chaotic, for arbitrary $n$. The basic ingredients are sets of periodic orbits that have nearly the same action and therefore provide constructive interference. We calculate explicitly the first correlation functions, to leading orders in their energy arguments, for both unitary and orthogonal symmetry classes. The results agree with corresponding predictions from random matrix theory, thereby giving solid support to the conjecture of universality.

Starting from a semiclassical approach recently developed for spectral correlation functions of quantum systems whose classical dynamics is chaotic, we focus on the case of broken time-reversal symmetry, the so-called unitary class. We obtain to all orders in perturbation theory the nonoscillatory parts of all correlation functions, showing that the off-diagonal contributions to these correlation functions cancel and the conjectured universality holds. The innovation that allows this calculation to be performed is the introduction of an auxiliary matrix model which is governed by the same diagrammatic rules as the semiclassical approach and which can be exactly solved.

Several recent papers have shown that reservoir computers are useful for analyzing and predicting dynamical systems. Reservoir computers have also been shown to be useful for various classification problems. In this work, a reservoir computer is used to identify one out of the 19 different Sprott systems. An advantage of reservoir computers for this problem is that no embedding is necessary. Some guidance on choosing the reservoir computer parameters is given. The dependance on number of points, number of reservoir nodes, and noise in identifying the Sprott systems is explored.

An efficient collective response to external perturbations is one of the most striking abilities of a biological system. One of the crucial aspect of this phenomenon is given by the information transfer, and resulting propagation of signals, within the group. In this respect the existence of density waves that propagate linearly on a flock of birds is well known. However, most aspects of this phenomenon are still not fully captured by theoretical models. In this work we present a model for the propagation of speed fluctuations inside a flock, which is able to reproduce the observed density waves. We study the full solution of the model in $d=1$, and we find a line in the parameter space along which the system relaxes as fast as possible without oscillating, resembling a generalized critical damping condition. By analyzing the parameters plane we show that this “critical damping” line indeed represents an attractor for a steepest descent dynamics of the return time of the system. Finally we propose a method to test the validity of the model through future experiments.

Spatially forced systems can exhibit coexistence and a rich interface dynamics between manipulable states. We show here how the propagation speed of a front into an unstable state can be modified through periodic space forcing. Based on optical feedback, we set up a quasi-one-dimensional forced experiment in a liquid-crystal cell. When changing the forcing parameters, fronts exhibit a ratchet motion. Unexpectedly, the average speed of fronts decreases when the strength of the forcing increases. Close to molecular reorientation transition, an amplitude equation allows characterizing analytically and numerically the observed dynamics.

The packing and flow of aspherical frictional particles are studied using discrete element simulations. Particles are superballs with shape ${\left|x\right|}^s+{\left|y\right|}^s+{\left|z\right|}^s=1$ that varies from sphere ($s=2$) to cube ($s=\infty$), constructed with an overlapping-sphere model. Both packing fraction, $\varphi$, and coordination number, $z$, decrease monotonically with microscopic friction $\mu$, for all shapes. However, this decrease is more dramatic for larger $s$ due to a reduction in the fraction of face-face contacts with increasing friction. For flowing grains, the dynamic friction $\tilde{\mu }$—the ratio of shear to normal stresses—depends on shape, microscopic friction, and inertial number $I.$ For all shapes, $\tilde{\mu }$ grows from its quasistatic value ${\tilde{\mu }}_0$ as $(\tilde{\mu }-{\tilde{\mu }}_0)=d{I}^{\alpha }$, with different universal behavior for frictional and frictionless shapes. For frictionless shapes the exponent $\alpha \approx 0.5$ and prefactor $d\approx 5{\tilde{\mu }}_0$ while for frictional shapes $\alpha \approx 1$ and $d$ varies only slightly. The results highlight that the flow exponents are universal and are consistent for all the shapes simulated here.

In this paper, we investigate the statistical behavior of Brownian particles in a deformable traveling-wave potential in the absence of external load. We model the deformation of the system by the modified Remoissenet-Peyrard on-site potential, which is distinguished by its sine-Gordon shape. We examine numerically the effect of the deformed on-site potential with traveling speeds on the transport properties in overdamped as well as underdamped Brownian particles. Using the Langevin Monte Carlo method, we show that the average velocity of Brownian particles is an increasing function of the shape parameter in the overdamped case, and a decreasing function of the shape parameter in the underdamped case. It is found that, in the overdamped case, the numerical behavior of the average velocity of Brownian particles validates its analytical results. In the presence of the deformable traveling-wave potential, for negative as well as positive values of the shape parameter, the underdamped case favors the transport properties in the medium. The average velocity needed to cross the potential barriers is lowest in the underdamped case. Moreover, the effective diffusion coefficient in both cases exhibits peaks, and the diffusion process enhancement is discussed for some values of the shape parameter. Finally, in the underdamped case, by using the Smoluchowski equation and the finite-element methods, we analyze the distribution of Brownian particles in the deformed system.

Scroll waves in reaction diffusion systems can be pinned to several unexcitable heterogeneities. The stable pinned filaments have highly enhanced lifetimes. An external gradient can be applied to unpin the scroll waves sequentially from the anchoring sites. As the number of pinning sites are increased, the strength of the field required to unpin the filament also increases. The time required for unpinning changes as a function of the number of anchors, the geometry in which they are arranged, and their placement relative to the external field direction. Experiments with the Belousov-Zhabotinsky reaction are supported by numerical simulations on a simple reaction diffusion model.