Random acceleration is a fundamental stochastic process encountered in many applications. In the one-dimensional version of the process a particle is randomly accelerated according to the Langevin equation $\ddot{x}\left(t\right)=\sqrt{2D}\xi \left(t\right)$, where $x\left(t\right)$ is the particle's coordinate, $\xi \left(t\right)$ is Gaussian white noise with zero mean, and $D$ is the particle velocity diffusion constant. Here, we evaluate the $A\to 0$ tail of the distribution $P_n\left(A\right|L)$ of the functional $I\left[x\left(t\right)\right]={\int }_0^T{x}^n\left(t\right)dt=A$, where $T$ is the first-passage time of the particle from a specified point $x=L$ to the origin, and $n\ge 0$. We employ the optimal fluctuation method akin to geometrical optics. Its crucial element is determination of the optimal path—the most probable realization of the random acceleration process $x\left(t\right)$, conditioned on specified $A, n$, and $L$. The optimal path dominates the $A\to 0$ tail of $P_n\left(A\right|L)$. We show that this tail has a universal essential singularity, $P_n(A\to 0|L)\sim exp(-\frac{{\alpha }_n{L}^{3n+2}}{D{A}^3})$, where ${\alpha }_n$ is an $n$-dependent number which we calculate analytically for $n=0$, 1, and 2 and numerically for other $n$. For $n=0$ our result agrees with the asymptotic of the previously found first-passage time distribution.

Even though the existence of nonconvergent evolution of the states of populations in ecological and evolutionary contexts is an undeniable fact, insightful game-theoretic interpretations of such outcomes are scarce in the literature of evolutionary game theory. As a proof-of-concept, we tap into the information-theoretic concept of relative entropy in order to construct a game-theoretic interpretation for periodic orbits in a wide class of deterministic discrete-time evolutionary game dynamics, primarily investigating the two-player two-strategy case. Effectively, we present a consistent generalization of the evolutionarily stable strategy—the cornerstone of the evolutionary game theory—and aptly term the generalized concept “information stable orbit.” The information stable orbit captures the essence of the evolutionarily stable strategy in that it compares the total payoff obtained against an evolving mutant with the total payoff that the mutant gets while playing against itself. Furthermore, we discuss the connection of the information stable orbit with the dynamical stability of the corresponding periodic orbit.

In this experimental paper, we demonstrate that turbulence can develop in a fluid system with background damping. For that purpose, we analyze dust acoustic waves, self-excited in a fluid complex plasma where the motion of individual microparticles was recorded with a high-speed video camera. We use the Wiener-Khinchin theorem to calculate the kinetic spectrum during different phases of the highly nonlinear periodic wave motion and show that a turbulent cascade develops at the phases of highest particle compression. We demonstrate that the energy cascade occurs despite the presence of a damping force due to the background neutral gas.

The structural diversity of the solute molecules involved in biomolecular processes necessitates the characterization of the forces between charged macromolecules beyond the point-ion description. From the field-theoretic partition function of an electrolyte confined between two anionic membranes, we derive a contact-value identity valid for general intramolecular solute structure and electrostatic coupling strength. In the electrostatic mean-field regime, the inner charge spread of the solute particles is shown to induce the twofold enhancement of the short-range Poisson-Boltzmann level membrane repulsion and a longer-range depletion attraction. Our contact theorem indicates that the twofold repulsion enhancement by solute size is equally present in the opposite strong-coupling regime of linear and spherical solute molecules. Upon the inclusion of the dielectric contrast between the electrolyte and the interacting membranes, the emerging polarization forces substantially amplify the solute specificity of the macromolecular interactions. Namely, the finite size of the dumbbell-like solute particles composed of similar terminal charges weakens the intermembrane repulsion. However, the extended structure of the solute molecules carrying opposite elementary charges such as ionized atoms and zwitterionic molecules enhances the membrane repulsion by several factors. We also show that these polarization forces can extend the range of the solute structure effects up to intermembrane distances exceeding the solute size by an order of magnitude. This radical alteration of the intermembrane interactions by the salt structure identifies the solute specificity as a key ingredient of the thermodynamic stability in colloidal systems.

Not every particle that forms a nematic liquid crystal makes a smectic. The particle tip is critical for this behavior. Ellipsoids do not make a smectic, but spherocylinders do. Similarly, only those $N$-CB alkylcyanobiphenyls with sufficiently long ($N\ge 8$ carbons) alkane tails form smectics. We understand the role of the particle tip in the smectic transition by means of a simple two-dimensional model. We model spherocylinders by “boubas” with rounded tips, and ellipsoids by “kikis” with pointed tips. The $N$-CB molecules are modeled by a small body with a polymer tail. We find that rounded tips and longer polymer tails lead to a smectic at lower densities by making the space between layers less accessible, destabilizing the nematic.

Prevailing diffusion-limited analyses of evaporating sessile droplets are facilitated by a quasisteady model for the evolution of vapor concentration in space and time. When attempting to employ that model in two dimensions, however, one encounters an impasse: the logarithmic growth of concentration at large distances, associated with the Green's function of Laplace's equation, is incompatible with the need to approach an equilibrium concentration at infinity. Observing that the quasisteady description breaks down at large distances, the diffusion problem is resolved using matched asymptotic expansions. Thus the vapor domain is conceptually decomposed into two asymptotic regions: one at the scale of the drop, where vapor transport is indeed quasisteady, and one at a remote scale, where the drop appears as a point singularity and transport is genuinely unsteady. The requirement of asymptotic matching between the respective regions furnishes a self-consistent description of the time-evolving evaporation process. Its solution provides the droplet lifetime as a universal function of a single physical parameter. Our scheme avoids the use of a remote artificial boundary, which introduces a nonremovable dependence upon a nonphysical parameter.

We analyze the impact of temperature on the diffusion coefficient of an inertial Brownian particle moving in a symmetric periodic potential and driven by a symmetric time-periodic force. Recent studies have revealed the low-friction regime in which the diffusion coefficient shows giant damped quasiperiodic oscillations as a function of the amplitude of the time-periodic force [I. G. Marchenko et al., Chaos 32, 113106 (2022)]. We find out that when temperature grows the diffusion coefficient increases at its minima; however, it decreases at the maxima within a finite temperature window. This curious behavior is explained in terms of the deterministic dynamics perturbed by thermal fluctuations and mean residence time of the particle in the locked and running trajectories. We demonstrate that temperature dependence of the diffusion coefficient can be accurately reconstructed from the stationary probability to occupy the running trajectories.

Resistance switching memory cells such as electrochemical metallization cells and valence change mechanism cells have the potential to revolutionize information processing and storage. However, the creation of deterministic resistance switching devices is a challenging problem that is still open. At present, the modeling of resistance switching cells is dominantly based on deterministic models that fail to capture the cycle-to-cycle variability intrinsic to these devices. Herewith we introduce a state probability distribution function and associated integrodifferential equation to describe the switching process consisting of a set of stochastic jumps. Numerical and analytical solutions of the equation have been found in two model cases. This work expands the toolbox of models available for resistance switching cells and related devices and enables a rigorous description of intrinsic physical behavior not available in other models.

This paper studies a set of globally coupled bistable oscillators, all subjected to the same weak periodic signal and identical coupling. The effect of mean field density (MFD) on global dynamics is analyzed. The oscillators switch from intra- to interwell motion as MFD increases, clearly demonstrating MFD-enhanced signal amplification. A maximum amplification also occurs at a moderate level of MFD, indicating that the response exhibits a nonmonotonic sensitivity to MFD. The MFD-enhanced response depends mainly on the signal intensity but not on the signal frequency or the network topology. The analytical investigation provides a simplified model to study the mechanism underlying this resonancelike behavior. It is shown that by modifying the bistability nature of the potential energy, the mean field density can promote well-to-well oscillations and larger amplitude motions. Finally, the robustness of this phenomenon to various signal waveforms is examined. It can therefore be used alternatively to efficiently amplify weak signals in practical situations with large network sizes.

We derive general analytical expressions for the time-averaged acoustic radiation force on a small spherical particle suspended in a fluid and located in an axisymmetric incident acoustic wave. We treat the cases of the particle being either an elastic solid or a fluid particle. The effects of particle vibrations, acoustic scattering, acoustic microstreaming, heat conduction, and temperature-dependent fluid viscosity are all included in the theory. Acoustic streaming inside the particle is also taken into account for the case of a fluid particle. No restrictions are placed on the widths of the viscous and thermal boundary layers relative to the particle radius. We compare the resulting acoustic radiation force with that obtained from previous theories in the literature, and we identify limits, where the theories agree, and specific cases of particle and fluid materials, where qualitative or significant quantitative deviations between the theories arise.

The objective of this work is to show that adiabatic processes can be very similar to isothermal ones. First, we show that the criteria for the compatibility of linear-response theory with the second law of thermodynamics for thermally isolated systems are the same as those for systems performing isothermal processes. Motivated by such a result, we explore the thermodynamic consequences of the time-average excess work, observing an unexpected existence of a well-defined relaxation time for thermally isolated systems that obeys the second law of thermodynamics. This is justified by recognizing that such systems, in the usual sense, present random relaxation time, which can be “averaged” by taking the time average of the relaxation function. Such a proceeding is very similar to what happens in isothermal processes, where a stochastic average must be done on the relaxation function to have a well-defined relaxation time. In the end, we analyze the Landau-Zener model from this new point of view, discussing the construction of slowly-varying processes from linear-response theory and observing negative entropy production rates for nonmonotonic and rapid protocols.

The stochastic thermodynamics of systems with a few degrees of freedom has been studied extensively so far. We would like to extend the study to systems with more degrees of freedom and even further-continuous fields with infinite degrees of freedom. The simplest case for a continuous stochastic field is the Edwards-Wilkinson elastic manifold. It is an exactly solvable model of which the heat statistics in the relaxation process can be calculated analytically. The cumulants require a cutoff spacing to avoid ultraviolet divergence. The scaling behavior of the heat cumulants with time and the system size as well as the large deviation rate function of the heat statistics in the large size limit is obtained.

The relation between spontaneous and stimulated brain activity is a fundamental question in neuroscience which has received wide attention in experimental studies. Recently, it has been suggested that the evoked response to external stimuli can be predicted from temporal correlations of spontaneous activity. Previous theoretical results, confirmed by the comparison with magnetoencephalography data for human brains, were obtained for the Wilson-Cowan model in the condition of balance of excitation and inhibition, a signature of a healthy brain. Here we extend previous studies to imbalanced conditions by examining a region of parameter space around the balanced fixed point. Analytical results are compared to numerical simulations of Wilson-Cowan networks. We evidence that in imbalanced conditions the functional form of the time correlation and response functions can show several behaviors, exhibiting also an oscillating regime caused by the emergence of complex eigenvalues. The analytical predictions are fully in agreement with numerical simulations, validating the role of cross-correlations in the response function. Furthermore, we identify the leading role of inhibitory neurons in controlling the overall activity of the system, tuning the level of excitability and imbalance.

We show that an ultra-high-pressure plasma can be generated when an aligned nanowire is irradiated by a laser with relativistic transparent intensity. Using a particle-in-cell simulation, we demonstrate that the expanded plasma following the $z$ pinch becomes relativistically transparent and compressed longitudinally by the oscillating component of the ponderomotive force. The compressed structure persists throughout the pulse duration with a maximum pressure of $40\mathrm{Tbar}$ when irradiated with a laser at an intensity of ${10}^{23}\mathrm{W}{\mathrm{cm}}^{-2}, 5\times$ higher than the $z$-pinch pressure. These results suggest an alternative approach to extending the current attainable pressure in the laboratory.

We propose a type of quantum statistics which we call inclusion statistics, in which particles tend to coalesce more than ordinary bosons. Inclusion statistics is defined in analogy with exclusion statistics, in which statistical exclusion is stronger than in Fermi statistics, but now extrapolating beyond Bose statistics, resulting in statistical inclusion. A consequence of inclusion statistics is that the lowest space dimension in which particles can condense in the absence of potentials is $d=2$, unlike $d=3$ for the usual Bose-Einstein condensation. This reduction in the dimension happens for any inclusion stronger than bosons, and the critical temperature increases with stronger inclusion. Possible physical realizations of inclusion statistics involving attractive interactions between bosons may be experimentally achievable.

By using the kicked Harper model, the effect of dynamical perturbations to the localized and ballistic phases in quasiperiodic lattice systems is investigated. The transition from the localized phase to diffusive phase via a critical subdiffusion $t^{\alpha }$ ($t$ is time) with $0<\alpha <1$ is observed. In addition, we confirm the existence of the transition from the ballistic phase to the diffusive phase via a critical superdiffusion with $1<\alpha <2$.

The Delta-Notch system plays a vital role in many areas of biology and typically forms a salt and pepper pattern in which cells strongly expressing Delta and cells strongly expressing Notch are alternately aligned via lateral inhibition. In this study, we consider cell rearrangement events, such as cell mixing and proliferation, that alter the spatial structure itself and affect the pattern dynamics. We model cell rearrangement events by a Poisson process and analyze the model while preserving the discrete properties of the spatial structure. We investigate the effects of the intermittent perturbations arising from these cell rearrangement events on the discrete spatial structure itself in the context of pattern formation and by using an analytical approach, coupled with numerical simulation. We find that the homogeneous expression pattern is stabilized if the frequency of cell rearrangement events is sufficiently large. We analytically obtain the balanced frequencies of the cell rearrangement events where the decrease of the pattern amplitude, as a result of cell rearrangement, is balanced by the increase in amplitude due to the Delta-Notch interaction dynamics. Our framework, while applied here to the specific case of the Delta-Notch system, is applicable more widely to other pattern formation mechanisms.

We study ab initio approaches for calculating x-ray Thomson scattering spectra from density functional theory molecular dynamics simulations based on a modified Chihara formula that expresses the inelastic contribution in terms of the dielectric function. We study the electronic dynamic structure factor computed from the Mermin dielectric function using an ab initio electron-ion collision frequency in comparison to computations using a linear-response time-dependent density functional theory (LR-TDDFT) framework for hydrogen and beryllium and investigate the dispersion of free-free and bound-free contributions to the scattering signal. A separate treatment of these contributions, where only the free-free part follows the Mermin dispersion, shows good agreement with LR-TDDFT results for ambient-density beryllium, but breaks down for highly compressed matter where the bound states become pressure ionized. LR-TDDFT is used to reanalyze x-ray Thomson scattering experiments on beryllium demonstrating strong deviations from the plasma conditions inferred with traditional analytic models at small scattering angles.

This paper introduces the location Pareto distribution as a natural extension of the power law distribution and gives a likelihood ratio test for choosing between the two models. Some properties of the distribution and test are thoroughly investigated, and applications to real data are provided. For large values of the observations the two models perform similarly; this explains why some classical approaches are very insensitive to the differentiation between them. The likelihood ratio test between the two models is simple to use and has a high level of discrimination power. It is recommended when the complementary cumulative distribution function exhibits linearity on a log-log scale.

The spatial distribution of cosmic ray (CR) particles in the interstellar medium (ISM) is of major importance in radio astronomy, where its knowledge is essential for the interpretation of observations, and in theoretical astrophysics, where CRs contribute to the structure and dynamics of the ISM. Local inhomogeneities in interstellar magnetic field strength and structure can affect the local diffusivity and ensemble dynamics of the CR particles. Magnetic traps (regions between magnetic mirrors located on the same magnetic line) can lead to especially strong and persistent features in the CR spatial distribution. Using test particle simulations, we study the spatial distribution of an ensemble of CR particles (both protons and electrons) in various magnetic field configurations, from an idealized axisymmetric trap to those that emerge in intermittent (dynamo-generated) random magnetic fields. We demonstrate that both the inhomogeneity in the CR sources and the energy losses by the CR particles can lead to persistent local inhomogeneities in the CR distribution and that the protons and electrons have different spatial distributions. Our results can have profound implications for the interpretation of the synchrotron emission from astronomical objects, and in particular its random fluctuations.