The effect of correlations in disorder variables is a largely unexplored topic in spin glass theory. We study this problem through a specific example of correlated disorder introduced in the Ising spin glass model. We prove that the distribution function of the magnetization along the Nishimori line in the present model is identical to the distribution function of the spin glass order parameter in the standard Edwards-Anderson model with symmetrically distributed independent disorder. This result means that if the Edwards-Anderson model exhibits replica symmetry breaking, the magnetization distribution in the correlated model has support on a finite interval, in sharp contrast to the conventional understanding that the magnetization distribution has, at most, two delta peaks. This unusual behavior challenges the traditional argument against replica symmetry breaking on the Nishimori line in the Edwards-Anderson model. In addition, we show that when temperature chaos is present in the Edwards-Anderson model, the ferromagnetic phase is strictly confined to the Nishimori line in the present model. These findings are valid not only for finite-dimensional systems but also for the infinite-range model, and highlight the need for a deeper understanding of disorder correlations in spin glass systems.

We consider two globally coupled populations of phase oscillators featuring as conformists and contrarians, respectively. By employing an asymmetric parameter for contrarians, we unravel the emergence of various collective dynamical states, including incoherent, chimera, phase clusters, quasiperiodic chimera, and frequency clusters states. Specifically, chimera, quasiperiodic chimera, and frequency clusters states emerge only for appropriate fractions of both conformists and contrarians, and for a large enough asymmetric parameter. We also show that the asymmetric parameter diminishes the spread of the bistable region and eventually leads to a second-order transition for larger coupling strengths of the contrarians. Further, the spread of the incoherent state decreases in the phase diagrams as the asymmetry between the contrarians is increased. Furthermore, libration of the collective phases onsets for the quasiperiodic chimera state and in the frequency clusters state. We deduce the evolution equations corresponding to the macroscopic order parameters using the finite-dimensional reduction by Watanabe and Strogatz. The analytical stability conditions obtained from the evolution equations for the macroscopic order parameters agree very well with the simulation boundaries of the dynamical states.

Methane hydrate deposits are one of the largest fractions of hydrocarbons in the Earth's crust. They are found mainly in ocean sediments, and the configuration of the deposits—at the largest (kilometer) and smallest (micrometer) scales—determines how and when gaseous methane is released. Here, using thermodynamic arguments, we show how the confined spaces of the sediment allow methane hydrate to coexist with both water and gas to create a three-phase region. We find that the hydrate pore occupancy changes depending on the depth of the three-phase region, due to changes in methane density of the gas phase. We estimate the thickness of three-phase regions (hydrate, gas, and water) within ocean sediments. We further show how this directly predicts how the presence of hydrate affects the flow properties of gaseous methane and water through porous media.

This paper investigates the thermal nonequilibrium effects on Richtmyer-Meshkov (RM) flow driven by a heavy forward-triangular bubble. Numerical laminar simulations are performed by utilizing the compressible dimensionless Navier-Fourier equations obtained from the Boltzmann-Curtiss transport equation of nonmonatomic gases that consider translational energy-rotational energy transfer. Three distinct gases, including monatomic argon, diatomic nitrogen, and polyatomic methane, envelop a forward-triangular bubble that is filled with sulfur hexafluoride. Simulations are performed with a shock Mach number of 1.2. The simulations demonstrate that the thermal nonequilibrium and flow characteristics of nonmonatomic gases cause significant changes in the flow fields, which lead to complicated wave patterns, bubble deformation, and vortex dynamics. Using contours and spatially integrated fields of vorticity generation, degree of nonequilibrium, enstrophy, dissipation rate, and kinetic energy, a thorough analysis of nonmonatomic gases is conducted. The nonmonatomic gases produce larger rolled-up vortex chains, longer outward jet forms, and enormous mixing zones with strong, large-scale expansion in contrast to monatomic gases. Furthermore, a quantitative analysis of the time variations of interface features reveals that nonmonatomic gases have enhanced interface features. Lastly, a quantitative investigation is conducted into the consequences of thermal nonequilibrium characteristics. Two patterns are seen in spatially integrated fields: a rising trend in response to an increase in the bulk viscosity ratio and a falling trend in response to an increase in the inverse power-law index.

Propagation of ultrarelativistically intense laser pulses in a self-trapping mode in a near critical density plasma makes it possible to produce electron bunches of extreme parameters appropriate for different state of the art applications. Based on three-dimensional particle-in-cell (PIC) simulations, it has been demonstrated how the best efficiency of electron acceleration in terms of the total charge of high-energy electrons and laser-to-electron conversion rate can be achieved. For a given laser pulse energy the universal way is a proper matching of laser hot spot size and electron plasma density to the laser pulse duration. The recommendation to achieve the highest yield of high-energy electrons is to compress the laser pulse as much as possible. As an example, compression of a pulse of a few tens of femtoseconds to the $\sim 10$ fs pulse leads to generation of the high-energy electron bunch with the highest total charge to exhibit conversion efficiency exceeding $50\%$ for the Joule-level laser pulse energies.

The thermodynamic properties of sI clathrate hydrates involving methane and carbon dioxide guest molecules have been investigated using Monte Carlo (MC) simulations in the grand canonical ensemble, and analytical cluster approximation (CA) theory. The CA approach is founded on the precise calculation of states within finite cells. Both the sI hydrate structure and the guest species were represented using a two-dimensional triangular lattice-gas model with single- and multiple-site occupancy. The investigation entailed monitoring the lattice coverage's dependence on the chemical potential (adsorption isotherm) and examining quantities like Helmholtz free energy, energy of the adsorbed phase, configurational entropy, and adsorption heat. Three distinct scenarios were considered, each dependent on the intra- and interspecies interactions. First, the study was restricted to an ideal clathrate hydrate, wherein lateral interactions were disregarded, and the system's properties are governed by entropy alone. Second, lateral interactions between the guest species and water molecules were introduced by employing the well-established Lorentz-Berthelot mixing rules. Lastly, repulsive lateral interactions were taken into account. In all cases, a remarkable agreement between the results obtained through CA and MC was observed, underscoring the significant potential of CA theory as a valuable tool for exploring cavity occupancy and selectivity in the sI clathrate hydrate formation process.

We consider the motion of a randomly accelerated particle in one dimension 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 position, $\xi \left(t\right)$ is Gaussian white noise with zero mean, and $D$ is the particle velocity diffusion constant. By employing the optimal fluctuation method, we study the short-time distribution $P(\mathcal{A}=A)$ of the functionals, $\mathcal{A}={\int }_0^{t_f}{x}^n\left(t\right)dt$, along constrained trajectories for a given time duration $t_f$, where $n$ is a positive integer. We consider two types of constraints: one called the total constraint, where the initial position and velocity and the final position and velocity are both fixed, and the other, called the partial constraint, where the initial position and velocity and the final position are fixed, and letting the final velocity be free. Via the variation of constrained action functionals, the resulting Euler-Lagrange equations are analytically solved for $n=1$ and 2, and the optimal path, that is, the most probable realization of the random acceleration process $x\left(t\right)$, conditioned on specified $A$ and $n$, are correspondingly obtained. For $n\ge 3$, a numerical scheme is proposed to find the optimal path. We show that, for $n=1, P\left(A\right)$ is a Gaussian distribution with the variance proportional to $D{t}_f^5$. For $n\ge 2, P\left(A\right)$ exhibits the non-Gaussian feature. In the small-$A$ limit, $P\left(A\right)$ shows an essential singularity, $-lnP\left(A\right)\sim A^{-3}$, and the optimal path localizes around the initial state over a long time window and then escapes to the final position sharply at a late time. For $A$ much larger than its typical value, there are multiple optimal paths with the same $A$ but with different actions (or probability densities). Among these degenerate paths, the one with the minimum action is dominant and the others are exponentially unlikely. All theoretical results are validated by simulating the effective Langevin equations governing the constrained random acceleration process.

We investigate the overdamped dynamics of a “passive” particle driven by nonreciprocal interaction with a “driver” Brownian particle. When the interaction between them is short-ranged, the long-time behavior of the driven particle is remarkably universal—the mean-squared displacement (MSD) and the typical position of the driven particle exhibit the same qualitative behaviors independent of the specific form of the potential. In particular, the MSD grows as $t^{1/2}$ in one dimension and $logt$ in two spatial dimensions. We compute the exact scaling functions for the position distribution in $d=1$ and 2. These functions are universal when the interaction is short-ranged. For long-ranged interactions, the MSD of the driven particle grows as $t^{\varphi }$ with exponent $\varphi$ depending on the tail of the potential.

The quantum phase transition of the one-dimensional long-range transverse-field Ising model is explored by combining the quantum Monte Carlo method and stochastic parameter optimization, specifically achieved by tuning correlation ratios so that space and imaginary time are isotropic. In our simulations, the simulator automatically determines the parameters to sample from, even without prior knowledge of the critical point and universality class. The leading-order finite-size corrections are eliminated by comparing two systems with different sizes; this procedure is also performed automatically. Varying the decay exponent of the long-range interaction, $\sigma$, we investigate $\sigma$ dependence of the dynamical exponent and the other critical exponents precisely in the mean-field, nonuniversal, and two-dimensional classical Ising universality regimes. We successfully obtained numerical evidence supporting $\sigma =7/4$ as the universality boundary between the latter two.

We discuss the spectral properties of microwave networks and quantum graphs with preserved and partially violated $\mathcal{T}$ invariance (time-reversal invariance) under an edge swap transformation. A chaotic tetrahedral quantum graph was simulated by the tetrahedral microwave network in which the swap transformation was realized by replacing one pair of edges $\left\{e_i\right\}$ and $\left\{e_j\right\}$ adjacent to different vertices $\left\{v_i\right\}$ and $\left\{v_j\right\}$. We show that the spectra ${\left\{{\nu }_n\right\}}_{n=1}^{\infty }$ and ${\left\{{\tilde{\nu }}_n\right\}}_{n=1}^{\infty }$ before and after an edge swap operation are level-2 interlaced. The experimental distribution $P\left(\mathrm{\Delta }N\right)$ of the spectral shift $\mathrm{\Delta }N=N\left(\nu \right)-\tilde{N}\left(\nu \right)$, where $N\left(\nu \right)$ and $\tilde{N}\left(\nu \right)$ are the counting functions for the original and swapped networks, was confirmed in the numerical calculations. For chaotic systems with partially violated $\mathcal{T}$ invariance, the cases of level-2 interlacing ($\mathrm{\Delta }N=\pm 2$) appear less frequently than for the systems with time reversal symmetry. Furthermore, the widths of the overlapping areas with $\mathrm{\Delta }N=\pm 2$ are getting narrower than for the system with preserved $\mathcal{T}$ invariance. The smaller susceptibility to the swap operation for networks and graphs with partially violated $\mathcal{T}$ invariance is likely caused by the stronger level repulsion in their spectra than in the systems with preserved $\mathcal{T}$ invariance leading to smaller rigidity of their spectra.

The deformed ${\tilde{\phi }}^{\left(6\right)}$ model is introduced based on the ${\phi }^4$ model using a deformation functional $f\left[\phi \right]$ including a free parameter $a$. The kink solutions in different sectors and their internal modes are obtained as functions of the deformation parameter and their characteristics are evaluated as well. It is shown that the kinks of the deformed model inherit some of their dynamical properties (like internal modes) from the standard ${\phi }^4$ potential and some of their characteristics from the ${\phi }^6$ model. The dynamics of kink-antikink (antikink-kink) scattering is investigated in different sectors with various kink initial conditions as well as different values of deformation parameter. According to the kinks' initial velocity, colliding kinks may be bound together or scatter from each other after the interaction. These two situations are distinguished by the critical velocity, which itself depends on the deformation parameter of the model. Due to the difference in the rest mass of kink solutions related to different sectors, interesting and sometimes rare phenomena are observed during the kink scattering and their interactions.

Controlling and understanding phenomena in coupled systems remains a significant challenge across diverse fields. This study investigates a simple globally coupled chemical system that exhibits a range of rich collective dynamics, from coherence to chimera states, controllable by a system parameter. We explore the effects of altering this control parameter using two different protocols. In protocol-I, a continuous variation of the control parameter leads to memory effects, resulting in two distinct sets of phenomena in the forward and reverse directions. In contrast, protocol-II, which includes a resetting feature, yields an entirely distinct collection of behaviors. Additionally, we capture the evolution of key elements of nonequilibrium thermodynamics associated with these dynamical states under both protocols, revealing distinct signatures for each. This work highlights the complexity and uniqueness of regulating coupled systems via control parameters compared to corresponding single systems, and it carries potential implications for the manipulation and application of collective behaviors.

Statistical physicists have long studied systems where the variable of interest spans many orders of magnitude, the classic example is the relaxation times of glassy materials, which are often found to follow power laws. A power-law dependence has been found for the probability of transmission of COVID-19, as a function of length of time a susceptible person is in contact with an infected person. This is in data from the United Kingdom's COVID-19 app. The amount of virus in infected people spans many orders of magnitude. Inspired by this, I assume that the power-law behavior found in COVID-19 transmission is due to the effective transmission rate varying over orders of magnitude from one contact to another. I then use a model from statistical physics to estimate that if a population all wear FFP2/N95 masks, this reduces the effective reproduction number for COVID-19 transmission by a factor of approximately nine.

Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some critical properties of the transition, in particular for heterogeneous substrates, have not been fully elucidated and contradictory results appear in the literature. In this paper we present, by means of a generating functions approach, a thorough and complete investigation of percolation critical properties in uncorrelated locally treelike random networks. We determine all critical exponents, the associated critical amplitude ratios, and the form of the cluster size distribution for networks of any level of heterogeneity. We uncover, in particular for highly heterogeneous networks, subtle crossover phenomena, nontrivial scaling forms, and violations of hyperscaling. In this way we clarify the origin of inconsistencies in the previous literature.

The leading eigenvalue $\lambda$ of the adjacency matrix of a graph exerts much influence on the behavior of dynamical processes on that graph. It is thus relevant to relate notions of importance of network structures to $\lambda$ and its associated eigenvectors. We study a previously derived measure of edge importance known as “dynamical importance,” which estimates how much $\lambda$ changes when one removes an edge from a graph or adds an edge to it. We examine the accuracy of this estimate for several undirected network structures and compare it to the relative change in $\lambda$ after an edge removal or edge addition. We then derive a first-order approximation of the change in the leading eigenvector. We also consider the effects of edge additions on Kuramoto dynamics on networks, and we express the Kuramoto order parameter in terms of dynamical importance. Through our analysis and computational experiments, we find that studying dynamical importance can improve understanding of the relationship between network perturbations and dynamical processes on networks.

An analytically solvable model of unsaturated lipid bilayer is derived by introducing finite bending angle of the unsaturated bond relative to straight part of the lipid chain considered previously in our model of semiflexible strings. It is found that the lateral pressure profile of unsaturated lipids has a distinct maximum in the unsaturated bond region due to the enhanced excluded volume effect caused by the bent bond, leading to an increase of entropic repulsion between the lipid chains. Simultaneously, just away from the unsaturated bond, some parts of the neighboring lipid chains have less probability to collide for geometrical reasons, causing depletion of entropic repulsion relative to the saturated lipid chains case and resulting in the local minima of the lateral pressure profile surrounding the maximum at the bent unsaturated bond. The lipid chain order parameter, the lateral pressure profile, and the area per lipid are computed for palmitoyl-oleoyl-phosphatidylcholine and compared with those for dipalmitoylphosphatidylcholine lipid bilayer.

Thermally bistable fluid tends to self-organize into clouds of hot and cold material, which are internally uniform and separated by thin conduction fronts. The evolution of these clouds has been studied for isobaric systems, but when pressure is instead treated as a dynamical quantity and allowed to evolve self-consistently, fundamentally different dynamics appear. Such a treatment is necessary in some laboratory plasmas, whose volume is constrained but whose pressure can vary. Solutions are derived for the evolution of clouds, accounting for pressure variation and interactions between conduction fronts. Additional stable configurations and secondary instabilities are derived, which may be relevant to fusion plasmas and to the study of photoionized plasma in the laboratory.

Response to an external perturbation characterizes the fundamental nature of equilibrium and nonequilibrium systems. The response properties have been expressed by the susceptibility and the precision given by the signal to noise ratio. In this Letter, we first derive a general response equality for precision that connects susceptibilities out of equilibrium for general observables to the Fisher information measuring a sensitivity to the perturbation. In particular, this fundamental result provides kinetic equality for susceptibility (KSE), a model-independent general equality among experimentally accessible quantities such as the time derivative of observables, the dynamical activity, and fluctuation for generic nonequilibrium systems. As special limiting cases, KSE reproduces the kinetic uncertainty relation and its extensions to multiple variables. We also show an equality between the susceptibility and the observable-action covariance. Hence, KSE provides a master relation of these nonequilibrium relations.

We develop a general transfer-matrix formalism for determining the growth rate of the Rayleigh-Taylor instability in a fluid system with spatially varying density and viscosity. We use this formalism to analytically and numerically treat the case of a stratified heterogeneous fluid. We introduce the inviscid-flow approximation in our transfer-matrix formalism to find analytic solutions in the limit of uniform kinematic viscosity for a stratified heterogeneous fluid. We discuss the applicability of these results and a related approximation that also yields analytical solutions in the large-viscosity limit.