The effects of an electric field on the flow patterns and defect dynamics of two-dimensional active nematic liquid crystals are numerically investigated. We found that field-induced director reorientation causes anisotropic active turbulence characterized by enhanced flow perpendicular to the electric field. The average flow speed and its anisotropy are maximized at an intermediate field strength. Topological defects in the anisotropic active turbulence are localized and show characteristic dynamics with simultaneous creation of two pairs of defects. A laning state characterized by stripe domains with alternating flow directions is found at a larger field strength near the transition to the uniformly aligned state. We obtained periodic oscillations between the laning state and active turbulence, which resembles an experimental observation of active nematics subject to anisotropic friction.

In this paper, we develop a general rectangular multiple-relaxation-time lattice Boltzmann (RMRT-LB) method for the Navier-Stokes equations (NSEs) and nonlinear convection-diffusion equation (NCDE) by extending our recent unified framework of the multiple-relaxation-time lattice Boltzmann (MRT-LB) method [Chai and Shi, Phys. Rev. E 102, 023306 (2020)], where an equilibrium distribution function (EDF) [Lu et al., Philos. Trans. R. Soc. A 369, 2311 (2011)] on a rectangular lattice is utilized. The anisotropy of the lattice tensor on a rectangular lattice leads to anisotropy of the third-order moment of the EDF, which is inconsistent with the isotropy of the viscous stress tensor of the NSEs. To eliminate this inconsistency, we extend the relaxation matrix related to the dynamic and bulk viscosities. As a result, the macroscopic NSEs can be recovered from the RMRT-LB method through the direct Taylor expansion method. Whereas the rectangular lattice does not lead to the change of the zero-, first- and second-order moments of the EDF, the unified framework of the MRT-LB method can be directly applied to the NCDE. It should be noted that the RMRT-LB model for NSEs can be derived on the $\mathrm{rD}d\mathrm{Q}q$ ($q$ discrete velocities in $d$-dimensional space, $d\ge 1$) lattice, including rD2Q9, rD3Q19, and rD3Q27 lattices, while there are no rectangular D3Q13 and D3Q15 lattices within this framework of the RMRT-LB method. Thanks to the block-lower triangular relaxation matrix introduced in the unified framework, the RMRT-LB versions (if existing) of the previous MRT-LB models can be obtained, including those based on raw (natural) moment, central moment, Hermite moment, and central Hermite moment. It is also found that when the parameter $c_s$ is an adjustable parameter in the standard or rectangular lattice, the present RMRT-LB method becomes a kind of MRT-LB method for the NSEs and NCDE, and the commonly used MRT-LB models on the $\mathrm{D}d\mathrm{Q}q$ lattice are only its special cases. We also perform some numerical simulations, and the results show that the present RMRT-LB method can give accurate results and also have a good numerical stability.

We study the de Almeida–Thouless (AT) line in the one-dimensional power-law diluted $XY$ spin-glass model, in which the probability that two spins separated by a distance $r$ interact with each other, decays as $1/r^{2\sigma }$. Tuning the exponent $\sigma$ is equivalent to changing the space dimension of a short-range model. We develop a heat bath algorithm to equilibrate $XY$ spins; using this in conjunction with the standard parallel tempering and overrelaxation sweeps, we carry out large-scale Monte Carlo simulations. For $\sigma =0.6$, which is in the mean-field regime above six dimensions—it is similar to being in 10 dimensions—we find clear evidence for an AT line. For $\sigma =0.75$ and $\sigma =0.85$, which are in the non-mean-field regime and similar to four and three dimensions, respectively, our data is like that found in previous studies of the Ising and Heisenberg spin glasses when reducing the temperature at fixed field. For $\sigma =0.75$, there is evidence from finite-size-scaling studies for an AT transition but for $\sigma =0.85$, the evidence for a transition is nonexistent. We have also studied these systems at fixed temperature varying the field and discovered that at both $\sigma =0.75$ and at $\sigma =0.85$ there is evidence of an AT transition! Confusingly, the correlation length and spin-glass susceptibility as a function of the field are both entirely consistent with the predictions of the droplet picture and hence the nonexistence of an AT line. In the usual finite-size critical point scaling studies used to provide evidence for an AT transition, there is seemingly good evidence for an AT line at $\sigma =0.75$ for small values of the system size $N$, which is strengthening as $N$ is increased, but for $N>2048$ the trend changes and the evidence then weakens as $N$ is further increased. We have also studied with fewer bond realizations the system at $\sigma =0.70$, which is the analog of a system with short-range interactions just below six dimensions, and found that it is similar in its behavior to the system at $\sigma =0.75$ but with larger finite-size corrections. The evidence from our simulations points to the complete absence of the AT line in dimensions outside the mean-field region and to the correctness of the droplet picture. Previous simulations which suggested there was an AT line can be attributed to the consequences of studying systems which are just too small. The collapse of our data to the droplet scaling form is poor for $\sigma =0.75$ and to some extent also for $\sigma =0.85$, when the correlation length becomes of the order of the length of the system, due to the existence of excitations which only cost a free energy of $O\left(1\right)$, just as envisaged in the TNT picture of the ordered state of spin glasses. However, for the case of $\sigma =0.85$ we can provide evidence that for larger system sizes, droplet scaling will prevail even when the correlation length is comparable to the system size.

We study large deviations of the one-point height $H$ of a stochastic interface, governed by the Golubović-Bruinsma equation, ${\partial }_{t}h=-\nu {\partial }_x^{4}h+(\lambda /2){\left({\partial }_{x}h\right)}^2+\sqrt{D}\xi (x,t)$, where $h(x,t)$ is the interface height at point $x$ and time $t$ and $\xi (x,t)$ is the Gaussian white noise. The interface is initially flat, and $H$ is defined by the relation $h(x=0,t=T)=H$. We focus on the short-time limit, $T\ll T_{\text{NL}}$, where $T_{\text{NL}}={\nu }^{5/7}{\left(D{\lambda }^2\right)}^{-4/7}$ is the characteristic nonlinear time of the system. In this limit typical, small fluctuations of $H$ are unaffected by the nonlinear term, and they are Gaussian. However, the large-deviation tails of the probability distribution $\mathcal{P}(H,T)$ “feel” the nonlinearity already at short times, and they are non-Gaussian and asymmetric. We evaluate these tails using the optimal fluctuation method (OFM). The lower tail scales as $-ln\mathcal{P}(H,T)\sim H^{5/2}/T^{1/2}$. It coincides with its analog for the Kardar-Parisi-Zhang (KPZ) equation, and we point out to the mechanism of this universality. The upper tail scales as $-ln\mathcal{P}(H,T)\sim H^{11/6}/T^{5/6}$, it is different from the upper tail of the KPZ equation. We also compute the large deviation function of $H$ numerically and verify our asymptotic results for the tails.

We study the active Potts model with either site occupancy restriction or on-site repulsion to explore jamming and kinetic arrest in a flocking model. The incorporation of such volume exclusion features leads to a surprisingly rich variety of self-organized spatial patterns. While bands and lanes of moving particles commonly occur without or under weak volume exclusion, strong volume exclusion along with low temperature, high activity, and large particle density facilitates jams due to motility-induced phase separation. Through several phase diagrams, we identify the phase boundaries separating the jammed and free-flowing phases and study the transition between these phases which provide us with both qualitative and quantitative predictions of how jamming might be delayed or dissolved. We further formulate and analyze a hydrodynamic theory for the restricted APM which predicts various features of the microscopic model.

Over the past decade, dynamic schemes have been proposed for the use of bistable systems in the design of logic devices. A bistable system in a noisy background can operate as a reliable logic gate in a moderate noise level, which is called a logical stochastic resonance (LSR). In this paper, we theoretically explore the emergence of LSR in general bistable systems and identify the dynamical mechanisms of LSR. The timescale relationship between the measured time and the mean first-pass time of two-state transitions is a key condition in determining whether the system is reliable. Furthermore, we demonstrate that the stability of the logic operation can be significantly improved by choosing the appropriate filtering method. Low-pass filtered noise-driven systems are more stable than Gaussian white noise. However, band-pass and high-pass filtered noise are harmful to the stability of the system due to the filtering of low-frequency components. Our theoretical and numerical simulation results offer perspectives for the development of logic devices.

We introduce a notion of emergence for macroscopic variables associated with highly multivariate microscopic dynamical processes. Dynamical independence instantiates the intuition of an emergent macroscopic process as one possessing the characteristics of a dynamical system “in its own right,” with its own dynamical laws distinct from those of the underlying microscopic dynamics. We quantify (departure from) dynamical independence by a transformation-invariant Shannon information-based measure of dynamical dependence. We emphasize the data-driven discovery of dynamically independent macroscopic variables, and introduce the idea of a multiscale “emergence portrait” for complex systems. We show how dynamical dependence may be computed explicitly for linear systems in both time and frequency domains, facilitating discovery of emergent phenomena across spatiotemporal scales, and outline application of the linear operationalization to inference of emergence portraits for neural systems from neurophysiological time-series data. We discuss dynamical independence for discrete- and continuous-time deterministic dynamics, with potential application to Hamiltonian mechanics and classical complex systems such as flocking and cellular automata.

Self-exciting point processes, widely used to model arrival phenomena in nature and society, are often difficult to identify. The estimation becomes even more challenging when arrivals are recorded only as bin counts on a finite partition of the observation interval. In this paper, we propose the recursive identification with sample correction (RISC) algorithm for the estimation of process parameters from time-censored data. In every iteration, a synthetic sample path is generated and corrected to match the observed bin counts. Then the process parameters update and a unique iteration is performed to successively approximate the stochastic characteristics of the observed process. In terms of finite-sample approximation error, the proposed RISC framework performs favorably over extant methods, as well as compared to a naïve locally uniform sample redistribution. The results of an extensive numerical experiment indicate that the reconstruction of an intrabin history based on the conditional intensity of the process is crucial for attaining superior performance in terms of estimation error.

Bose-Einstein condensation of a finite number of photons propagating inside a plasma-filled microcavity is investigated. The nonzero chemical potential is provided by the electrons, which induces a finite photon mass and allows condensation to occur. We derive an equation that models the evolution of the photon-mode occupancies, with Compton scattering taken into account as the mechanism of thermalization. The kinetic evolution of the photon spectrum is solved numerically, and we find evidence of condensation down to nanosecond timescales for typical microplasma conditions, $n_e\sim {10}^{14}–{10}^{15}{\text{cm}}^{-3}$. The critical temperature scales almost linearly with the number of photons, and we find high condensate fractions at microcavity-plasma temperatures, for experimentally achievable cavity lengths ($100–500\mu \mathrm{m}$) and photon numbers (${10}^{10}–{10}^{12}$).

In this paper, we analyze and numerically simulate mechanisms for generating directed rf radiation by a low-intensity laser pulse train (LPT) propagating in air. The LPT ionizes the air, forming a plasma filament. The ionization process relies on the background level of radioactivity which plays an important role in initiating a collisional ionization process. In our model a low-intensity LPT photoionizes background negative ions (produced by ambient ionizing radiation) and provides the seed electrons necessary to initiate collisional ionization. The intensity of the LPT is far below tunneling ionization levels. The ponderomotive forces associated with the LPT and self-fields drive plasma oscillations predominately in the radial direction. The driven radial electron currents in turn generate directed rf radiation. As the plasma density builds up on axis, the later portion of the LPT can defocus and limit the interaction length. The spectrum of the rf radiation consists of the fundamental frequency associated with the pulse separation time as well as harmonics. The rf generation mechanism is analyzed using fluid equations which incorporate, among other things, the effects of background radioactivity, photoionization, collisional ionization, ponderomotive and space-charge effects, and electron attachment–recombination processes. As an example, for a specific set of parameters, the rf spectrum and intensity are compared to experimental data.

This work proposes a discrete unified gas-kinetic wave-particle (DUGKWP) method for simulation of flows in all flow regimes. Unlike the discrete velocity method (DVM) and the direct simulation Monte Carlo (DSMC) method which solve the governing equations by either the deterministic method or the stochastic method, the DUGKWP combines the advantages of these two methods. In the DUGKWP, the information of microscopic particles as well as macroscopic flow variables are both evolved. Specifically, the microscopic particles are updated by the free-transport and resampling processes, while the macroscopic flow properties are evolved via solving the macroscopic governing equations of conservation laws with the finite volume method. According to the discrete characteristic solution to the Boltzmann-BGK equation utilized in the DUGKWP, in the highly rarefied flow regime, the motion of microscopic particles greatly determines the fluxes for the macroscopic governing equations. Conversely, for the continuum flow, no microscopic particle exists in the computational domain and the DUGKWP is degraded to the Navier-Stokes solver. Numerical studies validate that the DUGKWP can accurately predict the flow properties in all flow regimes. Furthermore, compared with the deterministic method, the DUGKWP enjoys superior efficiency with less memory consumption for both high-speed rarefied flows and flows close to the continuum regime.

Understanding the evolutionary stability of cooperation is a central problem in biology, sociology, and economics. There exist only a few known mechanisms that guarantee the existence of cooperation and its robustness to cheating. Here, we introduce a mechanism for the emergence of cooperation in the presence of fluctuations. We consider agents whose wealth changes stochastically in a multiplicative fashion. Each agent can share part of her wealth as a public good, which is equally distributed among all the agents. We show that, when agents operate with long-time horizons, cooperation produces an advantage at the individual level, as it effectively screens agents from the deleterious effect of environmental fluctuations.

We theoretically address crystals exhibiting first-order phase transformations subjected to a steadily propagating temperature gradient. The latter drives a nonisothermal propagation of a phase front. We theoretically demonstrate that for the phase transformations of the displacive type, the phase front always steadily follows the isotherm. In contrast, in the case of the order-disorder or hybrid phase transformations in a crystal containing pinning defects, one finds a velocity of the isotherm, the first critical velocity, at which the steady front motion becomes unstable, and a stick-slip front propagation starts. Upon reaching the second critical velocity, the stick-slip behavior vanishes, and the motion becomes steady again. Our results enable one to determine the activation energy of the leading order-disorder process from the measurements of the driven motion of the phase front. In light of these results, we discuss experimental findings for ${\mathrm{PbTiO}}_3$ and ${\mathrm{NaNbO}}_3$

The importance of roughness in the modeling of granular gases has been increasingly considered in recent years. In this paper, a freely evolving homogeneous granular gas of inelastic and rough hard disks or spheres is studied under the assumptions of the Boltzmann kinetic equation. The homogeneous cooling state is studied from a theoretical point of view using a Sonine approximation, in contrast to a previous Maxwellian approach. A general theoretical description is done in terms of $d_t$ translational and $d_r$ rotational degrees of freedom, which accounts for the cases of spheres ($d_t=d_r=3$) and disks ($d_t=2, d_r=1$) within a unified framework. The non-Gaussianities of the velocity distribution function of this state are determined by means of the first nontrivial cumulants and by the derivation of non-Maxwellian high-velocity tails. The results are validated by computer simulations using direct simulation Monte Carlo and event-driven molecular dynamics algorithms.

We suggest a new focus for turbulence studies—multimode correlations—which reveal the hitherto hidden nature of turbulent state. We apply this approach to shell models describing basic properties of turbulence. The family of such models allows one to study turbulence close to thermal equilibrium, which happens when the interaction time weakly depends on the mode number. As the number of modes increases, the one-mode statistics approaches Gaussian (like in weak turbulence), the occupation numbers grow, while the three-mode cumulant describing the energy flux stays constant. Yet we find that higher multimode cumulants grow with the order. We derive analytically and confirm numerically the scaling law of such growth. The sum of all squared dimensionless cumulants is equal to the relative entropy between the full multimode distribution and the Gaussian approximation of independent modes; we argue that the relative entropy could grow as the logarithm of the number of modes, similar to the entanglement entropy in critical phenomena. Therefore, the multimode correlations give the new way to characterize turbulence states and possibly divide them into universality classes.

This article revisits the fluctuation-dissipation relationship of a generalized Brownian particle constrained in a harmonic potential and immersed in a thermal bath whose degrees of freedom also interact with the external field. The generalized Langevin equation put forth herein keeps its original form. The different terms now depend on a compound strength related to those of the field and bath oscillators. The resulting theorem keeps Kubo's original form with the memory kernel depending on the frequency of the field. It has the consequence that friction is not a constant but is a function of the field frequency as predicted by molecular dynamics simulations. The position particle distribution and the Fokker-Planck equation associated with the generalized Langevin equation are also derived.

We have used an extended scaled-particle theory that incorporates four-body correlations through the fourth-order virial coefficient to analyze the orientational properties of a fluid of hard right isosceles triangles. This fluid has been analyzed by computer simulation studies, with clear indications of strong octatic correlations present in the liquid-crystal phase, although the more symmetric order tetratic phase would seem to be the most plausible candidate. Standard theories based on the second virial coefficient are unable to reproduce this behavior. Our extended theory predicts that octatic correlations, associated to a symmetry under global rotations of the oriented fluid by ${45}^{\circ }$, are highly enhanced, but not enough to give rise to a thermodynamically stable phase with strict octatic symmetry. We discuss different scenarios to improve the theoretical understanding of the elusive octatic phase in this intriguing fluid.

We present an analytical study on the effects of the transverse plasma gradient in the blowout regime of a plasma wakefield accelerator. The analysis departs from a simple ballistic model of plasma electrons and allows us to derive a complete analytic solution for the pseudopotential and, consequently, for the wakefield. We demonstrate that the transverse plasma gradient modifies the bubble shape and affects the wakefield; namely, the dipole plasma gradient results in a dipole component of the wakefield. Analysis suggests that, despite the asymmetry, the instability due to the fixed transverse plasma gradient is unlikely, as the total wakefield has a single stable point inside the bubble. The only effect that occurs is the shift of the electromagnetic center. We point out that random fluctuation of the transverse plasma gradient could become an issue.