We report on the prewavy (PW) instability in ac field-driven electrohydrodynamics that is induced in a nematic liquid crystal (NLC) sandwiched between parallel electrodes. The instability is characterized by a twist mode of the NLC director along the vertical orientation to the electrodes (i.e., the $z$ axis), generating a periodic pattern having a large wavelength (${\lambda }_{\mathrm{PW}}$) in the $xy$ plane. The PW periodic to the preferred director ${\mathit{n}}_0$ of the NLC should be distinguished from well-known electroconvection (EC) such as normal rolls (NRs) and abnormal rolls (ARs) with similar wave vectors. A reentrant PW (PW2) was discovered by employing well-adjusted optical conditions and a dynamic image-process method. The wavelength ${\lambda }_{\mathrm{PW}2}$ of the PW2 accompanying turbulent EC was measured as functions of the applied ac voltage and frequency, which was distinguished from ${\lambda }_{\mathrm{PW}1}$ of the primary PW (PW1) separated from the NR. Moreover, the appearance, disappearance, and reappearance of the PW were investigated for five frequency regions classified in the ac field-driven EC; it was found that the high frequency and high voltage causes competition between the rising mode (θ, tilting angle to the $xy$ plane) and twist mode (ϕ, in-plane angle to the $x$ axis) of the director through electrohydrodynamic coupling between the director field and flows. We discuss how the PW2 can arise by considering another twist mode known as AR instability.

A lattice Boltzmann model for multispecies flows with catalytic reactions is developed, which is valid from very low to very high surface Damköhler numbers (${\text{Da}}_{\text{s}}$). The previously proposed model for catalytic reactions [S. Arcidiacono, J. Mantzaras, and I. V. Karlin, Phys. Rev. E 78, 046711 (2008)], which is applicable for low-to-moderate ${\text{Da}}_{\text{s}}$ and encompasses part of the mixed kinetics and transport-controlled regime, is revisited and extended for the simulation of arbitrary kinetics-to-transport rate ratios, including strongly transport-controlled conditions (${\text{Da}}_{\text{s}}\to \infty$). The catalytic boundary condition is modified by bringing nonlocal information on the wall reactive nodes, allowing accurate evaluation of chemical rates even when the concentration of the deficient reactant at the wall becomes vanishingly small. The developed model is validated against a finite volume Navier-Stokes CFD (Computational Fluid Dynamics) solver for the total oxidation of methane in an isothermal channel-flow configuration. CFD simulations and lattice Boltzmann simulations with the old and new catalytic reaction models are compared against each other. The new model demonstrates a second order accuracy in space and time and provides accurate results at very high ${\text{Da}}_{\text{s}}$ ($\sim {\text{10}}^{\text{9}}$) where the old model fails. Moreover, to achieve the same accuracy at moderate-to-high ${\text{Da}}_{\text{s}}$ of $O\left(1\right)$, the new model requires $\sim 2^d\times N$ coarser grid than the original model, where $d$ is the spatial dimension and $N$ the number of species.

Here we consider a one-dimensional $q$-state Potts model with an external magnetic field and an anisotropic interaction that selects neighboring sites that are in the spin state 1. The present model exhibits unusual behavior in the low-temperature region, where we observe an anomalous vigorous change in the entropy for a given temperature. There is a steep behavior at a given temperature in entropy as a function of temperature, quite similar to first-order discontinuity, but there is no jump in the entropy. Similarly, second derivative quantities like specific heat and magnetic susceptibility also exhibit strong acute peaks similar to second-order phase transition divergence, but once again there is no singularity at this point. Correlation length also confirms this anomalous behavior at the same given temperature, showing a strong and sharp peak which easily one may confuse with a divergence. The temperature where this anomalous feature occurs we call the pseudocritical temperature. We have analyzed physical quantities, like correlation length, entropy, magnetization, specific heat, magnetic susceptibility, and distant pair correlation functions. Furthermore, we analyze the pseudocritical exponents that satisfy a class of universality previously identified in the literature for other one-dimensional models; these pseudocritical exponents are for correlation length $\nu =1$, specific heat $\alpha =3$, and magnetic susceptibility $\mu =3$.

We introduce a powerful analytic method to study the statistics of the number ${\mathcal{N}}_{\mathit{A}}\left(\gamma \right)$ of eigenvalues inside any smooth Jordan curve $\gamma \in \mathbb{C}$ for infinitely large non-Hermitian random matrices $\mathit{A}$. Our generic approach can be applied to different random matrix ensembles of a mean-field type, even when the analytic expression for the joint distribution of eigenvalues is not known. We illustrate the method on the adjacency matrices of weighted random graphs with asymmetric couplings, for which standard random-matrix tools are inapplicable, and obtain explicit results for the diluted real Ginibre ensemble. The main outcome is an effective theory that determines the cumulant generating function of ${\mathcal{N}}_{\mathit{A}}$ via a path integral along $\gamma$, with the path probability distribution following from the numerical solution of a nonlinear self-consistent equation. We derive expressions for the mean and the variance of ${\mathcal{N}}_{\mathit{A}}$ as well as for the rate function governing rare fluctuations of ${\mathcal{N}}_{\mathit{A}}\left(\gamma \right)$. All theoretical results are compared with direct diagonalization of finite random matrices, exhibiting an excellent agreement.

We propose a quantum Stirling heat engine with an ensemble of harmonic oscillators as the working medium. We show that the efficiency of the harmonic oscillator quantum Stirling heat engine (HO-QSHE) at a given frequency can be maximized at a specific ratio of the temperatures of the thermal reservoirs. In the low-temperature or equivalently high-frequency limit of the harmonic oscillators, the efficiency of the HO-QSHE approaches the Carnot efficiency. Further, we analyze a quantum Stirling heat engine with an ensemble of particle-in-a-box quantum systems as the working medium. Here both work and efficiency can be maximized at a specific ratio of temperatures of the thermal reservoirs. These studies will enable us to operate the quantum Stirling heat engines at its optimal performance. The theoretical study of the HO-QSHE would provide impetus for its experimental realization, as most real systems can be approximated as harmonic oscillators for small displacements near equilibrium.

We consider the scattering of the nonlinear Schrödinger equation bright soliton by a reflectionless Pöschl-Teller potential well. We show that at the sharp transition between quantum reflection and full transmission, a single-node bound state localized at the center of the potential forms and is fully occupied. The profile and energy of the trapped mode are calculated both numerically and analytically using a variational calculation. The critical speed for quantum reflection is then determined from a delicate balance between the energy of the incident soliton and the energy of the trapped mode. We investigate the stability of the trapped mode against perturbations in its profile and position which explains the sharpness of the transition and sheds some light on the physics of quantum reflection. We show that quantum reflection by exciting the multinode trapped modes is also possible.

Integrable nonlinear Schrödinger (NLS) systems provide a platform for exploring the propagation and interaction of nonlinear waves. Extreme events such as rogue waves (RWs) are currently of particular interest. However, the presence of disorder in these systems is sometimes unavoidable, for example, in the forms of turbulent current in the ocean and random fluctuation in optical media, and its influence remains less understood. Here, we report numerical experiments of two nearly-integrable NLS equations with the effect of disorder showing that the probability of RW occurrence can be significantly increased by adding weak system noise. Linear and nonlinear spectral analyses are proposed to qualitatively explain those findings. Our results are expected to shed light on the understanding of the interplay between disorder and nonlinearity, and may motivate new experimental works in hydrodynamics, nonlinear optics, and Bose-Einstein condensates.

Swarming patterns that emerge from the interaction of many mobile agents are a subject of great interest in fields ranging from biology to physics and robotics. In some application areas, multiple swarms effectively interact and collide, producing complex spatiotemporal patterns. Recent studies have begun to address swarm-on-swarm dynamics, and in particular the scattering of two large, colliding swarms with nonlinear interactions. To build on early numerical insights, we develop a self-propelled, rigid-body approximation that can be used to predict the parameters under which colliding swarms are expected to form a milling state. Our analytical method relies on the assumption that, upon collision, two swarms oscillate near a limit cycle, where each swarm rotates around the other while maintaining an approximately constant and uniform density. Using this approach we are able to predict the critical swarm-on-swarm interaction coupling, below which two colliding swarms merely scatter, as a function of physical swarm parameters. We show that the critical coupling gives a lower bound for all impact parameters, including head-on collision, and corresponds to a saddle-node bifurcation of a stable limit cycle in the uniform, constant density approximation. Our results are tested and found to agree with both small and large multiagent simulations.

We investigate spectral properties of turbulence in the solar wind that is a weakly collisional astrophysical plasma, accessible to in situ observations. Using the Helios search coil magnetometer measurements in the fast solar wind, in the inner heliosphere, we focus on properties of the turbulent magnetic fluctuations at scales smaller than the ion characteristic scales, the so-called kinetic plasma turbulence. At such small scales, we show that magnetic power spectra between 0.3 and 0.9 AU from the Sun have a generic shape $\sim f^{-8/3}exp(-f/f_d)$, where the dissipation frequency $f_d$ is correlated with the Doppler shifted frequency $f_{\rho e}$ of the electron Larmor radius. This behavior is statistically significant: all the observed kinetic spectra are well described by this model, with $f_d=f_{\rho e}/1.8$. Our results indicate that the electron gyroradius plays the role of the dissipation scale and marks the end of the electromagnetic cascade in the solar wind.

We study the distribution of lengths and other statistical properties of worms constructed by Monte Carlo worm algorithms in the power-law three-sublattice ordered phase of frustrated triangular and kagome lattice Ising antiferromagnets. Viewing each step of the worm construction as a position increment (step) of a random walker, we demonstrate that the persistence exponent $\theta$ and the dynamical exponent $z$ of this random walk depend only on the universal power-law exponents of the underlying critical phase and not on the details of the worm algorithm or the microscopic Hamiltonian. Further, we argue that the detailed balance condition obeyed by such worm algorithms and the power-law correlations of the underlying equilibrium system together give rise to two related properties of this random walk: First, the steps of the walk are expected to be power-law correlated in time. Second, the position distribution of the walker relative to its starting point is given by the equilibrium position distribution of a particle in an attractive logarithmic central potential of strength ${\eta }_m$, where ${\eta }_m$ is the universal power-law exponent of the equilibrium defect-antidefect correlation function of the underlying spin system. We derive a scaling relation, $z=(2-{\eta }_m)/(1-\theta )$, that allows us to express the dynamical exponent $z\left({\eta }_m\right)$ of this process in terms of its persistence exponent $\theta \left({\eta }_m\right)$. Our measurements of $z\left({\eta }_m\right)$ and $\theta \left({\eta }_m\right)$ are consistent with this relation over a range of values of the universal equilibrium exponent ${\eta }_m$ and yield subdiffusive ($z>2$) values of $z$ in the entire range. Thus, we demonstrate that the worms represent a discrete-time realization of a fractional Brownian motion characterized by these properties.

We report on the onset of antiresonant behavior of mass transport systems driven by time-dependent forces. Antiresonances arise from the coupling of a sufficiently high number of space-time modes of the force. The presence of forces having a wide space-time spectrum, a necessary condition for the formation of an antiresonance, is typical of confined systems with uneven and deformable walls that induce entropic forces dependent on space and time. We have analyzed, in particular, the case of polymer chains confined in a flexible channel and shown how they can be sorted and trapped. The presence of resonance-antiresonance pairs found can be exploited to design protocols able to engineer optimal transport processes and to manipulate the dynamics of nano-objects.

We study thermodynamic processes in contact with a heat bath that may have an arbitrary time-varying periodic temperature profile. Within the framework of stochastic thermodynamics, and for models of thermodynamic engines in the idealized case of underdamped particles in the low-friction regime subject to a harmonic potential, we derive explicit bounds as well as optimal control protocols that draw maximum power and achieve maximum efficiency at any specified level of power.

We propose a probability distribution for multivariate binary random variables. The probability distribution is expressed as principal minors of the parameter matrix, which is a matrix analogous to the inverse covariance matrix in the multivariate Gaussian distribution. In our model, the partition function, central moments, and the marginal and conditional distributions are expressed analytically. That is, summation over all possible states is not necessary for obtaining the partition function and various expected values, which is a problem with the conventional multivariate Bernoulli distribution. The proposed model has many similarities to the multivariate Gaussian distribution. For example, the marginal and conditional distributions are expressed in terms of the parameter matrix and its inverse matrix, respectively. That is, the inverse matrix represents a sort of partial correlation. The proposed distribution can be derived using Grassmann numbers, anticommuting numbers. Analytical expressions for the marginal and conditional distributions are also useful in generating random numbers for multivariate binary variables. Hence, we investigated sampling distributions of parameter estimates using synthetic datasets. The computational complexity of maximum likelihood estimation from observed data is proportional to the number of unique observed states, not to the number of all possible states as is required in the case of the conventional multivariate Bernoulli distribution. We empirically observed that the sampling distributions of the maximum likelihood estimates appear to be consistent and asymptotically normal.

We derive a Doi-Peliti field theory for free active Ornstein-Uhlenbeck particles, or, equivalently, free inertial Brownian particles, and present a way to diagonalize the quadratic part of the action and calculate the propagator. Unlike previous coarse-grained approaches this formulation correctly tracks particle identity and yet can easily be expanded to include potentials and arbitrary reactions.

We study diffusion of a Brownian particle in a two-dimensional periodic channel of abruptly alternating width. Our main result is a simple approximate analytical expression for the particle effective diffusivity, which shows how the diffusivity depends on the geometric parameters of the channel: lengths and widths of its wide and narrow segments. The result is obtained in two steps: first, we introduce an approximate one-dimensional description of particle diffusion in the channel, and second, we use this description to derive the expression for the effective diffusivity. While the reduction to the effective one-dimensional description is standard for systems of smoothly varying geometry, such a reduction in the case of abruptly changing geometry requires a new methodology used here, which is based on the boundary homogenization approach to the trapping problem. To test the accuracy of our analytical expression and thus establish the range of its applicability, we compare analytical predictions with the results obtained from Brownian dynamics simulations. The comparison shows excellent agreement between the two, on condition that the length of the wide segment of the channel is equal to or larger than its width.

The influence of a colored three-level input noise (trichotomous noise) on the spike generation of a perfect integrate-and-fire (PIF) model of neurons is studied. Using a first-passage-time formulation, exact expressions for the Laplace transform of the output interspike interval (ISI) density and for the statistical moments of the ISIs (such as the coefficient of variation, the skewness, the serial correlation coefficient, and the Fano factor) are derived. To model the anomalous subdiffusion that can arise from, e.g., the trapping properties of dendritic spines, the model is extended by including a random operational time in the form of an inverse strictly increasing Lévy-type subordinator, and exact formulas for ISI statistics are given for this case as well. Particularly, it is shown that at some parameter regimes, the ISI density exhibits a three-modal structure. The results for the extended model show that the ISI serial correlation coefficient and the Fano factor are nonmonotonic with respect to the input current, which indicates that at an intermediate value of the input current the variability of the output spike trains is minimal. Similarities and differences between the behavior of the presented models and the previously investigated PIF models driven by dichotomous noise are also discussed.

Different integral representations for the mass flux of inertial particles transported by turbulent gas flows have been proposed. These are discussed and analyzed. Each formulation provides its own insights into the underlying physical processes governing the resulting flux. However, none of the representations, as it stands, provides an explicit closed-form expression in terms of known statistical properties of the flow and parameters governing particle dynamics. We consider the representations in terms of their potential for reduction to closed-form models. To enable an analysis uncomplicated by the presence of many coupled interactions, we confine our attention to the classic test case of monodisperse particles in homogeneous, isotropic turbulent flows, and subject to a uniform gravitational field. The modification of the mean particle settling velocity resulting from their preferential sampling of fluid velocities is captured by the flux representations. A distribution-based symmetry analysis coupled with a correlation splitting technique is used to reduce and simplify the terms appearing in the flux integrals. This prompts a strategy for closure modeling of the resulting expressions in terms of correlations between the sampled fluid velocity and fluid strain-rate fields. Results from particle-trajectory-based simulations are presented to assess the potential of this closure strategy.

The numerical simulation of the development of a streamer discharge in a gap with an external longitudinal magnetic field was used to demonstrate the self-focusing of such discharges. Self-focusing is caused by a sharp deceleration of the radial ionization wave due to a change in the electron energy distribution function, a decrease in the average electron energy, the rate of gas ionization, and the electron mobility in crossed electric and magnetic fields as compared to the case of the discharge development without a magnetic field. The self-focusing effect of a streamer discharge in an external longitudinal magnetic field is observed for both positive and negative pulse polarities. The paper proposes an estimate of the critical value of the magnetic field, which makes it possible to control the development of pulsed high-voltage discharges at various gas pressures.

The generalized source term multiflux method (GSMFM) combined with Runge-Kutta ray tracing technique is developed to calculate arbitrary directional radiative intensity of graded-index media. In this method, the finite volume method is employed to solve source terms along the curved ray path determined by the Fermat principle. Runge-Kutta ray tracing technique is adopted to obtain the ray trajectory numerical solution in graded-index media. And the GSMFM is used to solve radiative intensity to be expected. One-dimensional and two-dimensional radiative heat transfer problems are investigated to verify the performance of this method. The numerical results show that the accuracy of the GSMFM is close to that of backward Monte Carlo (BMC) method, while the efficiency of GSMFM is much higher than that of the BMC. Therefore, the GSMFM developed can be considered as a promising method to solve arbitrary radiative intensity in graded-index media.