The nonequilibrium hydrodynamic correlations of a multiparticle-collision-dynamics (MPC) fluid in shear flow are studied by analytical calculations and simulations. The Navier-Stokes equations for a MPC fluid are linearized about the shear flow and the hydrodynamic modes are evaluated as an expansion in the wave vector. The shear-rate dependence and anisotropy of the transverse and longitudinal velocity correlations are analyzed. We demonstrate that hydrodynamic correlations in shear flow are anisotropic, specifically, the two transverse modes are no longer identical. In addition, our simulations reveal the directional dependence of the frequency and attenuation of the longitudinal velocity correlation function. Furthermore, the velocity autocorrelation functions of a tagged fluid particle in shear flow are determined. The simulation results for various hydrodynamic correlations agree very well with the theoretical predictions.

This article presents a calculation of the mean electromotive force arising from general small-scale magnetohydrodynamical turbulence, within the framework of the second-order correlation approximation. With the goal of improving understanding of the accretion disk dynamo, effects arising through small-scale magnetic fluctuations, velocity gradients, density and turbulence stratification, and rotation, are included. The primary result, which supplements numerical findings, is that an off-diagonal turbulent resistivity due to magnetic fluctuations can produce large-scale dynamo action—the magnetic analog of the “shear-current” effect. In addition, consideration of $\alpha$ effects in the stratified regions of disks gives the puzzling result that there is no strong prediction for a sign of $\alpha$, since the effects due to kinetic and magnetic fluctuations, as well as those due to shear and rotation, are each of opposing signs and tend to cancel each other.

It is well-known that a dilute one-dimensional (1D) gas of bosons with infinitely strong repulsive interactions behaves like a gas of free fermions. Just as with conduction electrons in metals, we consider a single-particle picture of the resulting dynamics, when the gas is isolated by enclosing it into a box with hard walls and preparing it in a special initial state. We show, by solving the nonstationary problem of a free particle in a 1D hard-wall box, that the single-particle state recurs in time, signaling the intuitively expected back-and-forth motion of a free particle moving in a confined space. Under suitable conditions, the state of the whole gas can then be made to recur if all the particles are put in the same initial momentum superposition. We introduce this problem here as a modern instance of the discussions giving rise to the famous recurrence paradox in statistical mechanics: on one hand, our results may be used to develop a poor man's interpretation of the recurrence of the initial state observed [T. Kinoshita et al., Nature 440, 900 (2006)] in trapped 1D Bose gases of cold atoms, for which our estimated recurrence time is in fair agreement with the period of the oscillations observed; but this experiment, on the other hand, has been substantially influential on the belief that an isolated quantum many-body system can equilibrate as a consequence of its own unitary nonequilibrium dynamics. Some ideas regarding the latter are discussed.

Mesoscopic thermoelectric heat engine is much anticipated as a device that allows us to utilize with high efficiency wasted heat inaccessible by conventional heat engines. However, the derivation of the heat current in this engine seems to be either not general or described too briefly, even inappropriately in some cases. In this paper, we give a clear-cut derivation of the heat current of the engine with suitable assumptions beyond the linear-response regime. It resolves the confusion in the definition of the heat current in the linear-response regime. After verifying that we can construct the same formalism as that of the cyclic engine, we find the following two interesting results within the Landauer-Büttiker formalism: the efficiency of the mesoscopic thermoelectric engine reaches the Carnot efficiency if and only if the transmission probability is finite at a specific energy and zero otherwise; the unitarity of the transmission probability guarantees the second law of thermodynamics, invalidating Benenti et al.'s argument in the linear-response regime that one could obtain a finite power with the Carnot efficiency under a broken time-reversal symmetry [Phys. Rev. Lett. 106, 230602 (2011)]. These results demonstrate how quantum mechanics constrains thermodynamics.

The velocity autocorrelation function (VAF), a key quantity in the atomic-scale dynamics of fluids, has been the first paradigmatic example of a long-time tail phenomenon, and much work has been devoted to detecting such long-lasting correlations and understanding their nature. There is, however, much more to the VAF than simply the evidence of this long-time dynamics. A unified description of the VAF from very short to long times, and of the way it changes with varying density, is still missing. Here we show that an approach based on very general principles makes such a study possible and opens the way to a detailed quantitative characterization of the dynamical processes involved at all time scales. From the analysis of molecular dynamics simulations for a slightly supercritical Lennard-Jones fluid at various densities, we are able to evidence the presence of distinct fast and slow decay channels for the velocity correlation on the time scale set by the collision rate. The density evolution of these decay processes is also highlighted. The method presented here is very general, and its application to the VAF can be considered as an important example.

We reexamine the snapshot entropy of the Ising and three-states Potts models on the $L\times L$ square lattice. Focusing on how to encode the spin snapshot, we find that the entropy at $T_c$ scales asymptotically as $S\sim (1/3)lnL$ that strongly reminds us of the entanglement entropy in one-dimensional quantum critical systems. This finding seems to support that the snapshot entropy after the proper encoding is related to the holographic entanglement entropy. On the other hand, the anomalous scaling $S_{\chi }\sim {\chi }^{\eta }ln\chi$ for the coarse-grained snapshot entropy holds even for the proper encoding. These features originate in the fact that the largest singular value of the snapshot matrix is regulated by the proper encoding.

In 1983, Felderhof, Ford, and Cohen gave microscopic explanation of the famous Clausius-Mossotti formula for the dielectric constant of nonpolar dielectric. They based their considerations on the cluster expansion of the dielectric constant, which relates this macroscopic property with the microscopic characteristics of the system. In this article, we analyze the cluster expansion of Felderhof, Ford, and Cohen by performing its resummation (renormalization). Our analysis leads to the ring expansion for the macroscopic characteristic of the system, which is an expression alternative to the cluster expansion. Using similarity of structures of the cluster expansion and the ring expansion, we generalize (renormalize) the Clausius-Mossotti approximation. We apply our renormalized Clausius-Mossotti approximation to the case of the short-time transport properties of suspensions, calculating the effective viscosity and the hydrodynamic function with the translational self-diffusion and the collective diffusion coefficient. We perform calculations for monodisperse hard-sphere suspensions in equilibrium with volume fraction up to $45\%$. To assess the renormalized Clausius-Mossotti approximation, it is compared with numerical simulations and the Beenakker-Mazur method. The results of our renormalized Clausius-Mossotti approximation lead to comparable or much less error (with respect to the numerical simulations) than the Beenakker-Mazur method for the volume fractions below $\varphi \approx 30\%$ (apart from a small range of wave vectors in hydrodynamic function). For volume fractions above $\varphi \approx 30\%$, the Beenakker-Mazur method gives in most cases lower error than the renormalized Clausius-Mossotti approximation.

The prediction of electrostatic forces (EFs) between biological cells still poses challenges of great scientific importance, e.g., cell recognition, electroporation (EP), and mechanosensing. Frequency-domain finite element simulations explore a variety of cell configurations in the range of parameters typical for eukaryotic cells. Here, by applying an electric field to a pair of layered concentric shells, a prototypical model of a biological cell, we provide numerical evidence that the instantaneous EF changes from repulsion to attraction as the drive frequency of the electric field is varied. We identify crossover frequencies and discuss their dependence as a function of field frequency, conductivity of the extracellular medium, and symmetry of the configuration of cells. We present findings which suggest that the spectrum of EFs depends sensitively on the configuration of cells. We discuss the signatures of the collective behavior of systems with many cells in the spectrum of the EF and highlight a few of the observational consequences that this behavior implies. By looking at different cell configurations, we are able to show that the repulsion-to-attraction transition phenomenon is largely associated with an asymmetric electrostatic screening at very small separation between cells. These findings pave the way for the experimental observation of the electromagnetic properties of efficient and simple models of biological tissues.

Messages conveyed by media act as a major drive in shaping attitudes and inducing opinion shift. On the other hand, individuals are strongly affected by peer pressure while forming their own judgment. We solve a general model of opinion dynamics where individuals either hold one of two alternative opinions or are undecided and interact pairwise while exposed to an external influence. As media pressure increases, the system moves from pluralism to global consensus; four distinct classes of collective behavior emerge, crucially depending on the outcome of direct interactions among individuals holding opposite opinions. Observed nontrivial behaviors include hysteretic phenomena and resilience of minority opinions. Notably, consensus could be unachievable even when media and microscopic interactions are biased in favor of the same opinion: The unfavored opinion might even gain the support of the majority.

We present a procedure to systematically design the connection parameters that will induce amplitude death in oscillator networks with time-varying delay connections. The parameters designed by the procedure are valid in oscillator networks with any network topology and with any connection delay. The validity of the design procedure is confirmed by numerical simulation. We also consider a partial time-varying delay connection, which has both time-invariant and time-varying delays. The effectiveness of the partial connection is shown theoretically and numerically.

The distribution of relative velocities between particles provides invaluable information on the rates and characteristics of particle collisions. We show that the theoretical model of Gustavsson and Mehlig [K. Gustavsson and B. Mehlig, J. Turbul. 15, 34 (2014)], within its anticipated limits of validity, can predict the joint probability density function of relative velocities and separations of identical inertial particles in isotropic turbulent flows with remarkable accuracy. We also quantify the validity range of the model. The model matches two limits (or two types) of relative motion between particles: one where pair diffusion dominates (i.e., large coherence between particle motion) and one where caustics dominate (i.e., large velocity differences between particles at small separations). By using direct numerical simulation combined with Lagrangian particle tracking, we assess the model prediction in homogeneous and isotropic turbulence. We demonstrate that, when sufficient caustics are present at a given separation and the particle response time is significantly smaller than the integral time scales of the flow, the distribution exhibits the same universal power-law form dictated by the correlation dimension as predicted by the model of Gustavsson and Mehlig. In agreement with the model, no strong dependency on the Taylor-based Reynolds number is observed.

Extending from the model proposed by Vasel-Be-Hagh et al. [J. Fluid Mech. 769, 522 (2015)], a perturbation analysis is performed to modify Turner's radius by taking into account the viscous effect. The modified radius includes two terms; the zeroth-order solution representing the effect of buoyancy, and the first-order perturbation correction describing the influence of viscosity. The zeroth-order solution is explicit Turner's radius; the first-order perturbation modification, however, includes the drag coefficient, which is unknown and of interest. Fitting the photographically measured radius into the modified equation yields the time history of the drag coefficient of the corresponding buoyant vortex ring. To give further clarification, the proposed model is applied to calculate the drag coefficient of a buoyant vortex ring at a Bond number of approximately 85; a similar procedure can be applied at other Bond numbers.

Generalized-ensemble simulations, such as replica exchange and serial generalized-ensemble methods, are powerful simulation tools to enhance sampling of free energy landscapes in systems with high energy barriers. In these methods, sampling is enhanced through instantaneous transitions of replicas, i.e., copies of the system, between different ensembles characterized by some control parameter associated with thermodynamical variables (e.g., temperature or pressure) or collective mechanical variables (e.g., interatomic distances or torsional angles). An interesting evolution of these methodologies has been proposed by replacing the conventional instantaneous (trial) switches of replicas with noninstantaneous switches, realized by varying the control parameter in a finite time and accepting the final replica configuration with a Metropolis-like criterion based on the Crooks nonequilibrium work (CNW) theorem. Here we revise these techniques focusing on their correlation with the CNW theorem in the framework of Markovian processes. An outcome of this report is the derivation of the acceptance probability for noninstantaneous switches in serial generalized-ensemble simulations, where we show that explicit knowledge of the time dependence of the weight factors entering such simulations is not necessary. A generalized relationship of the CNW theorem is also provided in terms of the underlying equilibrium probability distribution at a fixed control parameter. Illustrative calculations on a toy model are performed with serial generalized-ensemble simulations, especially focusing on the different behavior of instantaneous and noninstantaneous replica transition schemes.

In this paper, a regularized lattice Boltzmann model for a class of nonlinear convection-diffusion equations with variable coefficients is proposed. The main idea of the present model is to introduce a set of precollision distribution functions that are defined only in terms of macroscopic moments. The Chapman-Enskog analysis shows that the nonlinear convection-diffusion equations can be recovered correctly. Numerical tests, including Fokker-Planck equations, Buckley-Leverett equation with discontinuous initial function, nonlinear convection-diffusion equation with anisotropic diffusion, are carried out to validate the present model, and the results show that the present model is more accurate than some available lattice Boltzmann models. It is also demonstrated that the present model is more stable than the traditional single-relaxation-time model for the nonlinear convection-diffusion equations.

We model the cytoskeleton as a fractal network by identifying each segment with a simple Kelvin-Voigt element with a well defined equilibrium length. The final structure retains the elastic characteristics of a solid or a gel, which may support stress, without relaxing. By considering a very simple regular self-similar structure of segments in series and in parallel, in one, two, or three dimensions, we are able to express the viscoelasticity of the network as an effective generalized Kelvin-Voigt model with a power law spectrum of retardation times $\mathcal{L}\sim {\tau }^{\alpha }$. We relate the parameter $\alpha$ with the fractal dimension of the gel. In some regimes $\left(0<\alpha <1\right)$, we recover the weak power law behaviors of the elastic and viscous moduli with the angular frequencies $G^{\prime }\sim G^{\prime \prime }\sim w^{\alpha }$ that occur in a variety of soft materials, including living cells. In other regimes, we find different power laws for $G^{\prime }$ and $G^{\prime \prime }$.

Bouncing walking droplets possess fascinating properties due to their peculiar wave-particle interaction leading to unexpected quantumlike behaviors. We propose a study consisting in droplets walking along annular cavities. We show that, in this geometry, they spontaneously form a string of synchronized bouncing droplets that share a common coherent wave propelling the group at a speed faster than single walkers. The formation of this coherent wave and the collective droplet behaviors are captured by a model. Those are at the opposite of the ones found in two-dimensional geometries. Our results shed light on walking dynamics.

We present a formulation of the model of laser-plasma interaction (LPI) at hydrodynamical scales that couples the plasma dynamics with linear and nonlinear LPI processes, including the creation and propagation of high-energy electrons excited by parametric instabilities and collective effects. This formulation accounts for laser beam refraction and diffraction, energy absorption due to collisional and resonant processes, and hot electron generation due to the stimulated Raman scattering, two-plasmon decay, and resonant absorption processes. Hot electron (HE) transport and absorption are described within the multigroup angular scattering approximation, adapted for transversally Gaussian electron beams. This multiscale inline LPI-HE model is used to interpret several shock ignition experiments, highlighting the importance of target preheating by HEs and the shortcomings of standard geometrical optics when modeling the propagation and absorption of intense laser pulses. It is found that HEs from parametric instabilities significantly increase the shock pressure and velocity in the target, while decreasing its strength and the overall ablation pressure.

The relative stability of two-dimensional soft quasicrystals in systems with two length scales is examined using a recently developed projection method, which provides a unified numerical framework to compute the free energy of periodic crystal and quasicrystals. Accurate free energies of numerous ordered phases, including dodecagonal, decagonal, and octagonal quasicrystals, are obtained for a simple model, i.e., the Lifshitz-Petrich free-energy functional, of soft quasicrystals with two length scales. The availability of the free energy allows us to construct phase diagrams of the system, demonstrating that, for the Lifshitz-Petrich model, the dodecagonal and decagonal quasicrystals can become stable phases, whereas the octagonal quasicrystal stays as a metastable phase.