The goal of the present paper is the investigation of the final evolution of anisotropic regular structures and turbulence at large Reynolds number in the multidimensional Burgers equation. We show that we have local isotropization at small scales of the velocity and potential fields inside cellular zones. For periodic waves, we have simple decay inside a frozen structure. The global structure at large times is determined by the initial correlations and for short range correlated fields we have isotropization of turbulence. Finally, we consider the final behavior of the field, when the processes of nonlinear beating interactions become frozen, and the evolution of the field is determined only by the linear dissipation.

We give a solution of the Riemann problem in relativistic hydrodynamics in the case of ultrarelativistic equation of state and nonvanishing components of the velocity tangent to the initial discontinuity. Simplicity of the ultrarelativistic equation of state (the pressure being directly proportional to the energy density) allows us to express this solution in analytical terms. The result can be used both to construct and test numerical schemes for relativistic Euler equations in $\left(3+1\right)$ dimensions.

The dynamics of a long, two-dimensional vapor bubble confined in the gap between two superheated or subcooled parallel plates is analyzed theoretically. The unsteady expansion and/or contraction of the bubble is driven by mass transfer between the liquid and the vapor. The analysis uses the approach developed by Wilson et al. [J. Fluid Mech. 391, 1 (1999)] for a situation with “large” gaps and “small” superheating or subcooling to consider a situation with small gaps and large superheating or subcooling in which the mass transfer from or to the semicircular nose of the bubble is comparable to that from or to the thin liquid films on the plates. In order to permit a (semi-) analytical treatment the analysis is restricted to low Prandtl number liquids. When both plates are superheated the bubble always expands. In this case there are two possible constant-velocity continuous-film solutions for the expansion of the bubble, namely, an unstable fast mode and a stable slow mode. The evolution of the bubble is calculated numerically for a range of values of the parameters. In particular, these calculations show that eventually the bubble expands either with the constant velocity of the slow mode or exponentially. When both plates are subcooled the bubble always collapses to zero length in a finite time. When one plate is subcooled and the other plate is superheated the situation is rather more complicated. If the magnitude of the subcooling is less than that of the superheating then if the magnitude of the subcooling is greater than a critical value then a variety of complicated behaviors (including the possibility of an unexpected “waiting time” behavior in which the bubble remains almost stationary for a finite period of time) can occur before the bubble eventually collapses to a finite length in an infinite time, whereas if it is less than this critical value then the bubble always expands and eventually does so exponentially. If the magnitude of the subcooling is greater than that of the superheating then the bubble always collapses to zero length in a finite time.

A multiterm solution of the Boltzmann equation has been developed and used to calculate transport coefficients of charged-particle swarms in gases under the influence of electric and magnetic fields crossed at arbitrary angles when nonconservative collisions are present. The hierarchy resulting from a spherical-harmonic decomposition of the Boltzmann equation in the hydrodynamic regime is solved numerically by representing the speed dependence of the phase-space distribution function in terms of an expansion in Sonine polynomials about a Maxwellian velocity distribution at an internally determined temperature. Results are given for electron swarms in certain collisional models for ionization and attachment over a range of angles between the fields and field strengths. The implicit and explicit effects of ionization and attachment on the electron-transport coefficients are considered using physical arguments. It is found that the difference between the two sets of transport coefficients, bulk and flux, resulting from the explicit effects of nonconservative collisions, can be controlled either by the variation in the magnetic field strengths or by the angles between the fields. In addition, it is shown that the phenomena of ionization cooling and/or attachment cooling/heating previously reported for dc electric fields carry over directly to the crossed electric and magnetic fields. The results of the Boltzmann equation analysis are compared with those obtained by a Monte Carlo simulation technique. The comparison confirms the theoretical basis and numerical integrity of the moment method for solving the Boltzmann equation and gives a set of well-established data that can be used to test future codes and plasma models.

The metamaterial presented by Yan et al. [Phys. Rev. E 77, 056604 (2008)] is claimed to exhibit a superwide band of negative refraction. However, a retrieval procedure of the refractive index including the phase advance of a propagating plane wave shows that the material provides two distinct narrow bands with a negative refractive index instead of a single superwide band and thus the central claim of the paper is incorrect.

The superwide-band negative refraction of the symmetrical E-shaped structure designed by Yan et al. [Phys. Rev. E 77, 056604 (2008)] may not exist. While we accepted the validity of scattering parameter simulations completely, the process of retrieving material parameters could not be justified.

It is known that, in the order-parameter space $S^2/Z_2$ (a typical example being a uniaxial nematic liquid crystal in three dimensions), a $-1/2$ wedge disclination line and a $+1/2$ one are topologically equivalent and can thus be transformed continuously into each other. Here we report the realization of this transformation in a simulation of a cholesteric blue phase under an electric field.

It is a big challenge in the analysis of experimental data to disentangle the unavoidable measurement noise from the intrinsic dynamical noise. Here we present a general operational method to extract measurement noise from stochastic time series even in the case when the amplitudes of measurement noise and uncontaminated signal are of the same order of magnitude. Our approach is based on a recently developed method for a nonparametric reconstruction of Langevin processes. Minimizing a proper non-negative function, the procedure is able to correctly extract strong measurement noise and to estimate drift and diffusion coefficients in the Langevin equation describing the evolution of the original uncorrupted signal. As input, the algorithm uses only the two first conditional moments extracted directly from the stochastic series and is therefore suitable for a broad panoply of different signals. To demonstrate the power of the method, we apply the algorithm to synthetic as well as climatological measurement data, namely, the daily North Atlantic Oscillation index, shedding light on the discussion of the nature of its underlying physical processes.

We present a general method to study the nonequilibrium behavior of Casimir-type fluctuation-induced forces for classical free scalar field theories. In particular, we analyze the temporal evolution of the force toward its equilibrium value when the field dynamics is given by a general class of overdamped stochastic dynamics (including the model A and model B classes). The steady-state force is also analyzed for systems which have nonequilibrium steady states, for instance, where they are driven by colored noise. The key to the method is that the out of equilibrium force is computed by specifying an energy of interaction between the field and the surfaces in the problem. In general, we find that there is a mapping of the dynamical problem onto a corresponding static one and in the case where the latter can be solved, the full dynamical behavior of the force can be extracted. The method is used to compute the nonequilibrium Casimir force induced between two parallel plates by a fluctuating field, in the cases of Dirichlet, Neumann, and mixed boundary conditions. Various other examples, such as the fluctuation-induced force between inclusions in fluctuating media, are discussed.

In applying vibration-transit (V-T) theory of liquid dynamics to the thermodynamic properties of monatomic liquids, the point has been reached where an improved model is needed for the small $\left(\sim 10\mathrm{\%}\right)$ transit contribution. Toward this goal, an analysis of the available high-temperature experimental entropy data for elemental liquids was recently completed [D. C. Wallace, E. D. Chisolm, and N. Bock, Phys. Rev. E 79, 051201 (2009)]. This analysis yields a common curve of transit entropy vs $T/{\theta }_{\text{tr}}$, where $T$ is temperature and ${\theta }_{\text{tr}}$ is a scaling temperature for each element. In the present paper, a statistical mechanics model is constructed for the transit partition function, and is calibrated to the experimental transit entropy curve. The model has two scalar parameters, and captures the temperature scaling of experiment. The calibrated model fits the experimental liquid entropy to high accuracy at all temperatures. With no additional parameters, the model also agrees with both experiment and molecular dynamics for the internal energy vs. $T$ for Na. With the calibrated transit model, V-T theory provides equations subject to ab initio evaluation for thermodynamic properties of monatomic liquids. This will allow the range of applicability of the theory, and its overall accuracy, to be determined. More generally, the hypothesis of V-T theory, which divides the many-atom potential energy valleys into random and symmetric classes, can also be tested for its application beyond monatomic systems.

Whether strange nonchaotic attractors (SNAs) can typically arise in non-skew-product maps has been a crucial question for more than two decades. Recently, it was shown that SNAs arise in a particular non-skew-product map related to quasiperiodically driven continuous dynamical systems [R. Badard, Chaos, Solitons Fractals 28, 1327 (2006); Chaos 18, 023127 (2008)]. In the present paper, we derive Badard’s non-skew-product map from a periodically driven continuous dynamical system with spatially quasiperiodic potential and investigate onset mechanisms of SNAs in the map. In particular, we focus on a transition route to intermittent SNAs, where SNAs appear after pair annihilations of stable and unstable fixed points located on a ring-shaped invariant curve. Then the mean residence time and rotation numbers have a logarithmic singularity. Finally, we discuss the existence of SNAs in a special class of non-skew-product maps.

The behavior of the dielectric constant $\epsilon$ of pure fluids and binary mixtures near liquid-gas and liquid-liquid critical points is studied within the concept of complete scaling of asymmetric fluid-fluid criticality. While mixing of the electric field into the scaling fields plays a role, pressure mixing is crucial as the asymptotic behavior of the coexistence-curve diameter in the $\epsilon \text{—}T$ plane is concerned. Specifically, it is found that the diameters, characterized by a ${\left|T-T_c\right|}^{1-\alpha }$ singularity in the previous scaling formulation [J. V. Sengers, D. Bedeaux, P. Mazur, and S. C. Greer, Physica A 104, 573 (1980)], gain a more dominant ${\left|T-T_c\right|}^{2\beta }$ term, whose existence is shown to be supported by literature experimental data. The widely known ${\left|T-T_c\right|}^{1-\alpha }$ singularity of $\epsilon$ along the critical isopleth in the one-phase region is found to provide information on the effect of electric fields on the liquid-liquid critical temperature: from experimental data it is inferred that $T_c$ usually decreases as the magnitude of the electric field is enhanced. Furthermore, the behavior of mixtures along an isothermal path of approach to criticality is also analyzed: theory explains why the observed anomalies are remarkably higher than those associated to the usual isobaric path.

The long-time limit behavior of the variance and the correlation function for the output signal of a fractional oscillator with fluctuating eigenfrequency subjected to a periodic force is considered. The influence of a fluctuating environment is modeled by a multiplicative white noise and by an additive noise with a zero mean. The viscoelastic-type friction kernel with memory is assumed as a power-law function of time. The exact expressions of stochastic resonance (SR) characteristics such as variance and signal-to-noise ratio (SNR) have been calculated. It is shown that at intermediate values of the memory exponent the energetic stability of the oscillator is significantly enhanced in comparison with the cases of strong and low memory. A multiresonancelike behavior of the variance and SNR as functions of the memory exponent is observed and a connection between this effect and the memory-induced enhancement of energetic stability is established. The effect of memory-induced energetic stability encountered in case the harmonic potential is absent, is also discussed.

In this paper, we propose a transparent subordination approach to anomalous diffusion processes underlying the nonexponential relaxation. We investigate properties of a coupled continuous-time random walk that follows from modeling the occurrence of jumps with compound counting processes. As a result, two different diffusion processes corresponding to over- and undershooting operational times, respectively, have been found. We show that within the proposed framework, all empirical two-power-law relaxation patterns may be derived. This work is motivated by the so-called “less typical” relaxation behavior observed, e.g., for gallium-doped ${\text{Cd}}_{0.99}{\text{Mn}}_{0.01}\text{Te}$ mixed crystals.

The Brownian motion of a particle in a harmonic potential, which is simultaneously exposed either to a linear shear flow or to a plane Poiseuille flow is investigated. In the shear plane of both flows the probability distribution of the particle becomes anisotropic and the dynamics is changed in a characteristic manner compared to a trapped particle in a quiescent fluid. The particle distribution takes either an elliptical or a parachute shape or a superposition of both depending on the mean particle position in the shear plane. Simultaneously, shear-induced cross-correlations between particle fluctuations along orthogonal directions in the shear plane are found. They are asymmetric in time. In Poiseuille flow thermal particle fluctuations perpendicular to the flow direction in the shear plane induce a shift of the particle’s mean position away from the potential minimum. Two complementary methods are suggested to measure shear-induced cross-correlations between particle fluctuations along orthogonal directions.

The densest local packings of $N$ identical nonoverlapping spheres within a radius $R_{min}\left(N\right)$ of a fixed central sphere of the same size are obtained using a nonlinear programming method operating in conjunction with a stochastic search of configuration space. The knowledge of $R_{min}\left(N\right)$ in $d$-dimensional Euclidean space ${\mathbb{R}}^d$ allows for the construction both of a realizability condition for pair-correlation functions of sphere packings and an upper bound on the maximal density of infinite sphere packings in ${\mathbb{R}}^d$. In this paper, we focus on the two-dimensional circular disk problem. We find and present the putative densest packings and corresponding $R_{min}\left(N\right)$ for selected values of $N$ up to $N=348$ and use this knowledge to construct such a realizability condition and an upper bound. We additionally analyze the properties and characteristics of the maximally dense packings, finding significant variability in their symmetries and contact networks, and that the vast majority differ substantially from the triangular lattice even for large $N$. Our work has implications for packaging problems, nucleation theory, and surface physics.

We experimentally report the elastic response of an assembly of ${\text{SiO}}_2$ powders under a shear oscillation strain by a modified inverted torsion pendulum with a Couette-like setup. We find that the shear restoring force displayed by ${\text{SiO}}_2$ assembly is of strong amplitude dependence, which is ascribed to the dynamic behavior of the stress network inside and could be used to classify the states of the ${\text{SiO}}_2$ assembly, i.e., elastic solid, plastic solid, viscoelastic solid, and viscous fluid. The underlying mechanisms for different states of the ${\text{SiO}}_2$ assembly are tentatively proposed.