Current implementations of fluctuating ideal-gas descriptions with the lattice Boltzmann methods are based on a fluctuation dissipation theorem, which, while greatly simplifying the implementation, strictly holds only for zero mean velocity and small fluctuations. We show how to derive the fluctuation dissipation theorem for all $\mathbf{k}$, which was done only for $\mathbf{k}=0$ in previous derivations. The consistent derivation requires, in principle, locally velocity-dependent multirelaxation time transforms. Such an implementation is computationally prohibitively expensive but, with a small computational trick, it is feasible to reproduce the correct FDT without overhead in computation time. It is then shown that the previous standard implementations perform poorly for non vanishing mean velocity as indicated by violations of Galilean invariance of measured structure factors. Results obtained with the method introduced here show a significant reduction of the Galilean invariance violations.

Using extensive numerical analysis of the fiber bundle model with equal load sharing dynamics we studied the finite-size scaling forms of the relaxation times against the deviations of applied load per fiber from the critical point. Our most crucial result is we have not found any $\ln \left(N\right)$ dependence of the average relaxation time $\langle T(\sigma ,N)\rangle$ in the precritical state. The other results are as follows: (i) The critical load ${\sigma }_c\left(N\right)$ for the bundle of size $N$ approaches its asymptotic value ${\sigma }_c\left(\infty \right)$ as ${\sigma }_c\left(N\right)={\sigma }_c\left(\infty \right)+A{N}^{-1/\nu }$. (ii) Right at the critical point the average relaxation time $\langle T({\sigma }_c\left(N\right),N)\rangle$ scales with the bundle size $N$ as $\langle T({\sigma }_c\left(N\right),N)\rangle \sim N^{\eta }$ and this behavior remains valid within a small window of size $\left|\Delta \sigma \right|\sim N^{-\zeta }$ around the critical point. (iii) When $1/N<\left|\Delta \sigma \right|<100N^{-\zeta }$ the finite-size scaling takes the form $\langle T(\sigma ,N)\rangle /N^{\eta }\sim \mathcal{G}\left[\{{\sigma }_c\left(N\right)-\sigma \}{N}^{\zeta }\right]$ so in the limit of $N\to \infty$ one has $\langle T\left(\sigma \right)\rangle \sim {(\sigma -{\sigma }_c)}^{-\tau }$. The high precision of our numerical estimates led us to verify that $\nu =3/2$, conjecture that $\eta =1/3$, $\zeta =2/3$, and, therefore, $\tau =1/2$.

We present numerical and theoretical results concerning the technologically important process of evolution of high-aspect-ratio profiles due to surface diffusion under thermal treatment. We show how a broad class of initial gratings adopt, after a short transient stage, a typical shape that can be accurately described as a curve whose curvature has only two single Fourier modes as a function of the arc-length parameter. Moreover, we introduce a set of evolution equations for the relevant parameters that accounts very accurately for both morphological and kinetic aspects of the transformation processes for these curves in a wide region in parameter space. Regarding the decay of rectangular gratings, our numerical results show the existence of geometrically related classes that asymptotically approach to the same trajectory in parameter space. Gratings belonging to the same class pass through the same sequence of morphologies before reaching the final equilibrium state.

In the present paper we study the mechanism that leads to the formation of regular patterns of energy localization and complete recurrent energy transport in the homogeneous systems of anharmonic oscillators and oscillatory chains subjected to a state of sonic vacuum. The basic model under investigation comprises a system of purely anharmonic oscillators as well as oscillatory chains given to a localized excitation where the initial energy is imported to one of the oscillators or oscillatory chains. The results of numerical simulations reveal the existence of a strong classical beating phenomenon, characterized by complete, recurrent, resonant energy exchanges between the oscillators and oscillatory chain and this in the state of sonic vacuum where no regular resonant frequencies can be defined. In this study we show that formation of the recurrent energy exchanges in this highly degenerate model is strictly stipulated by the system parameters. Thus, for instance, choosing the parameter of coupling below a certain threshold leads to significant energy localization on one of the oscillators or oscillatory chains. However, increasing the strength of coupling above the threshold leads to the formation of a strong beating response. The analytical study pursued in this paper predicts the origin of formation of a strong beating phenomenon and provides the necessary conditions on the system parameter for its excitation. Moreover, careful analysis of the beating phenomenon reveals the qualitatively different global bifurcation undergone by this type of highly nonstationary regime. The theoretical study is further extended to the system of coupled purely anharmonic lattices. Thus we show analytically and numerically that excitation of some particular solutions (e.g., spatially periodic standing waves and standing breathers) on one of the lattices results in the formation of similar patterns of energy (wave) localization as well as the regime of complete recurrent interchain energy transport. In particular we demonstrate that the formation of these regimes is solely affected by a particular choice of system parameters. The results of the analytical study are found to be in very good agreement with those of numerical simulations.

This paper proposes the concept of pinning noise and then investigates the phenomenon of stochastic resonance of coupled complex systems driven by pinning noise, where the noise has an $\alpha$-stable distribution. Two kinds of pinning noise are taken into account: partial noise and switching noise. In particular, we establish a connection between switching noise and global noise when Gaussian noise is considered. It is shown that switching noise can not only achieve a stronger resonance effect, but it is also more robust to induce the resonance effect than partial noise.

We study statistics of entanglement generated by quantum chaotic dynamics. Using an ensemble of the very large number ($\gtrsim {10}^7$) of quantum states obtained from the temporally evolving coupled kicked tops, we verify that the estimated one-body distribution of the squared Schmidt eigenvalues for the quantum chaotic dynamics can agree surprisingly well with the analytical one for the universality class of the random matrices described by the fixed trace ensemble (FTE). In order to quantify this agreement, we introduce the $L^1$ norm of the difference between the one-body distributions for the quantum chaos and FTE and use it as an indicator of the dynamical randomness. As we increase the scaled coupling constant, the $L^1$ difference decreases. When the effective Planck constant is not small enough, the decrease saturates, which implies quantum suppression of dynamical randomness. On the other hand, when the effective Planck constant is small enough, the decrease of the $L^1$ difference continues until it is masked by statistical fluctuation due to finiteness of the ensemble. Furthermore, we carry out two statistical analyses, the ${\chi }^2$ goodness of fit test and an autocorrelation analysis, on the difference between the distributions to seek for dynamical remnants buried under the statistical fluctuation. We observe that almost all fluctuating deviations are statistical. However, even for well-developed quantum chaos, unexpectedly, we find a slight nonstatistical deviation near the largest Schmidt eigenvalue. In this way, the statistics of Schmidt eigenvalues enables us to measure dynamical randomness of quantum chaos with reference to the random matrix theory of FTE.

We study the absorption of an intense electromagnetic wave in a plasma by inverse bremsstrahlung, in the relativistic quantum regime, by using the Klein-Gordon (KG) equation. We examine the following points: (1) the solutions of the KG equation in the absence of collisions; (2) the transition probabilities between electron momentum states, and (3) the effective collision frequency in the weak and strong field limits.

The principle of hierarchical design is a prominent theme in many natural systems where mechanical efficiency is of importance. Here we establish the properties of a particular hierarchical structure, showing that high mechanical efficiency is found in certain loading regimes. We show that in the limit of gentle loading, the optimal hierarchical order increases without bound. We show that the scaling of material required for stability against loading to be withstood can be altered in a systematic, beneficial manner through manipulation of the number of structural length scales optimized upon. We establish the relationship between the Hausdorff dimension of the optimal structure and loading for which the structure is optimized. Practicalities of fabrication are discussed and examples of hierarchical frames of the same geometry constructed from solid beams are shown.

We examine the general problem of light transport initiated by oblique illumination of a turbid medium with a collimated beam. This situation has direct relevance to the analysis of cloudy atmospheres, terrestrial surfaces, soft condensed matter, and biological tissues. We introduce a solution approach to the equation of radiative transfer that governs this problem, and develop a comprehensive spherical harmonics expansion method utilizing Fourier decomposition (SHEF${}_N$). The SHEF${}_N$ approach enables the solution of problems lacking azimuthal symmetry and provides both the spatial and directional dependence of the radiance. We also introduce the method of sequential-order smoothing that enables the calculation of accurate solutions from the results of two sequential low-order approximations. We apply the SHEF${}_N$ approach to determine the spatial and angular dependence of both internal and boundary radiances from strongly and weakly scattering turbid media. These solutions are validated using more costly Monte Carlo simulations and reveal important insights regarding the evolution of the radiant field generated by oblique collimated beams spanning ballistic and diffusely scattering regimes.

We propose a lattice Boltzmann (LB) model for the convection-diffusion equation (CDE) and show that the CDE can be recovered correctly from the model by the Chapman-Enskog analysis. The most striking feature of the present LB model is that it enables the collision process to be implemented locally, making it possible to retain the advantage of the lattice Boltzmann method in the study of the heat and mass transfer in complex geometries. A local scheme for computing the heat and mass fluxes is then proposed to replace conventional nonlocal finite-difference schemes. We further validate the present model and the local scheme for computing the flux against analytical solutions to several classical problems, and we show that both the model for the CDE and the computational scheme for the flux have a second-order convergence rate in space. It is also demonstrated the present model is more accurate than existing LB models for the CDE.

We study the zigzag transition in a system of particles with screened electrostatic interaction, submitted to a thermal noise. At finite temperature, this configurational phase transition is an example of noisy supercritical pitchfork bifurcation. The measurements of transverse fluctuations allow a complete description of the bifurcation region, which takes place between the deterministic threshold and a thermal threshold beyond which thermal fluctuations do not allow the system to flip between the symmetric zigzag configurations. We show that a divergence of the saturation time for the transverse fluctuations allows a precise and unambiguous definition of this thermal threshold. Its evolution with the temperature is shown to be in good agreement with theoretical predictions from noisy bifurcation theory.

Unlike other natural network systems, assortativity can be observed in most human social networks; however, it has been reported that a social dilemma situation represented by a 2×2 prisoner's dilemma game favors dissortativity to enhance cooperation. Our simulations successfully reveal that a public goods game with coevolution for both agents’ strategy and network topology encourages assortativity, although it only slightly enhances cooperation as compared to a 2×2 donor and recipient game with a strong dilemma to be solved. This outcome occurs because the network dynamics in a multiplayer game discourages emerging cooperation unlike its beneficial result in a 2×2 prisoner's dilemma game.

The aim of this paper is to identify the forces that govern the dynamic behavior of polydisperse granular systems under high electric fields in air media. In a previous paper, we reported the changes in the morphology and dynamics of grain structures under a frequency and amplitude variable voltage and summarized them in a diagram [L. M. Salvatierra et al., Chem. Phys. Lett. 481, 194 (2009)]. In the present article, we investigate the influence of the grain size distribution and the speed of voltage increase during tests. We explain the main transitions observed in the diagram in terms of the change in grain size and the frequency-dependent electrical response, related to electrophoretic and dielectrophoretic interactions.

Reactivity boundaries that divide the destination and the origin of trajectories are of crucial importance to reveal the mechanism of reactions. We investigate whether such reactivity boundaries can be extracted for higher index saddles in terms of a nonlinear canonical transformation successful for index-one saddles by using a model system with an index-two saddle. It is found that the true reactivity boundaries do not coincide with those extracted by the transformation taking into account a nonlinearity in the region of the saddle even for small perturbations, and the discrepancy is more pronounced for the less repulsive direction of the index-two saddle system. The present result indicates an importance of the global properties of the phase space to identify the reactivity boundaries, relevant to the question of what reactant and product are in phase space, for saddles with index more than one.

A bottleneck situation in one-lane traffic flow is typically modelled with a constant demand of entering cars. However, in practice this demand may depend on the density of cars in the bottleneck. The present paper studies a simple bimodal realization of this mechanism to which we refer to as density-feedback control (DFC): If the actual density in the bottleneck is above a certain threshold, the reservoir density of possibly entering cars is reduced to a different constant value. By numerical solution of the discretized viscid Burgers equation a rich stationary phase diagram is found. In order to maximize the flow, which is the goal of typical traffic-management strategies, we find the optimal choice of the threshold. Analytical results are verified by computer simulations of the microscopic totally asymmetric exclusion process with DFC.

We perform experiments with 72 electronic limit-cycle oscillators, globally coupled via a linear or nonlinear feedback loop. While in the linear case we observe a standard Kuramoto-like synchronization transition, in the nonlinear case, with increase of the coupling strength, we first observe a transition to full synchrony and then a desynchronization transition to a quasiperiodic state. However, in this state the ensemble remains coherent so that the amplitude of the mean field is nonzero, but the frequency of the mean field is larger than frequencies of all oscillators. Next, we analyze effects of common periodic forcing of the linearly or nonlinearly coupled ensemble and demonstrate regimes when the mean field is entrained by the force whereas the oscillators are not.

A measure to estimate the direct and directional coupling in multivariate time series is proposed. The measure is an extension of a recently published measure of conditional mutual information from mixed embedding (MIME) for bivariate time series. In the proposed measure of partial MIME (PMIME), the embedding is on all observed variables and it is optimized in explaining the response variable. It is shown that PMIME detects correctly direct coupling and outperforms the (linear) conditional Granger causality and the partial transfer entropy. We demonstrate that PMIME does not rely on significance test and embedding parameters and the number of observed variables has no effect on its statistical accuracy; it may only slow the computations. The importance of these points is shown in simulations and in an application to epileptic multichannel scalp electroencephalograms.

The off-axis emergence of vortex breakdown (VB) is revealed. The steady axisymmetric flow in a vertical sealed cylinder, which is partially filled with water and the rest is filled with air, is driven by the rotating bottom disk. The numerical simulations show that VB can emerge away from the rotation axis, interface, and walls. As the rotation intensifies, VB first develops in the water region. If the water height is less (larger) than nearly one half of the cylinder radius, VB emerges off (on) the axis. As the rotation further increases, the off-axis VB ring touches the interface and then a thin countercirculation layer develops in the air flow above the water VB domain. This two-fluid VB ring shrinks (it even disappears in a very shallow whirlpool) as the interface approaches the bottom disk.