We study in momentum-conserving systems, how nonintegrable dynamics may affect thermal transport properties. As illustrating examples, two one-dimensional (1D) diatomic chains, representing 1D fluids and lattices, respectively, are numerically investigated. In both models, the two species of atoms are assigned two different masses and are arranged alternatively. The systems are nonintegrable unless the mass ratio is one. We find that when the mass ratio is slightly different from one, the heat conductivity may keep significantly unchanged over a certain range of the system size and as the mass ratio tends to one, this range may expand rapidly. These results establish a new connection between the macroscopic thermal transport properties and the underlying dynamics.

We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit of large system sizes is shown to be very well-approximated by a Fokker-Planck-like equation, or equivalently by a set of stochastic difference equations. This formalism is applied to the specific case of two species: one predator species and its prey species. Quasicycles, stochastic cycles sustained and amplified by the demographic noise, previously found in continuous-time predator-prey models are shown to exist, and their behavior predicted from a linear noise analysis is shown to be in very good agreement with simulations. The effects of the noise on other attractors in the corresponding deterministic map, such as periodic cycles, quasiperiodicity, and chaos, are also investigated.

The temperature dependences of α relaxation time ${\tau }_{\alpha }(T)$ of three glass-forming liquids (salol, $o$-terphenyl, and α-picoline) were investigated by a depolarized light scattering technique. A detailed description of ${\tau }_{\alpha }(T)$ near $T_A$, the temperature of the transition from the Arrhenius law at high temperatures to a non-Arrhenius behavior of ${\tau }_{\alpha }(T)$ at lower temperatures, was done. It was found that this transition is quite sharp. If the transition is described as switching from the Arrhenius law to the Vogel-Fulcher-Tammann law, it occurs within the temperature range of about 15 K or less. Most of the known expressions for ${\tau }_{\alpha }(T)$ cannot describe this sharp transition. Our analysis revealed that this transition can be described either as a discontinuous transition in the spirit of the frustration-limited domain theory [D. Kivelson, G. Tarjus, X. Zhao, and S. A. Kivelson, Phys. Rev. E 53, 751 (1996)], implying a phase transition, or by a phenomenological expression recently suggested [B. Schmidtke, N. Petzold, R. Kahlau, M. Hofmann, and E. A. Rössler, Phys. Rev. E 86, 041507 (2012)], where the activation energy includes the term depending exponentially on temperature.

We have studied spectral properties of a cholesteric liquid crystal with a combined defect consisting of a nanocomposite layer and a twist. The nanocomposite layer is made of metallic nanoballs dispersed in a transparent matrix and featuring effective resonant permittivity. A solution has been found for the transmission spectrum of circularly polarized waves in the structure. We have analyzed spectral splitting of the defect mode in the band gap of the cholesteric when its frequency coincides with the nanocomposite resonant frequency. Defect modes have characteristics strongly dependent on the magnitude and the sign of the phase difference of the cholesteric helix on both sides of the defect layer. It has been found that the band gap width and the position and localization degree of defect modes can be effectively controlled by external fields applied to the cholesteric.

We provide a family of transparent tight-binding models with nontrivial potentials and site-dependent hopping parameters. Their feasibility is discussed in electromagnetic resonators, dielectric slabs, and quantum-mechanical traps. In the second part of the paper, the arrays are obtained through a generalization of supersymmetric quantum mechanics in discrete variables. The formalism includes a finite-difference Darboux transformation applied to the scattering matrix of a periodic array. A procedure for constructing a hierarchy of discrete Hamiltonians is indicated and a particular biparametric family is given. The corresponding potentials and hopping functions are identified as solitary waves, pointing to a discrete spinorial generalization of the Korteweg-deVries family.

Typically, the force between paramagnetic particles in a uniform magnetic field is calculated using either dipole-based models or the Maxwell stress tensor combined with Laplace's equation for magnetostatics. Dipole-based models are fast but involve many assumptions, leading to inaccuracies in determining forces for clusters of particles. The Maxwell stress tensor yields an exact force calculation, but solving Laplace's equation is very time consuming. Here, we present a more elaborate dipole-based model: the micro-mutual-dipolar model. Our model has a time complexity that is similar to that of other dipole-based models but is much more accurate especially when used to calculate the force of small aggregates. Using this model, we calculate the force between two paramagnetic spheres in a uniform magnetic field and a circular rotational magnetic field and compare our results with those of other models. The forces for three-particle and ten-particle systems dispersed in two-dimensional (2D) space are examined using the same model. We also apply this model to calculate the force between two paramagnetic disks dispersed in 2D space. The micro-mutual-dipolar model is demonstrated to be useful for force calculations in dynamic simulations of small clusters of particles for which both accuracy and efficiency are desirable.

A parametric study on the simulation of a single aluminum (Al) particle settling in water is conducted using various sets of interactive parameters between Al and water particles, so that a systematic method can be established to describe the hydrodynamic interaction between an Al particle and the fluid in a large range of particle sizes. The force parameters and the cutoff have been correlated to the terminal settling velocity of the Al particle in the dissipative particle dynamics simulation, so that the classic Stokes' law can be used to determine those parameters. Two empirical equations are developed to calculate the minimum repulsive force parameter in terms of the number density and radius, respectively. In addition, the correlation between the cutoff and the Al particle radius has been obtained by linear curve fitting. The radial distribution functions of Al and water particles are computed to examine the relative spacing among solid and fluid particles. The present approach is general and can also be extended to study particle motion of other types of particles and fluids. This study will be a baseline for the investigation of multiple particles settling in a viscous fluid.

The development of condensed-phase detonation instabilities is simulated using moving window molecular dynamics and a generic AB model of a high explosive. It is found that an initially planar detonation front with one-dimensional flow can become unstable through development of transverse perturbations resulting in highly inhomogeneous and complex two- and three-dimensional distributions of pressure and other variables within the detonation front. Chemical reactions are initiated in localized transverse shock fronts and Mach stems with a pressure and temperature higher than those predicted by classic Zel'dovich, von Neumann, and Doering detonation theory. The two-dimensional cellular and transverse and three-dimensional pulsating detonation structures are found by varying the physico-chemical properties of AB energetic material, sample geometry, and boundary conditions. The different regimes of condensed-phase detonation that can develop from instabilities within a planar detonation front exhibit structures, although at a much smaller scale, that are similar to those observed in gases and diluted liquids.

The resistance between two nodes in general position on a fan network with $n$ radial lines and $m$ transverse lines is determined. Also a similar result of Izmailian, Kenna, and Wu [J. Phys. A: Math. Theor. 47, 035003 (2014)] for an $m\times n$ cobweb network is reproduced, but the method used here is significantly different. It avoids the use of the Kirchhoff matrix, requires the solution of just one instead of two eigenvalue problems, and results directly in only a single summation. Further, the current distribution is given explicitly as a byproduct of the method. The method is the same as that used by Tan, Zhou, and Yang [J. Phys. A: Math. Theor. 46, 195202 (2013)] to find the cobweb resistance between center and perimeter for $1\le m\le 3$ and general $n$. Proof of their conjecture for general $m$ is discussed.

We derive generalized Langevin equations for the translational and rotational motion of a heated Brownian particle from the fluctuating hydrodynamics of its nonisothermal solvent. The temperature gradient around the particle couples to the hydrodynamic modes excited by the particle itself so that the resulting noise spectrum is governed by a frequency-dependent temperature. We show how the effective temperatures at which the particle coordinates and (angular) velocities appear to be thermalized emerge from this central quantity.

A kinetic theory describing the motion of an impurity particle in a degenerate Tonks-Girardeau gas is presented. The theory is based on the one-dimensional Boltzmann equation. An iterative procedure for solving this equation is proposed, leading to the exact solution in a number of special cases and to an approximate solution with the explicitly specified precision in a general case. Previously we reported that the impurity reaches a nonthermal steady state, characterized by an impurity momentum $p_{\infty }$ depending on its initial momentum $p_0$ [E. Burovski, V. Cheianov, O. Gamayun, and O. Lychkovskiy, Phys. Rev. A 89, 041601(R) (2014)]. In the present paper the detailed derivation of $p_{\infty }\left(p_0\right)$ is provided. We also study the motion of an impurity under the action of a constant force $F$. It is demonstrated that if the impurity is heavier than the host particles, $m_{\mathrm{i}}>m_h$, damped oscillations of the impurity momentum develop, while in the opposite case, $m_{\mathrm{i}}<m_h$, oscillations are absent. The steady-state momentum as a function of the applied force is determined. In the limit of weak force it is found to be force independent for a light impurity and proportional to $\sqrt{F}$ for a heavy impurity.

Quasistationary states of long-range interacting systems have been studied at length over the last 15 years. It is known that the collisional terms of the Balescu-Lenard and Landau equations vanish for one-dimensional systems in homogeneous states, thus requiring a new kinetic equation with a proper dependence on the number of particles. Here we show that the scalings discussed in the literature are mainly due either to small size effects or the use of unsuitable variables to describe the dynamics. The scaling obtained from both simulations and theoretical considerations is proportional to the square of the number of particles, and a general form for the kinetic equation valid for the homogeneous regime is obtained. Numerical evidence is given for the Hamiltonian mean field and ring models, and a kinetic equation valid for the homogeneous state is obtained for the former system.

Shearing of two-dimensional wet foam is simulated using an introduced numerical model, and results are compared to those of experiments. This model features realistically deformable bubbles, which distinguishes it from previously used models for wet foam. The internal bubble dynamics and their contact interactions are also separated in the model, making it possible to investigate the effects of the related microscale properties of the model on the macroscale phenomena. Validity of model assumptions was proved here by agreement between the simulated and measured Herschel-Bulkley rheology, and shear-induced relaxation times. This model also suggests a relationship between the shear stress and normal stress as well as between the average degree of bubble deformation and applied shear stress. It can also be used to analyze suspensions of bubbles and solid particles, an extension not considered in this work.

Motivated by the fact that the same social dilemma can be perceived differently by different players, we here study evolutionary multigames in structured populations. While the core game is the weak prisoner's dilemma, a fraction of the population adopts either a positive or a negative value of the sucker's payoff, thus playing either the traditional prisoner's dilemma or the snowdrift game. We show that the higher the fraction of the population adopting a different payoff matrix the more the evolution of cooperation is promoted. The microscopic mechanism responsible for this outcome is unique to structured populations, and it is due to the payoff heterogeneity, which spontaneously introduces strong cooperative leaders that give rise to an asymmetric strategy imitation flow in favor of cooperation. We demonstrate that the reported evolutionary outcomes are robust against variations of the interaction network, and they also remain valid if players are allowed to vary which game they play over time. These results corroborate existing evidence in favor of heterogeneity-enhanced network reciprocity, and they reveal how different perceptions of social dilemmas may contribute to their resolution.

We discuss the occurrence of chimera states in networks of nonlocally coupled bistable oscillators, in which individual subsystems are characterized by the coexistence of regular (a fixed point or a limit cycle) and chaotic attractors. By analyzing the dependence of the network dynamics on the range and strength of coupling, we identify parameter regions for various chimera states, which are characterized by different types of chaotic behavior at the incoherent interval. Besides previously observed chimeras with space-temporal and spatial chaos in the incoherent intervals we observe another type of chimera state in which the incoherent interval is characterized by a central interval with standard space-temporal chaos and two narrow side intervals with spatial chaos. Our findings for the maps as well as for time-continuous van der Pol–Duffing's oscillators reveal that this type of chimera states represents characteristic spatiotemporal patterns at the transition from coherence to incoherence.

Accurate knowledge of the optical properties of a warm dense deuterium-tritium (DT) mixture is important for reliable design of inertial confinement fusion (ICF) implosions using radiation-hydrodynamics simulations. The opacity of a warm dense DT shell essentially determines how much radiation from hot coronal plasmas can be deposited in the DT fuel of an imploding capsule. Even for the simplest species of hydrogen, the accurate calculation of their opacities remains a challenge in the warm-dense matter regime because strong-coupling and quantum effects play an important role in such plasmas. With quantum-molecular-dynamics (QMD) simulations, we have derived a first-principles opacity table (FPOT) of deuterium (and the DT mixture by mass scaling) for a wide range of densities from ${\rho }_{\mathrm{D}}=0.5$ to $673.518\mathrm{g}/{\mathrm{cm}}^3$ and temperatures from $T=5000\mathrm{K}$ up to the Fermi temperature $T_{\mathrm{F}}$ for each density. Compared with results from the astrophysics opacity table (AOT) currently used in our hydrocodes, the FPOT of deuterium from our QMD calculations has shown a significant increase in opacity for strongly coupled and degenerate plasma conditions by a factor of 3–100 in the ICF-relevant photon-energy range. As conditions approach those of classical plasma, the opacity from the FPOT converges to the corresponding values of the AOT. By implementing the FPOT of deuterium and the DT mixture into our hydrocodes, we have performed radiation-hydrodynamics simulations for low-adiabat cryogenic DT implosions on the OMEGA laser and for direct-drive-ignition designs for the National Ignition Facility. The simulation results using the FPOT show that the target performance (in terms of neutron yield and energy gain) could vary from ∼10% up to a factor of ∼2 depending on the adiabat of the imploding DT capsule; the lower the adiabat, the more variation is seen in the prediction of target performance when compared to the AOT modeling.

In this paper, we generalize the unified approach proposed in Zhang et al. [J. Zhang, Z. Xu, and X. Wu, Phys. Rev. E 78, 026709 (2008)] to design the nonlinear local absorbing boundary conditions (LABCs) for the nonlinear Schrödinger equation with wave operator on unbounded domains. In fact, based on the methodology underlying the unified approach, we first split the original equation into two parts—the linear equation and the nonlinear equation—then achieve a one-way operator to approximate the linear equation to make the wave outgoing, and finally combine the one-way operator with the nonlinear equation to achieve the nonlinear LABCs. The stability of the equation with the nonlinear LABCs is also analyzed by introducing some auxiliary variables, and some numerical examples are presented to verify the accuracy and effectiveness of our proposed method.

Systems driven by $\alpha$-stable noises could be very different from their Gaussian counterparts. Stationary states in single-well potentials can be multimodal. Moreover, a potential well needs to be steep enough in order to produce stationary states. Here it is demonstrated that two-dimensional (2D) systems driven by bivariate $\alpha$-stable noises are even more surprising than their 1D analogs. In 2D systems, intriguing properties of stationary states originate not only due to heavy tails of noise pulses, which are distributed according to $\alpha$-stable densities, but also because of properties of spectral measures. Consequently, 2D systems are described by a whole family of Langevin and fractional diffusion equations. Solutions of these equations bear some common properties, but also can be very different. It is demonstrated that also for 2D systems potential wells need to be steep enough in order to produce bounded states. Moreover, stationary states can have local minima at the origin. The shape of stationary states reflects symmetries of the underlying noise, i.e., its spectral measure. Finally, marginal densities in power-law potentials also have power-law asymptotics.

The celebrated Einstein relation between the diffusion coefficient $D$ and the drift velocity $v$ is violated in nonequilibrium circumstances. We analyze how this violation emerges for the simplest example of a Brownian motion on a lattice, taking into account the interplay between the periodicity, the randomness, and the asymmetry of the transition rates. Based on the nonequilibrium fluctuation theorem the $v/D$ ratio is found to be a nonlinear function of the affinity. Hence it depends in a nontrivial way on the microscopics of the sample.