We study Brownian motion of a single millimeter size bead confined in a quasi-two-dimensional horizontal channel with built-in anisotropy and asymmetry. Channel asymmetry is implemented by ratchet walls while anisotropy is introduced using a channel base that is grooved along the channel axis so that a bead can acquire a horizontal impulse perpendicular to the longitudinal direction when it collides with the base. When energy is injected to the channel by vertical vibration, the combination of asymmetric walls and anisotropic base induces an effective force which drives the bead into biased diffusive motion along the channel axis with diffusivity and drift velocity increase with vibration strength. The magnitude of this driving force, which can be measured in experiments on a tilted channel, is found to be consistent with those obtained from dynamic mobility and position probability distribution measurements. These results are explained by a simple collision model that suggests the random kinetic energy transfer between different translational degrees of freedom may be turned into useful work in the presence of asymmetry and anisotropy.

The influence of periodic shear deformation on nonaffine atomic displacements in an amorphous solid is examined via molecular dynamics simulations. We study the three-dimensional Kob-Andersen binary mixture model at a finite temperature. It is found that when the material is periodically strained, most of the atoms undergo repetitive nonaffine displacements with amplitudes that are broadly distributed. We show that particles with large amplitudes of nonaffine displacements are organized into compact clusters. With increasing strain amplitude, spatial correlations of nonaffine displacements become increasingly long-ranged, although they remain present even in a quiescent system due to thermal fluctuations.

The effects of compressibility on Rayleigh-Taylor instability (RTI) are investigated by inspecting the interplay between thermodynamic and hydrodynamic nonequilibrium phenomena (TNE, HNE, respectively) via a discrete Boltzmann model. Two effective approaches are presented, one tracking the evolution of the local TNE effects and the other focusing on the evolution of the mean temperature of the fluid, to track the complex interfaces separating the bubble and the spike regions of the flow. It is found that both the compressibility effects and the global TNE intensity show opposite trends in the initial and the later stages of the RTI. Compressibility delays the initial stage of RTI and accelerates the later stage. Meanwhile, the TNE characteristics are generally enhanced by the compressibility, especially in the later stage. The global or mean thermodynamic nonequilibrium indicators provide physical criteria to discriminate between the two stages of the RTI.

We extend the application of the adaptive resolution technique (AdResS) to liquid systems composed of alkane chains of different lengths. The aim of the study is to develop and test the modifications of AdResS required in order to handle the change of representation of large molecules. The robustness of the approach is shown by calculating several relevant structural properties and comparing them with the results of full atomistic simulations. The extended scheme represents a robust prototype for the simulation of macromolecular systems of interest in several fields, from material science to biophysics.

We comment on the main result given by Ourabah et al. [Phys. Rev. E 92, 032114 (2015)], noting that it can be derived as a special case of the more general study that we have provided in [Quantum Inf Process 15, 3393 (2016)]. Our proof of the nondecreasing character under projective measurements of so-called generalized $(h,\varphi )$ entropies (that comprise the Kaniadakis family as a particular case) has been based on majorization and Schur-concavity arguments. As a consequence, we have obtained that this property is obviously satisfied by Kaniadakis entropy but at the same time is fulfilled by all entropies preserving majorization. In addition, we have seen that our result holds for any bistochastic map, being a projective measurement a particular case. We argue here that looking at these facts from the point of view given in [Quantum Inf Process 15, 3393 (2016)] not only simplifies the demonstrations but allows for a deeper understanding of the entropic properties involved.

We rely on our proof of the nondecreasing character of quantum Kaniadakis entropy under projective measurement [Phys. Rev. E 92, 032114 (2015)], and we put it into perspective with the results of Bosyk et al. [Quantum Inf Process 15, 3393 (2016)]. Our method, adopted for the proof that Kaniadakis entropy does not decrease under a projective measurement, is based on Jensen's inequalities, while the method proposed by the authors of the Comment represents another alternative and clearly correct method to prove the same thing. Furthermore, we clarify that our interest in Kaniadakis entropy is due to the fact that this entropy has a transparent physical significance, emerging within the special relativity.

The existence of a zealot who stays a cooperator irrespective of the result of an interaction has been reported to add “social viscosity” to a population and thereby helps increase the cooperation level in prisoner's dilemma games, which premises the so-called well-mixed situation of a population. We found that this is not always true when a spatial structure, i.e., connecting agent, is introduced. Deploying zealots is counterproductive, especially when the underlying topology is homogenous, similar to that of a lattice. Our simulation reveals how the existence of never-converting cooperators destroys rather than boosts cooperation. We explain detailed mechanisms behind this interesting finding by referring to our previously presented concepts with respect to evolutionary dynamic processes for spatial games under the names enduring and expanding periods.

We numerically determine the global entropy for heat-conducting states, which is connected to the so-called excess heat considered as a basic quantity for steady-state thermodynamics in nonequilibrium. We adopt an efficient method to estimate the global entropy from the bare heat current and find that the obtained entropy agrees with the familiar local equilibrium hypothesis well. Our method possesses a wider applicability than local equilibrium and opens a possibility to compare thermodynamic properties of complex systems in nonequilibrium with those in the local equilibrium. We further investigate the global entropy for heat-conducting states and find that it exhibits both extensive and additive properties; however, the two properties do not degenerate each other differently from those at equilibrium. The separation of the extensivity and additivity makes it difficult to apply powerful thermodynamic methods to the nonequilibrium steady states.

The one-dimensional Ising spin-glass model with power-law long-range interactions is a useful proxy model for studying spin glasses in higher space dimensions and for finding the dimension at which the spin-glass state changes from having broken replica symmetry to that of droplet behavior. To this end we have calculated the exponent that describes the difference in free energy between periodic and antiperiodic boundary conditions. Numerical work is done to support some of the assumptions made in the calculations and to determine the behavior of the interface free-energy exponent of the power law of the interactions. Our numerical results for the interface free-energy exponent are badly affected by finite-size problems.

A goal of many epidemic models is to compute the outcome of the epidemics from the observed infected early dynamics. However, often, the total number of infected individuals at the end of the epidemics is much lower than predicted from the early dynamics. This discrepancy is argued to result from human intervention or nonlinear dynamics not incorporated in standard models. We show that when variability in infection rates is included in standard susciptible-infected-susceptible ($\mathrm{SIS}$) and susceptible-infected-recovered ($\mathrm{SIR}$) models the total number of infected individuals in the late dynamics can be orders lower than predicted from the early dynamics. This discrepancy holds for $\mathrm{SIS}$ and $\mathrm{SIR}$ models, where the assumption that all individuals have the same sensitivity is eliminated. In contrast with network models, fixed partnerships are not assumed. We derive a moment closure scheme capturing the distribution of sensitivities. We find that the shape of the sensitivity distribution does not affect $R_0$ or the number of infected individuals in the early phases of the epidemics. However, a wide distribution of sensitivities reduces the total number of removed individuals in the $\mathrm{SIR}$ model and the steady-state infected fraction in the $\mathrm{SIS}$ model. The difference between the early and late dynamics implies that in order to extrapolate the expected effect of the epidemics from the initial phase of the epidemics, the rate of change in the average infectivity should be computed. These results are supported by a comparison of the theoretical model to the Ebola epidemics and by numerical simulation.

Modeling isolated dislocations is challenging due to their long-ranged strain fields. Flexible boundary condition methods capture the correct long-range strain field of a defect by coupling the defect core to an infinite harmonic bulk through the lattice Green function (LGF). To improve the accuracy and efficiency of flexible boundary condition methods, we develop a numerical method to compute the LGF specifically for a dislocation geometry; in contrast to previous methods, where the LGF was computed for the perfect bulk as an approximation for the dislocation. Our approach directly accounts for the topology of a dislocation, and the errors in the LGF computation converge rapidly for edge dislocations in a simple cubic model system as well as in BCC Fe with an empirical potential. When used within the flexible boundary condition approach, the dislocation LGF relaxes dislocation core geometries in fewer iterations than when the perfect bulk LGF is used as an approximation for the dislocation, making a flexible boundary condition approach more efficient.

Recently Guérout et al. [Phys. Rev. E 93, 022108 (2016)] advocated that the lossless plasma model has to be redefined as the limit of the Drude model when the relaxation parameter goes to zero. It was claimed that the previously used plasma model cannot correctly describe the Casimir pressure between two plates made of both nonmagnetic and magnetic metals and has to be replaced with the redefined one. We show that the suggested redefinition does not satisfy necessary physical requirements imposed on the dielectric permittivity. We also present a plausible explanation for the fact that the lossless plasma model describes the Casimir pressure correctly even though it does not match the optical and electrical properties of metals.

We reply to the “Comment on ‘Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic mirrors.' ” We believe the comment misrepresents our papers, and fails to provide a plausible resolution to the conflict between theory and experiment.

The antiferromagnetic Ising model is investigated on the twenty 2-uniform lattices using the Monte Carlo method based on the Wang-Landau algorithm and the Metropolis algorithm to study the geometric frustration effect systematically. Based on the specific heat, the residual entropy, and the Edwards-Anderson freezing order parameter, the ground states of them were determined. In addition to the long-range-ordered phase and the spin ice phase found in the Archimedean lattices, two more phases were found. The partial long-range order is long-range order with exceptional disordered sites, which give extensive residual entropy. In the partial spin ice phase, the partial freezing phenomenon appears: A majority of sites are frozen without long-range order, but the other sites are fluctuating even at zero temperature. The spin liquid ground state was not found in the 2-uniform lattices.

Driven diffusive systems are important models in nonequilibrium state statistical mechanics. This paper studies an asymmetric exclusion process model with nearest rear neighbor interactions associated with energy. The exact flux expression of the model is obtained by a cluster mean-field method. Based on the flux expression, the properties of the fundamental diagram have been investigated in detail. To probe the energy's influence on the coarsening process of the system, Monte Carlo simulations are carried out to acquire the monotonic phase boundary in energy-density space. Above the phase boundary, the system is inhomogeneous and the normalized residence distribution $p\left(s\right)$ is nonmonotonically decreasing. Under the phase boundary, the system is homogeneous and $p\left(s\right)$ is monotonically decreasing. Further study comparatively shows that the system has turned into a microscopic inhomogeneous state from a homogeneous state before the system current arrives at maximum, if nearest rear neighbor interactions are strong. Our findings offer insights to deeply understand the dynamic features of nonequilibrium state systems.

How landscape fragmentation affects ecosystems diversity and stability is an important and complex question in ecology with no simple answer, as spatially separated habitats where species live are highly dynamic rather than just static. Taking into account the species dispersal among nearby connected habitats (or patches) through a common dynamic environment, we model the consumer-resource interactions with a ring type coupled network. By characterizing the dynamics of consumer-resource interactions in a coupled ecological system with three fundamental mechanisms such as the interaction within the patch, the interaction between the patches, and the interaction through a common dynamic environment, we report the occurrence of various collective behaviors. We show that the interplay between the dynamic environment and the dispersal among connected patches exhibits the mechanism of generation of oscillations, i.e., rhythmogenesis, as well as suppression of oscillations, i.e., amplitude death and oscillation death. Also, the transition from homogeneous steady state to inhomogeneous steady state occurs through a codimension-2 bifurcation. Emphasizing a network of a spatially extended system, the coupled model exposes the collective behavior of a synchrony-stability relationship with various synchronization occurrences such as in-phase and out-of-phase.

We consider a two-component, two-dimensional nonlinear Schrödinger system with unequal dispersion coefficients and self-defocusing nonlinearities, chiefly with equal strengths of the self- and cross-interactions. In this setting, a natural waveform with a nonvanishing background in one component is a vortex, which induces an effective potential well in the second component, via the nonlinear coupling of the two components. We show that the potential well may support not only the fundamental bound state, but also multiring excited radial state complexes for suitable ranges of values of the dispersion coefficient of the second component. We systematically explore the existence, stability, and nonlinear dynamics of these states. The complexes involving the excited radial states are weakly unstable, with a growth rate depending on the dispersion of the second component. Their evolution leads to transformation of the multiring complexes into stable vortex-bright solitons ones with the fundamental state in the second component. The excited states may be stabilized by a harmonic-oscillator trapping potential, as well as by unequal strengths of the self- and cross-repulsive nonlinearities.

Localization of energy in oscillator arrays has been of interest for a number of years, with special attention paid to the role of nonlinearity and discreteness in the formation of localized structures. This work examines a different type of energy localization arising due to the presence of dissipation in nonlinear resonance arrays. As a basic model, we consider a Klein-Gordon chain of finite length subjected to a harmonic excitation applied at an edge of the chain. It is shown that weak dissipation may be a key factor preventing the emergence of resonance in the entire chain, even if its nondissipative analog is entirely captured into resonance. The resulting process in the dissipative oscillator array represents large-amplitude resonant oscillations in a part of the chain adjacent to the actuator and small-amplitude oscillations in the distant part of the chain. The conditions of the emergence of resonance as well as the conditions of energy localization are derived. An agreement between the obtained analytical results and numerical simulations is demonstrated.

The relation between the onset of chaos and critical phenomena, like quantum phase transitions (QPTs) and excited-state quantum phase transitions (ESQPTs), is analyzed for atom-field systems. While it has been speculated that the onset of hard chaos is associated with ESQPTs based in the resonant case, the off-resonant cases, and a close look at the vicinity of the QPTs in resonance, show clearly that both phenomena, ESQPTs and chaos, respond to different mechanisms. The results are supported in a detailed numerical study of the dynamics of the semiclassical Hamiltonian of the Dicke model. The appearance of chaos is quantified calculating the largest Lyapunov exponent for a wide sample of initial conditions in the whole available phase space for a given energy. The percentage of the available phase space with chaotic trajectories is evaluated as a function of energy and coupling between the qubit and bosonic part, allowing us to obtain maps in the space of coupling and energy, where ergodic properties are observed in the model. Different sets of Hamiltonian parameters are considered, including resonant and off-resonant cases.

Analytical expressions are derived for aerodynamic drag force on small cylinders in the free molecule flow using the gas-kinetic theory. The derivation considers the effect of intermolecular interactions between the cylinder and gas media. Two limiting collision models, specular and diffuse scattering, are investigated in two limiting cylinder orientations with respect to the drift velocity. The earlier solution of Dahneke [B. E. Dahneke, J. Aerosol Sci. 4, 147 (1973)] is shown to be a special case of the current expressions in the rigid-body limit of collision. Drag force expressions are obtained for cylinders that undergo Brownian rotation and for those that align with the drift velocity. The validity of the theoretical expressions is tested against experimental mobility data available for carbon nanotubes.