Superaging and Subaging Phenomena in a Nonequilibrium Critical Behavior of the Structurally Disordered Two-Dimensional XY Model

A Monte Carlo numerical simulation of the specific features of nonequilibrium critical behavior is carried out for the two-dimensional structurally disordered XY model during its evolution from a low-temperature initial state. On the basis of the analysis of the two-time dependence of autocorrelation functions and dynamic susceptibility for systems with spin concentrations of p = 1.0, 0.9, and 0.6, aging phenomena characterized by a slowing down of the relaxation system with increasing waiting time and the violation of the fluctuation–dissipation theorem (FDT) are revealed. The values of the universal limiting fluctuation–dissipation ratio (FDR) are obtained for the systems considered. As a result of the analysis of the two-time scaling dependence for spin–spin and connected spin autocorrelation functions, it is found that structural defects lead to subaging phenomena in the behavior of the spin–spin autocorrelation function and superaging phenomena in the behavior of the connected spin autocorrelation function.     

Marginal Effect of Structural Defects on the Nonequilibrium Critical Behavior of the Two-Dimensional Ising Model

The influence of various initial magnetizations m0 and structural defects on the nonequilibrium critical behavior of the two-dimensional Ising model is numerically simulated by Monte Carlo methods. Based on analysis of the time dependence of magnetization and the two-time dependences of autocorrelation function and dynamic susceptibility, we revealed the influence of logarithmic corrections and the crossover phenomena of percolation behavior on the nonequilibrium characteristics and the critical exponents. Violation of the fluctuation–dissipation theorem is studied, and the limiting fluctuation–dissipation ratio is calculated for the case of high-temperature initial state. The influence of various initial states on the limiting fluctuation–dissipation ratio is investigated. The nonequilibrium critical dynamics of weakly disordered systems with spin concentrations p ≥ 0.9 is shown to belong to the universality class of the nonequilibrium critical behavior of the pure model and to be characterized by the same critical exponents and the same limiting fluctuation–dissipation ratios. The nonequilibrium critical behavior of systems with p ≤ 0.85 demonstrates that the universal characteristics of the nonequilibrium critical behavior depend on the defect concentration and the dynamic scaling is violated, which is related to the influence of the crossover effects of percolation behavior.     

Aging effects in the nonequilibrium behavior of multilayer magnetic superstructures

A numerical Monte Carlo study of the nonequilibrium behavior of multilayer magnetic superstructures consisting of alternating magnetic and nonmagnetic nanolayers is performed. The calculated two-time autocorrelation function and the staggered magnetization of the structure at its evolution starting from various initial states are analyzed. The analysis reveals aging effects characterized by a slowing down of the relaxation and correlation characteristics in the system with the waiting time. It is shown that, in contrast to bulk magnetic systems, the aging effects in magnetic superstructures arise not only near the ferromagnetic ordering temperature T _c in the films but also within a wide temperature range at T ≤ T _c.     

Dynamical regimes in the dissipative particle dynamics model

We discuss theoretically the behavior of the velocity autocorrelation function in the dissipative particle dynamics (DPD) model. Two dynamical regimes are identified depending on the dimensionless model parameters. For low values of the dimensional friction, a mean field behavior is observed in which the kinetic theory for the DPD model provides good predictions. For high values of the friction, collective hydrodynamic effects are dominant. We have performed numerical simulations that validate the theory presented.     

Analysis of the Effect of Different Initial States and Structural Defects on the Characteristics of the Nonequilibrium Critical Behavior of the 3D Ising Model

The effect of different initial values m₀ of magnetization and structural defects on the nonequilibrium critical behavior of the 3D Ising model have been analyzed numerically using the Monte Carlo method. Analysis of the two-time dependences of the autocorrelation function and dynamic susceptibility has revealed a substantial influence of the initial states on the aging effects that are characterized by anomalous retardation of relaxation and correlation in the system upon an increase in the waiting time. We have studied the violations of the fluctuation–dissipation theorem and calculated the limiting fluctuation–dissipation ratio. It is shown that in the nonequilibrium critical behavior of the 3D Ising model, two universality subclasses corresponding to the evolution of the system from the high-temperature (with m₀ = 0) and low-temperature (with m₀ = 1) initial states with the values of the limiting fluctuation–dissipation ratio typical of these states can be singled out.     

Monte Carlo Study of the Effect of Initial States and Structural Defects on Nonequilibrium Critical Behavior of the Three-Dimensional Ising Model

The effect of various initial magnetizations m₀ and structural defects the nonequilibrium critical behavior of the three-dimensional Ising model is numerically studied. Based on an analysis of the time dependence of the magnetization and the two-time dependence of the autocorrelation function and dynamic susceptibility, the significant effect of initial states on relaxation magnetizations and aging effects characterized by anomalous relaxation inhibition and correlation in the system with increasing waiting time was revealed. The fluctuation–dissipation theorem violation was studied, and the values of the limit fluctuation–dissipation ratio (FDR) are calculated. It is shown that two universality subclasses can be distinguished in the nonequilibrium critical behavior of the three-dimensional Ising model with random initial magnetization m₀ These subclasses correspond to the system evolution from the high-temperature (m₀ = 0) and low-temperature (m₀ = 1) initial states with limit FDRs characteristic of these states.     

A Gentle Stochastic Thermostat for Molecular Dynamics

We discuss a dynamical technique for sampling the canonical measure in molecular dynamics. We present a method that generalizes a recently proposed scheme (Samoletov et al., J. Stat. Phys. 128:1321–1336, 2007), and which controls temperature by use of a device similar to that of Nosé dynamics, but adds random noise to improve ergodicity. In contrast to Langevin dynamics, where noise is added directly to each physical degree of freedom, the new scheme relies on an indirect coupling to a single Brownian particle. For a model with harmonic potentials, we show under a mild non-resonance assumption that we can recover the canonical distribution. In spite of its stochastic nature, experiments suggest that it introduces a relatively weak perturbative effect on the physical dynamics, as measured by perturbation of temporal autocorrelation functions. The kinetic energy is well controlled even in the early stages of a simulation.     

Absence of logarithmic scaling in the ageing behaviour of the 4D spherical model

The non-equilibrium dynamics of the kinetic spherical model with a non-conserved order-parameter, quenched to T≤T_c from a fully disordered initial state, is studied at its upper critical dimension d=d^*=4. In the scaling limit where both the waiting time s and the observation time t are large and the ratio y=t/s>1 is fixed, the scaling functions of the two-time autocorrelation and autoresponse functions do not contain any logarithmic correction factors and the typical size of correlated domains scales for large times as L(t)∼t^1/2.     

Activity Phase Transition for Constrained Dynamics

We consider two cases of kinetically constrained models, namely East and FA-1f models. The object of interest of our work is the activity A(t){\mathcal {A}(t)} defined as the total number of configuration changes in the interval [0, t] for the dynamics on a finite domain. It has been shown in Garrahan et al. (J Phys A 42:075007, 2009; Phys Rev Lett 98:195702, 2007) that the large deviations of the activity exhibit a non-equilibrium phase transition in the thermodynamic limit and that reducing the activity is more likely than increasing it due to a blocking mechanism induced by the constraints. In this paper, we study the finite size effects around this first order phase transition and analyze the phase coexistence between the active and inactive dynamical phases in dimension 1. In higher dimensions, we show that the finite size effects are determined by the dimension and the choice of the boundary conditions.     

Brownian motion in a fluid in elongational flow

Brownian motion of a spherical particle in stationary elongational flow is studied. We derive the Langevin equation together with the fluctuation-dissipation theorem for the particle from nonequilibrium fluctuating hydrodynamics to linear order in the elongation-rate-dependent inverse penetration depths. We then analyze how the velocity autocorrelation function as well as the mean square displacement are modified by the elongational flow. We find that for times small compared to the inverse elongation rate the behavior is similar to that found in the absence of the elongational flow. Upon approaching times comparable to the inverse elongation rate the behavior changes and one passes into a time domain where it becomes fundamentally different. In particular, we discuss the modification of thet ^–3/2 long-time tail of the velocity autocorrelation function and comment on the resulting contribution to the mean square displacement. The possibility of defining a diffusion coefficient in both time domains is discussed.     

Electrohydrodynamic wave-packet collapse and soliton instability for dielectric fluids in (2 + 1)-dimensions

In this paper we introduce a modified lattice Boltzmann model (LBM) with the capability of mimicking a fluid system with dynamic heterogeneities. The physical system is modeled as a one-dimensional fluid, interacting with finite-lifetime moving obstacles. Fluid motion is described by a lattice Boltzmann equation and obstacles are randomly distributed semi-permeable barriers which constrain the motion of the fluid particles. After a lifetime delay, obstacles move to new random positions. It is found that the non-linearly coupled dynamics of the fluid and obstacles produces heterogeneous patterns in fluid density and non-exponential relaxation of two-time autocorrelation function.Received: 19 March 2004, Published online: 29 June 2004PACS: 47.11. + j Computational methods in fluid dynamics - 05.70.Ln Nonequilibrium and irreversible thermodynamics     

Calculation of the fluctuation-dissipation ratio for the nonequilibrium critical behavior of disordered systems

The values of a new universal parameter characterizing a nonequilibrium critical behavior, namely, the fluctuation-dissipation ratio specifying a fundamental relation between the dynamic response function and the correlation function, are calculated for the disordered three-dimensional Ising model. The analysis of the two-time dependence for autocorrelation functions and the ac susceptibility for the systems with spin densities p = 1.0, 0.8, and 0.6 shows the aging effects characterized by the anomalous slowing of relaxation in the system with the growth of the waiting time and the violation of the fluctuation-dissipation theorem. To improve the accuracy of the ac susceptibility calculations, the “thermal bath” technique has been used without introducing the applied magnetic field in the simulation. It has been shown that the structural defects lead to the pronounced enhancement of the aging effects.     

Five Dimensional Domain Walls in a Scalar-Tensor Theory of Gravitation

Five dimensional Kaluza-Klein space-time is considered in the presence of thick domain walls in the framework of scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A 113:467, [1986]). Exact cosmological model, which represents a stiff domain wall, is presented. Some physical and kinematical properties of the model are also discussed.     

Molecular dynamics investigation of structural phase transitions

A two dimensional model exhibiting a structural phase transition is described, and results of molecular dynamics calculations on the model are presented. The static properties indicate a second order phase transition and show the growth of large ordered regions as the transition is approached. The spectral function for the order parameter autocorrelation function has an intense central peak near the transition.     

A Higher Dimensional Cosmic Domain Wall in Brans-Dicke Theory of Gravitation

Five dimensional Kaluza-Klein Space-time is considered in the presence of thick domain walls in the scalar-tensor theory formulated by Brans and Dicke (Phys. Rev. 124:925, 1961). Exact cosmological model, in this theory, is presented with the help of special law of variation proposed by Berman (Nuovo Cim. B 74:182, 1983) for Hubble’s parameter. Some physical and kinematical properties of the model are also discussed.     

Aging in the glass phase of a two-dimensional random periodic elastic system

Using the renormalization group method we investigate the nonequilibrium relaxation of the (Cardy-Ostlund) 2D random sine-Gordon model, which describes pinned arrays of lines. Its statics exhibit a marginal (theta = 0) glass phase for T < Tg described by a line of fixed points. We obtain the universal scaling functions for two-time dynamical response and correlations near Tg for various initial conditions, as well as the autocorrelation exponent. The fluctuation dissipation ratio is found to be nontrivial and continuously dependent on T.     

Higher Dimensional LRS Bianchi Type-I Domain Walls in a Scalar-Tensor Theory of Gravitation

An exact higher dimensional LRS Bianchi type-I cosmological model is obtained in presence of thick domain walls in a scalar tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A113:467, 1985). Some physical and kinematical properties of the models are also discussed.     

Monte Carlo investigations of the influence of structural defects on aging effects and the violation of the fluctuation-dissipation theorem for a nonequilibrium critical behavior in the three-dimensional Ising model

The specific features of a nonequilibrium critical behavior in the three-dimensional structurally disordered Ising model have been studied numerically by the Monte Carlo method. An analysis of the two-time dependence of the autocorrelation function and the dynamic susceptibility for systems with spin concentrations p = 0.8 and 0.6 has revealed the aging effects, which are characterized by a slowing down of the relaxation of the system with an increase in the waiting time, and the violation of the fluctuation-dissipation theorem. The values of the universal limit of fluctuation-dissipation ratio for the considered systems have been obtained using the Monte Carlo method. It has been shown that the presence of structural defects in the system leads to an enhancement of the aging effects and to an increase of the values of the limit of fluctuation-dissipation ratio.     

Kaluza-Klein Cosmological Model in f(R,T) Gravity

A five dimensional Kaluza-Klein space-time is considered in the presence of perfect fluid source in f(R,T) gravity proposed by Harko et al. ( [gr-qc], 2011). A cosmological model with a negative constant deceleration parameter with an appropriate choice of a function f(T) is presented. To find a determinate solution of the field equations it is assumed that scalar of expansion is proportional to the shear scalar of the space time. The physical behavior of the model is also studied.