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Convergence analysis of Markov chain Monte Carlo methods in high-dimensional statistical applications is increasingly recognized. In this paper, we develop general mixing time bounds for Metropolis-Hastings algorithms on discrete spaces by…
We consider the Ising model on a small-world network, where the long-range interaction strength $J_2$ is in general different from the local interaction strength $J_1$, and examine its relaxation behaviors as well as phase transitions. As…
We study the continuum limit of a family of kinetic Monte Carlo models of crystal surface relaxation that includes both the solid-on-solid and discrete Gaussian models. With computational experiments and theoretical arguments we are able to…
Random sequential adsorption with diffusional relaxation, of two by two square objects on the two-dimensional square lattice is studied by Monte Carlo computer simulation. Asymptotically for large lattice sizes, diffusional relaxation…
We theoretically investigate the relaxation dynamics of a nearly-flat binary lipid bilayer membrane by taking into account the membrane tension, hydrodynamics of the surrounding fluid, inter-monolayer friction and mutual diffusion in each…
The density relaxation phenomenon is modeled using both Monte Carlo and dissipative MD simulations to investigate the effects of regular taps applied to a vessel having a planar floor filled with monodisperse spheres. Results suggest the…
We study the relaxation properties of the Kondo lattice model using the nonequilibrium dynamical mean field formalism in combination with the non-crossing approximation. The system is driven out of equilibrium either by a magnetic field…
We report a Monte Carlo investigation of the effect of a lattice of antidots on spin relaxation in twodimensional electron systems. The spin relaxation time is calculated as a function of geometrical parameters describing the antidot…
We consider stochastic spin-flip dynamics for: (i) monotone discrete surfaces in Z^3 with planar boundary height and (ii) the one-dimensional discrete Solid-on-Solid (SOS) model confined to a box. In both cases we show almost optimal bounds…
We have studied kinetics of random sequential adsorption of mixtures on a square lattice using Monte Carlo method. Mixtures of linear short segments and long segments were deposited with the probability $p$ and $1-p$, respectively. For…
The finite-size scaling method in the equilibrium Monte Carlo(MC) simulations and the finite-time scaling method in the nonequilibrium-relaxation simulations are compromised. MC time data of various physical quantities are scaled by the MC…
We report extensive simulations of the relaxation dynamics of a self-avoiding polymer confined inside a cylindrical pore. In particular, we concentrate on examining how confinement influences the scaling behavior of the global relaxation…
We discuss the relaxation time (inverse spectral gap) of the one dimensional $O(N)$ model, for all $N$ and with two types of boundary conditions. We see how its low temperature asymptotic behavior is affected by the topology. The…
We consider the relaxation process and the out-of-equilibrium dynamics of natural generalizations to arbitrary dimensions of the well known one dimensional East process. These facilitated models are supposed to catch some of the main…
Using theories of phase ordering kinetics and of renormalization group, we derive analytically the relaxation times of the long wave-length fluctuations of a phase-separated domain boundary in the vicinity of (and below) the critical…
We consider the adsorption kinetics of a regular block-copolymer of total length $N$ and block size $M$ at a selective liquid-liquid interface in the limit of strong localization. We propose a simple analytic theory based on scaling…
On the basis of physical considerations we propose a one-dimensional discrete lattice model for the density relaxation of granular materials under tapping. Solving the difference equation numerically, we find a logarithmic time-dependence…
We use Monte Carlo simulations to study polymer melts consisting of fully flexible and moderately stiff chains in the bond fluctuation model at a volume fraction $0.5$. In order to reduce the local density fluctuations, we test a…
A mean-field kinetic model suggests that the relaxation dynamics of wormlike micellar networks is a long and complex process due to the problem of reducing the number of free end-caps (or dangling ends) while also reaching an equilibrium…
Using results of a Monte Carlo simulation of the Sherrington-Kirkpatrick model, we try to characterize the slow disorder samples, namely we analyze visually the correlation between the relaxation time for a given disorder sample $J$ with…