Numerical simulation of Ginzburg-Landau-Langevin equations

This work is concerned with non-equilibrium phenomena, with focus on the numerical simulation of the relaxation of non-conserved order parameters described by stochastic kinetic equations known as Ginzburg-Landau-Langevin (GLL) equations. We propose methods for solving numerically these type of equations, with additive and multiplicative noises. Illustrative applications of the methods are presented for different GLL equations, with emphasis on equations incorporating memory effects

Numerical approximation of the Ginzburg-Landau equation with memory effects in the dynamics of phase transitions

We consider the out-of-equilibrium time evolution of a nonconserved order parameter using the Ginzburg-Landau equation including memory effects. Memory effects are expected to play important role on the nonequilibrium dynamics for fast phase transitions, in which the time scales of the rapid phase conversion are comparable to the microscopic time scales. We consider two numerical approximation schemes based on Fourier collocation and finite difference methods and perform a numerical analysis with respect to the existence, stability and convergence of the schemes. We present results of direct numerical simulations for one and three spatial dimensions, and examine numerically the stability and convergence of both approximation schemes. (C) 2008 Elsevier B.V. All rights reserved.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

NOISE and ULTRAVIOLET DIVERGENCES in SIMULATIONS of GINZBURG-LANDAU-LANGEVIN TYPE of EQUATIONS

The time evolution of an order parameter towards equilibrium can be described by nonlinear Ginzburg-Landau (GL) type of equations, also known as time-dependent nonlinear Schrodinger equations. Environmental effects of random nature are usually taken into account by noise sources, turning the GL equations into stochastic equations. Noise sources give rise to lattice-spacing dependence of the solutions of the stochastic equations. We present a systematic method to renormalize the equations on a spatial lattice to obtain lattice-spacing independent solutions. We illustrate the method in approximation schemes designed to treat nonlinear and nonlocal GL equations that appear in real time thermal field theory and stochastic quantization.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Univ Estadual Paulista, Inst Fis Teor, BR-01140070 São Paulo, BrazilUniv Fed Sao Joao Del Rei, Dept Ciencias Nat, BR-36301000 Sao Joao Del Rei, MG, BrazilUniversidade Federal de São Paulo, Dept Informat Saude, Escola Paulista Med, BR-04023062 São Paulo, BrazilUniversidade Federal de São Paulo, Dept Informat Saude, Escola Paulista Med, BR-04023062 São Paulo, BrazilWeb of Scienc