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Title: Estudo numérico da equação de Kardar, Parisi e Zhang
Keywords: Integração numérica;  Equação diferencial estocástica;  Rugosidade (Superfície);  Numerical integration;  Stochastic differential equation;  Roughness (surface)
Issue Date: 4-Mar-2009
Abstract: We integrate numerically the Kardar-Parisi-Zhang (KPZ) equation in one and two dimensions using the usual finite differences scheme and the replacement of |∇h|2 by exponentially decreasing functions of that quantity. In one dimension the study showed that the discretization scheme adopted by us was able to solve the two major problems found with the usual discretization: numerical instabilities and inconsistency between the parameters of the discretized and the continuum version. Our study advences over previous works on the KPZ equation, which usually treated those problems apart. In two dimensions, we evaluated and confirmed the universality of steady state height and roughness distributions in KPZ class by a sistematic variation of the equation s parameters. Estimates of kurtosis and skewness of steady state height and roughness distributions were provided. We also obtained roughness exponents estimates. We observed the weak scaling corrections behavior of steady state roughness distributions and verified the evidence of stretched exponentials tails of such distributions. Our results confirm previous estimates from lattice models, showing their reliability as representatives of the KPZ class.
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