Anomaly in Numerical Integrations of the KPZ Equation and Improved Discretization

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We demonstrate and explain that conventional finite difference schemes for direct numerical integration do not approximate the continuum Kardar-Parisi-Zhang (KPZ) equation due to microscopic roughness. The effective diffusion coefficient is found to be inconsistent with the nominal one. We propose a novel discretization in 1+1 dimensions which does not suffer from this deficiency and elucidates the reliability and limitations of direct integration approaches.
14 pages, 3 figures, RevTex

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Statistical Mechanics

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http://salesiana.dossiersoluciones.com/handle/123456789/151909

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cond-mat/9709008
 http://arxiv.org/abs/cond-mat/9709008

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arXiv