Numerical solution of the Kardar-Parisi-Zhang equation with a long-range spatially correlated noise

Minchun Wu, K. Y.R. Billah, Masanobu Shinozuka

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9 Scopus citations

Abstract

The Kardar-Parisi-Zhang (KPZ) equation for stochastic surface growth is numerically integrated in the presence of a long-range spatially correlated noise and the scaling behavior of the growing surfaces is investigated. A robust methodology for simulating the colored noise directly from uniform random variates is used with the discretized KPZ equation. The sample functions are expressed in terms of harmonic functions and the powerful fast Fourier transform is used. The growth exponents α and β are calculated and the results are compared with the predictions by Medina et al. [Phys. Rev. A 39, 3053 (1989)], Zhang [Phys. Rev. B 42, 4897 (1990)], and with the numerical results of Amar et al. [Phys. Rev. A 43, R4548 (1991)] and Peng et al. [Phys. Rev. A 44, R2239 (1991)]. The agreement of the present results with the theoretical prediction by Medina et al. shows that the current method of colored noise simulation is uniquely effective.

Original languageEnglish
Pages (from-to)995-998
Number of pages4
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume51
Issue number2
DOIs
StatePublished - 1995

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