TY - JOUR
T1 - Numerical solution of the Kardar-Parisi-Zhang equation with a long-range spatially correlated noise
AU - Wu, Minchun
AU - Billah, K. Y.R.
AU - Shinozuka, Masanobu
PY - 1995
Y1 - 1995
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevE.51.995
DO - 10.1103/PhysRevE.51.995
M3 - Article
AN - SCOPUS:0042013172
SN - 1063-651X
VL - 51
SP - 995
EP - 998
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 2
ER -