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

Journal Article · Tue Jan 31 23:00:00 EST 1995 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.51.995· OSTI ID:6640107

Wu, M ^[1]; Billah, K Y.R. ^[2]; Shinozuka, M ^[3]

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1. Physics Department, Princeton University, Princeton, New Jersey 08544 (United States)
2. Department of Civil, Environmental and Coastal Engineering, Stevens Institute of Technology, Hoboken, New Jersey 07030 (United States)
3. Department of Civil Engineering and Operations Research, Princeton University, Princeton, New Jersey 08544 (United States)

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 [alpha] and [beta] are calculated and the results are compared with the predictions by Medina [ital et] [ital al]. [Phys. Rev. A 39, 3053 (1989)], Zhang [Phys. Rev. B 42, 4897 (1990)], and with the numerical results of Amar [ital et] [ital al]. [Phys. Rev. A 43, R4548 (1991)] and Peng [ital et] [ital al]. [Phys. Rev. A 44, R2239 (1991)]. The agreement of the present results with the theoretical prediction by Medina [ital et] [ital al]. shows that the current method of colored noise simulation is uniquely effective.

• OSTI ID: 6640107
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 51:2; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COATINGS
CORRELATION FUNCTIONS
CRYSTAL GROWTH
DIFFUSION
FOURIER TRANSFORMATION
FUNCTIONS
GROWTH
INTEGRAL TRANSFORMATIONS
MECHANICS
NOISE
NUMERICAL SOLUTION
SCALING LAWS
STATISTICAL MECHANICS
STOCHASTIC PROCESSES
SURFACE PROPERTIES
SURFACE TENSION
TRANSFORMATIONS
VAPOR DEPOSITED COATINGS