Ch. Lam et Lm. Sander, EXACT SCALING IN SURFACE GROWTH WITH POWER-LAW NOISE, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 48(2), 1993, pp. 979-987
We investigate a continuum formulation of surface growth following the
Kardar-Parisi-Zhang equation [Phys. Rev. Lett. 56, 889 (1986)] with a
power-law distribution of the magnitudes of regional advances. This f
ormulation describes Zhang's ballistic-deposition model [J. Phys. (Par
is) 51, 2129 (1990)] with power-law noise and possibly recent fluid-di
splacement experiments. Our exact theory predicts a transition of the
scaling behavior from power-law-noise domination to a Gaussian-noise r
egime as the power increases. An apparent contradiction with previous
simulations is due to a logarithmic correction to the scaling at the t
ransition and to anomalous-growth effects. Analogous scaling behaviors
are derived for the Edwards-Wilkinson model [Proc. R. Soc. London Ser
. A 381, 17 (1982)] with power-law noise. Our results are supported by
simulations.