Surface growth models with a random-walk-like nonlocality.
To understand the effects of a random-walk-like nonlocality on the dynamical scaling properties of surface growths, a stochastic growth model in which the height difference triangle up h((i,i+1))=|h(i)-h(i+1)| of a chosen nearest neighbor column pair (i,i+1) is decreased by one unit is introduced and studied by simulations. The probability P((i,i+1)) of choosing a column pair (i,i+1) on a one-dimensional substrate is assigned as P((i,i+1))=e(kappa triangle up h((i,i+1)))/ summation operator (L)(j=1)e(kappa triangle up h((j,j+1))). On a substrate of given size L, the dynamical scaling property satisfies a normal scaling behavior as W=L(alpha)f(t/L(z)), when kappa is very small. If kappa becomes moderately large, the scaling property with the dynamic exponent z=1 as in diffusion-limited erosion appears. If kappa becomes very large, no surface roughening is found.
Yoon
S Y
SY
Department of Physics and Research Institute of Basic Sciences, Kyung Hee University, Seoul 130-701, Korea. ykim@khu.ac.kr
Kim
Yup
Y