Dynamical scaling of the surface of finite-density ballistic aggregation.

Abstract

We study the roughness of aggregates that are formed by ballistic deposition with nonzero flux density of incoming particles. The flux density is controlled by a parameter 0\ensuremath{\le}p\ensuremath{\le}1. The scaling behavior of the interfacial width \ensuremath{\xi} does not depend on p and is the same as \ensuremath{\xi} found in a variety of other, related models. For short times \ensuremath{\xi}\ensuremath{\propto}${t}^{1/3}$ for a one-dimensional substrate and \ensuremath{\xi}\ensuremath{\propto}${t}^{0.22}$ for two-dimensional ones. The latter is not consistent with various theoretical predictions. Rough numerical estimates for the long-time exponent are also presented. In addition, we derive a relation between the width of the geometrical boundary of the aggregate and the width of the active region of growth. This relation, true for models in which the active zone is asymptotically correlated to the surface of the aggregate, is verified by our simulations.