Numerical study of the development of bulk scale-free structures upon growth of self-affine aggregates.

Abstract

During the last decade, self-affine geometrical properties of many growing aggregates, originated in a wide variety of processes, have been well characterized. However, little progress has been achieved in the search of a unified description of the underlying dynamics. Extensive numerical evidence is given showing that the bulk of aggregates formed upon ballistic aggregation and random deposition with surface relaxation processes can be broken down into a set of infinite scale invariant structures called "trees." These two types of aggregates have been selected because it has been established that they belong to different universality classes: those of Kardar-Parisi-Zhang and Edward-Wilkinson, respectively. Exponents describing the spatial and temporal scale invariance of the trees can be related to the classical exponents describing the self-affine nature of the growing interface. Furthermore, those exponents allow us to distinguish either the compact or noncompact nature of the growing trees. Therefore, the measurement of the statistic of the process of growing trees may become a useful experimental technique for the evaluation of the self-affine properties of some aggregates.