A numerical study of the development of bulk scale-free structures upon growth of self-affine aggregates

摘要

During the last decade, self-affine geometrical properties of many growingaggregates, originated in a wide variety of processes, have been wellcharacterized. However, little progress has been achieved in the search of aunified description of the underlying dynamics. Extensive numerical evidencehas been given showing that the bulk of aggregates formed upon ballisticaggregation and random deposition with surface relaxation processes can bebroken down into a set of infinite scale invariant structures called "trees".These two types of aggregates have been selected because it has beenestablished that they belong to different universality classes: those ofKardar-Parisi-Zhang and Edward-Wilkinson, respectively. Exponents describingthe spatial and temporal scale invariance of the trees can be related to theclassical exponents describing the self-affine nature of the growing interface.Furthermore, those exponents allows us to distinguish either the compact ornon-compact nature of the growing trees. Therefore, the measurement of thestatistic of the process of growing trees may become a useful experimentaltechnique for the evaluation of the self-affine properties of some aggregates.