Cluster aggregation by shortest path travel

Abstract

The authors have studied a new growth process of cluster aggregation. In this process, particles are released randomly from a hypersphere enclosing the cluster and stick to those perimeter sites of the growing cluster which are closest (at shortest distance) to the releasing sites. They find D=1.62+or−0.09 for d=2 and D=2.02+or−0.13 for d=3 for the fractal dimensions D of such aggregates in Euclidean dimension d. Using Hentschel's mean-field theory, for generalised cluster aggregations, they argue that these aggregates should have the least fractal dimension (because of maximum screening present in this model) among all the aggregation models in which particles coming from outside form the aggregates. The mean-field values of D predicted by the theory are shown to be comparable with observation.