PARTICLE-CLUSTER AGGREGATION WITH FRACTAL PARTICLE TRAJECTORIES AND ON FRACTAL SUBSTRATES

Abstract

ABSTRACT Several generalizations of the Witten-Sander model for diffusion limited aggregation have been investigated. Using Levy flight particle trajectories, clusters with a continuous range of effective fractal dimensionalities (D) between the limits of the Witten-Sander (D−5/3 for d = 2) and Void-Sutherland models (D ⋍ 2.0 for d = 2) can be generated. The effective dimensionality varies continuously with the exponent which described the distribution of step lengths in the Levy flight trajectory, but there does not seem to be a unique (1:1) relationship between the dimensionality of the trajectory and the dimensionality of the cluster. Several models for diffusion limited aggregation on 2d percolation clusters have been investigated. If both the growing aggregate and the mobile particles are confined to the percolation cluster, the growing aggregate has a limiting (low concentration) fractal dimensionality of about 1.40±0.10. If the growing aggregate is restricted to the percolation cluster, but the mobile particles are completely unrestricted, the aggregate covers the percolation cluster densely (D⋍1.89). If the aggregate is confined to the percolation cluster, but the only restriction on the mobile particles is that they may not visit sites already occupied by the growing aggregate, we estimate that the aggregate has a fractal dimensionality of about 1.75. Similar simulations have also been carried out on 3d percolation clusters and other fractal lattices.