Aggregation in a mixture of Brownian and ballistic wandering particles

In this paper, we analyze the scaling properties of a model that has as limiting cases the diffusion-limited aggregation (DLA) and the ballistic aggregation (BA) models. This model allows us to control the radial and angular scaling of the patterns, as well as their gap distributions. The particles added to the cluster can follow either ballistic trajectories, with probability Pba, or random ones, with probability Prw=1-Pba. The patterns were characterized through several quantities, including those related to the radial and angular scaling. The fractal dimension as a function of Pba continuously increases from df approximately 1.72 (DLA dimensionality) for Pba=0 to df approximately 2 (BA dimensionality) for Pba. However, the lacunarity and the active zone width exhibit a distinct behavior: they are convex functions of Pba with a maximum at Pba approximately 1/2. Through the analysis of the angular correlation function, we found that the difference between the radial and angular exponents decreases continuously with increasing Pba and rapidly vanishes for Pba>1/2, in agreement with recent results concerning the asymptotic scaling of DLA clusters.