Aggregation in a mixture of Brownian and ballistic wandering particles

Details Aggregation in a mixture of Brownian and ballistic wandering particles Aggregation in a mixture of Brownian and ballistic wandering particles

2006-04-10

arxiv.org/abs/cond-mat/0604256v1

Phys. Rev. E 73, 051401 (2006) url: http://link.aps.org/doi/10.1103/PhysRevE.73.051401

Physics

Condensed Matter

Statistical Mechanics

7 pages, 6 figures. accepted for publication on PRE

Scientific paper

10.1103/PhysRevE.73.051401

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 $P_{ba}$, or random ones, with probability $P_{rw}=1-P_{ba}$. The patterns were characterized through several quantities, including those related to the radial and angular scaling. The fractal dimension as a function of $P_{ba}$ continuously increases from $d_f\approx 1.72$ (DLA dimensionality) for $P_{ba}=0$ to $d_f\approx 2$ (BA dimensionality) for $P_{ba}=1$. However, the lacunarity and the active zone width exhibt a distinct behavior: they are convex functions of $P_{ba}$ with a maximum at $P_{ba}\approx1/2$. Through the analysis of the angular correlation function, we found that the difference between the radial and angular exponents decreases continuously with increasing $P_{ba}$ and rapidly vanishes for $P_{ba}>1/2$, in agreement with recent results concerning the asymptotic scaling of DLA clusters.

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