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Aggregation in a mixture of Brownian and ballistic wandering particles

S. G. Alves

S. C. Ferreira, Jr.^*

Departamento de Física, Universidade Federal de Minas Gerais, CP 702, 30161-970, Belo Horizonte, Minas Gerais, Brazil

Departamento de Física, Universidade Federal Viçosa, 36571-000, Viçosa, Minas Gerais, Brazil

^*Email address: silviojr@ufv.br

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Phys. Rev. E 73, 051401 – Published 1 May, 2006

DOI: https://doi.org/10.1103/PhysRevE.73.051401

Abstract

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 exhibit a distinct behavior: they are convex functions of $P_{ba}$ with a maximum at $P_{ba} \approx 1 ∕ 2$ . Through the analysis of the angular correlation function, we found that the difference between the radial and angular exponents decreases continuously with increasing $P_{ba}$ and rapidly vanishes for $P_{ba} > 1 ∕ 2$ , in agreement with recent results concerning the asymptotic scaling of DLA clusters.

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Aggregation in a mixture of Brownian and ballistic wandering particles

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References (24)

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