Aggregation in a mixture of Brownian and ballistic wandering particles

TL;DR

This paper investigates a model blending diffusion-limited and ballistic aggregation to understand how particles' trajectories influence pattern formation, revealing continuous changes in fractal dimension and distinct behaviors in lacunarity and active zone width.

Contribution

It introduces a unified model controlling radial and angular scaling in aggregation patterns, bridging DLA and BA models, and analyzes how particle trajectories affect pattern properties.

Findings

Fractal dimension increases from ~1.72 to 2 as P_ba increases from 0 to 1.

Lacunarity and active zone width peak at P_ba≈1/2.

Angular and radial exponents converge for P_ba>1/2.

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 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.