Morphological transition between diffusion-limited and ballistic aggregation growth patterns

Abstract

In this work, the transition between diffusion-limited and ballistic aggregation models was revisited using a model in which biased random walks simulate the particle trajectories. The bias is controlled by a parameter $\lambda$, which assumes the value $\lambda =0$ (1) for ballistic (diffusion-limited) aggregation model. Patterns growing from a single seed were considered. In order to simulate large clusters, a new efficient algorithm was developed. For $\lambda \ne 0$, the patterns are fractal on the small length scales, but homogeneous on the large ones. We evaluated the mean density of particles $\bar{\rho }$ in the region defined by a circle of radius $r$ centered at the initial seed. As a function of $r$, $\bar{\rho }$ reaches the asymptotic value ${\rho }_0(\lambda )$ following a power law $\bar{\rho }={\rho }_0+A{r}^{-\gamma }$ with a universal exponent $\gamma =0.46(2)$, independent of $\lambda$. The asymptotic value has the behavior ${\rho }_0\sim |1-\lambda {|}^{\beta }$, where $\beta =0.26(1)$. The characteristic crossover length that determines the transition from DLA- to BA-like scaling regimes is given by $\xi \sim |1-\lambda {|}^{-\nu }$, where $\nu =0.61(1)$, while the cluster mass at the crossover follows a power law $M_{\xi }\sim |1-\lambda {|}^{-\alpha }$, where $\alpha =0.97(2)$. We deduce the scaling relations $β=\n uγ$ and $\beta =2\nu -\alpha$ between these exponents.

7 pages, 8 figures

References in corpus (2)

• Multiparticle Biased DLA with surface diffusion: a comprehensive model of electrodeposition
• Effects of the Screening Breakdown in the Diffusion-Limited Aggregation Model

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