Attracted Diffusion-Limited Aggregation

TL;DR

This study uses Monte Carlo simulations to explore how an attractive plane influences diffusion-limited aggregation patterns, revealing how fractal dimensions vary with attraction strength and enabling control over cluster morphology.

Contribution

It introduces a model of DLA with an attractive plane, demonstrating how attraction strength affects fractal dimensions and cluster morphology in 2D and 3D.

Findings

Fractal dimension depends on attraction strength for small mbda.

In the non-attracting case, 3D patterns match ordinary DLA.

Intermediate mbda yields quasi-2D structures.

Abstract

In this paper, we present results of extensive Monte Carlo simulations of diffusion-limited aggregation (DLA) with a seed placed on an attractive plane as a simple model in connection with the electrical double layers. We compute the fractal dimension of the aggregated patterns as a function of the attraction strength \alpha. For the patterns grown in both two and three dimensions, the fractal dimension shows a significant dependence on the attraction strength for small values of \alpha, and approaches to that of the ordinary two-dimensional (2D) DLA in the limit of large \alpha. For non-attracting case with \alpha=1, our results in three dimensions reproduce the patterns of 3D ordinary DLA, while in two dimensions our model leads to formation of a compact cluster with dimension two. For intermediate \alpha, the 3D clusters have quasi-2D structure with a fractal dimension very close to that of the ordinary 2D-DLA. This allows one to control morphology of a growing cluster by tuning a single external parameter \alpha.