Iterative conformal mapping approach to diffusion-limited aggregation with surface tension effect

TL;DR

This paper introduces a conformal mapping method to model diffusion-limited aggregation with surface tension, revealing a transition from compact to fractal growth and confirming fractal dimensions.

Contribution

It presents a novel iterative conformal mapping approach that incorporates surface tension effects into DLA models, enabling analysis of growth regimes and fractal properties.

Findings

Cluster transitions from compact to fractal growth

Fractal dimension of area and perimeter coincide

Method effectively models surface tension effects

Abstract

We present a simple method for incorporating the surface tension effect into an iterative conformal mapping model of two-dimensional diffusion-limited aggregation. A curvature-dependent growth probability is introduced and the curvature is given by utilizing the branch points of a conformal map. The resulting cluster exhibits a crossover from compact to fractal growth. In the fractal growth regime, it is confirmed, by the conformal map technique, that the fractal dimension of its area and perimeter length coincide.