Morphological diagram of diffusion driven aggregate growth in plane: competition of anisotropy and adhesion

TL;DR

This study investigates two-dimensional diffusion-driven aggregate growth, analyzing how anisotropy and adhesion influence fractal dimensions and universality classes, revealing distinct growth behaviors and asymptotic fractal dimensions.

Contribution

It introduces a detailed analysis of off-lattice and antenna method clusters with varying growth directions, showing how anisotropy affects fractal dimensions and universality classes in aggregate growth.

Findings

High anisotropy clusters tend to have fractal dimension 3/2.

Off-lattice and low anisotropy clusters have fractal dimension around 1.710.

Noise reduction can change the universality class of DLA clusters.

Abstract

Two-dimensional structures grown with Witten and Sander algorithm are investigated. We analyze clusters grown off-lattice and clusters grown with antenna method with $N_{fp}=3,4,5,6,7$ and 8 allowed growth directions. With the help of variable probe particles technique we measure fractal dimension of such clusters $D(N)$ as a function of their size $N$. We propose that in the thermodynamic limit of infinite cluster size the aggregates grown with high degree of anisotropy ($N_{fp}=3,4,5$) tend to have fractal dimension $D$ equal to 3/2, while off-lattice aggregates and aggregates with lower anisotropy ($N_{fp}>6$) have $D \approx 1.710$. Noise-reduction procedure results in the change of universality class for DLA. For high enough noise-reduction value clusters with $N_{fp} \ge 6$ have fractal dimension going to $3/2$ when $N\rightarrow\infty$.