Analysis of patterns formed by two-component diffusion limited aggregation

TL;DR

This paper studies how initial patterns influence the structure of two-component diffusion limited aggregation clusters, revealing a critical distance beyond which initial periodicity is lost and randomness prevails.

Contribution

It introduces an analysis of pattern influence on two-component DLA and proposes an approach to describe the evolution of cluster branches.

Findings

Initial patterns are visible near the substrate within a certain distance.

Beyond a critical distance, the initial pattern is lost and randomness dominates.

The initial pattern can be detected only within approximately 1.5 times its characteristic size.

Abstract

We consider diffusion limited aggregation of particles of two different kinds. It is assumed that a particle of one kind may adhere only to another particle of the same kind. The particles aggregate on a linear substrate which consists of periodically or randomly placed particles of different kinds. We analyze the influence of initial patterns on the structure of growing clusters. It is shown that at small distances from the substrate, the cluster structures repeat initial patterns. However, starting from a critical distance the initial periodicity is abruptly lost, and the particle distribution tends to a random one. An approach describing the evolution of the number of branches is proposed. Our calculations show that the initial patter can be detected only at the distance which is not larger than approximately one and a half of the characteristic pattern size.