Scaling laws in the diffusion limited aggregation of persistent random walkers

TL;DR

This paper studies how particles performing persistent random walks form aggregates, revealing a crossover between ballistic and diffusion-limited growth and identifying a key scaling relation between aggregate size and persistence length.

Contribution

It introduces a detailed analysis of the scaling laws governing aggregation of persistent random walkers, highlighting a novel relation between aggregate morphology and walk persistence.

Findings

Identification of a crossover between ballistic and diffusion-limited aggregation.

Discovery of a non-trivial scaling relation $\xi extasciitilde\ell^{1.25}$.

Observation of morphological transition in aggregates.

Abstract

We investigate the diffusion limited aggregation of particles executing persistent random walks. The scaling properties of both random walks and large aggregates are presented. The aggregates exhibit a crossover between ballistic and diffusion limited aggregation models. A non-trivial scaling relation $\xi\sim\ell^{1.25}$ between the characteristic size $\xi$, in which the cluster undergoes a morphological transition, and the persistence length $\ell$, between ballistic and diffusive regimes of the random walk, is observed.