Effects of the Screening Breakdown in the Diffusion-Limited Aggregation Model

TL;DR

This paper investigates how replacing random steps with fixed-length flights in a modified DLA model affects pattern formation, revealing a transition from compact to fractal structures and identifying scaling behaviors and noise characteristics.

Contribution

Introduces a new on-lattice DLA extension with fixed-length flights, analyzing its impact on pattern morphology and scaling properties, including the transition from compact to fractal clusters.

Findings

Patterns exhibit DLA-like scaling at small flight lengths.

Clusters transition from round to fractal as flight size increases.

Wavelength selection and 1/k noise observed away from transition.

Abstract

Several models based on the diffusion-limited aggregation (DLA) model were proposed and their scaling properties explored by computational and theoretical approaches. In this paper, we consider a new extension of the on-lattice DLA model in which the unitary random steps are replaced by random flights of fixed length. This procedure reduces the screening for particle penetration present in the original DLA model and, consequently, generates new pattern classes. The patterns have DLA-like scaling properties at small length of the random flights. However, as the flight size increases, the patterns are initially round and compact but become fractal for sufficiently large clusters. Their radius of gyration and number of particles at the cluster surface scale asymptotically as in the original DLA model. The transition between compact and fractal patterns is characterized by wavelength selection, and $1/k$ noise was observed far from the transition.