Multiscaling analysis and width of the active zone of large off-lattice DLA

TL;DR

This paper investigates the multiscaling properties of large off-lattice DLA clusters, revealing a continuous dependence of multiscaling dimensions on position in smaller clusters and a sharp drop in larger clusters, highlighting size-dependent behavior.

Contribution

It provides new insights into the multiscaling behavior of off-lattice DLA, especially in very large clusters, and compares size-dependent behaviors.

Findings

Continuous multiscaling dimensions in smaller clusters

Sharp drop of multiscaling dimensions in very large clusters

Size-dependent multiscaling behavior observed

Abstract

We measure the multiscaling behavior of large off-lattice diffusion limited aggregates (DLA). In contrast to previous studies we now find a continuous dependence of the multiscaling dimensions $D(x)$ on the relative distance $x=r/R_g$ to the center of the cluster. This result agrees with measurements on smaller clusters. Furthermore we report the multiscaling behavior and the behavior of the width of the active zone of one very large off-lattice DLA cluster with 50 million particles. Here we find a sharp drop of the multiscaling dimensions for large $x$ instead of a continuous behavior.