Orientation of particle attachment and local isotropy in diffusion limited aggregation (DLA)

TL;DR

This study uses large-scale simulations to analyze the orientation of particle attachment in diffusion-limited aggregation, revealing that large clusters are locally isotropic, contrary to previous beliefs, and providing a new phenomenological model.

Contribution

It introduces extensive off-lattice DLA simulations and demonstrates that attachment angles become isotropic in large clusters, challenging prior conclusions based on correlation measurements.

Findings

Attachment angle distribution approaches a cosine form as cluster size increases.

Amplitude of the cosine distribution decreases as a power-law with cluster size.

Large DLA clusters are locally isotropic, contradicting earlier density correlation results.

Abstract

We simulate 50 off-lattice DLA clusters, one million particles each. The probability distribution of the angle of attachment of arriving particles with respect to the local radial direction is obtained numerically. For increasing cluster size, $N$, the distribution crosses over extremely accurately to a cosine, whose amplitude decreases towards zero as a power-law in $N$. From this viewpoint, asymptotically large DLA clusters are locally $isotropic$. This contradicts previous conclusions drawn from density-density correlation measurements [P. Meakin, and T. Viscek, Phys. Rev. A {\bf 32}, 685 (1985)]. We present an intuitive phenomenological model random process for our numerical findings.