Off-lattice Noise Reduced Diffusion-limited Aggregation in Three Dimensions

TL;DR

This study uses off-lattice noise reduction to accurately analyze three-dimensional diffusion-limited aggregation clusters, confirming known fractal dimensions and revealing detailed asymptotic properties and correction exponents.

Contribution

It introduces a noise reduction method for better estimation of asymptotic properties of 3D DLA clusters, providing new measurements of correction exponents and universal asymptotes.

Findings

Fractal dimension approximately 2.50

Asymptotic relative penetration depth around 0.122

Universal asymptotes in multipole powers

Abstract

Using off-lattice noise reduction it is possible to estimate the asymptotic properties of diffusion-limited aggregation clusters grown in three dimensions with greater accuracy than would otherwise be possible. The fractal dimension of these aggregates is found to be 2.50 +/- 0.01, in agreement with earlier studies, and the asymptotic value of the relative penetration depth is 0.122 +/- 0.002. The multipole powers of the growth measure also exhibit universal asymptotes. The fixed point noise reduction is estimated to be \epsilon = 0.0035 meaning that large clusters can be identified with a low noise regime. The slowest correction to scaling exponents are measured for a number of properties of the clusters, and the exponent for the relative penetration depth and quadrupole moment are found to be significantly different from each other. The relative penetration depth exhibits the slowest correction to scaling of all quantities, which is consistent with a theoretical result derived in two dimensions.