Growth and form of noise-reduced diffusion-limited aggregation

Abstract

The model of noise-reduced diffusion-limited aggregation is analyzed in detail using classical methods of conformal mappings. It is shown that there are two phases of growth, compact and fractal, and the transition between them depends only weakly on the level of noise reduction. Detailed descriptions of the rate of growth, mass-to-size scaling, mass distribution, and shape of the clusters in both the compact and the fractal phases are presented. The results of the theoretical analysis are compared to extensive numerical simulations, and agreement down to fine details is reported.