Deviations from Self-Similarity in Plane DLA and the “Infinite Drift” Scenario

Abstract

The behavior of very large clusters of diffusion-limited aggregation (DLA) was investigated to help discriminate between the two geometric scenarios recently described by Mandelbrot: finite transient and infinite drift. Using 50 DLA clusters of 1 million particles, we follow the increase during growth of the maximum radius of the clusters and of various relative moments. One can distinguish two regions: an inactive completely grown core and an active growing region. In the growing region, scale factors were defined the moments of the atoms distances from the original "seed". They do not cross-over to the behavior characteristic of self-similarity for finite sizes and support the novel "drift" scenario that postulate an infinite continuing "transient". The moment's "misbehavior" may help understand the disagreement between previous estimates of the clusters' fractal dimension.