Scaling exponent of the maximum growth probability in diffusion-limited aggregation
Statistical Mechanics
2009-11-07 v1 Disordered Systems and Neural Networks
Abstract
An early (and influential) scaling relation in the multifractal theory of Diffusion Limited Aggregation(DLA) is the Turkevich-Scher conjecture that relates the exponent \alpha_{min} that characterizes the ``hottest'' region of the harmonic measure and the fractal dimension D of the cluster, i.e. D=1+\alpha_{min}. Due to lack of accurate direct measurements of both D and \alpha_{min} this conjecture could never be put to serious test. Using the method of iterated conformal maps D was recently determined as D=1.713+-0.003. In this Letter we determine \alpha_{min} accurately, with the result \alpha_{min}=0.665+-0.004. We thus conclude that the Turkevich-Scher conjecture is incorrect for DLA.
Cite
@article{arxiv.cond-mat/0212177,
title = {Scaling exponent of the maximum growth probability in diffusion-limited aggregation},
author = {Mogens H. Jensen and Joachim Mathiesen and Itamar Procaccia},
journal= {arXiv preprint arXiv:cond-mat/0212177},
year = {2009}
}
Comments
4 pages, 5 figures