Scaling exponent of the maximum growth probability in diffusion-limited aggregation

Details Scaling exponent of the maximum growth probability in diffusion-limited aggregation Scaling exponent of the maximum growth probability in diffusion-limited aggregation

2002-12-09

arxiv.org/abs/cond-mat/0212177v1

Physical Review E 67, 042402 (2003)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 5 figures

Scientific paper

10.1103/PhysRevE.67.042402

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.

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