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

Mogens H. Jensen·Joachim Mathiesen·Itamar Procaccia
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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 α_{min} that characterizes the ``hottest'' region of the harmonic measure and the fractal dimension D of the cluster, i.e. D=1+α_{min}. Due to lack of accurate direct measurements of both D and α_{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 α_{min} accurately, with the result α_{min}=0.665+-0.004. We thus conclude that the Turkevich-Scher conjecture is incorrect for DLA.

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Mogens H. Jensen, Joachim Mathiesen, Itamar Procaccia. 2002-12-09. Scaling exponent of the maximum growth probability in diffusion-limited aggregation. https://doi.org/10.1103/physreve.67.042402

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