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Jensen MH, Mathiesen J, Procaccia I. Scaling exponent of the maximum growth probability in diffusion-limited aggregation. Phys Rev E Stat Nonlin Soft Matter Phys. 2003;67(4):042402doi: 10.1103/PhysRevE.67.042402.
Jensen, M. H., Mathiesen, J., & Procaccia, I. (2003). Scaling exponent of the maximum growth probability in diffusion-limited aggregation. Physical review. E, Statistical, nonlinear, and soft matter physics, 67(4), 042402. https://doi.org/10.1103/PhysRevE.67.042402
Jensen, Mogens H, et al. "Scaling exponent of the maximum growth probability in diffusion-limited aggregation." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 67,4 (2003): 042402. doi: https://doi.org/10.1103/PhysRevE.67.042402
Jensen MH, Mathiesen J, Procaccia I. Scaling exponent of the maximum growth probability in diffusion-limited aggregation. Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Apr;67(4):042402. doi: 10.1103/PhysRevE.67.042402. Epub 2003 Apr 17. PMID: 12786408.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Apr;67(4):042402. doi: 10.1103/PhysRevE.67.042402. Epub 2003 Apr 17.

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

Physical review. E, Statistical, nonlinear, and soft matter physics

Mogens H Jensen, Joachim Mathiesen, Itamar Procaccia

Affiliations

  1. The Niels Bohr Institute, Blegdamsvej 17, Copenhagen, Denmark.

PMID: 12786408 DOI: 10.1103/PhysRevE.67.042402

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 a serious test. Using the method of iterated conformal maps, D was recently determined as D=1.713+/-0.003. In this paper, 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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