Diffusion-limited aggregation on hierarchical lattice with multifractal heterogeneity

Takashi Nagatani
Phys. Rev. A 41, 999 – Published 1 January 1990
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Abstract

A renormalization-group theory is developed to study the multifractal structure of the growth probability distribution in the diffusion-limited aggregation on the multifractal lattice proposed by Meakin [Phys. Rev. A 36, 2833 (1987)]. The hierarchical lattices with two classes of multifractal heterogeneity are constructed using a diamond generator with two sets of weights P1=1, P2=Q, P3=Q2, and P4=Q3 and P1=1, P2=1, P3=Q, and P4=Q. Multifractal scaling exponents of the growth probability distribution are calculated using a finite-lattice renormalization. The effect of the multifractal heterogeneity on the growth probability distribution is considered. It is shown that the multifractal heterogeneity has important effects on the multifractal structure of the growth probability distribution.

  • Received 7 September 1989

DOI:https://doi.org/10.1103/PhysRevA.41.999

©1990 American Physical Society

Authors & Affiliations

Takashi Nagatani

  • College of Engineering, Shizuoka University, Hamamatsu 432, Japan

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Issue

Vol. 41, Iss. 2 — January 1990

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