Volume 48, Number 5, December 1999
|Page(s)||547 - 553|
|Section||Condensed matter: structure, mechanical and thermal properties|
|Published online||01 September 2002|
Conformal theory of the dimensions of diffusion-limited aggregates
Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
Accepted: 23 September 1999
We employ the recently introduced conformal iterative construction of Diffusion-Limited Aggregates (DLA) to study the multifractal properties of the harmonic measure. The support of the harmonic measure is obtained from a dynamical process which is complementary to the iterative cluster growth. We use this method to establish the existence of a series of random scaling functions that yield, via the thermodynamic formalism of multifractals, the generalized dimensions Dq of DLA for . The scaling function is determined just by the last stages of the iterative growth process which are relevant to the complementary dynamics. Using the scaling relation , we estimate the fractal dimension of DLA to be .
PACS: 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions
© EDP Sciences, 1999
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