Europhys. Lett, 48 (5), pp. 547-553 (1999)
Conformal theory of the dimensions of diffusion-limited aggregates
B. Davidovich and I. Procaccia
Department of Chemical Physics, The Weizmann Institute of Science
Rehovot 76100, Israel
(received 2 June 1999; accepted in final form 23 September 1999)
PACS. 64.60Ak - Renormalization-group, fractal, and percolation studies of phase transitions.
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 D3=D0/2, we estimate the fractal dimension of DLA to be .
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