Europhys. Lett.
Volume 48, Number 5, December 1999
Page(s) 547 - 553
Section Condensed matter: structure, mechanical and thermal properties
Published online 01 September 2002
DOI: 10.1209/epl/i1999-00518-y

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 $q\ge 1$. 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 $D_0=1.69\pm 0.03$.


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