Issue |
Europhys. Lett.
Volume 48, Number 5, December 1999
|
|
---|---|---|
Page(s) | 547 - 553 | |
Section | Condensed matter: structure, mechanical and thermal properties | |
DOI | https://doi.org/10.1209/epl/i1999-00518-y | |
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
Received:
2
June
1999
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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