Diffusion-limited aggregation as branched growth
- 21 February 1994
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 72 (8) , 1228-1231
- https://doi.org/10.1103/physrevlett.72.1228
Abstract
I present a first-principles theory of diffusion-limited aggregation in two dimensions. A renormalized mean-field approximation gives the form of the unstable manifold for branch competition, following the method of Halsey and Leibig [Phys. Rev. A 46, 7793 (1992)]. This leads to a result for the cluster dimensionality, D≊1.66, which is close to numerically obtained values. In addition, the multifractal exponent τ(3)=D in this theory, in agreement with a proposed ‘‘electrostatic’’ scaling law.Keywords
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