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Diffusion-Limited Aggregation as Branched Growth

Published online by Cambridge University Press:  03 September 2012

Thomas C. Halsey
Thomas C. Halsey*
Affiliation:
Exxon Research and Engineering, Route 22 East, Annandale, NJ 08801
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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. Quenched and annealed multifractal dimensions can also be computed in this theory; the multifractal dimension τ(3) = D, in agreement with a proposed “electro- static” scaling law.

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Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 367: Symposium P – Fractal Aspects of Materials , 1994, 23
Copyright
Copyright © Materials Research Society 1995

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References

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