Diffusion-controlled aggregation in the continuum approximation

R. Ball; M. Nauenberg; T. A. Witten, Jr

doi:10.1103/PhysRevA.29.2017

Diffusion-controlled aggregation in the continuum approximation

R. Ball, M. Nauenberg, and T. A. Witten, Jr.

Phys. Rev. A 29, 2017 – Published 1 April 1984

Abstract

A numerical solution and analytic approximation are obtained for the mean-field continuum equations corresponding to diffusion-controlled aggregation. For $d > 2$ an asymptotic solution is found with the density of the cluster varying as the inverse radius, which suggests a Hausdorff dimension $D = d - 1$ .

Received 26 October 1983

DOI:https://doi.org/10.1103/PhysRevA.29.2017

Authors & Affiliations

R. Ball

Institute for Theoretical Physics, University of California, Santa Barbara, California 93106
Cavendish Laboratory, Cambridge CB3 OHE, England

M. Nauenberg

Institute for Theoretical Physics, University of California, Santa Barbara, California 93106
School of Natural Science, University of California at Santa Cruz, Santa Cruz, California 95060

T. A. Witten, Jr.

Institute for Theoretical Physics, University of California, Santa Barbara, California 93106
Theoretical and Mathematical Sciences Laboratory, Exxon Research and Engineering Company, Annandale, New Jersey 08801

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Vol. 29, Iss. 4 — April 1984

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