Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-23T15:38:09.192Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Witten, T.A. Jr., and Sander, L.M., Phys. Rev. Lett. 47, 1400 (1981); P. Meakin, Phys. Rev. A 27, 1495 (1983).Google Scholar
2. Brady, R. and Ball, R.C., Nature (London) 309, 225 (1984); L. Niemeyer, L. Pietronero, and H.J. Wiesmann, Phys. Rev. Lett. 52, 1033 (1984); J. Nittmann, G. Daccord, and H.E. Stanley, Nature (London) 314, 141 (1985).Google Scholar
3. This question is also the focus of real-space studies such as Pietronero, L., Erzan, A., and Evertsz, C., Phys. Rev. Lett. 61, 861 (1988); Physica A 151, 207 (1988), and X.R. Wang, Y. Shapir and M. Rubenstein, Phys. Rev. A 39, 5974 (1989); J. Phys. A 22, L507 (1989).Google Scholar
4. Halsey, T.C. and Leibig, M., Phys. Rev. A 46, 7793 (1992); T.C. Halsey, Phys. Rev. Lett. 72, 1228 (1994).Google Scholar
5. Turkevich, L. and Scher, H., Phys. Rev. Lett. 55, 1026 (1985); Phys. Rev. A 33, 786 (1986); see also R. Ball, R. Brady, G. Rossi, and B.R. Thompson, Phys. Rev. Lett. 55, 1406 (1985), and T.C. Halsey, P. Meakin, and I. Procaccia, Phys. Rev. Lett. 56, 854 (1986).Google Scholar
6. Halsey, T.C., Phys. Rev. Lett. 59, 2067 (1987); Phys. Rev. A 38, 4749 (1988).Google Scholar
7. The fact that there are no loops follows from the fact that every particle has a unique parent, which is true in off-lattice versions of DLA.Google Scholar
9. Halsey, T.C., Phys. Rev. A 35, 3512 (1987).Google Scholar
10. Halsey, T.C., Honda, K., and Duplantier, B., unpublished.Google Scholar