Structure of large two-dimensional square-lattice diffusion-limited aggregates: Approach to asymptotic behavior
Efficient algorithms have been used to grow large (4 x 10/sup 6/ site) diffusion-limited aggregation (DLA) clusters on two-dimensional (2D) square lattices. As the clusters grow larger, their envelope grows, from a more or less round shape characteristic of small clusters, through a diamond shape characteristic of clusters containing about 10/sup 5/ sites, into a cross shape. Results from about 25 clusters indicate that the exponents describing the length l and width w of the four major arms vary continuously with M (the cluster mass) over the range 10/sup 3/<4 x 10/sup 6/. We find that the effective exponent ..nu../sub X/ = dln(l)/dln(M) increases systematically from 0.585 to 0.61 at the highest mass. This may be consistent with a limiting value of (2/3) (as found for uniaxially biased DLA in two dimensions) but only with large corrections to scaling in our range of M. The exponent ..nu../sub perpendicular/ = dln(w)/dln(M) decreases systematically, to about 0.48 at M = 4 x 10/sup 6/. Our results are consistent with an asymptotic (scaling) fractal geometry for square-lattice DLA but suggest that these fractals are neither self-similar nor homogeneous.
- Research Organization:
- Central Research and Development Department, E.I. du Pont de Nemours and Company, Wilmington, Delaware 19898
- OSTI ID:
- 5914829
- Journal Information:
- Phys. Rev. A; (United States), Vol. 35:12
- Country of Publication:
- United States
- Language:
- English
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