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Structure of large two-dimensional square-lattice diffusion-limited aggregates : approach to asymptotic behavior
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Meakin, Paul, 1944-, Ball, R. C., Ramanlal, P. and Sander, Leonard M. (Leonard Michael). (1987) Structure of large two-dimensional square-lattice diffusion-limited aggregates : approach to asymptotic behavior. Physical Review A (General Physics), Vol.35 (No.12). pp. 5233-5239. ISSN 0556-2791
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Official URL: http://dx.doi.org/10.1103/PhysRevA.35.5233
Abstract
Efficient algorithms have been used to grow large (4×106 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 105 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 103<M<4×106. We find that the effective exponent ν?=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 ν⊥=dln(w)/dln(M) decreases systematically, to about 0.48 at M=4×106. 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.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
| Divisions: | Faculty of Science > Physics |
| Library of Congress Subject Headings (LCSH): | Lattice theory, Aggregation (Chemistry), Asymptotic symmetry (Physics), Fractals |
| Journal or Publication Title: | Physical Review A (General Physics) |
| Publisher: | American Physical Society |
| ISSN: | 0556-2791 |
| Date: | 1987 |
| Volume: | Vol.35 |
| Number: | No.12 |
| Page Range: | pp. 5233-5239 |
| Identification Number: | 10.1103/PhysRevA.35.5233 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Funder: | United States. Dept. of Energy (DOE) |
| Grant number: | DE-FG02-85ER45189 (DoE) |
| URI: | http://wrap.warwick.ac.uk/id/eprint/39426 |
Data sourced from Thomson Reuters' Web of Knowledge
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