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Structure of large two-dimensional square-lattice diffusion-limited aggregates : approach to asymptotic behavior
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Meakin, Paul, Ball, Robin, Ramanlal, P. and Sander, Leonard M. (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. doi:10.1103/PhysRevA.35.5233 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 | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||
Official Date: | 1987 | ||||
Dates: |
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Volume: | Vol.35 | ||||
Number: | No.12 | ||||
Page Range: | pp. 5233-5239 | ||||
DOI: | 10.1103/PhysRevA.35.5233 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Funder: | United States. Dept. of Energy (DOE) | ||||
Grant number: | DE-FG02-85ER45189 (DoE) |
Data sourced from Thomson Reuters' Web of Knowledge
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