Structure of large two-dimensional square-lattice diffusion-limited aggregates : approach to asymptotic behavior
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. ISSN 0556-2791Full text not available from this repository.
Official URL: http://dx.doi.org/10.1103/PhysRevA.35.5233
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|
|Page Range:||pp. 5233-5239|
|Funder:||United States. Dept. of Energy (DOE)|
|Grant number:||DE-FG02-85ER45189 (DoE)|
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