Two, three and four-dimensional diffusion-limited aggregation models

Susan Tolman and Paul Meakin

Physica A: Statistical Mechanics and its Applications, 1989, vol. 158, issue 3, 801-816

Abstract: Two, three and four-dimensional diffusion-limited aggregation (DLA) models with noise reduction and with growth probabilities proportional to small integer powers (η) of the harmonic measure have been investigated using improved algorithms. The results obtained from these simulations provide the basis for a more decisive test of theoretical results than ordinary DLA simulations alone. Using off-lattice models, effective fractal dimensionalities (D) of about 1.41 and 1.29 were found for η = 2 and 3 respectively for a two dimensional (d=2) embedding space. For d=3, D≌2.13 for η=2 and D≌1.90 for η=3. Similarly, for d = 4, D ≌ 2.97 for η = 2 and D ≌ 2.74 for η = 3. For the noise reduced DLA lattice models our results are consistent with the idea that D⩾d−1 in the asymptotic (s→∞, m→∞) limit where s is the cluster size and m is the noise reduction parameter. However, for d=4, the effective fractal dimensionality is quite close to 3 for m=30.

Date: 1989
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:158:y:1989:i:3:p:801-816

DOI: 10.1016/0378-4371(89)90492-5

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