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

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  • Tolman, Susan
  • Meakin, Paul

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.

Suggested Citation

  • Tolman, Susan & Meakin, Paul, 1989. "Two, three and four-dimensional diffusion-limited aggregation models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 158(3), pages 801-816.
    • Handle: RePEc:eee:phsmap:v:158:y:1989:i:3:p:801-816
    DOI: 10.1016/0378-4371(89)90492-5
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    1. Ohta, Shigetoshi & Ohta, Takao & Kawasaki, Kyozi, 1984. "Dynamics of topological defects in critical binary fluids, metamagnets and 3He-4He mixtures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(1), pages 1-24.
    2. Pietronero, L. & Erzan, A. & Evertsz, C., 1988. "Theory of Laplacian fractals: Diffusion limited aggregation and dielectric breakdown model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 151(2), pages 207-245.
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    Cited by:

    1. Nicolás-Carlock, J.R. & Solano-Altamirano, J.M. & Carrillo-Estrada, J.L., 2020. "The dynamics of the angular and radial density correlation scaling exponents in fractal to non-fractal morphodynamics," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    2. Marsili, M. & Pietronero, L., 1991. "Fixed scale transformation approach to the multifractcal properties of the growth probabilities in the dielectric breakdown model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 175(1), pages 31-46.
    3. Marsili, M. & Pietronero, L., 1991. "Properties of the growth probability for the dielectric breakdown model in cylinder geometry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 175(1), pages 9-30.

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