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Fractal dimension of the trunk of a diffusion limited aggregation cluster

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  • Pikhitsa, P.

Abstract

The mean-field approximation (the Flory method) is used to obtain the fractal dimension of the trunk of a diffusion limited aggregation (DLA) cluster. The screening length (the characteristic length of a void) of the cluster is larger than in the case of growing percolation clusters in which intersections are forbidden. It makes the trunk of the DLA cluster comparatively more straight. The fractal dimension Df is found to be Df = (1 + 14d2)/[1 + 18d(d + 1)] in d-dimensional space. The limit Df = 2 takes place at the upper critical dimension dc = ∞, which is expected for DLA clusters.

Suggested Citation

  • Pikhitsa, P., 1993. "Fractal dimension of the trunk of a diffusion limited aggregation cluster," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 196(3), pages 317-319.
    • Handle: RePEc:eee:phsmap:v:196:y:1993:i:3:p:317-319
    DOI: 10.1016/0378-4371(93)90197-C
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    References listed on IDEAS

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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.
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