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IOP Publishing, Journal of Physics A: Mathematical and General, 16(27), p. L579-L583

DOI: 10.1088/0305-4470/27/16/003

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Fractal Dimensions of Confined Clusters in Two-Dimensional Directed Percolation

Journal article published in 1994 by C. Kaiser, L. Turban ORCID
This paper is available in a repository.
This paper is available in a repository.

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Abstract

The fractal structure of directed percolation clusters, grown at the percolation threshold inside parabolic-like systems, is studied in two dimensions via Monte Carlo simulations. With a free surface at y=± Cx^k and a dynamical exponent z, the surface shape is a relevant perturbation when k<1/z and the fractal dimensions of the anisotropic clusters vary continuously with k. Analytic expressions for these variations are obtained using a blob picture approach. Comment: 6 pages, Plain TeX file, epsf, 3 postscript-figures