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Fractal Dimensions of Confined Clusters in Two-Dimensional Directed Percolation

C. Kaiser·L. Turban
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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=\pm 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.

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C. Kaiser, L. Turban. 1997-09-08. Fractal Dimensions of Confined Clusters in Two-Dimensional Directed Percolation. https://doi.org/10.1088/0305-4470%2F27%2F16%2F003

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