Fractal Dimensions of Confined Clusters in Two-Dimensional Directed Percolation
C. Kaiser (1, 2), L. Turban (2) ((1) F. U. Berlin, (2) Henri, Poincare University, Nancy)
TL;DR
This study investigates how the fractal dimensions of directed percolation clusters in two dimensions change when confined within parabolic boundaries, revealing continuous variation influenced by boundary shape.
Contribution
It provides analytic expressions for the variation of fractal dimensions of confined clusters based on boundary shape parameters, using a blob picture approach.
Findings
Fractal dimensions vary continuously with boundary shape parameter k.
Analytic expressions for fractal dimension variations are derived.
Surface shape acts as a relevant perturbation when k<1/z.
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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