Statistical topography of rough surfaces: “Oceanic coastlines” as generalizations of percolation clustersJ. Kalda
CENS, Institute of Cybernetics, Tallinn University of Technology - Akadeemia tee 21, 12618 Tallinn, Estonia, EU
received 15 April 2008; accepted in final form 16 October 2008; published November 2008
published online 14 November 2008
A new fractal subset of random surfaces, the “oceanic coastline”, is defined. For Gaussian surfaces with negative Hurst exponent (H < 0), “oceanic coastlines” are mapped to the percolation clusters of the (correlated) percolation problem. In the case of rough self-affine surfaces (H 0), the fractal dimension of the “oceanic coastline” dc is calculated via Monte Carlo simulations as a function of the exponent H. For H = 0, the result dc 1.896 coincides with the analytic value for the percolation problem (91/48), suggesting a super-universality of dc for the correlated percolation problem.
68.35.Ct - Interface structure and roughness.
64.60.ah - Percolation.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
© EPLA 2008