Volume 84, Number 4, November 2008
|Number of page(s)||6|
|Section||Condensed Matter: Structural, Mechanical and Thermal Properties|
|Published online||14 November 2008|
Statistical topography of rough surfaces: “Oceanic coastlines” as generalizations of percolation clusters
CENS, Institute of Cybernetics, Tallinn University of Technology - Akadeemia tee 21, 12618 Tallinn, Estonia, EU
Corresponding author: firstname.lastname@example.org
Accepted: 16 October 2008
A new fractal subset of random surfaces, the “oceanic coastline”, is defined. For Gaussian surfaces with negative Hurst exponent (), “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 , 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.
PACS: 68.35.Ct – Interface structure and roughness / 64.60.ah – Percolation / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EPLA, 2008
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