Volume 84, Number 4, November 2008
Article Number 46003
Number of page(s) 6
Section Condensed Matter: Structural, Mechanical and Thermal Properties
Published online 14 November 2008
EPL, 84 (2008) 46003
DOI: 10.1209/0295-5075/84/46003

Statistical topography of rough surfaces: “Oceanic coastlines” as generalizations of percolation clusters

J. 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 $\geq$ 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 $\approx$ 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