| Issue |
EPL
Volume 84, Number 4, November 2008
|
|
|---|---|---|
| Article Number | 46003 | |
| Number of page(s) | 6 | |
| Section | Condensed Matter: Structural, Mechanical and Thermal Properties | |
| DOI | https://doi.org/10.1209/0295-5075/84/46003 | |
| 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: kalda@ioc.ee
Received:
15
April
2008
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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