English

Oceanic coastline and super-universality of percolation clusters

Statistical Mechanics 2007-05-23 v2

Abstract

New fractal subset of a rough surface, the ``oceanic coastline'', is defined. For random Gaussian surfaces with negative Hurst exponent H<0H<0, ``oceanic coastlines'' are mapped to the percolation clusters of the (correlated) percolation problem. In the case of rough self-affine surfaces (H0H \ge 0), the fractal dimension of the ``oceanic coastline'' dcd_c is calculated numerically as a function of the roughness exponent HH (using a novel technique of minimizing finite-size effects). For H=0, the result dc1.896d_c \approx 1.896 coincides with the analytic value for the percolation problem (91/48), suggesting a super-universality of dcd_c for correlated percolation problem.

Keywords

Cite

@article{arxiv.cond-mat/0210650,
  title  = {Oceanic coastline and super-universality of percolation clusters},
  author = {Jaan Kalda},
  journal= {arXiv preprint arXiv:cond-mat/0210650},
  year   = {2007}
}

Comments

4 pages (Grammatically revised)