Scaling Relations for Contour Lines of Rough Surfaces

Details Scaling Relations for Contour Lines of Rough Surfaces Scaling Relations for Contour Lines of Rough Surfaces

2009-07-05

arxiv.org/abs/0907.0881v1

Phys. Rev. E 80, 011115 (2009)

Physics

Condensed Matter

Statistical Mechanics

17 pages, 5 figures, accepted for PRE

Scientific paper

Equilibrium and non-equilibrium growth phenomena, e.g., surface growth, generically yields self-affine distributions. Analysis of statistical properties of these distributions appears essential in understanding statistical mechanics of underlying phenomena. Here, we analyze scaling properties of the cumulative distribution of iso-height loops (i.e., contour lines) of rough self-affine surfaces in terms of loop area and system size. Inspired by the Coulomb gas methods, we find the generating function of the area of the loops. Interestingly, we find that, after sorting loops with respect to their perimeters, Zipf-like scaling relations hold for ranked loops. Numerical simulations are also provided in order to demonstrate the proposed scaling relations.

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