Scaling relations for contour lines of rough surfaces.

Equilibrium and nonequilibrium 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.

• Publication year

  2009

• Venue

  Physical review. E, Statistical, nonlinear, and soft matter physics

• Publication date

  2009-07-05

• Fields of study

  Mathematics, Materials Science, Physics, Medicine

• Identifiers
  DOI 10.1103/PHYSREVE.80.011115arXiv 0907.0881PMID 19658661
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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