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Updated: Jun 21, 2026

Determination of Aggregate Surface Morphology at the Interfacial Transition Zone (ITZ)
Published on: December 16, 2019
Scaling relations for contour lines of rough surfaces
M A Rajabpour1, S M Vaez Allaei
1Institute for Studies in Theoretical Physics and Mathematics, Tehran 19395-5531, Iran. rajabpour@ipm.ir
Abstract:
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.
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