Eur. Phys. J. B 29, 211-215 (2002)
https://doi.org/10.1140/epjb/e2002-00288-4

Self-affine random surfaces

¹ American University in Bulgaria, 2700 Blagoevgrad, Bulgaria
² Institute of Electronics, BAS, 1784 Sofia, Bulgaria

Corresponding author: ^a oyordanov@aubg.bg

Received: 3 October 2001
Revised: 5 March 2002
Published online: 2 October 2002

Abstract

We consider general d-dimensional random surfaces that are characterized by power-law power spectra defined in both infinite and finite spectral regions. The first type of surfaces belongs to the class of ideal fractals, whereas the second possess both the smallest and the largest scales and physically is more realistic. For both types we calculate the structure functions (SF) exactly; in addition for the second type we obtain the SF's asymptotic expansions. On this basis we show that the surfaces are (in statistical sense) self-affine and approximately self-affine, respectively. Depending on the value of the spectral exponent, we find imbalance between the finite size effects which results in systematic discrepancy in the scaling properties between the two types of surfaces. Explicit expressions for the topothesy, and in the case of second type of surfaces for the large correlation length and cross-over distances are also derived.