Volume 37, Number 8, March II 1997
|Page(s)||523 - 528|
|Section||Classical areas of phenomenology|
|Published online||01 September 2002|
Harmonic field distribution on self-affine surfaces
Laboratoire de Physique et Mécanique des Milieux Hétérogènes, Ecole Supérieure de Physique et de Chimie Industrielles, 10 rue Vauquelin, 75231 Paris Cedex 05, France
Accepted: 31 January 1997
The aim of this study is to analyse the statistical properties of harmonic fields V in the vicinity of a self-affine Gaussian equipotential boundary. It is shown that the statistical distribution of , in the limit of a vanishing amplitude, is a normal law. As the amplitude increases the distribution develops an exponential tail, hence the field gradient displays a power law distribution. The exponent of the power law varies continuously with the lower scale cut-off of the self-affine regime, and the roughness amplitude A as , where ζ is the roughness exponent. The latter form is revealed from a second-order perturbation expansion on the roughness amplitude, and directly through numerical simulations in two dimensions using a conformal mapping technique.
PACS: 44.30.+v – Heat transfer in inhomogeneous media, in porous media, and through interfaces / 66.10.Cb – Diffusion and thermal diffusion / 61.43.Hv – Fractals; macroscopic aggregates (including diffusion-limited aggregates)
© EDP Sciences, 1997
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