| Issue |
Europhys. Lett.
Volume 37, Number 8, March II 1997
|
|
|---|---|---|
| Page(s) | 523 - 528 | |
| Section | Classical areas of phenomenology | |
| DOI | https://doi.org/10.1209/epl/i1997-00185-0 | |
| 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
Received:
3
October
1996
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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