Europhys. Lett.
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 DOI: 10.1209/epl/i1997-00185-0

Europhys. Lett, 37 (8), pp. 523-528 (1997)

Harmonic field distribution on self-affine surfaces

D. Vandembroucq and S. Roux

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)

PACS. 44.30 - Heat transfer in inhomogeneous media, in porous media, and through interfaces.
PACS. 66.10Cb - Diffusion and thermal diffusion.
PACS. 61.43Hv - Fractals; macroscopic aggregates (including diffusion-limited aggregates).


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 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.

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