Correlation dimension of self-similar surfaces and application to Kirchhoff integrals
Résumé
For surfaces generated by a class of asymptotically self-similar processes we define a probability measure, supported by the surface. We show that the correlation dimension of that surface measure is linked to the self-similarity exponent almost surely. This result is applied to the Kirchhoff integral well known in scattering from rough surfaces. We show that a certain average of the scattered intensity exhibits almost surely a scaling that allows us to recover the self-similarity index of the surface in an experiment involving only one sample of the surface.
Domaines
Physique mathématique [math-ph]Origine | Fichiers produits par l'(les) auteur(s) |
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