Correlation dimension of self-similar surfaces and application to Kirchhoff integrals - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Physics A: Mathematical and General (1975 - 2006) Année : 2003

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.
Fichier principal
Vignette du fichier
KirchhoffB.pdf (196.93 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00083207 , version 1 (10-07-2016)

Licence

Identifiants

Citer

Charles-Antoine Guérin, Matthias Holschneider. Correlation dimension of self-similar surfaces and application to Kirchhoff integrals. Journal of Physics A: Mathematical and General (1975 - 2006), 2003, 36 (34), pp.9067-9079. ⟨10.1088/0305-4470/36/34/309⟩. ⟨hal-00083207⟩
929 Consultations
111 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More