Radiative transfer limit of two-frequency Wigner distribution for random parabolic waves: An exact solution

Albert C. Fannjiang

doi:10.1016/j.crhy.2007.01.001

Physics/Mathematical physics, theoretical physics

Radiative transfer limit of two-frequency Wigner distribution for random parabolic waves: An exact solution
[Limite du transfert radiatif de la distribution de Wigner à deux fréquences pour des ondes paraboliques aléatoires : une solution exacte]

Présenté par : Jacques Villain

Albert C. Fannjiang ¹

¹ Department of Mathematics, University of California, Davis, CA 95616, USA

Comptes Rendus. Physique, Volume 8 (2007) no. 2, pp. 267-271.

Résumé
Abstract

Dans cette Note nous établissons la limite auto-moyennante dans le regime du transfert radiatif pour la distribution de Wigner á deux fréquences dans le cas classique d'ondes en milieu aléatoires. Suivant le rapport de la longueur d'onde à la longueur de corrélation l'équation limite est soit une équation intégrale de type Boltzmann soit une équation différentielle de type Fokker–Planck dans l'espace des phases. L'équation limite est utilisée pour estimer trois paramètres physiques : l'étalement spatial, la longueur de cohérence et la largeur de bande cohérente. Dans le cas longitudinal l'équation de type Fokker–Planck admet une solution exacte.

The present Note establishes the self-averaging, radiative transfer limit for the two-frequency Wigner distribution for classical waves in random media. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmann-like integral equation or a Fokker–Planck-like differential equation in the phase space. The limiting equation is used to estimate three physical parameters: the spatial spread, the coherence length and the coherence bandwidth. In the longitudinal case, the Fokker–Planck-like equation can be solved exactly.

Reçu le : 2006-09-25
Accepté le : 2006-11-28
Publié le : 2007-02-09

DOI : 10.1016/j.crhy.2007.01.001

Keywords: Radiative transfer, Two-frequency Wigner distribution, Spatial spread, Coherence length, Coherence bandwidth
Mot clés : Transfert radiatif, Distribution de Wigner á deux fréquences, Étalement spatial, Longueur de cohérence, Largeur de bande cohérente

Affiliations des auteurs :

Albert C. Fannjiang ¹

¹ Department of Mathematics, University of California, Davis, CA 95616, USA

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Albert C. Fannjiang. Radiative transfer limit of two-frequency Wigner distribution for random parabolic waves: An exact solution. Comptes Rendus. Physique, Volume 8 (2007) no. 2, pp. 267-271. doi : 10.1016/j.crhy.2007.01.001. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2007.01.001/

Bibliographie
Cité par

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Cité par Sources :

^⁎ The research is supported in part by National Science Foundation Grant No. DMS-0306659, ONR Grant N00014-02-1-0090 and Darpa Grant N00014-02-1-0603.

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