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Upscaling of the wave propagation equation in random media: applications in geophysics and railway engineering

le 19 mai 2016

Régis Cottereau Laboratoire MSSMat, CNRS, CentraleSupelec, Université Paris Saclay interviendra lors du séminaire du LMT à l'ENS Cachan.

Depending on the relative magnitudes of the wavelength , correlation length
`c and propagation length L, wave propagation in random media leads to very
di erent physical behaviors. In the low-frequency regime (  L), classical ho-
mogenization for rapidly uctuating properties (`c  ) predicts a wave propa-
gation regime with slowly-uctuating homogenized coecients, and anisotropic
behavior. In the higher frequency regime (  L), the wave eld is not sta-
tistically stable and energy densities are more meaningful. The appropriate
mathematical tool is then the Wigner measure of the displacement eld, which
is a wavenumber resolved energy density. In the stochastic regime (  `c), the
Wigner measure veri es a radiative transfer equation. In the long-time limit,
this regime is well approximated by di usion equations. Finally, when the am-
plitude of the uctuations of the properties are large, localization can occur.
In this regime, the energy is trapped close to the source and cannot propagate
away. This talk will briey introduce these di erent regimes of wave propagation
in random media and illustrate their appearance in two applications. In geo-
physics, we will discuss the inuence of the anisotropy of the slowly-
background on the radiative transfer regime. In railway engineering, we will
illustrate the e ect of localization on the waves generated in the surroundings
of a ballasted railway track.
Type :
Séminaires - conférences
Lieu(x) :
Campus de Cachan
Amphi e-média
Bâtiment Léonard De Vinci - ENS Cachan
61, avenue du Président Wilson 94230 Cachan
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