-----------------------------------------------------------

Applied Mathematics Colloquium

Friday, September 23,  2005, 11:30 am
Cullimore Lecture Hall II
New Jersey Institute of Technology

Radiative transfer equations and applications

Guillaume Bal

Department of Applied Physics and Applied Mathematics

Columbia University

Abstract

Radiative transfer equations have long been used to model the energy density of waves in random media, with applications in light propagating through turbulent atmospheres, underwater acoustics, and elastic wave propagation in the Earth's crust to name a few. In this talk I will derive such models from first principles, i.e., from equations for the wave fields in the high frequency regime. A very useful tool in such a derivation is the Wigner transform applied to the wave fields. I will also show how the correlations of two wave fields propagating in possibly different media can be estimated in the high frequency regime and present applications of the theory to the understanding of time reversed waves propagating in highly heterogeneous media. Finally I will present recent numerical simulations performed on parallel architectures of two-dimensional acoustic wave propagation in random media on large domains (on the order of 500 times 500 wavelengths) and show the very good accuracy of the macroscopic radiative transfer models to describe the energy density of the acoustic waves. Applications to detection and imaging of buried inclusions in highly cluttered environment will also be mentioned.