Differential Equations Seminar

Radiative transfer is widely used to describe wave propagation in heterogeneous media. The mathematical theory in open space (i.e., in the absence of boundaries) is well established. However, understanding the coupling of surface waves propagating along boundaries and body waves that propagate deep in the medium remains a challenge. I will present a novel mathematical analysis of such coupling in a waveguide. The waveguide has a thin, weakly randomly heterogeneous layer near the top boundary and a thick homogeneous layer beneath it. It supports two types of propagating modes: those that are trapped in the thin layer and model surface waves and those that penetrate deep in the waveguide and model body waves. We derive from first principles a radiative transfer equation that quantifies the mode power exchange and study in detail the multiscale dynamics of the power exchange and the onset of equipartition of energy.

(joint work with Josselin Garnier (Ecole Polytechnique) and Knut Solna (UC Irvine)) Speaker(s): Liliana Borcea (University of Michigan)