Seminar Event Detail


Differential Equations

Date:  Thursday, March 10, 2016
Location:  4088 East Hall (4:00 PM to 5:00 PM)

Title:  Electromagnetic wave propagation in random media

Abstract:   We study Maxwell's equations in media with small random fluctuations of the electric permittivity, to obtain a detailed mathematical characterization of the statistics of the electric and magnetic fields at long distances of propagation. We introduce a novel wide-angle wave propagation regime, which is mathematically justified by scaling assumptions. In this regime, we obtain a decomposition of the waves in transverse electric and magnetic modes with random amplitudes. These amplitudes account for the cumulative scattering effects in the medium, and satisfy a system of stochastic differential equations which can be analyzed with the Markov limit theorem. The result is an explicit quantification of the randomization of the waves due to scattering, an understanding of polarization effects, and a mathematical justification of the radiative transport equations with polarization.

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Speaker:  Liliana Borcea
Institution:  Univ. of Michigan

Event Organizer:     

 

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