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Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics$
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G. F. Roach, I. G. Stratis, and A. N. Yannacopoulos

Print publication date: 2012

Print ISBN-13: 9780691142173

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691142173.001.0001

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(p.275) Chapter Fourteen Homogenisation
Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

G. F. Roach

I. G. Stratis

A. N. Yannacopoulos

Princeton University Press

This chapter presents a theory of homogenisation for random bianisotropic media exhibiting an ergodic structure. It shows that for such a medium there exists a homogenised system of the Maxwell type. To begin, the chapter presents an introduction to the necessary notions from the theory of ergodicity that will be used in this treatment of homogenisation. It then showcases a model for a random complex medium, on which this chapter's analysis will be based. The chapter also details a formal two-scale approach to set ideas and understand the basic mechanisms that will lead to a homogenised system, as well as to identify the coefficients of the homogenised system. Finally, this chapter presents some rigorous results on the homogenisation of random complex electromagnetic media.

Keywords:   homogenisation, random bianisotropic media, ergodicity, random complex medium, two-scale approach, homogenised system, random complex electromagnetic media

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