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The Maxwell Equations and Constitutive Relations

G. F. Roach, I. G. Stratis, and A. N. Yannacopoulos

in Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691142173
eISBN:
9781400842650
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142173.003.0002
Subject:
Mathematics, Applied Mathematics

This chapter first introduces the constitutive relations which are commonly used in electromagnetic theory for the mathematical modelling of complex electromagnetic media. These constitutive ... More


Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

G. F. Roach, I. G. Stratis, and A. N. Yannacopoulos

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691142173
eISBN:
9781400842650
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142173.001.0001
Subject:
Mathematics, Applied Mathematics

Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important ... More


Well Posedness

G. F. Roach, I. G. Stratis, and A. N. Yannacopoulos

in Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691142173
eISBN:
9781400842650
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142173.003.0012
Subject:
Mathematics, Applied Mathematics

This chapter first presents a model for the Maxwell equations for complex random media in terms of stochastic integrodifferential equations. It then provides the appropriate functional framework that ... More


Homogenisation

G. F. Roach, I. G. Stratis, and A. N. Yannacopoulos

in Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691142173
eISBN:
9781400842650
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142173.003.0014
Subject:
Mathematics, Applied Mathematics

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. ... More


Controllability

G. F. Roach, I. G. Stratis, and A. N. Yannacopoulos

in Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691142173
eISBN:
9781400842650
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142173.003.0013
Subject:
Mathematics, Applied Mathematics

This chapter addresses the problem of controllability for stochastic complex electromagnetic media. The starting point is the stochastic integrodifferential equations that model the evolution of the ... More


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