Mathematical Analysis of Deterministic and Stochastic by G. F. Roach

By G. F. Roach

Electromagnetic complicated media are synthetic fabrics that have an effect on the propagation of electromagnetic waves in remarkable methods no longer frequently visible in nature. due to their wide selection of significant purposes, those fabrics were intensely studied during the last twenty-five years, frequently from the views of physics and engineering. yet a physique of rigorous mathematical conception has additionally steadily built, and this can be the 1st ebook to give that idea.

Designed for researchers and complex graduate scholars in utilized arithmetic, electric engineering, and physics, this e-book introduces the electromagnetics of complicated media via a scientific, state of the art account in their mathematical concept. The ebook combines the research of good posedness, homogenization, and controllability of Maxwell equations complemented with constitutive kin describing advanced media. The booklet treats deterministic and stochastic difficulties either within the frequency and time domain names. It additionally covers computational facets and scattering difficulties, between different very important subject matters. specific appendices make the e-book self-contained when it comes to mathematical necessities, and available to engineers and physicists in addition to mathematicians.

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Extra info for Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics (Princeton Series in Applied Mathematics)

Example text

For simplicity the randomness is assumed to be spatial only. In the above uω = u(·, ω) is a general notation for a random field u : Ω → V , where (Ω, F , P ) is a probability space and V is a properly selected function space. The probability space (Ω, F , P ) is a model for the spatial randomness of the medium; we will return to specific examples later on. The random nature of the medium is used to model imperfections of the medium due to its construction, experimental mis-specifications of the medium properties, etc.

Otherwise, there is an extra term18 proportional to u, which may be incorporated in the definition of the operator MA , leading to minor modifications to the mathematical treatment. The boundary conditions, as well as the divergence free character of the electromagnetic field, can be included in the definition of the operator M in appropriately selected function spaces. The well posedness of such problems will be studied in Chapter 7. 7 Controllability and optimal control problems Ch. 8 Consider a complex medium, confined within the domain O ⊂ R3 , considered to be sufficiently smooth.

In the case of perfect conductor boundary condition, f = 0. As for the time-dependent case, using the constitutive relations we may obtain a system involving only the fields E, H. 1). This equation is a static equation. 21) in order to associate D, B with E, H. 27), which remain unaltered. 15 After dropping the subscripts DBF . 32) k 2 = 2 εF µF , γ 2 = k2 (1 − β 2 k 2 )−1 , √ and J is an external force. Note that k is just an abbreviation for εF µF and not a wave number16 . 28). 29). 22) between the parameters of the medium in the DBF and the Telegen approximation, and in this way their equivalence.

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