Mathematical analysis of deterministic and stochastic problems in complex media electromagnetics
by Roach, G. F., (Gary Francis)
"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 applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory. Designed for researchers and …
Read More ↓Title Statements
- Full title :Mathematical analysis of deterministic and stochastic problems in complex media electromagnetics / Gary F. Roach, Ioannis G. Stratis, Athanasios N. Yannacopoulos.
Summary
"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 applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory.
Designed for researchers and advanced graduate students in applied mathematics, electrical engineering, and physics, this book introduces the electromagnetics of complex media through a systematic, state-of-the-art account of their mathematical theory. The book combines the study of well posedness, homogenization, and controllability of Maxwell equations complemented with constitutive relations describing complex media. The book treats deterministic and stochastic problems both in the frequency and time domains. It also covers computational aspects and scattering problems, among other important topics. Detailed appendices make the book self-contained in terms of mathematical prerequisites, and accessible to engineers and physicists as well as mathematicians."--Pub. desc.
Edition Statements
- Publication Date:2012.
Publication Statements
- Publisher(s):Princeton University Press
- Place of Publication:Princeton
- Language:eng
- Publication Date:2012.
The Physical Object
- Description:xv, 382 pages : : illustrations ; : 25 cm.
Edition Identifiers
- ISBN:9780691142173, 0691142173
- oclc:ocn758646782
- LC Classification:QC760.4.M37
- Dewey Decimal:537.01/519
Table of Contents
Chapter 1. Complex Media -- Chapter 2. The Maxwell Equations and Constitutive Relations ; Fundamentals ; Constitutive relations ; The Maxwell equations in complex media: A variety of problems -- Chapter 3. Spaces and Operators ; Function spaces ; Standard difierential and trace operators ; Function spaces for electromagnetics ; Traces ; Various decompositions ; Compact embeddings ; The operators of vector analysis revisited ; The Maxwell operator -- PART 2. TIME-HARMONIC DETERMINISTIC PROBLEMS -- Chapter 4. Well Posedness ; Solvability of the interior problem ; The eigenvalue problem ; Low chirality behaviour ; Comments on exterior domain problems ; Towards numerics -- Chapter 5. Scattering Problems: Beltrami Fields and Solvability ; Elliptic, circular and linear polarisation of waves ; Beltrami fields -- The Bohren decomposition ; Scattering problems: Formulation ; An introduction to BIEs ; Properties of Beltrami fields ; Solvability ; Generalised Muller's BIEs ; Low chirality approximations.
Chapter 6. Scattering Problems: A Variety of Topics ; Important concepts of scattering theory ; Back to chiral media: Scattering relations and the far-field operator ; Using dyadics ; Hergl…
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