Electromagnetism of Continuous Media
Mathematical Modelling and Applications
Series: Oxford Mathematical Monographs;
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Product details:
- Publisher OUP Oxford
- Date of Publication 5 June 2003
- ISBN 9780198527008
- Binding Hardback
- No. of pages688 pages
- Size 241x161x38 mm
- Weight 1068 g
- Language English
- Illustrations 13 figures 0
Categories
Short description:
The wide application of technologies in new mechanical, electronic and biomedical systems calls for materials and structures with non-conventional properties (e.g materials with 'memory'). Of equal importance is the understanding of the physical behaviour of these materials and consequently developing mathematical modelling techniques for prediction.
This self contained text discusses the mathematical modelling used with these types of electromagnetic materials. It provides a carefully structured, coherent, and comprehensive treatment of electromagnetism of continuous media. The authors provide a systematic review of known subjects along with original results about thermodynamics of electromagnetic materials, well-posedness of initial boundary-value problems, variational settings, and wave propagation. Models of non-linear materials, non-local materials (superconductors), and hysteretic (magnetic) materials are also developed in detail.
Long description:
For graduate students and researchers, this self contained text provides a carefully structured, coherent, and comprehensive treatment of the mathematical modelling in electromagnetism of continuous media. The authors provide a systematic review of known subjects along with many original results.
Part I reviews basic notions and approaches in electromagnetism (Maxwell's equations, Green's functions, harmonic fields, dispersive effects) and emphasizes the physical motivation for the modelling of non-conventional materials. The frequency-dependent properties (such as conductivity, polarizability, and magnetizability), which enter wave diffraction and dispersion, are shown, and these lead to a discussion of models of materials with fading memory in the time domain.
Part II develops the thermodynamics of electromagnetic and thermoelectromagnetic materials with memory and provides a systematic account of thermodynamic restrictions. Existence, uniqueness and stability problems are investigated. Also, variational formulations and wave propagation solution are established.
Part III is devoted to more involved models which are motivated by the interest in materials and structures with non-conventional properties. The mathematical modelling deals with non-linearity, non-locality and hysteresis. In non-linear materials attention is focussed on the generation of harmonics and in discontinuity waves. Non-locality is examined in a general way and hence is applied to superconductivity. Hysteresis is developed for magnetism. A review of known schemes is given along with new results about the modelling of hysteresis loops. The wide application of technologies in new mechanical, electronic and biomedical systems calls for materials and structures with non-conventional properties (e.g materials with 'memory'). Of equal importance is the understanding of the physical behaviour of these materials and consequently developing mathematical modelling techniques for prediction.
Includes appendices that include some properties of Bessel functions, Fourier transforms and Sobolev spaces, compact operators and eigenfunctions, differential operators in curvilinear coordinates, and finite formulation of electromagnetism.
This ample monograph deals with mathematical models for electromagnetic phenomena in media exhibiting nonconventional characteristics. There is a wealth of material divided into several parts.
Table of Contents:
Preface
Electromagnetic fields
Green's functions and retarded potentials
Time-harmonic fields
Models of materials with memory
Thermodynamics of simple electromagnetic systems
Thermoelectromagnetic systems
Existence and uniqueness
Wave propagation
Extremum principles
Problems in nonlinear electromagnetism
Nonlocal electromagnetism and superconductivity
Magnetic hysteresis
Some properties of Bessel functions
Fourier transforms and Sobolev spaces
Compact operators and eigenfunctions
Differential operators in curvilinear coordinates
Finite formulation of electromagnetism
