Electromagnetism of Continuous Media: Mathematical Modelling and Applications by Mauro FabrizioElectromagnetism of Continuous Media: Mathematical Modelling and Applications by Mauro Fabrizio

Electromagnetism of Continuous Media: Mathematical Modelling and Applications

byMauro Fabrizio, Angelo Morro

Hardcover | March 1, 2004

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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 originalresults.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 areestablished.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 harmonicsand 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 newmechanical, 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 forprediction.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.
Mauro Fabrizio is a Professor of Rational Mechanics, Department of Mathematics, University of Bologna, Italy. Angelo Morro is a Professor of Mathematical Physics, DIBE, University of Genoa, Italy.
Title:Electromagnetism of Continuous Media: Mathematical Modelling and ApplicationsFormat:HardcoverDimensions:686 pages, 9.21 × 6.14 × 1.52 inPublished:March 1, 2004Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198527004

ISBN - 13:9780198527008

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Table of Contents

PrefacePart I: Basic Notions in Electromagnetism1. Electromagnetic fields2. Green's functions and retarded potentials3. Time-harmonic fields4. Models of materials with memoryPart II: Thermodynamics and Mathematical Problems5. Thermodynamics of simple electromagnetic systems6. Thermoelectromagnetic systems7. Existence and uniqueness8. Wave propagation9. Extremum principlesPart III: Nonlinearity and Nonlocality10. Problems in nonlinear electromagnetism11. Nonlocal electromagnetism and superconductivity12. Magnetic hysteresisAppendicesA. Some properties of Bessel functionsB. Fourier transforms and Sobolev spacesC. Compact operators and eigenfunctionsD. Differential operators in curvilinear coordinatesE. Finite formulation of electromagnetism

Editorial Reviews

`... a worthy continuation of well-known works on electromagnetic theory such as Stratton and Smythe, although the notation is not always quite the same.'Zentralblatt MATH