Overview

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.

Full Product Details

Author:   Mauro Fabrizio (, Professor of Rational Mechanics, Department of Mathematics, University of Bologna, Italy) ,  Angelo Morro (, Professor of Mathematical Physics, DIBE, University of Genoa, Italy)
Publisher:   Oxford University Press
Imprint:   Oxford University Press
Dimensions:   Width: 16.10cm , Height: 3.90cm , Length: 24.10cm
Weight:   1.068kg
ISBN:  

9780198527008

ISBN 10:   0198527004
Pages:   688
Publication Date:   05 June 2003
Audience:   College/higher education ,  Tertiary & Higher Education
Format:   Hardback
Publisher's Status:   Active
Availability:   To order  
Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us.

Table of Contents

Preface Part I: Basic Notions in Electromagnetism1: Electromagnetic fields 2: Green's functions and retarded potentials 3: Time-harmonic fields 4: Models of materials with memory Part II: Thermodynamics and Mathematical Problems5: Thermodynamics of simple electromagnetic systems 6: Thermoelectromagnetic systems 7: Existence and uniqueness 8: Wave propagation 9: Extremum principles Part III: Nonlinearity and Nonlocality10: Problems in nonlinear electromagnetism 11: Nonlocal electromagnetism and superconductivity 12: Magnetic hysteresis AppendicesA: Some properties of Bessel functions B: Fourier transforms and Sobolev spaces C: Compact operators and eigenfunctions D: Differential operators in curvilinear coordinates E: Finite formulation of electromagnetism

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

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. Mathematical Reviews There is a wealth of material. Mathematical Reviews The book is well written and the printing is excellent ... It can be thoroughly recommended. Zentralblatt MATH

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions