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Electromagnetism of continuous media : mathematical modelling and applications

Author: Mauro Fabrizio; Angelo Morro
Publisher: Oxford : Oxford University Press, 2003.
Edition/Format:   Print book : EnglishView all editions and formats
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The wide application of technologies in mechanical, electronic and biomedical systems calls for materials and structures with non-conventional properties. This text discusses the mathematical  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Mauro Fabrizio; Angelo Morro
ISBN: 0198527004 9780198527008
OCLC Number: 51668468
Description: xvii, 668 pages : illustrations ; 24 cm
Contents: Part 1 Basic Notions in Electromagnetism --
1 Electromagnetic fields 3 --
1.1 Historical remarks 3 --
1.2 Basic principles and balance laws 5 --
1.2.1 Local balance equations 6 --
1.3 Dipole moments and balance laws in matter 9 --
1.4 Macroscopic properties and constitutive equations 12 --
1.4.1 Forced current, magnetic current and magnetic charge 14 --
1.4.2 Duality principle 15 --
1.5 Lorentz-invariant form of Maxwell's equations 16 --
1.5.1 The Lorentz force 20 --
1.5.2 Electromagnetic stress and momentum 21 --
1.5.3 Electromagnetism based on three principles 23 --
1.6 Poynting's theorem and balance of energy 23 --
1.7 Balance laws in matter and discontinuous fields 26 --
1.8 Boundary conditions 32 --
1.9 Consequences of the Clausius-Duhem inequality 34 --
1.9.1 Other choices of independent variables 36 --
1.10 Electromagnetic potentials 37 --
1.11 Differential equations for the electromagnetic fields 42 --
1.12 Force, torque and energy of dipoles 45 --
1.13 Electromagnetism of deformable media 51 --
1.13.1 Electrodynamics of moving media 51 --
1.13.2 Electrodynamics of deformable media 52 --
2 Green's functions and retarded potentials 55 --
2.1 Green's formula and distributional solutions 55 --
2.2 The Fourier transform of distributions 58 --
2.3 Green's function for the harmonic oscillator 61 --
2.4 Green's function for the wave equation 64 --
2.4.1 One-dimensional wave equation 65 --
2.4.2 Two-dimensional wave equation 66 --
2.4.3 Three-dimensional wave equation 67 --
2.5 Green's function for the reduced wave equation 69 --
2.6 Green's function for the lossy wave equation 70 --
2.7 Retarded potentials 73 --
2.8 Kirchhoff's solution 76 --
2.9 Integral formulae for the electromagnetic field 78 --
2.10 Electric dipole fields 81 --
2.11 Lienard-Wiechert potentials and point charge radiation 83 --
2.12 Initial-value problem for the wave equation 89 --
2.13 Initial-value problem for the telegraph equation 95 --
2.14 Boundary-value problem for the telegraph equation 99 --
3 Time-harmonic fields 101 --
3.1 Fields and potentials 101 --
3.2 Helmholtz's theorem 104 --
3.3 Energy balance 106 --
3.3.1 Uniqueness 108 --
3.3.2 Energy density 109 --
3.4 Green's functions for Helmholtz's equation 111 --
3.5 Green's tensor 113 --
3.6 Helmholtz's equation and waves 115 --
3.7 Huygens' principle 123 --
3.8 Time-harmonic plane waves 125 --
3.9 Reciprocity 128 --
3.10 Superposition of waves and group velocity 130 --
3.11 Doppler effect, dispersion and convection of light 137 --
3.12 Signal velocity 139 --
3.13 The method of stationary phase 142 --
4 Models of materials with memory 146 --
4.1 A motivation of memory from waves in water 146 --
4.2 Simple models of material behaviour 148 --
4.2.1 Dielectrics 148 --
4.2.2 Debye model of dielectrics 150 --
4.2.3 Bound electrons in a magnetic field 153 --
4.2.4 Radiation damping 155 --
4.2.5 Magnetic materials 157 --
4.2.6 Ferroelectric materials 161 --
4.2.7 Molecular crystals with permanent dipoles 162 --
4.2.8 Metals 163 --
4.2.9 Ionosphere 164 --
4.2.10 Magnetosphere 167 --
4.2.11 A mixture description of plasmas 169 --
4.3 Kinetic approach to a plasma model 170 --
4.4 Restrictions placed by the Clausius-Duhem inequality 175 --
4.5 Causality and Kramers-Kronig relations 177 --
4.6 Approximate consequences of the Kramers-Kronig relations 181 --
4.7 Integral theorems 184 --
4.8 Causality conditions 187 --
Part 2 Thermodynamics and Mathematical Problems --
5 Thermodynamics of simple electromagnetic systems 195 --
5.1 Electromagnetic systems 195 --
5.2 Materials with fading memory 199 --
5.2.1 Dielectrics with memory 199 --
5.2.2 Conductors with memory 202 --
5.3 Thermodynamic laws 204 --
5.4 Reversibility 205 --
5.5 Principle of electromagnetic energy dissipation 208 --
5.5.1 Equivalent formulations of the minimum free energy 214 --
5.6 Dielectrics and rate-type electromagnetic materials 217 --
5.7 Thermodynamic restrictions on linear systems 220 --
5.8 Free enthalpy of linear systems with memory 226 --
5.8.1 Free enthalpies and free energies for dielectrics with memory 228 --
5.8.2 Free enthalpies and free energies for conductors with memory 239 --
5.9 Topologies for the history space 242 --
5.9.1 Dielectrics with memory 242 --
5.9.2 Conductors with memory 250 --
5.10 Electric conduction in the ionosphere 251 --
5.10.1 Free energies and free enthalpies 252 --
5.11 Dissipativity at interfaces 254 --
6 Thermoelectromagnetic systems 260 --
6.1 Review of previous approaches 260 --
6.1.1 Electromagnetic systems without memory 263 --
6.2 Simple materials 264 --
6.3 Thermodynamic laws 266 --
6.4 Linear approximation with respect to the temperature 271 --
6.5 Examples of internal pseudo-energies 274 --
6.6 Linear systems with memory 279 --
6.6.1 Thermoelectromagnetic dielectrics 279 --
6.6.2 Free enthalpy of a thermoelectromagnetic dielectric 282 --
6.7 Linear thermoelectromagnetic dielectrics 283 --
6.8 Maximum free enthalpy 287 --
6.9 The discrete spectrum model 289 --
6.10 Thermoelectromagnetic conductors 291 --
6.11 Onsager's reciprocal relations 292 --
6.11.1 Application to thermoelectric phenomena 295 --
7 Existence and uniqueness 297 --
7.1 Some function spaces in electromagnetism 297 --
7.2 Stationary solutions in one-dimensional resonators 304 --
7.3 Stationary solutions in a resonator 305 --
7.4 Stationary solutions in conductors 308 --
7.5 Stationary fields with dissipative boundary conditions 312 --
7.6 Static solutions 314 --
7.7 The quasi-static problem 320 --
7.8 The evolution problem 323 --
7.8.1 Domain of dependence inequality 327 --
7.8.2 Uniqueness theorems 330 --
7.8.4 Existence of strict solutions 334 --
7.9 Existence and uniqueness for dielectrics with memory 338 --
7.10 Asymptotic behaviour in dielectrics with memory 341 --
7.11 Domain of dependence for dielectrics with memory 343 --
7.12 Absorbing boundary conditions 345 --
7.13 Existence and uniqueness for absorbing boundaries 348 --
7.14 Asymptotic behaviour for absorbing boundaries 354 --
7.15 A counterexample to asymptotic stability 358 --
7.16 Maxwell's equations as a constrained system 361 --
7.17 Spatial decay estimates 366 --
7.18 Spatial decay for dielectrics with memory 371 --
7.19 Thermoelectromagnetic systems 373 --
7.19.1 Thermoelectromagnetic conductors 374 --
8 Wave propagation 382 --
8.1 Plane waves 382 --
8.2 Linear and circular polarization 387 --
8.3 Reflection-transmission of waves between dielectrics 389 --
8.4 Reflectivity and transmissivity 396 --
8.5 Reflection and transmission between dissipative media 399 --
8.5.1 Upgoing and downgoing waves 402 --
8.5.2 Reflected and transmitted waves 404 --
8.6 Magnetohydrodynamic waves 405 --
8.7 Waves in anisotropic materials 409 --
8.7.1 Anisotropic dielectrics 410 --
8.7.2 Gyrotropic media 413 --
8.8 Plane wavefronts 417 --
8.9 Speed of propagation in materials with memory 421 --
8.10 Decay in materials with memory 423 --
9 Extremum principles 427 --
9.1 Some function spaces 427 --
9.2 Variational formulation for a system of equations 429 --
9.3 Models of electromagnetic media 433 --
9.3.1 Dielectrics 434 --
9.3.2 Conductors 434 --
9.3.3 Materials with memory 434 --
9.3.4 Boundary conditions 435 --
9.4 Extremum principles for static problems 437 --
9.4.1 Electrostatic problem 437 --
9.4.2 Magnetostatic problem 439 --
9.4.3 Electromagnetostatic problem 440 --
9.4.4 Electromagnetostatic problem with dissipative boundary conditions 442 --
9.5 Rayleigh's variational principles 443 --
9.5.1 Resonance frequencies 444 --
9.5.2 Wave numbers 447 --
9.6 Stationary formulae and Rayleigh-Ritz procedure 449 --
9.7 Least action principle 452 --
9.7.1 The least-action principle in empty space 452 --
9.7.2 Lagrangians involving the electromagnetic tensor 456 --
9.7.3 Electromagnetic Lagrangian 459 --
9.7.4 Lagrangian for nonlinear dielectrics 462 --
9.8 Functionals for initial-value problems 464 --
9.9 Functionals in the Laplace-tranform domain 467 --
9.9.1 Reiss-type principles 470 --
9.9.2 Constrained variational formulations 475 --
Part 3 Nonlinearity and Nonlocality --
10 Problems in nonlinear electromagnetism 481 --
10.1 Modelling in nonlinear optics 481 --
10.2 Nonlinear constitutive equations with memory 485 --
10.2.1 Nonlinear models for anisotropic media 486 --
10.2.2 Isotropic dielectrics 488 --
10.3 Volterra series 491 --
10.3.1 Sinusoidal inputs 493 --
10.3.2 Gaussian noise input 495 --
10.4 A model of nonlinear materials 497 --
10.5 Luxembourg effect 499 --
10.6 Plane waves in nonlinear media 502 --
10.6.1 Second harmonic 504 --
10.6.2 Phase conjugation 505 --
10.7 Generation of harmonics through perturbation methods 507 --
10.8 Simple waves 514 --
10.9 Hyperbolic systems and shock formation 518 --
10.10 The Bernoulli equation for the weak-wave amplitude 525 --
10.11 Speed of shocks 532 --
10.12 Shocks in dielectrics with instantaneous response 534 --
10.12.1 Shock evolution and constitutive properties 535 --
10.12.2 Shocks of small amplitude 537 --
10.13 Shocks in dielectrics with memory 537 --
11 Nonlocal electromagnetism and superconductivity 542 --
11.1 Remarks on the entropy inequality 542 --
11.2 Balance laws and second law 544 --
11.3 Dielectric bodies with quadrupoles 549 --
11.4 Nonlocal dielectrics with memory 551 --
11.5 Strictly nonlocal materials 555 --
11.6 Superconductivity 557 --
11.6.1 Basic phenomena 557.
Responsibility: Mauro Fabrizio and Angelo Morro.
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