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| Basic Notions in Electromagnetism | |
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| Electromagnetic fields | |
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| Historical remarks | |
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| Basic principles and balance laws | |
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| Local balance equations | |
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| Dipole moments and balance laws in matter | |
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| Macroscopic properties and constitutive equations | |
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| Forced current, magnetic current and magnetic charge | |
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| Duality principle | |
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| Lorentz-invariant form of Maxwell's equations | |
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| The Lorentz force | |
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| Electromagnetic stress and momentum | |
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| Electromagnetism based on three principles | |
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| Poynting's theorem and balance of energy | |
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| Balance laws in matter and discontinuous fields | |
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| Boundary conditions | |
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| Consequences of the Clausius-Duhem inequality | |
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| Other choices of independent variables | |
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| Electromagnetic potentials | |
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| Differential equations for the electromagnetic fields | |
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| Force, torque and energy of dipoles | |
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| Electromagnetism of deformable media | |
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| Electrodynamics of moving media | |
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| Electrodynamics of deformable media | |
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| Green's functions and retarded potentials | |
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| Green's formula and distributional solutions | |
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| The Fourier transform of distributions | |
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| Green's function for the harmonic oscillator | |
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| Green's function for the wave equation | |
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| One-dimensional wave equation | |
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| Two-dimensional wave equation | |
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| Three-dimensional wave equation | |
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| Green's function for the reduced wave equation | |
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| Green's function for the lossy wave equation | |
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| Retarded potentials | |
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| Kirchhoff's solution | |
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| Integral formulae for the electromagnetic field | |
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| Electric dipole fields | |
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| Lienard-Wiechert potentials and point charge radiation | |
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| Initial-value problem for the wave equation | |
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| Initial-value problem for the telegraph equation | |
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| Boundary-value problem for the telegraph equation | |
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| Time-harmonic fields | |
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| Fields and potentials | |
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| Helmholtz's theorem | |
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| Energy balance | |
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| Uniqueness | |
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| Energy density | |
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| Green's functions for Helmholtz's equation | |
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| Green's tensor | |
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| Helmholtz's equation and waves | |
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| Huygens' principle | |
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| Time-harmonic plane waves | |
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| Reciprocity | |
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| Superposition of waves and group velocity | |
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| Doppler effect, dispersion and convection of light | |
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| Signal velocity | |
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| The method of stationary phase | |
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| Models of materials with memory | |
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| A motivation of memory from waves in water | |
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| Simple models of material behaviour | |
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| Dielectrics | |
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| Debye model of dielectrics | |
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| Bound electrons in a magnetic field | |
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| Radiation damping | |
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| Magnetic materials | |
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| Ferroelectric materials | |
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| Molecular crystals with permanent dipoles | |
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| Metals | |
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| Ionosphere | |
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| Magnetosphere | |
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| A mixture description of plasmas | |
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| Kinetic approach to a plasma model | |
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| Restrictions placed by the Clausius-Duhem inequality | |
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| Causality and Kramers-Kronig relations | |
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| Approximate consequences of the Kramers-Kronig relations | |
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| Integral theorems | |
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| Causality conditions | |
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| Thermodynamics and Mathematical Problems | |
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| Thermodynamics of simple electromagnetic systems | |
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| Electromagnetic systems | |
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| Materials with fading memory | |
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| Dielectrics with memory | |
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| Conductors with memory | |
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| Thermodynamic laws | |
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| Reversibility | |
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| Principle of electromagnetic energy dissipation | |
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| Equivalent formulations of the minimum free energy | |
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| Dielectrics and rate-type electromagnetic materials | |
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| Thermodynamic restrictions on linear systems | |
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| Free enthalpy of linear systems with memory | |
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| Free enthalpies and free energies for dielectrics with memory | |
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| Free enthalpies and free energies for conductors with memory | |
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| Topologies for the history space | |
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| Dielectrics with memory | |
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| Conductors with memory | |
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| Electric conduction in the ionosphere | |
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| Free energies and free enthalpies | |
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| Dissipativity at interfaces | |
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| Thermoelectromagnetic systems | |
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| Review of previous approaches | |
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| Electromagnetic systems without memory | |
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| Simple materials | |
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| Thermodynamic laws | |
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| Linear approximation with respect to the temperature | |
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| Examples of internal pseudo-energies | |
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| Linear systems with memory | |
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| Thermoelectromagnetic dielectrics | |
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| Free enthalpy of a thermoelectromagnetic dielectric | |
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| Linear thermoelectromagnetic dielectrics | |
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| Maximum free enthalpy | |
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| The discrete spectrum model | |
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| Thermoelectromagnetic conductors | |
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| Onsager's reciprocal relations | |
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| Application to thermoelectric phenomena | |
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| Existence and uniqueness | |
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| Some function spaces in electromagnetism | |
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| Stationary solutions in one-dimensional resonators | |
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| Stationary solutions in a resonator | |
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| Stationary solutions in conductors | |
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| Stationary fields with dissipative boundary conditions | |
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| Static solutions | |
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| The quasi-static problem | |
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| The evolution problem | |
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| Domain of dependence inequality | |
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| Uniqueness theorems | |
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| Existence | |
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| Existence of strict solutions | |
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| Existence and uniqueness for dielectrics with memory | |
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| Asymptotic behaviour in dielectrics with memory | |
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| Domain of dependence for dielectrics with memory | |
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| Absorbing boundary conditions | |
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| Existence and uniqueness for absorbing boundaries | |
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| Asymptotic behaviour for absorbing boundaries | |
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| A counterexample to asymptotic stability | |
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| Maxwell's equations as a constrained system | |
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| Spatial decay estimates | |
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| Spatial decay for dielectrics with memory | |
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| Thermoelectromagnetic systems | |
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| Thermoelectromagnetic conductors | |
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| Wave propagation | |
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| Plane waves | |
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| Linear and circular polarization | |
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| Reflection-transmission of waves between dielectrics | |
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| Reflectivity and transmissivity | |
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| Reflection and transmission between dissipative media | |
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| Upgoing and downgoing waves | |
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| Reflected and transmitted waves | |
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| Magnetohydrodynamic waves | |
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| Waves in anisotropic materials | |
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| Anisotropic dielectrics | |
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| Gyrotropic media | |
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| Plane wavefronts | |
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| Speed of propagation in materials with memory | |
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| Decay in materials with memory | |
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| Extremum principles | |
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| Some function spaces | |
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| Variational formulation for a system of equations | |
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| Models of electromagnetic media | |
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| Dielectrics | |
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| Conductors | |
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| Materials with memory | |
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| Boundary conditions | |
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| Extremum principles for static problems | |
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| Electrostatic problem | |
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| Magnetostatic problem | |
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| Electromagnetostatic problem | |
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| Electromagnetostatic problem with dissipative boundary conditions | |
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| Rayleigh's variational principles | |
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| Resonance frequencies | |
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| Wave numbers | |
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| Stationary formulae and Rayleigh-Ritz procedure | |
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| Least action principle | |
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| The least-action principle in empty space | |
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| Lagrangians involving the electromagnetic tensor | |
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| Electromagnetic Lagrangian | |
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| Lagrangian for nonlinear dielectrics | |
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| Functionals for initial-value problems | |
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| Functionals in the Laplace-tranform domain | |
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| Reiss-type principles | |
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| Constrained variational formulations | |
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| Nonlinearity and Nonlocality | |
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| Problems in nonlinear electromagnetism | |
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| Modelling in nonlinear optics | |
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| Nonlinear constitutive equations with memory | |
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| Nonlinear models for anisotropic media | |
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| Isotropic dielectrics | |
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| Volterra series | |
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| Sinusoidal inputs | |
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| Gaussian noise input | |
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| A model of nonlinear materials | |
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| Luxembourg effect | |
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| Plane waves in nonlinear media | |
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| Second harmonic | |
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| Phase conjugation | |
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| Generation of harmonics through perturbation methods | |
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| Simple waves | |
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| Hyperbolic systems and shock formation | |
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| The Bernoulli equation for the weak-wave amplitude | |
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| Speed of shocks | |
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| Shocks in dielectrics with instantaneous response | |
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| Shock evolution and constitutive properties | |
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| Shocks of small amplitude | |
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| Shocks in dielectrics with memory | |
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| Nonlocal electromagnetism and superconductivity | |
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| Remarks on the entropy inequality | |
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| Balance laws and second law | |
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| Dielectric bodies with quadrupoles | |
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| Nonlocal dielectrics with memory | |
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| Strictly nonlocal materials | |
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| Superconductivity | |
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| Basic phenomena | |
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| The London equations | |
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| An improvement of the London theory | |
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| Two nonlocal models | |
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| Nonlocal properties of superconductivity | |
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| Superconductors with memory | |
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| The London gauge | |
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| The Ginzburg-Landau theory | |
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| Quasi-stationary model | |
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| Evolution model | |
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| Magnetic hysteresis | |
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| Micromagnetics | |
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| Domain wall motion | |
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| Evaluation of the magnetization at a given field | |
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| Solution for major and minor loops | |
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| Remarks about mathematical models for hysteresis | |
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| General requirements | |
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| Rate-type models | |
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| A Preisach-type model | |
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| Two 'bilinear' models | |
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| The Coleman-Hodgdon model | |
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| History-rate type models | |
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| An example | |
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| History-integral type models | |
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| The Bouc model | |
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| The Preisach model | |
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| Appendices | |
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| Some properties of Bessel functions | |
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| Fourier transform and Sobolev spaces | |
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| Fourier transform | |
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| Introduction to Sobolev spaces | |
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| Distributions | |
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| Fourier transform of distributions | |
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| Compact operators and eigenfunctions | |
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| Compact operators | |
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| Eigenfunctions in spatially homogeneous resonators | |
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| Differential operators in curvilinear coordinates | |
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| Differentiation | |
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| Gradient, divergence, curl and the Laplacian | |
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| Orthogonal curvilinear coordinates | |
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| Finite formulation of electromagnetism | |
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| Field laws in global form | |
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| Bibliography | |
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| Index | |