Electrodynamics of Continua

(Volume II).- 9 Elastic Ferromagnets.- 9.0. An Overview of Basic Equations.- 9.1. Scope of the Chapter.- 9.2. Model of Interactions.- A. Gyroscopic Nature of the Spin Density.- B. Spin-Lattice Model of Interactions.- 9.3. Balance Equations.- A. Global Balance Equations.- B. Local Balance Equations.- C. The Clausius-Duhem (C-D) Inequality.- D. Boundary Conditions.- 9.4. Constitutive Theory.- A. Saturated Ferromagnetic Elastic Insulators.- B. Free Energy.- C. Correspondence Between the Microscopic Model and the Continuous Representation.- D. Infinitesimal Strains.- E. Centrosymmetric Cubic Crystals.- F. Uniaxial Crystals.- G. Elementary Dissipative Processes.- H. Small Fields Superposed on a Constant Bias Magnetic Field.- 9.5. Resume of Basic Equations.- 9.6. Coupled Magnetoelastic Waves in Ferromagnets.- A. Preliminary Remarks.- B. Plane Harmonic Waves.- C. Damping of Magnetoelastic Waves.- D. Magnetoelastic Faraday Effect.- 9.7. Applications of the Magnon-Phonon Coupling.- A. Pumping and Temporal Magnon-Phonon Conversion.- B. Drift-Type Amplification of Magnetoelastic Waves.- 9.8. Other Works.- A. Continuum Descriptions of Ferromagnetic Deformable Bodies.- B. Wave Propagation.- C. Ferrimagnetic Deformable Bodies.- Problems.- 10 Magnetohydrodynamics.- 10.1. Scope of the Chapter.- 10.2. Basic Equations of Electromagnetic Fluids.- 10.3. Magnetohydrodynamic Approximation.- 10.4. Perfect Magnetohydrodynamics.- A. Field Equations.- B. "Frozen-In" Fields.- C. Bernoulli's Equation in Magnetohydrodynamics.- D. Kelvin's Circulation Theorem in Magnetohydrodynamics.- E. Alfven Waves.- F. Generalized Hugoniot Condition.- 10.5. Incompressible Viscous Magnetohydrodynamic Flow.- A. Magnetohydrodynamic Poiseuille Flow.- B. Magnetohydrodynamic Couette Flow.- 10.6. One-Dimensional Compressible Flow.- 10.7. Shock Waves in Magnetohydrodynamics.- A. Classification of Magnetohydrodynamic Shock Waves.- B. Shock Structure.- 10.8. Magnetohydrodynamic Equilibria.- 10.9. Equilibrium of Magnetic Stars.- 10.10. Magnetohydrodynamic Stability.- A. The Energy Method.- B. Equilibrium States and Perturbations.- C. Quantities Conserved in the Perturbation.- D. Elementary Perturbations.- E. Change in the Energy Integrals.- F. Application to the Linear Pinch.- Problems.- 11 Eleetrohydrodynamics.- 11.1. Scope of the Chapter.- 11.2. Field Equations.- 11.3. Charge Relaxation.- 11.4. Stability Condition.- 11.5. Helmholtz and Bernoulli Equations.- A. Generalization of the Helmholtz Equation.- B. Vorticity Generation in a Space-Charge-Loaded Electric Field.- C. Generalization of Bernoulli' of Basic Equations.- 9.6. Coupled Magnetoelastic Waves in Ferromagnets.- A. Preliminary Remarks.- B. Plane Harmonic Waves.- C. Damping of Magnetoelastic Waves.- D. Magnetoelastic Faraday Effect.- 9.7. Applications of the Magnon-Phonon Coupling.- A. Pumping and Temporal Magnon-Phonon Conversion.- B. Drift-Type Amplification of Magnetoelastic Waves.- 9.8. Other Works.- A. Continuum Descriptions of Ferromagnetic Deformable Bodies.- B. Wave Propagation.- C. Ferrimagnetic Deformable Bodies.- Problems.- 10 Magnetohydrodynamics.- 10.1. Scope of the Chapter.- 10.2. Basic Equations of Electromagnetic Fluids.- 10.3. Magnetohydrodynamic Approximation.- 10.4. Perfect Magnetohydrodynamics.- A. Field Equations.- B. "Frozen-In" Fields.- C. Bernoulli's Equation in Magnetohydrodynamics.- D. Kelvin's Circulation Theorem in Magnetohydrodynamics.- E. Alfven Waves.- F. Generalized Hugoniot Condition.- 10.5. Incompressible Viscous Magnetohydrodynamic Flow.- A. Magnetohydrodynamic Poiseuille Flow.- B. Magnetohydrodynamic Couette Flow.- 10.6. One-Dimensional Compressible Flow.- 10.7. Shock Waves in Magnetohydrodynamics.- A. Classification of Magnetohydrodynamic Shock Waves.- B. Shock Structure.- 10.8. Magnetohydrodynamic Equilibria.- 10.9. Equilibrium of Magnetic Stars.- 10.10. Magnetohydrodynamic Stability.- A. The Energy Method.- B. Equilibrium States and Perturbations.- C. Quantities Conserved in the Perturbation.- D. Elementary Perturbations.- E. Change in the Energy Integrals.- F. Application to the Linear Pinch.- Problems.- 11 Eleetrohydrodynamics.- 11.1. Scope of the Chapter.- 11.2. Field Equations.- 11.3. Charge Relaxation.- 11.4. Stability Condition.- 11.5. Helmholtz and Bernoulli Equations.- A. Generalization of the Helmholtz Equation.- B. Vorticity Generation in a Space-Charge-Loaded Electric Field.- C. Generalization of Bernoulli's Equations.- 11.6. Equilibrium of a Free Interface.- 11.7. Effect of Free Charges at an Interface.- 11.8. Electrohydrodynamic Stability.- 11.9. Electrohydrodynamic Flow in a Circular Cylindrical Conduit.- 11.10. Electrogasdynamic Energy Converter.- Problems.- 12 Ferrofluids.- 12.1. Scope of the Chapter.- 12.2. Constitutive Equations of Ferromagnetic Fluids.- 12.3. Theory of Ferrofluids.- A. Equilibrium Constitutive Equations.- B. Nonequilibrium Constitutive Equations.- C. Balance Laws.- 12.4. Existence and Stability of a Constant Magnetization in a Moving Ferrofluid.- 12.5. Ferrohydrodynamic Approximation.- 12.6. Some General Theorems in Ferrohydrodynamics.- A. Generalization of the Helmholtz Equation.- B. Generalization of the Bernoulli Equation.- 12.7. Ferrohydrostatics.- A. Equilibrium of a Free Surface.- B. Energy Conversion.- 12.8. Ferrohydrodynamic Flow of Nonviscous Fluids.- A. Preliminary Remarks.- B. Steady Two-Dimensional Source Flow.- 12.9. Simple Shear of a Viscous Ferrofluid.- 12.10. Stagnation-Point Flow of a Viscous Ferrofluid.- 12.11. Interfacial Stability of Ferrofluids.- 12.12. Other Problems in Ferrofluids.- Problems.- 13 Memory-Dependent Electromagnetic Continua.- 13.1. Scope of the Chapter.- 13.2. Constitutive Equations.- 13.3. Thermodynamics of Materials with Continuous Memory.- 13.4. Quasi-Linear and Linear Theories.- A. Quadratic Memory Dependence.- B. Finite-Linear Theory.- C. Linear Theory.- D. Linear Isotropic Materials.- E. General Polynomial Constitutive Equations.- 13.5. Rigid Bodies.- A. Continuous Memory.- B. Polynomial Constitutive Equations.- 13.6. Dispersion and Absorption.- 13.7. A Simple Atomic Model.- 13.8. Free Motion of an Electron Under Magnetic Field.- 13.9. Electromagnetic Waves in Memory-Dependent Solids.- 13.10. Electromagnetic Waves in Isotropic Viscoelastic Materials.- 13.11. Nonlinear Atomic Models for Polarization.- 13.12. Constitutive Equations of Birefringent Viscoelastic Materials.- A. Rate-Dependent Materials.- B. Linear, Continuous Memory of Strains.- 13.13. Propagation of Waves in Birefringent Viscoelastic Materials.- 13.14. Photoviscoelasticity.- Problems.- 14 Nonlocal Electrodynamics of Elastic Solids.- 14.1. Scope of the Chapter.- 14.2. Constitutive Equations.- 14.3. Thermodynamics.- 14.4. Linear Theory.- 14.5. Material Symmetry.- 14.6. Nature of Nonlocal Moduli.- 14.7. Nonlocal Rigid Solids.- 14.8. Electromagnetic Waves.- 14.9. Point Charge.- 14.10. Rigid Magnetic Solids.- 14.11. Superconductivity.- 14.12. Piezoelectric Waves.- 14.13. Infrared Dispersion and Lattice Vibrations.- 14.14. Memory-Dependent Nonlocal Electromagnetic Elastic Continua.- 14.15. Linear Nonlocal Theory for Electromagnetic Elastic Solids.- 14.16. Natural Optical Activity.- 14.17. Anomalous Skin Effects.- Problems.- 15 Relativistic Electrodynamics of Continua.- 15.1. Scope of the Chapter.- 15.2. Space-Time, Notation.- A. Space-Time.- B. Special Relativity.- C. General Relativity.- D. Inertial Frames and Rest Frame.- E. Proper Time, Timelikeness.- F. Space and Time Decomposition.- G. Antisymmetric Tensors and Axial Four-Vectors.- 15.3. Relativistic Kinematics of Continua.- A. Motion, Strain Tensors.- B. Relativistic Rate of Strain.- C. Contravariant Convective Time Derivative.- 15.4. Covariant Formulation of Maxwell's Equations in Matter.- A. Electromagnetic Fields.- B. Integral Formulation of Maxwell's Equations.- C. Four-Vector Formulation of Maxwell's Equations.- 15.5. Relativistically Invariant Balance Laws.- 15.6. Electromagnetic Interactions with Matter.- 15.7. Thermoelastic Electromagnetic Insulators.- 15.8. Electromagnetic Fluids.- A. General Nondissipative Case.- B. Linear Electromagnetic Constitutive Equations.- C. Elementary Dissipative Processes.- D. Relativistic Perfect Magnetohydrodynamics.- 15.9. Further Problems in the Relativistic Electrodynamics of Continua.- Problems.- References.