Electrodynamics of Continua II

This is the second volume of a two-volume set presenting a unified approach to the electrodynamics of continua, based on the principles of contemporary continuum of physics. The first volume was devoted mainly to the development of the theory and applications to deformable solid media. This volume extends the developments of the first volume to richer and newer grounds. It contains discussions on fluid media, magnetohydrodynamics, eletrohydrodynamics and media with more complicated structures. With the discussion, in the last two chapters, of memory-dependent materials and non-local E-M theory, the authors account for the nonlocal effects arising from motions and fields of material points at past times and at spatially distant points. This discussion is included here to stimulate further research in these important fields, which are presently in development stages. The second volume is self-contained and can be studied without the help of volume I. A section summarizing the constitutive equations and the underlying physical ideas, which were presented in more detail in the first volume, is included. This volume may be used as a basis for several graduate courses in engineering schools, applied mathematics and physics departments. It also contains fresh ideas and will stimulate further research in the directions the authors outline.

(Volume II). - 9 Elastic Ferromagnets. - 9. 0. An Overview of Basic Equations. - 9. 1. Scope of the Chapter. - 9. 2. Model of Interactions. - 9. 3. Balance Equations. - 9. 4. Constitutive Theory. - 9. 5. Résumé of Basic Equations. - 9. 6. Coupled Magnetoelastic Waves in Ferromagnets. - 9. 7. Applications of the Magnon-Phonon Coupling. - 9. 8. Other Works. - 10 Magnetohydrodynamics. - 10. 1. Scope of the Chapter. - 10. 2. Basic Equations of Electromagnetic Fluids. - 10. 3. Magnetohydrodynamic Approximation. - 10. 4. Perfect Magnetohydrodynamics. - 10. 5. Incompressible Viscous Magnetohydrodynamic Flow. - 10. 6. One-Dimensional Compressible Flow. - 10. 7. Shock Waves in Magnetohydrodynamics. - 10. 8. Magnetohydrodynamic Equilibria. - 10. 9. Equilibrium of Magnetic Stars. - 10. 10. Magnetohydrodynamic Stability. - 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. - 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. - 12 Ferrofluids. - 12. 1. Scope of the Chapter. - 12. 2. Constitutive Equations of Ferromagnetic Fluids. - 12. 3. Theory of Ferrofluids. - 12. 4. Existence and Stability of a Constant Magnetization in a Moving Ferrofluid. - 12. 5. Ferrohydrodynamic Approximation. - 12. 6. Some General Theorems in Ferrohydrodynamics. - 12. 7. Ferrohydrostatics. - 12. 8. Ferrohydrodynamic Flow of Nonviscous Fluids. - 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. - 13 Memory-Dependent ElectromagneticContinua. - 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. - 13. 5. Rigid Bodies. - 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. - 13. 13. Propagation of Waves in Birefringent Viscoelastic Materials. - 13. 14. Photoviscoelasticity. - 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. - 15 Relativistic Electrodynamics of Continua. - 15. 1. Scope of the Chapter. - 15. 2. Space-Time, Notation. - 15. 3. Relativistic Kinematics of Continua. - 15. 4. Covariant Formulation of Maxwell s Equations in Matter. - 15. 5. Relativistically Invariant Balance Laws. - 15. 6. Electromagnetic Interactions with Matter. - 15. 7. Thermoelastic Electromagnetic Insulators. - 15. 8. Electromagnetic Fluids. - 15. 9. Further Problems in the Relativistic Electrodynamics of Continua. - References.