Electrodynamics of Continua II : Fluids and Complex Media

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.- 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. Résumé 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. Alfvén 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.