Topics in Nonlinear Physics

Nonlinear Problems in Physics.- Nonlinear Problems in Physics.- The Nonlinear Field Theories in Mechanics.- 1. Thermodynamics of Homogeneous Processes.- 2. Kinematics. Changes of Frame.- 3. Force and Work, Laws of Motion.- 4. Constitutive Equations. Simple Materials.- 5. The Isotropy Group.- 6. Solids, Isotropic Materials, Fluids, Fluid Crystals.- 7. Motions with Constant Stretch History.- 8. The Stress System in Viscometric Flows of Incompressible Fluids.- 9. Dynamical Conditions in Viscometric Flows.- 10. Impossibility of Rectilinear Plow in Pipes.- 11. Elastic Materials.- 12. Non-Homogeneous Universal Solutions for Incompressible Elastic Bodies.- 13. Hyperelastic Materials.- 14. Work Theorems in Hyperelasticity.- 15. Thermomechanics. Equipresence.- 16. Thermodynamics of Simple Materials with Fading Memory.- 17. Wave Motions. Compatibility.- 18. Wave Propagation in Dissipative Materials.- to Nonequilibrium Statistical Physics.- 1. Introduction.- 2. Phenomenological Approach - Thermodynamics of Irreversible Processes.- 3. Statistical Mechanics - General Method.- 4. Boltzmann Situations.- 5. Generalized Boltzmann Situations.- 6. NonBoltzmann Situations.- 7. Irreversibility.- 8. Entropy.- 9. Concluding Remarks.- Appendix I. The General Evolution Equation and Projection Operators.- Appendix II. Nonanalytic Density Behavior of Transport Coefficients.- Interactions in a Classical Relativistic Plasma.- Preface.- 1. Introduction.- 2. Lorentz-Invariant Statistical Mechanical Formalism for a Classical Relativistlc Plasma Interacting with an Electromagnetic Field.- 3. Formal Approach to the Phenomenological Electrodynamics of Plasmas.- 4. Kinetic Approach to the Electrodynamics of Homogeneous Systems.- 5. Kinetic Approach to Phenomenological Radiation Laws for HomogeneousSystems.- Nonlinear Optics.- 1. Phenomenological Survey of Nonlinear Optical Effects.- 2. Wave Propagation in Nonlinear Media.- 3. Boundary Conditions and Coupling Between Light Waves in a Dispersive Medium.- 4. Stimulated Brillouin, Raman and Rayleigh Scattering Effects.- 5. Quantum Mechanical Calculation of Nonlinear Susceptibilities. Lamb's Theory of Coupled Laser Modes.- Lectures on Homogeneous Turbulence.- Preface.- 1. Introduction.- 2. The Description of Homogeneous Turbulence.- 3. Structure and Invariance of the Large Eddies.- 4. The Problem of Decay.- 5. The Universal Equilibrium Theory (Kolmogorov).- 6. "Burgerlence".- 7. The Structure of Turbulence.- 8. Quasianalytical Theories of Turbulence.- 9. Concluding Remarks.- Superspace and the Nature of Quantum Geometrodynamics.- Allowable History Selected out of Arena of Dynamics by Constructive Interference.- Three Dimensions, Not Four.- Superspace.- Wave Packet in Superspace and its Propagation.- "Spacetime" a Concept of Limited Validity.- The Planck Length and Gravitational Collapse.- Quantum Fluctuations in Geometry of Space.- Fluctuations Superposed on Classical Background.- Extrapolate Geometrodynamics to the Planck Scales of Distances?.- Electricity as Lines of Force Trapped in the Topology of Space.- The Energy of the Vacuum.- A Particle as a Geometrodynamical Exciton.- Problem 1. "Derivation" of "Einstein-Hamilton-Jacobi Equation".- Problem 2. Structure of Superspace.- Fixed Topology Excludes GMD Account of Particles and Fields.- Formalism of Field When Treated as "Foreign and Physical".- The Orientation Entanglement Relation or "Version".- Alternative Spin Structures in a Multiply Connected Space.- The Multisheeted Character of Superspace.- Electromagnetlsm as a Statistical Aspectof Geometry? Other Questions.- The Example of 2-Geometries.- Other Aspects of Superspace.- Tangent Vectors on Superspace and the Classical Initial Value Problem.- Problem 3. Initial Conditions.- References.