Ebook: Mean Field Theories and Dual Variation

This text concerns continuum mechanics, electrodynamics and the mechanics of electrically polarized media, and gravity. Its accessible approach formulates theories according to the principle of least action, a concise method that makes the physical content of classical subjects intelligible to advanced undergraduates and graduate students. 1976 edition ch. 1. Duality - Sealed Variation -- Chemotaxis -- Thermal Transport -- Collapse Formation -- Mean Field Hierarchy -- Stationary State -- Localization and Symmetrization -- Rescaling -- Mass Quantization -- Blowup Rate -- Blowup in Infinite Time -- Time Relaxation -- Geometric Flow -- Toland Duality -- Exponential Nonlinearity -- Full System of Chemotaxis -- Lagrangian -- Variational Equivalence -- Spectral Equivalence -- Stability -- Gradient Systems with Duality -- Entropy Functional -- Zygmund Space -- Phenomenology -- Non-Convex Evolution -- Gradient and Skew-Gradient Systems -- Skew-Gradient Systems with Duality -- Semi-Unfolding-Minimality -- Kuhn-Tucker Duality -- Thermodynamics -- Stefan Problem -- Thermal Equilibrium -- Penrose-Fife Theory -- Non-Equilibrium -- Phase Fields -- Fix-Caginalp Equation -- Penrose-Fife Equation -- Coupled Cahn-Hilliard Equation -- Shape Memory Alloys -- Time Map -- ch. 2. Scaling - Revealing Hierarchy -- Self-Interacting Continuum -- Self-Gravitating Fluids -- Equilibrium -- Plasma Confinement -- Stable Equilibrium -- Related Problems -- Particle Kinetics -- Vortex -- Boltzmann Relation -- Ensemble -- Turbulence -- Kramers-Moyal Expansion -- Kinetic Theory -- Gauge Field -- Field Theory -- Exponential Nonlinearity Revisited -- Scaling Invariance -- Liouville-Bandle Theory -- Alexandroff-Bol's Inequality -- Pre-Scaled Analysis -- Entire Solution -- Blowup Analysis -- Higher-Dimensional Blowup -- Semilinear Parabolic Equation -- Method of Duality -- Higher-Dimensional Quantization -- Dimension Control of the Blowup Set