PHASE TRANSITION DYNAMICS

By CHARLOTTE THOMPSON

CONTENTS PART ONE: STATICS SPIN SYSTEMS AND ?UIDS SPIN MODELS ONE-COMPONENT ?UIDS BINARY ?UID MIXTURES APPENDIX 1A CORRELATIONS WITH THE STRESS TENSOR REFERENCES CRITICAL PHENOMENA AND SCALING GENERAL ASPECTS CRITICAL PHENOMENA IN ONE-COMPONENT ?UIDS CRITICAL PHENOMENA IN BINARY ?UID MIXTURES 4HE NEAR THE SUPER?UID TRANSITION APPENDIX 2A CALCULATION IN NON-AZEOTROPIC CASES MEAN ?ELD THEORIES LANDAU THEORY TRICRITICAL BEHAVIOR BRAGG–WILLIAMS APPROXIMATION VAN DER WAALS THEORY MEAN ?ELD THEORIES FOR POLYMERS AND GELS APPENDIX 3A FINITE-STRAIN THEORY ADVANCED THEORIES IN STATICS GINZBURG–LANDAU–WILSON FREE ENERGY MAPPING ONTO ?UIDS STATIC RENORMALIZATION GROUP THEORY TWO-PHASE COEXISTENCE AND SURFACE TENSION VORTICES IN SYSTEMS WITH A COMPLEX ORDER PARAMETER APPENDIX 4A CALCULATION OF THE CRITICAL EXPONENT ? APPENDIX 4B RANDOM PHASE APPROXIMATION FOR POLYMERS APPENDIX 4C RENORMALIZATION GROUP EQUATIONS FOR N-COMPONENT SYSTEMS APPENDIX 4D CALCULATION OF A FREE-ENERGY CORRECTION APPENDIX 4E CALCULATION OF THE STRUCTURE FACTORS APPENDIX 4F SPECI?C HEAT IN TWO-PHASE COEXISTENCE PART TWO: DYNAMIC MODELS AND DYNAMICS IN ?UIDS AND POLYMERS DYNAMIC MODELS LANGEVIN EQUATION FOR A SINGLE PARTICLE NONLINEAR LANGEVIN EQUATIONS WITH MANY VARIABLES SIMPLE TIME-DEPENDENT GINZBURG–LANDAU MODELS LINEAR RESPONSE APPENDIX 5A DERIVATION OF THE FOKKER–PLANCK EQUATION APPENDIX 5B PROJECTION OPERATOR METHOD APPENDIX 5C TIME REVERSAL SYMMETRY IN EQUILIBRIUM TIME-CORRELATION FUNCTIONS APPENDIX 5D RENORMALIZATION GROUP CALCULATION IN PURELY DISSIPATIVE DYNAMICS APPENDIX 5E MICROSCOPIC EXPRESSIONS FOR THE STRESS TENSOR AND ENERGY CURRENT DYNAMICS IN ?UIDS HYDRODYNAMIC INTERACTION IN NEAR-CRITICAL ?UIDS CRITICAL DYNAMICS IN ONE-COMPONENT ?UIDS PISTON EFFECT SUPERCRITICAL ?UID HYDRODYNAMICS CRITICAL DYNAMICS IN BINARY ?UID MIXTURES CRITICAL DYNAMICS NEAR THE SUPER?UID TRANSITION 4HE NEAR THE SUPER?UID TRANSITION IN HEAT ?OW APPENDIX 6A DERIVATION OF THE REVERSIBLE STRESS TENSOR APPENDIX 6B CALCULATION IN THE MODE COUPLING THEORY APPENDIX 6C STEADY-STATE DISTRIBUTION IN HEAT ?OW APPENDIX 6D CALCULATION OF THE PISTON EFFECT DYNAMICS IN POLYMERS AND GELS VISCOELASTIC BINARY MIXTURES DYNAMICS IN GELS HETEROGENEITIES IN THE NETWORK STRUCTURE APPENDIX 7A SINGLE-CHAIN DYNAMICS IN A POLYMER MELT APPENDIX 7B TWO-?UID DYNAMICS OF POLYMER BLENDS APPENDIX 7C CALCULATION OF THE TIME-CORRELATION FUNCTION APPENDIX 7D STRESS TENSOR IN POLYMER SOLUTIONS APPENDIX 7E ELIMINATION OF THE TRANSVERSE DEGREES OF FREEDOM APPENDIX 7F CALCULATION FOR WEAKLY CHARGED POLYMERS APPENDIX 7G SURFACE MODES OF A UNIAXIAL GEL PART THREE: DYNAMICS OF PHASE CHANGES PHASE ORDERING AND DEFECT DYNAMICS PHASE ORDERING IN NONCONSERVED SYSTEMS INTERFACE DYNAMICS IN NONCONSERVED SYSTEMS SPINODAL DECOMPOSITION IN CONSERVED SYSTEMS INTERFACE DYNAMICS IN CONSERVED SYSTEMS HYDRODYNAMIC INTERACTION IN ?UIDS SPINODAL DECOMPOSITION AND BOILING IN ONE-COMPONENT ?UIDS ADIABATIC SPINODAL DECOMPOSITION PERIODIC SPINODAL DECOMPOSITION VISCOELASTIC SPINODAL DECOMPOSITION IN POLYMERS AND GELS VORTEX MOTION AND MUTUAL FRICTION APPENDIX 8A GENERALIZATIONS AND VARIATIONS OF THE POROD LAW APPENDIX 8B THE PAIR CORRELATION FUNCTION IN THE NONCONSERVED CASE APPENDIX 8C THE KAWASAKI–YALABIK–GUNTON THEORY APPLIED TO PERIODIC QUENCH APPENDIX 8D THE STRUCTURE FACTOR TAIL FOR N = APPENDIX 8E DIFFERENTIAL GEOMETRY APPENDIX 8F CALCULATION IN THE LANGER–BAR-ON–MILLER THEORY APPENDIX 8G THE STEFAN PROBLEM FOR A SPHERE AND A CIRCLE APPENDIX 8H THE VELOCITY AND PRESSURE CLOSE TO THE INTERFACE APPENDIX 8I CALCULATION OF VORTEX MOTION NUCLEATION DROPLET EVOLUTION EQUATION BIRTH OF DROPLETS GROWTH OF DROPLETS NUCLEATION IN ONE-COMPONENT ?UIDS NUCLEATION AT VERY LOW TEMPERATURES VISCOELASTIC NUCLEATION IN POLYMERS INTRINSIC CRITICAL VELOCITY IN SUPER?UID HELIUM APPENDIX 9A RELAXATION TO THE STEADY DROPLET DISTRIBUTION APPENDIX 9B THE NUCLEATION RATE NEAR THE CRITICAL POINT APPENDIX 9C THE ASYMPTOTIC SCALING FUNCTIONS IN DROPLET GROWTH APPENDIX 9D MOVING DOMAINS IN THE DISSIPATIVE REGIME APPENDIX 9E PISTON EFFECT IN THE PRESENCE OF GROWING DROPLETS APPENDIX 9F CALCULATION OF THE QUANTUM DECAY RATE 10 PHASE TRANSITION DYNAMICS IN SOLIDS PHASE SEPARATION IN ISOTROPIC ELASTIC THEORY PHASE SEPARATION IN CUBIC SOLIDS ORDER–DISORDER AND IMPROPER MARTENSITIC PHASE TRANSITIONS PROPER MARTENSITIC TRANSITIONS MACROSCOPIC INSTABILITY SURFACE INSTABILITY APPENDIX 10A ELIMINATION OF THE ELASTIC ?ELD APPENDIX 10B ELASTIC DEFORMATION AROUND AN ELLIPSOIDAL DOMAIN APPENDIX 10C ANALYSIS OF THE JAHN–TELLER COUPLING APPENDIX 10D NONLOCAL INTERACTION IN 2D ELASTIC THEORY APPENDIX 10E MACROSCOPIC MODES OF A SPHERE APPENDIX 10F SURFACE MODES ON A PLANAR SURFACE 11 PHASE TRANSITIONS OF ?UIDS IN SHEAR ?OW NEAR-CRITICAL ?UIDS IN SHEAR SHEAR-INDUCED PHASE SEPARATION COMPLEX ?UIDS AT PHASE TRANSITIONS IN SHEAR ?OW SUPERCOOLED LIQUIDS IN SHEAR ?OW APPENDIX 11 A CORRELATION FUNCTIONS IN VELOCITY GRADIENT