Nonlinear Phenomena at Phase Transitions and Instabilities

Anharmonic Properties near Structural Phase Transitions.- Intention and Summary.- I. From early Experiments to the New View.- a) Classical and Nonclassical Behaviour.- b) Central-Peak Research.- c) Computer Simulation, and Anharmonic Theory.- d) The New View.- II. Recent Consolidating Results.- a) Anharmonicity at TC in SrTiO3.- b) Displacive-Order-Disorder Crossover in Ferroelectric Oxides.- c) Evidence for Precursor Order in RbCaF3 and KMnF3.- d) Dynamic Components in SrTiO3.- e) Critical Dyamics in KMnF3.- III. Incommensurate Systems.- The Theory of Structural Phase Transitions: Universality and Quasi-Elastic Scattering Phenomena.- Preamble.- 1. Background.- 1.1 A Simple Model and the Basic Observables.- 1.2 General Theory of Scaling Susceptibilities.- 2. Novel Universal Quantities.- 2.1 Adiabatic and Isothermal Susceptibilities.- 2.2 The Onset of Superlattice Scattering.- 3. Universal Patterns of Short Range Order.- 3.1 Introduction.- 3.2 General Theory of the Block Coordinate p.d.f.- 3.3 One Dimension: Exact Results.- 3.4 Two and Three Dimensions: Approximate Results.- 3.5 Discussion.- 3.6 Summary and Prospects.- Dynamic Correlations in the Ordered Phase of Perovskites.- I. Introduction.- II. Model.- III. Dynamic Correlations below TC.- IV. Results and Conclusions.- Phason Light Scattering in BaMnF4.- Nonlinear Excitations in Some Anharmonic Lattice Models.- 1) Introduction.- 2) Nonlinear Excitations in a model Ferroelectric gl Static Solutions 33 Stationary Solutions.- Stability of Static Periodons.- The Periodon-Phonon Coupling.- 3) Some Remarks on Toda-Lattice.- Solitons in The One-Dimensional Planar Ferromagnet CsNiF3.- 1. Abstract.- 2. Introduction.- 3. Experiment.- 4. Data evalutation.- On The Possibility to Create Nonthermal Solitons in a One-Dimensional Magnetic Sine Gordon System.- 1. Introduction.- 2. The Model.- 3. Results.- 4. Discussion.- Transport and Fluctuations in Linear Arrays of Multistable Systems.- I. Classification of Multistable Systems.- II. Open Systems.- Thermal Instabilities in Electrical Conductors.- Chains of Phase Couples and Externally Synchronized Oscillators.- III. Transport in The Driven Sine-Gordon Chain.- Propagation Velocity of Driven Kinks.- The Steady State Density of Kinks.- IV. Fluctuations in The Sine-Gordon Chain.- The Kink Counting Approach.- The Hydrodynamic Approach.- Universality.- Appendix: The Simplicity of Transport in the Smoluchowski Equation.- Non-Linear Thermal Convection.- 1. Introduction.- 2. The Basic Equations and Boundary Conditions.- 3. The Linear Theory.- a. The Horizontally Unbounded Layer.- b. The Effect of Lateral Walls.- 4. Non-Linear Convection.- 4.1 Perturbation Approach.- 4.2 Numerical Approaches.- 4.3 Comparison with Experiments.- 4.4 The mean field theory.- 5. Convection in a Small Prandtl Number Fluid.- Nematic Instability Induced by An Elliptical Shear.- I. Experimental Apparatus.- II. Instability Mechanism.- III. Modification of The Convective Structure on Increasing the Control Parameter N.- IV. The Time Evolution of The Convective Structure at Fixed N.- Instabilities and Fluctuations.- 1. Role of Fluctuations.- 2. Description of Random Processes.- 3. Phase Transitions.- 4. The Laser Instability.- 5. The Transition to Chaos in Optics.- 6. Instability Transients.- 7. Fluctuations in Hydrodynamic Instabilities.- Steady States, Limit Cycles and The Onset of Turbulence. A Few Model Calculations and Exercises.- 1. Introduction: From Steady States to Chaos in The Time Evolution of Non-Linear Systems.- 1.1 Background.- 1.2 Landau Picture of The Onset of (Quasiperiodic Gaussian) Turbulence.- 1.3 Lorenz Model, Discrete Maps and Related Matters.- 2. Steady States, Limit Cycles and Phase Transition picture.- 2.1 Steady States and Their Stability.- 2.2 Phase Transition Picture: An Illustration of Phase Coexistence. Tricritical points, Triple Points, Etc. in Convective Instability.- 2.3 Limit Cycles and Their Stability.- 3. Strange Attractors.- 3.1 Fractal Dimension: An Illustration.- 3.2 Lyapunov Characteristic Exponents.- 3.3 Exercise: Lorenz Model.- 3.4 Exercise: Two-Component Lorenz Model.- 4. Discrete Maps: Feigenbaum's Cascade and Pomeau's Intermittencies.- 4.1 Period-Doubling Cascades.- 4.2 Pomeau's Intermittencies.- The Physical Mechanism of Oscillatory and Finite Amplitude Instabilities in Systems with Competing Effects.- I. Introduction.- II. Oscillatory Instability.- III. Finite Amplitude Instability.- IV. Concluding Remarks.- Investigation of Fluctuations and Oscillatory States in Rayleigh-Benard Systems by Neutron Scattering.- 1. Introduction.- 2. Observations of Oscillatory States in a Homeotropic Nematic Sample.- A Rayleigh-Benard Experiment: Helium in a Small Box.- I. The Experiment.- II. Basics of Convection: Busse Theory.- III. The Wavenumber Selection: Effect of Side Walls and The Dynamics of a 3 Rolls to 2 rolls Transition.- IV. The Oscillatory Instability.- V. Two Oscillators: Entrainment and Locking.- VI. Routes to Turbulent Convection.- Period Doubling Bifurcation Route to Chaos.- Space-Time Symmetry in Doubly Periodic Circular Couette Flow.- 1. Introduction.- 2. Review of Experimental Results.- 3. Theory.- The Structure and Dynamics of Non-Stationary Taylor-Vortex Flow.- Pattern Formation During Crystal Growth: Theory.- 1. Introduction.- 2. Dendrites.- 3. Directional Solidification.- 4. Eutectics.- Electrothermal Instabilities at Magnetic Critical Points.- Abstract.- 1. Electronic Transport Coefficients at TC.- 2. Differential Negative Resistivity Conditions near TC.- 3. Continuously Forced Ballast Resistor.- Instabilities During Crystal Growth: Experiments.- 1. Introduction.- 2. Normal Growth and Lateral Growth.- The Nonfaceted - Faceted Transition.- The Solid-Vapor Interface.- The Solid-Solution Interface.- The Solid-Melt Interface.- 3. Sharp Interface-Diffuse Interface.- Light Scattering at the Solid Liquid Interface.- Quasi Eleastic Light Scattering Technique.- Light Scattering at the Ice-Water Interface.- Intensity Hysteresis and Dynamics.- Transient Phenomena.- Light Scattering at the Solid-Liquid Interfaces of D2O and Salol.- 4. Growth Into Supercooled Melt.- Growth of Dendrites.- 5. The Dynamics of Freezing and Melting.- Periodic Fluctuations at The Solid Liquid Interface of Salol.- 1. Introduction.- 2. Experimental.- 3. Observations.- 4. Oscillatory Scattering.- 5. Diffusive Scattering.- On The Dynamics of Epitaxial Phase Transformations.- 1. Surface Molecular Dynamics (SMD).- 2. Surface-Liquid Systems.- The Pinning of a Domain Wall by Weakened Bonds in Two Dimensions.- 1. Introduction.- 2. Solution of The Model.- 3. Discussion.- Melting in Two Dimensions.- I. Introduction.- Theoretical Background.- II. Dislocation Mediated Melting.- Dislocation Mediated Melting at a Smooth Substrate.- Periodic Substrate Potentials.- III. Fluid Phases.- Experiments and Computer Simulations.- IV. Doslocation Theory of Liquid Crystal Films.- Molecular Dynamics Study of 2-D Melting: Long Range Potentials.- 1. Introduction.- 2. Molecular Dynamics (MD).- 3. Results.- a) Coulomb System.- b) Dipolar System.- Experimental Studies of Two Dimensional Melting.- 1. Introduction.- 2. Crytalline Order and Melting in 2D.- 3. Exoerimental 2D Phase Diagrams.- 4. Diffraction Lineshapes in the 2D Solid Phase.- 5. Incommensurate Melting.- 6. Commensurate Melting.- 7. Conclusion.- An Unusual Polymorphism in the 2D Melting: The Smectic F and I Phases.- 1. Structure of the SG Phase.- 2. Structure of the 2d SF and SI Phase.- 3. Analysis of the 2d Order.- 4. The SI and SF Phases and the 2d Melting Theory.- Participants.