Nonlinear Phenomena at Phase Transitions and Instabilities [E-Book] / edited by T. Riste.
This NATO Advanced Study Institute, held in Geilo between March 29th and April 9th 1981, was the sixth in a series devoted to the subject of phase transitions and instabilities. The present institute was intended to provide a forum for discussion of the importance of nonlinear phenomena associated w...
Saved in:
Full text |
|
Personal Name(s): | Riste, T., editor |
Imprint: |
Boston, MA :
Springer,
1982
|
Physical Description: |
XII, 481 p. 82 illus. online resource. |
Note: |
englisch |
ISBN: |
9781468441277 |
DOI: |
10.1007/978-1-4684-4127-7 |
Series Title: |
/* Depending on the record driver, $field may either be an array with
"name" and "number" keys or a flat string containing only the series
name. We should account for both cases to maximize compatibility. */?>
NATO Advanced Study Institutes Series ;
77 |
Subject (LOC): |
- 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-Bénard 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.