Nonlinear Phenomena at Phase Transitions and Instabilities edited by Tormod 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...

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Bibliographic Details
Corporate Author:	SpringerLink (Online service)
Other Authors:	Riste, Tormod (Editor)
Format:	eBook
Language:	English
Published:	New York, NY : Springer US : Imprint: Springer, 1982.
Edition:	1st ed. 1982.
Series:	Nato Science Series B:, Physics, 77 Springer eBook Collection.
Subjects:	Solid state physics. Spectroscopy. Microscopy. Electronic resources (E-books)
Online Access:	Click to view e-book
Holy Cross Note:	Loaded electronically. Electronic access restricted to members of the Holy Cross Community.

Table of Contents:

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.

Nonlinear Phenomena at Phase Transitions and Instabilities edited by Tormod Riste.

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