Ebook: New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena: The Geometry of Nonequilibrium

The basic aim of the NATO Advanced Research Workshop on "New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena: The Geometry of Nonequilibrium" was to bring together researchers from various areas of physics to review and explore new ideas regarding the organisation of systems driven far from equilibrium. Such systems are characterized by a close relationship between broken spatial and tempo­ ral symmetries. The main topics of interest included pattern formation in chemical systems, materials and convection, traveling waves in binary fluids and liquid crystals, defects and their role in the disorganisa­ tion of structures, spatio-temporal intermittency, instabilities and large-scale vortices in open flows, the mathematics of non-equilibrium systems, turbulence, and last but not least growth phenomena. Written contributions from participants have been grouped into chapters addressing these different areas. For additional clarity, the first chapter on pattern formation has been subdivided into sections. One of the main concerns was to focus on the unifying features between these diverse topics. The various scientific communities repre­ sented were encouraged to discuss and compare their approach so as to mutually benefit their respective fields. We hope that, to a large degree, these goals have been met and we thank all the participants for their efforts. The workshop was held in Cargese (Corsica, France) at the Institut d'Etudes Scientifiques from August 2nd to August 12th, 1988. We greatly thank Yves Pomeau and Daniel Walgraef who, as members of the organising committee, gave us valuable advice and encouragements.

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Content:
Front Matter....Pages i-x
Chemical Waves in Oscillatory Media....Pages 1-9
Pattern Dynamics by Interaction of Chemical Waves and Hydrodynamic Flows....Pages 11-19
Sustained Non-Equilibrium Patterns in a One-Dimensional Reaction-Diffusion Chemical System....Pages 21-23
Pattern Selection and Symmetry Competition in Materials Instabilities....Pages 25-32
Numerical Simulation of Persistent Slip Band Formation....Pages 33-36
Transitions to More Complex Patterns in Thermal Convection....Pages 37-45
Rayleigh-Benard Convection at Finite Rayleigh Number in Large Aspect Ratio Boxes....Pages 47-50
Transition between Different Symmetries in Rayleigh-Benard Convection....Pages 51-54
Non Linear Analysis of Traveling Waves in Binary Convection....Pages 55-60
Temporal Modulation of a Subcritical Bifurcation to Travelling Waves....Pages 61-64
Experiments with Travelling Waves in Electrohydrodynamic Convection....Pages 65-67
The Degenerate Amplitude Equation Near the Codimension-2 Point in Binary Fluid Convection....Pages 69-72
Travelling Waves in Axisymmetric Convection....Pages 73-75
About Confined States, Noise-Sustained Structures and Slugs....Pages 77-83
Localized Structures Generated by Subcritical Instabilities: Counterprogating Waves....Pages 85-87
From the Chaos to Quasiregular Patterns....Pages 89-93
Interfacial Instabilities and Waves in the Presence of a Transverse Electric Current....Pages 95-102
Modulated Taylor Vortex Flow....Pages 103-106
Recent Results on the Non-Linear Dynamics of Curved Premixed Flames....Pages 107-109
Patterns and Defects in Liquid Crystals....Pages 111-124
Defects and Transition to Disorder in Space-Time Patterns of Non-Linear Waves....Pages 125-135
Defect-Mediated Turbulence in Spatio-Temporal Patterns....Pages 137-144
Mean Flows and the Onset of Time-Dependence in Convection....Pages 145-157
Experiment on Pattern Evolution in the 2-D Mixing Layer....Pages 159-169
A Two Dimensional Model of Pattern Evolution in Mixing Layers....Pages 171-180
Some Statistical Properties of Defects in Complex Ginzburg-Landau Equations....Pages 181-183
Vortex Dynamics in a Coupled Map Lattice....Pages 185-192
Spatio Temporal Intermittency in Rayleigh-Benard Convection in an Annulus....Pages 193-198
Transition to Turbulence via Spatiotemporal Intermittency: Modeling and Critical Properties....Pages 199-214
Phase Turbulence, Spatiotemporal Intermittency and Coherent Structures....Pages 215-225
Properties of Quasi One-Dimensional Rayleigh Benard Convection....Pages 227-235
Probabilistic Cellular Automaton Models for a Fluid Experiment....Pages 237-239
Space-Time Chaos and Coherent Structures in the Coupled Map Lattices....Pages 241-242
Topological Defects in Vortex Streets Behind Tapered Circular Cylinders at Low Reynolds Numbers....Pages 243-250
Large-Eddy Simulation of a Three-Dimensional Mixing Layer....Pages 251-258
The Effect of Nonlinearity and Forcing on Global Modes....Pages 259-274
Mathematical Justification of Steady Ginzburg-Landau Equation Starting from Navier-Stokes....Pages 275-286
Non Linear Spatial Analysis: Application to the Study of Flows Subjected to Thermocapillary Effects....Pages 287-289
Discretizations and Jacobian in Functional Integrals....Pages 291-293
Homoclinic Bifurcations in Ordinary and Partial Differential Equations....Pages 295-303
Large-Scale Vortex Instability in Helical Convective Turbulence....Pages 305-312
Generation of Large Scale Structures in Three-Dimensional Anisotropic Incompressible Flow Lacking Parity-Invariance....Pages 313-314
A New Universal Scaling for Fully Developed Turbulence: The Distribution of Velocity Increments....Pages 315-319
Vortex Dynamics and Singularities in the 3-D Euler Equations....Pages 321-325
Directional Growth in Viscous Fingering....Pages 327-337
New Results in Dendritic Crystal Growth....Pages 339-341
Microstructural Transitions During Directional Solidification of a Binary Alloy....Pages 343-345
Nonstationary Cell Shapes in Directional Solidification....Pages 347-349
Back Matter....Pages 351-357

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Content:
Front Matter....Pages i-x
Chemical Waves in Oscillatory Media....Pages 1-9
Pattern Dynamics by Interaction of Chemical Waves and Hydrodynamic Flows....Pages 11-19
Sustained Non-Equilibrium Patterns in a One-Dimensional Reaction-Diffusion Chemical System....Pages 21-23
Pattern Selection and Symmetry Competition in Materials Instabilities....Pages 25-32
Numerical Simulation of Persistent Slip Band Formation....Pages 33-36
Transitions to More Complex Patterns in Thermal Convection....Pages 37-45
Rayleigh-Benard Convection at Finite Rayleigh Number in Large Aspect Ratio Boxes....Pages 47-50
Transition between Different Symmetries in Rayleigh-Benard Convection....Pages 51-54
Non Linear Analysis of Traveling Waves in Binary Convection....Pages 55-60
Temporal Modulation of a Subcritical Bifurcation to Travelling Waves....Pages 61-64
Experiments with Travelling Waves in Electrohydrodynamic Convection....Pages 65-67
The Degenerate Amplitude Equation Near the Codimension-2 Point in Binary Fluid Convection....Pages 69-72
Travelling Waves in Axisymmetric Convection....Pages 73-75
About Confined States, Noise-Sustained Structures and Slugs....Pages 77-83
Localized Structures Generated by Subcritical Instabilities: Counterprogating Waves....Pages 85-87
From the Chaos to Quasiregular Patterns....Pages 89-93
Interfacial Instabilities and Waves in the Presence of a Transverse Electric Current....Pages 95-102
Modulated Taylor Vortex Flow....Pages 103-106
Recent Results on the Non-Linear Dynamics of Curved Premixed Flames....Pages 107-109
Patterns and Defects in Liquid Crystals....Pages 111-124
Defects and Transition to Disorder in Space-Time Patterns of Non-Linear Waves....Pages 125-135
Defect-Mediated Turbulence in Spatio-Temporal Patterns....Pages 137-144
Mean Flows and the Onset of Time-Dependence in Convection....Pages 145-157
Experiment on Pattern Evolution in the 2-D Mixing Layer....Pages 159-169
A Two Dimensional Model of Pattern Evolution in Mixing Layers....Pages 171-180
Some Statistical Properties of Defects in Complex Ginzburg-Landau Equations....Pages 181-183
Vortex Dynamics in a Coupled Map Lattice....Pages 185-192
Spatio Temporal Intermittency in Rayleigh-Benard Convection in an Annulus....Pages 193-198
Transition to Turbulence via Spatiotemporal Intermittency: Modeling and Critical Properties....Pages 199-214
Phase Turbulence, Spatiotemporal Intermittency and Coherent Structures....Pages 215-225
Properties of Quasi One-Dimensional Rayleigh Benard Convection....Pages 227-235
Probabilistic Cellular Automaton Models for a Fluid Experiment....Pages 237-239
Space-Time Chaos and Coherent Structures in the Coupled Map Lattices....Pages 241-242
Topological Defects in Vortex Streets Behind Tapered Circular Cylinders at Low Reynolds Numbers....Pages 243-250
Large-Eddy Simulation of a Three-Dimensional Mixing Layer....Pages 251-258
The Effect of Nonlinearity and Forcing on Global Modes....Pages 259-274
Mathematical Justification of Steady Ginzburg-Landau Equation Starting from Navier-Stokes....Pages 275-286
Non Linear Spatial Analysis: Application to the Study of Flows Subjected to Thermocapillary Effects....Pages 287-289
Discretizations and Jacobian in Functional Integrals....Pages 291-293
Homoclinic Bifurcations in Ordinary and Partial Differential Equations....Pages 295-303
Large-Scale Vortex Instability in Helical Convective Turbulence....Pages 305-312
Generation of Large Scale Structures in Three-Dimensional Anisotropic Incompressible Flow Lacking Parity-Invariance....Pages 313-314
A New Universal Scaling for Fully Developed Turbulence: The Distribution of Velocity Increments....Pages 315-319
Vortex Dynamics and Singularities in the 3-D Euler Equations....Pages 321-325
Directional Growth in Viscous Fingering....Pages 327-337
New Results in Dendritic Crystal Growth....Pages 339-341
Microstructural Transitions During Directional Solidification of a Binary Alloy....Pages 343-345
Nonstationary Cell Shapes in Directional Solidification....Pages 347-349
Back Matter....Pages 351-357
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