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

ISBN-13: 9781468474817 / Angielski / Miękka / 2012 / 357 str.

Pierre Coullet; Patrick Huerre

Opis

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.

Spis treści

Pattern Formation.- Chemical Waves.- Chemical Waves in Oscillatory Media.- Pattern Dynamics by Interaction of Chemical Waves and Hydrodynamic Flows.- Sustained Non-Equilibrium Patterns in a One-Dimensional Reaction-Diffusion Chemical System.- Materials Instabilities.- Pattern Selection and Symmetry Competition in Materials Instabilities.- Numerical Simulation of Persistent Slip Band Formation.- Rayleigh-Benard Convection.- Transitions to More Complex Patterns in Thermal Convection.- Rayleigh-Benard Convection at Finite Rayleigh Number in Large Aspect Ratio Boxes.- Transition Between Different Symmetries in Rayleigh-Benard Convection.- Traveling Waves.- Nonlinear Analysis of Traveling Waves in Binary Convection.- Temporal Modulation of a Subcritical Bifurcation to Travelling Waves.- Experiments with Travelling Waves in Electrohydrodynamic Convection.- The Degenerate Amplitude Equation Near the Codimension-2 Point in Binary Fluid Convection.- Travelling Waves in Axisymetric Convection.- About Confined States, Noise-Sustained Structures and Slugs.- Localized Structures Generated by Subcritical Instabilities: Counterpropagating Waves.- Other Areas of Interest.- From the Chaos to Quasiregular Patterns.- Interfacial Instabilities and Waves in the Presence of a Transverse Electric Current.- Modulated Taylor Vortex Flow.- Recent Results on the Non-Linear Dynamics of Curved Premixed Flames.- Defects and Spatio-Temporal Complexity.- Patterns and Defects in Liquid Crystals.- Defects and Transition to Disorder in Space-Time Patterns of Non-Linear Waves.- Defect-Mediated Turbulence in Spatio-Temporal Patterns.- Mean Flows and the Onset of Time-Dependence in Convection.- Experiment on Pattern Evolution in the 2-D Mixing Layer.- A Two Dimensional Model of Pattern Evolution in Mixing Layers.- Some Statistical Properties of Defects in Complex Ginzburg-Landau Equations.- Vortex Dynamics in a Coupled Map Lattice.- Spatio-Temporal Intermittency.- Spatio Temporal Intermittency in Rayleigh-Benard Convection in an Annulus.- Transition to Turbulence Via Spatiotemporal Intermittency: Modeling and Critical Properties.- Phase Turbulence, Spatiotemporal Intermittency and Coherent Structures.- Properties of Quasi One-Dimensional Rayleigh Benard Convection.- Probabilistic Cellular Automaton Models for a Fluid Experiment.- Space-Time Chaos and Coherent Structures in the Coupled Map Lattices.- Spatially-Developing Non-Equilibrium Systems.- Topological Defects in Vortex Streets Behind Tapered Circular Cylinders at Low Reynolds Numbers.- Large-Eddy Simulation of a Three-Dimensional Mixing Layer.- The Effect of Nonlinearity and Forcing on Global Modes.- Mathematics of Non Equilibrium.- Mathematical Justification of Steady Ginzburg-Landau Equation Starting from Navier-Stokes.- Non Linear Spatial Analysis: Application to the Study of Flows Subjected to Thermocapillary Effects.- Discretizations and Jacobian in Functional Integrals.- Homoclinic Bifurcations in Ordinary and Partial Differential Equations.- Turbulence.- Large-Scale Vortex Instability in Helical Convective Turbulence.- Generation of Large Scale Structures in Three-Dimensional Anisotropie Incompressible Flow Lacking Parity-Invariance.- A New Universal Scaling for Fully Developed Turbulence: The Distribution of Velocity Increments.- Vortex Dynamics and Singularities in the 3-D Euler Equations.- Growth Phenomena.- Directional Growth in Viscous Fingering.- New Results in Dendritic Crystal Growth.- Microstructural Transitions During Directional Solidification of a Binary Alloy.- Nonstationary Cell Shapes in Directional Solidification.