Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems

ISBN-13: 9781468457957 / Angielski / Miękka / 2012 / 569 str.

F. H. Busse; L. Kramer

Opis

This volume contains papers contributed to the NATO Advanced Research Workshop "Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems" held in Streitberg, Fed. Rep. Germany, Sept. 24 through 30, 1989. The purpose of the rather long title has been to focus attention on a particularly fruitful direction of research within the broad field covered by terms like Nonlinear Dynamics or Non-Equilibrium Systems. After physicists have been occupied for several decades mainly with the microscopic structure of matter, recent years have witnessed a resurgence of interest in macroscopic patterns and dynamics. Research on these latter phenomena has not been dormant, of course, since fluid dynamicists interested in the origin of turbulence, meteorologists studying weather patterns and numerous other scientists have continued to advance the understanding of the structures relevant to their disciplines. The recent progress in the dynamics of nonl inear systems wi th few degrees of freedom and the discovery of universal laws such as the Feigenbaum scaling of period-doubling cascades has given rise to new hopes for the understanding of common principles underlying the spontaneous formation of structures in extended continuous systems.

Spis treści

Nonlinear Dynamics in Simple Fluids.- Spatial and Dynamical Properties of 1-D Rayleigh-Bénard Convection.- Dimensions and Lyapunov Spectra from Measured Time Series of Taylor-Couette Flow.- Dynamical Behaviour of Taylor Vortices with Superimposed Axial Flow.- Externally Modulated Hydrodynamic Systems.- Sideband Instability of Waves With Periodic Boundary Conditions.- Transition to Chaos in Non-Parallel Two-Dimensional Flow in a Channel.- Drifting Convection Rolls Induced by Spatial Modulation.- Convection in a Rotating Cylindrical Annulus with Rigid Boundaries.- Binary Fluid Convection.- Complex Demodulation Techniques for Experiments on Traveling-Wave Convection.- Convection in Binary Liquids with Soret Effect: What we can learn from Laser Doppler Velocimetry Experiments.- Boundary Layer Analysis of Traveling Waves in Binary Convection.- Nonlinear Convection in Binary Mixtures.- Structure and Dynamics of Nonlinear Convective States in Binary Fluid Mixtures.- Onset of Soret and Dufour Driven Convection in Binary Fluid Mixtures.- Experimental Study of Binary Fluid Convection in a Quasi 1-Dimensional Cell without Reflections from the Sidewalls.- Two-Phase Flows.- Interfacial Oscillations and Solitons Driven by the Marangoni Effect.- Couette Flows, Rollers, Emulsions, Tall Taylor Cells, Phase Separation and Inversion, and a Chaotic Bubble in Taylor-Couette Flow of Two Immiscible Liquids.- Traveling Waves in a Partly Solidified Mixture.- Localized Structures and Defects.- Phase-Mean Drift Equation for Convection Patterns in Large Aspect Ratio Containers.- Modulated Traveling Waves in Nonequilibrium Systems.- Confined States in Phase Dynamics.- Small-Scale Excitations in Large Systems.- Bound States of Interacting Localized Structures.- Nonlinear Dynamics of Particle-Like States of Multidimensional Fields.- Caustics of Nonlinear Waves and Related Questions.- Phase Dynamics and Propagation of Dislocations.- Nonlinear Dynamics in Reacting Fluids, Nematics, and Solids.- Spirals in Excitable Chemical Media: From Archimedian to Non-Archimedian Geometry.- Chemical Pattern Dynamics by Chemically Induced Hydrodynamic Flow.- Stability of Travelling Waves in the Belousov-Zhabotinskii Reaction.- The Formation and Propagation of Fronts at the Electric Field Induced Bend Fredericksz Transition.- The Dynamics of Transient Structures in the Fredericksz Transition.- Sideband Instability of Modulated Traveling Wave Convection.- Spatial Instabilities and Defect Ordering in Solids.- Mutual Interplay Between the Break-up of Spatial Order and the Onset of Low-Dimensional Temporal Chaos in an Exemplary Semiconductor System.- Electroconvection in a Freely Suspended Film of Smectic A Liquid Crystal.- Symmetry, Resonance, and Chaos.- Symmetry Breaking in Nonlinear Convection.- Chaos and the Effect of Noise for the Double Hopf Bifurcation with 2:1 Resonance.- Codimension 2 Bifurcation in Binary Convection With Square Symmetry.- Dynamics of Slowly Varying Wavetrains in Finite Geometry.- Kinks and Solitons in the Generalized Ginzburg-Landau Equation.- Onset of Chaos in the Generalized Ginzburg-Landau Equation.- Turbulence and Linear Stability in a Discrete Ginzburg-Landau Model.- On the Stability of Parametrically Excited Standing Waves.- Nonlinear Problems of Crystal Growth and Front Propagation.- Directional Solidification of Transparent Eutectic Alloys.- Directional Solidification of a Faceted Crystal.- Routes to Cell Formation and Hidden Ramps in Directional Solidification.- Influence of an External Periodic Flow on Dendritic Crystal Growth.- Pattern Growth: From Smooth Interfaces to Fractal Structures.- The Printer’s Instability: The Dynamical Regimes of Directional Viscous Fingering.- Front Propagation into Unstable States: Some Recent Developments and Surprises.- Structures in Turbulent Flows.- Collapsing Solutions in the 3-D Euler Equations.- Large Magnetic Reynolds Number Dynamo Action in Steady Spatially Periodic Flows.- On Spatial Structure of Kolmogorov Spectra of Weak Turbulence.- Spatiotemporal Intermittency.- On the Scale-Invariant Theory of Developed Hydrodynamic Turbulence Kolmogorov Type.- Contributors.