Ebook: Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems

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.

---

---

Content:
Front Matter....Pages i-xii
Spatial and Dynamical Properties of 1 — D Rayleigh-Benard Convection....Pages 1-6
Dimensions and Lyapunov Spectra From Measured Time Series of Taylor-Couette Flow....Pages 7-19
Dynamical Behaviour of Taylor Vortices with Superimposed Axial Flow....Pages 21-29
Externally Modulated Hydrodynamic Systems....Pages 31-43
Sideband Instability of Waves with Periodic Boundary Conditions....Pages 45-50
Transition to Chaos in Non-Parallel Two-Dimensional Flow in a Channel....Pages 51-60
Drifting Convection Rolls Induced by Spatial Modulation....Pages 61-65
Convection in a Rotating Cylindrical Annulus with Rigid Boundaries....Pages 67-72
Complex Demodulation Techniques for Experiments on Traveling-Wave Convection....Pages 73-91
Convection in Binary Liquids with Soret Effect: What We Can Learn from Laser Doppler Velocimetry Experiments....Pages 93-100
Boundary Layer Analysis of Traveling Waves in Binary Convection....Pages 101-107
Nonlinear Convection in Binary Mixtures....Pages 109-129
Structure and Dynamics of Nonlinear Convective States in Binary Fluid Mixtures....Pages 131-148
Onset of Soret and Dufour Driven Convection in Binary Fluid Mixtures....Pages 149-153
Experimental Study of Binary Fluid Convection in a Quasi 1-Dimensional Cell without Reflections from the Sidewalls....Pages 155-158
Interfacial Oscillations and Solitons Driven by the Marangoni Effect....Pages 159-167
Couette Flows, Rollers, Emulsions, Tall Taylor Cells, Phase Separation and Inversion, and a Chaotic Bubble in Taylor-Couette Flow of Two Immiscible Liquids....Pages 169-189
Traveling Waves in a Partly Solidified Mixture....Pages 191-196
Phase-Mean Drift Equation for Convection Patterns in Large Aspect Ratio Containers....Pages 197-209
Modulated Traveling Waves in Nonequilibrium Systems....Pages 211-220
Confined States in Phase Dynamics....Pages 221-229
Small-Scale Excitations in Large Systems....Pages 231-236
Bound States of Interacting Localized Structures....Pages 237-243
Nonlinear Dynamics of Particle-Like States of Multidimensional Fields....Pages 245-259
Caustics of Nonlinear Waves and Related Questions....Pages 261-269
Phase Dynamics and Propagation of Dislocations....Pages 271-283
Spirals in Excitable Chemical Media: From Archimedian to Non-Archimedian Geometry....Pages 285-292
Chemical Pattern Dynamics by Chemically Induced Hydrodynamic Flow....Pages 293-297
Stability of Travelling Waves in the Belousov-Zhabotinskii Reaction....Pages 299-311
The Formation and Propagation of Fronts at the Electric Field Induced Bend Freedericksz Transition....Pages 313-318
The Dynamics of Transient Structures in the Fredericksz Transition....Pages 319-325
Sideband Instability of Modulated Traveling Wave Convection....Pages 327-332
Spatial Instabilities and Defect Ordering in Solids....Pages 333-342
Mutual Interplay between the Break-Up of Spatial Order and the Onset of Low-Dimensional Temporal Chaos in an Exemplary Semiconductor System....Pages 343-350
Electroconvection in a Freely Suspended Film of Smectic a Liquid Crystal....Pages 351-357
Symmetry Breaking in Nonlinear Convection....Pages 359-374
Chaos and the Effect of Noise for the Double Hopf Bifurcation with 2:1 Resonance....Pages 375-384
Codimension 2 Bifurcation in Binary Convection with Square Symmetry....Pages 385-398
Dynamics of Slowly Varying Wavetrains in Finite Geometry....Pages 399-410
Kinks and Solitons in the Generalized Ginzburg-Landau Equation....Pages 411-417
Onset of Chaos in the Generalized Ginzburg-Landau Equation....Pages 419-424
Turbulence and Linear Stability in a Discrete Ginzburg-Landau Model....Pages 425-435
On the Stability of Parametrically Excited Standing Waves....Pages 437-443
Directional Solidification of Transparent Eutectic Alloys....Pages 445-450
Directional Solidification of a Faceted Crystal....Pages 451-456
Routes to Cell Formation and Hidden Ramps in Directional Solidification....Pages 457-473
Influence of an External Periodic Flow on Dendritic Crystal Growth....Pages 475-479
Pattern Growth: From Smooth Interfaces to Fractal Structures....Pages 481-486
The Printer’s Instability: The Dynamical Regimes of Directional Viscous Fingering....Pages 487-497
Front Propagation into Unstable States: Some Recent Developments and Surprises....Pages 499-508
Collapsing Solutions in the 3-D Euler Equations....Pages 509-513
Large Magnetic Reynolds Number Dynamo Action in Steady Spatially Periodic Flows....Pages 515-539
On Spatial Structure of Kolmogorov Spectra of Weak Turbulence....Pages 541-544
Spatiotemporal Intermittency....Pages 545-552
On the Scale-Invariant Theory of Developed Hydrodynamic Turbulence Kolmogorov Type....Pages 553-562
Back Matter....Pages 563-569

---

Content:
Front Matter....Pages i-xii
Spatial and Dynamical Properties of 1 — D Rayleigh-Benard Convection....Pages 1-6
Dimensions and Lyapunov Spectra From Measured Time Series of Taylor-Couette Flow....Pages 7-19
Dynamical Behaviour of Taylor Vortices with Superimposed Axial Flow....Pages 21-29
Externally Modulated Hydrodynamic Systems....Pages 31-43
Sideband Instability of Waves with Periodic Boundary Conditions....Pages 45-50
Transition to Chaos in Non-Parallel Two-Dimensional Flow in a Channel....Pages 51-60
Drifting Convection Rolls Induced by Spatial Modulation....Pages 61-65
Convection in a Rotating Cylindrical Annulus with Rigid Boundaries....Pages 67-72
Complex Demodulation Techniques for Experiments on Traveling-Wave Convection....Pages 73-91
Convection in Binary Liquids with Soret Effect: What We Can Learn from Laser Doppler Velocimetry Experiments....Pages 93-100
Boundary Layer Analysis of Traveling Waves in Binary Convection....Pages 101-107
Nonlinear Convection in Binary Mixtures....Pages 109-129
Structure and Dynamics of Nonlinear Convective States in Binary Fluid Mixtures....Pages 131-148
Onset of Soret and Dufour Driven Convection in Binary Fluid Mixtures....Pages 149-153
Experimental Study of Binary Fluid Convection in a Quasi 1-Dimensional Cell without Reflections from the Sidewalls....Pages 155-158
Interfacial Oscillations and Solitons Driven by the Marangoni Effect....Pages 159-167
Couette Flows, Rollers, Emulsions, Tall Taylor Cells, Phase Separation and Inversion, and a Chaotic Bubble in Taylor-Couette Flow of Two Immiscible Liquids....Pages 169-189
Traveling Waves in a Partly Solidified Mixture....Pages 191-196
Phase-Mean Drift Equation for Convection Patterns in Large Aspect Ratio Containers....Pages 197-209
Modulated Traveling Waves in Nonequilibrium Systems....Pages 211-220
Confined States in Phase Dynamics....Pages 221-229
Small-Scale Excitations in Large Systems....Pages 231-236
Bound States of Interacting Localized Structures....Pages 237-243
Nonlinear Dynamics of Particle-Like States of Multidimensional Fields....Pages 245-259
Caustics of Nonlinear Waves and Related Questions....Pages 261-269
Phase Dynamics and Propagation of Dislocations....Pages 271-283
Spirals in Excitable Chemical Media: From Archimedian to Non-Archimedian Geometry....Pages 285-292
Chemical Pattern Dynamics by Chemically Induced Hydrodynamic Flow....Pages 293-297
Stability of Travelling Waves in the Belousov-Zhabotinskii Reaction....Pages 299-311
The Formation and Propagation of Fronts at the Electric Field Induced Bend Freedericksz Transition....Pages 313-318
The Dynamics of Transient Structures in the Fredericksz Transition....Pages 319-325
Sideband Instability of Modulated Traveling Wave Convection....Pages 327-332
Spatial Instabilities and Defect Ordering in Solids....Pages 333-342
Mutual Interplay between the Break-Up of Spatial Order and the Onset of Low-Dimensional Temporal Chaos in an Exemplary Semiconductor System....Pages 343-350
Electroconvection in a Freely Suspended Film of Smectic a Liquid Crystal....Pages 351-357
Symmetry Breaking in Nonlinear Convection....Pages 359-374
Chaos and the Effect of Noise for the Double Hopf Bifurcation with 2:1 Resonance....Pages 375-384
Codimension 2 Bifurcation in Binary Convection with Square Symmetry....Pages 385-398
Dynamics of Slowly Varying Wavetrains in Finite Geometry....Pages 399-410
Kinks and Solitons in the Generalized Ginzburg-Landau Equation....Pages 411-417
Onset of Chaos in the Generalized Ginzburg-Landau Equation....Pages 419-424
Turbulence and Linear Stability in a Discrete Ginzburg-Landau Model....Pages 425-435
On the Stability of Parametrically Excited Standing Waves....Pages 437-443
Directional Solidification of Transparent Eutectic Alloys....Pages 445-450
Directional Solidification of a Faceted Crystal....Pages 451-456
Routes to Cell Formation and Hidden Ramps in Directional Solidification....Pages 457-473
Influence of an External Periodic Flow on Dendritic Crystal Growth....Pages 475-479
Pattern Growth: From Smooth Interfaces to Fractal Structures....Pages 481-486
The Printer’s Instability: The Dynamical Regimes of Directional Viscous Fingering....Pages 487-497
Front Propagation into Unstable States: Some Recent Developments and Surprises....Pages 499-508
Collapsing Solutions in the 3-D Euler Equations....Pages 509-513
Large Magnetic Reynolds Number Dynamo Action in Steady Spatially Periodic Flows....Pages 515-539
On Spatial Structure of Kolmogorov Spectra of Weak Turbulence....Pages 541-544
Spatiotemporal Intermittency....Pages 545-552
On the Scale-Invariant Theory of Developed Hydrodynamic Turbulence Kolmogorov Type....Pages 553-562
Back Matter....Pages 563-569
....