| Preface |
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xv | |
| Acknowledgements |
|
xix | |
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Equations, General Concepts and Methods of Analysis |
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1 | (62) |
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Pattern Formation and Nonlinear Dynamics |
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1 | (5) |
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Some Fundamental Concepts: Pattern, Interrelation and Scale |
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2 | (2) |
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PDEs, Symmetry and Nonequilibrium Phenomena |
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4 | (2) |
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The Navier-Stokes Equations |
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6 | (15) |
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A satisfying Microscopic Derivation of the Balance Equations |
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6 | (1) |
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A Statistical Mechanical Theory of Transport Processes |
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7 | (2) |
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9 | (1) |
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10 | (1) |
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The Total Energy Equation |
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11 | (2) |
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The Budget of Internal Energy |
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13 | (1) |
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13 | (2) |
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Some Considerations About the Dynamics of Vorticity |
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15 | (3) |
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Incompressible Formulation of the Balance Equations |
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18 | (1) |
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Nondimensional Form of the Equations for Thermal Problems |
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19 | (2) |
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Energy Equality and Dissipative Structures |
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21 | (4) |
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Flow Stability, Bifurcations and Transition to Chaos |
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25 | (2) |
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Linear Stability Analysis: Principles and Methods |
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27 | (9) |
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Conditional Stability and Infinitesimal Disturbances |
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27 | (1) |
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The Exponential Matrix and the Eigenvalue Problem |
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28 | (2) |
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Linearization of the Navier-Stokes Equations |
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30 | (2) |
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A Simple Example: The Stability of a Parallel Flow with an Inflectional Velocity Profile |
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32 | (3) |
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Weaknesses and Limits of the Linear Stability Approach |
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35 | (1) |
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36 | (4) |
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A Global Budget for the Generalized Disturbance Energy |
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36 | (3) |
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39 | (1) |
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Numerical Integration of the Navier-Stokes Equations |
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40 | (6) |
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41 | (1) |
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Primitive Variables Methods |
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42 | (4) |
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Some Universal Properties of Chaotic States |
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46 | (12) |
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Feigenbaum, Ruelle-Takens and Manneville-Pomeau Scenarios |
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46 | (1) |
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Phase Trajectories, Attractors and Strange Attractors |
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47 | (1) |
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The Lorenz Model and the Butterfly Effect |
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48 | (3) |
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A Possible Quantification of SIC: The Lyapunov Spectrum |
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51 | (2) |
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The Mandelbrot Set: The Ubiquitous Connection Between Chaos and Fractals |
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53 | (5) |
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58 | (5) |
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Classical Models, Characteristic Numbers and Scaling Arguments |
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63 | (32) |
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Buoyancy Convection and the Boussinesq Model |
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64 | (2) |
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66 | (4) |
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A Definition of Microgravity |
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66 | (1) |
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67 | (1) |
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Surface Tension-driven Flows |
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68 | (1) |
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Acceleration Disturbances on Orbiting Platforms and Vibrational Flows |
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68 | (2) |
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70 | (8) |
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The Genesis and Relevant Nondimensional Numbers |
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71 | (4) |
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Microzone Facilities and Microscale Experimentation |
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75 | (1) |
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A Paradigm Model: The Liquid Bridge |
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75 | (3) |
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Exact Solutions of the Navier-Stokes Equations for Thermal Problems |
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78 | (11) |
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Thermogravitational Convection: The Hadley Flow |
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80 | (1) |
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80 | (3) |
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83 | (1) |
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83 | (2) |
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The Infinitely Long Liquid Bridge |
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85 | (1) |
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86 | (3) |
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Conductive, Transition and Boundary-layer Regimes |
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89 | (6) |
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Examples of Thermal Fluid Convection and Pattern Formation in Nature and Technology |
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95 | (24) |
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Technological Processes: Small-scale Laboratory and Industrial Setups |
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95 | (8) |
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Crystal Growth from the Melt: Typical Techniques |
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96 | (5) |
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Detrimental Effects Induced by Convective Phenomena |
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101 | (2) |
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Examples of Thermal Fluid Convection and Pattern Formation at the Mesoscale |
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103 | (1) |
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Planetary Structure and Dynamics: Convective Phenomena |
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103 | (5) |
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Earth's `Layered' Structure |
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103 | (1) |
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Earth's Mantle Convection |
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104 | (1) |
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104 | (2) |
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106 | (1) |
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The Icy Galilean Satellites |
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107 | (1) |
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Atmospheric and Oceanic Phenomena |
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108 | (11) |
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A Fundamental Model: The Hadley Circulation |
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108 | (2) |
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Mesoscale Shallow Cellular Convection: Collection of Clouds and Related Patterns |
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110 | (2) |
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The Planetary Boundary Layer |
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112 | (4) |
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Atmospheic Convection in Other Solar System Bodies |
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116 | (3) |
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Thermogravitational Convection: The Rayleigh-Benard Problem |
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119 | (76) |
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Nonconfined Fluid Layers and Ideal Straight Rolls |
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119 | (5) |
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The Linearized Problem: Primary Convective Modes |
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119 | (3) |
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Systems Heated from Above: Internal Gravity Waves |
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122 | (2) |
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124 | (9) |
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Toroidal-Poloidal Decomposition |
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125 | (2) |
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The Zoo of Secondary Modes |
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127 | (6) |
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Some Considerations About the Role of Dislocation Dynamics |
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133 | (2) |
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Tertiary and Quatenary Modes of Convection |
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135 | (3) |
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138 | (4) |
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Spiral Defect Chaos, Hexagons and Squares |
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142 | (7) |
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Convection with Lateral Walls |
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149 | (2) |
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151 | (6) |
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Distinct Modes of Convection and Possible Symmetries |
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151 | (4) |
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Higher Modes of Convection and Oscillatory Regimes |
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155 | (2) |
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Three-dimensional Parallelepipedic Enclosures: Classification of Solutions and Possible Symmetries |
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157 | (8) |
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160 | (1) |
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The Onset of Time Dependence |
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161 | (4) |
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The Circular Cylindrical Problem |
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165 | (8) |
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Moderate Aspect Ratios: Azimuthal Structure and Effect of Lateral Boundary Conditions |
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165 | (5) |
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Small Aspect Ratios: Targets and PanAm Textures |
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170 | (3) |
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Spirals: Genesis, Properties and Dynamics |
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173 | (6) |
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175 | (1) |
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175 | (1) |
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Multi-armed Spirals and Spiral Core Instability |
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176 | (3) |
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From Spirals to SDC: The Extensive Chaos Problem |
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179 | (3) |
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Three-dimensional Convection in a Spherical Shell |
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182 | (13) |
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Possible Patterns of Convection and Related Symmetries |
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183 | (1) |
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183 | (2) |
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185 | (3) |
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188 | (7) |
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The Dynamics of Thermal Plumes and Related Regimes of Motion |
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195 | (20) |
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195 | (1) |
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196 | (6) |
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The Diffusive-Viscous Regime |
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197 | (1) |
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The Viscous-Nondiffusive Regime |
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198 | (1) |
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The Inviscid-Diffusive Regime |
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198 | (2) |
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The Inviscid-Nondiffusive Regime |
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200 | (1) |
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Sinous Instabilities Created by Horizontal Shear |
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200 | (1) |
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201 | (1) |
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The Flywheel Mechanism: The `Wind' of Turbulence |
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202 | (6) |
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Upwelling and Downward Jets and Alternating Eruption of Thermal Plumes |
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203 | (1) |
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204 | (1) |
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The Origin of the Large-scale Circulation: The Childress and Villermaux Theories |
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205 | (3) |
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The Role of Thermal Diffusion in Turbulent Rayleigh-Benard Convection |
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208 | (1) |
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Multiplume Configurations Originated from Disrete Sources of Buoyancy |
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208 | (7) |
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Systems Heated from the Side: The Hadley Flow |
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215 | (56) |
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The Infinite Horizontal Layer |
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215 | (13) |
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The Hadley Flow and its General Perturbing Mechanisms |
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216 | (3) |
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Hydrodynamic Modes and Oscillatory Longitudinal Rolls |
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219 | (4) |
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223 | (2) |
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Competition of Disturbances and Tertiary Modes of Convection |
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225 | (3) |
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Two-dimensional Horizontal Enclosures |
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228 | (19) |
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Geometric Constraints and Multiplicity of Solutions |
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228 | (7) |
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Instabilities Originating from Boundary Layers and Patterns with Internal Waves |
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235 | (12) |
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The Infinite Vertical Layer: Cats-eye Patterns and Temperature Waves |
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247 | (6) |
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Three-dimensional Parallelepipedic Enclosures |
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253 | (9) |
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Cylindrical Geometries under Various Heating Conditions |
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262 | (9) |
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Thermogravitational Convection in Inclined Systems |
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271 | (18) |
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Inclined Layer Convection |
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272 | (7) |
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The Codimension-two Point |
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273 | (2) |
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Tertiary and High-order Modes of Convection |
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275 | (4) |
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Inclined Side-Heated Slots |
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279 | (10) |
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Stationary Longitudinal Long-Wavelength Instability |
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281 | (1) |
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Stationary Transversal Instability |
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282 | (2) |
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Oscillatory Longitudinal Long-wavelength Instability |
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284 | (1) |
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Stationary Longitudinal Short-wavelength Instability |
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284 | (1) |
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Oscillatory Longitudinal Instability |
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284 | (2) |
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Interacting Longitudinal and Transversal Multicellular Modes |
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286 | (3) |
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Thermovibrational Convection |
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289 | (28) |
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Equations and Relevant Parameters |
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289 | (1) |
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290 | (1) |
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291 | (2) |
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High Frequencies and the Thermovibrational Theory |
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293 | (1) |
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States of Quasi-equilibrium and Related Stability |
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294 | (5) |
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The Vibrational Hydrostatic Conditions |
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294 | (1) |
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The Linear Stability Problem |
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295 | (2) |
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Solutions for the Infinite Layer |
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297 | (2) |
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Primary and Secondary Patterns of Symmetry |
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299 | (4) |
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Medium and Low Frequecies: Possible Regimes and Flow Patterns |
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303 | (14) |
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Synchronous, Subharmonic and Nonperiodic Response |
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303 | (2) |
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Reduced Equations and Related Ranges of Validity |
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305 | (12) |
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Marangoni-Benard Convection |
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317 | (24) |
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317 | (3) |
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High Prandtl Number Liquids: Patterns with Hexagons, Squares and Triangles |
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320 | (5) |
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Liquid Metals: Inverted Hexagons and High-order Solutions |
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325 | (1) |
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Effects of Lateral Confinement |
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326 | (8) |
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328 | (3) |
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331 | (3) |
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Temperature Gradient Inclination |
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334 | (7) |
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Thermocapillary Convection |
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341 | (86) |
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Basic Features of Steady Marangoni Convection |
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342 | (3) |
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Stationary Multicellular Flow and Hydrothermal Waves |
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345 | (23) |
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Basic Velocity Profiles: The Linear and Return Flows |
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346 | (1) |
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Linear Stability Analysis |
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346 | (8) |
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Weakly Nonlinear Analysis |
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354 | (5) |
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Boundary Effects: 2D and 3D Numerical Studies |
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359 | (9) |
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368 | (7) |
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375 | (52) |
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375 | (3) |
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Liquid Metals and Semiconductor Melts |
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378 | (1) |
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The First Bifurcation: Structure of the Secondary 3D Steady Flow |
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379 | (2) |
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Effect of Geometric Parameters |
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381 | (8) |
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A Generalized Theory for the Azimuthal Wavenumber |
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389 | (1) |
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The Second Bifurcation: Tertiary Modes of Convection |
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390 | (3) |
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High Prandtl Number Liquids |
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393 | (6) |
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Standing Waves and Travelling Waves |
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399 | (8) |
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Symmetric and Asymmetric Oscillatory Modes of Convection |
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407 | (5) |
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412 | (5) |
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The Hydrothermal Mechanism in Liquid Bridges |
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417 | (4) |
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Noncylindrical Liquid Bridges |
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421 | (2) |
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The Intermediate Range of Prandtl Numbers |
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423 | (4) |
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Mixed Buoyancy-Marangoni Convection |
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427 | (90) |
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The Canonical Problem: The Infinite Horizontal Layer |
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429 | (7) |
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Finite-sized Systems Filled with Liquid Metals |
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436 | (13) |
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Typical Terrestrial Laboratory Experiments with Transparent Liquids |
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449 | (1) |
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The Rectangular Liquid Layer |
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450 | (8) |
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Waves and Multicellular Patterns |
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450 | (6) |
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Tertiary Modes of Convection: OMC and HTW with Spatiotemporal Dislocations |
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456 | (2) |
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Effects Originating from the Walls |
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458 | (10) |
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Lateral Boundaries as a Permanent Stationary Disturbance |
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459 | (1) |
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Collision Phenomena of HTW and Wall-generated Steady Patterns |
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460 | (4) |
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Streaks Generated by a Lift-up Process and Instabilities of a Mechanical Nature |
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464 | (4) |
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468 | (7) |
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Volume Driving Actions and Rising Thermal Plumes |
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470 | (1) |
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Aiding Marangoni and Buoyant Flows |
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470 | (2) |
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Counteracting Driving Forces and Separation Phenomena |
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472 | (2) |
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Surface Driving Actions and Vertical Temperature Gradients |
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474 | (1) |
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475 | (16) |
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Target-like Wave Patterns (HW2) |
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476 | (2) |
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Waves with Spiral Pattern (HW1) |
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478 | (2) |
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480 | (3) |
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Progression Towards Chaos and Fractal Behaviour |
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483 | (4) |
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The Reverse Annular Configuration: Incoherent Spatial Dynamics |
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487 | (1) |
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Some Considerations About the Role of Curvature, Heating Direction and Gravity |
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488 | (3) |
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The Liquid Bridge on the Ground |
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491 | (26) |
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492 | (7) |
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Heating from Above or from Below |
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499 | (11) |
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The Route to Aperiodicity |
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510 | (7) |
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Hybrid Regimes with Vibrations |
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517 | (64) |
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RB Convection with Vertical Shaking |
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519 | (6) |
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Complex Order, Quasi-Periodic Crystals and Superlattices |
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525 | (8) |
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527 | (2) |
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Purely Subharmonic Patterns |
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529 | (1) |
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Coexistence and Complex Order |
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529 | (4) |
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RB Convection with Horizontal or Oblique Shaking |
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533 | (5) |
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Laterally Heated Systems and Parametric Resonances |
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538 | (12) |
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The Infinite Horizontal Layer |
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538 | (6) |
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Domains with vertical Walls |
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544 | (4) |
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The Infinite Vertical Layer |
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548 | (2) |
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550 | (1) |
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Control of Thermogravitational Convenction |
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550 | (11) |
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Cell Orientation as a Means to Mitigate Convective Disturbances on Orbiting Platforms |
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551 | (2) |
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Control of Convection Patterning and Intensity in Shallow Enclosures |
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553 | (6) |
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Modulation of Thermal Boundary Conditions |
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559 | (2) |
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Mixed Marangoni-Thermovibrational Convection |
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561 | (14) |
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561 | (5) |
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Control of Convection Patterning and Intensity in Shallow Enclosures |
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566 | (1) |
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Control of Hydrothermal Waves |
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567 | (8) |
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Modulation of Marangoni-Benard Convection |
|
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575 | (6) |
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Flow Control by Magnetic Fields |
|
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581 | (28) |
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Static and Uniform Magnetic Fields |
|
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582 | (2) |
|
Physical Principles and Governing Equations |
|
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582 | (2) |
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|
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584 | (1) |
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Historical Developments and Current Status |
|
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584 | (20) |
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Stabilization of Thermogravitational Flows |
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584 | (13) |
|
Stabilization of Surface Tension-driven Flows |
|
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597 | (7) |
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Roatating Magnetic Fields |
|
|
604 | (3) |
|
Gradients of Magnetic Fields and Virtual Microgravity |
|
|
607 | (2) |
| References |
|
609 | (50) |
| Index |
|
659 | |
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