Pattern Formation in Liquid Crystals

4.3 Stability Analysis and Basic Mechanisms.- 4.3.1 Stability Analysis.- 4.3.2 The Pieranski-Guyon Mechanism.- 4.4 Shear Flow Instabilities with the Director Perpendicular to the Shear Plane.- 4.4.1 Simple Shear Flow.- 4.4.2 Alternating Shear Flows.- 4.4.3 Poiseuille Flow.- 4.5 Flow Instabilities with the Director Initially Parallel to the Shear Plane.- 4.6 Elliptical Shear Instability in Homeotropic Configuration.- 4.6.1 Experimental Results.- 4.6.2 Theoretical Account.- 4.7 Further Developments.- Appendix A: Linear stability problem when the director is perpendicular to the shear plane.- Appendix B: Elliptical Shear Equations.- References.- 5 Experiments on Thermally Driven Convection.- 5.1 Introduction.- 5.1.1 Instability Mechanisms.- 5.1.2 Stability Analysis.- 5.1.3 Pattern Formation.- 5.1.4 Materials.- 5.2 Planar Alignment and a Horizontal Magnetic Field.- 5.2.1 Introductory Remarks.- 5.2.2 Theoretical Predictions.- 5.2.3 Experimental Results.- 5.3 Homeotropic Alignment and a Vertical Magnetic Field.- 5.3.1 General Remarks.- 5.3.2 Heating from Below.- 5.3.3 Heating from Above.- 5.4 Two-Phase Convection.- 5.4.1 Theoretical Predictions.- 5.4.2 Experimental results.- Appendix A: Experimental Methods.- Appendix B: Physical Properties of 5CB.- References.- 6 Electrohydrodynamic Instabilities in Nematic Liquid Crystals.- 6.1 Introduction.- 6.1.1 General Considerations.- 6.1.2 Theoretical preliminaries.- 6.2 Planar alignment: linear theory.- 6.2.1 Conduction regime.- 6.2.2 Dielectric regime.- 6.3 Planar alignment: nonlinear theory.- 6.3.1 Results of Ginzburg-Landau Equation (GLE).- 6.3.2 Beyond the GLE.- 6.4 Homeotropic alignment.- 6.4.1 Case C.- 6.4.2 Case F.- 6.5 Concluding remarks.- References.- 7 Mesophase Growth.- 7.1 Introduction.- 7.2 The Mullins-Sekerka Instability.- 7.2.1 Undercooled Pure Material.- 7.2.2 Thin Layer of a Binary Alloy in a Temperature Gradient.- 7.3 Directional Growth Experiments.- 7.3.1 The Initial Instability.- 7.3.2 Secondary Instabilities.- 7.3.3 Tertiary and Higher Instabilities.- 7.3.4 Other Experimental Systems.- 7.4 Free-Growth Experiments.- 7.4.1 Microscopic-Solvability Theory.- 7.4.2 Dendritic Growth at the Discotic-Isotropic Interface.- 7.4.3 Dendritic Growth in Other Mesophase Systems.- 7.5 Prospects.- References.- 8 Viscous Fingering.- 8.1 Introduction.- 8.2 Theoretical Background.- 8.3 Experiments.- 8.3.1 Isotropic Systems.- 8.3.2 Anisotropic Systems.- 8.4 Concluding Remarks.- References.- 9 Thermal Fluctuations in Pattern Forming Instabilities.- 9.1 Introduction.- 9.2 Macroscopic Stochastic Equations for Thermal Noise.- 9.3 Stochastic Amplitude Equations.- 9.4 Theoretical Results.- 9.4.1 Rayleigh-Bénard Convection.- 9.4.2 Taylor-Couette Flow.- 9.4.3 Planar Electrohydrodynamic Convection.- 9.5 Experimental Results.- 9.6 Discussion.- References.