Pattern Formation in Liquid Crystals

1 Introduction to Pattern Formation in Nonequilibrium Systems.- 1.1 General Remarks.- 1.2 A Simple Model.- 1.3 Pattern Formation in Liquid Crystals.- References.- 2 Hydrodynamics and Electrohydrodynamics of Liquid Crystals.- 2.1 Introduction.- 2.2 Symmetries and Broken Symmetries.- 2.3 Statics.- 2.4 Dynamics.- 2.5 Electrohydrodynamics.- 2.6 Additions to Nematodynamics.- 2.7 Director-Type Degrees of Freedom.- References.- 3 General Mathematical Description of Pattern-Forming Instabilities.- 3.1 Introductory Remarks.- 3.2 Linear Analysis.- 3.3 The Landau Equation.- 3.4 The Ginzburg—Landau Equations.- 3.5 Extended Weakly Nonlinear Analysis.- 3.6 From Order Parameter to Amplitude Equations.- 3.7 Concluding Remarks.- References.- 4 Flow Instabilities in Nematics.- 4.1 Introduction.- 4.2 Continuous Description of Nematics and Viscometry.- 4.3 Stability Analysis and Basic Mechanisms.- 4.4 Shear Flow Instabilities with the Director Perpendicular to the Shear Plane.- 4.5 Flow Instabilities with the Director Initially Parallel to the Shear Plane.- 4.6 Elliptical Shear Instability in Homeotropic Configuration.- 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.- 5.2 Planar Alignment and a Horizontal Magnetic Field.- 5.3 Homeotropic Alignment and a Vertical Magnetic Field.- 5.4 Two-Phase Convection.- Appendix A: Experimental Methods.- Appendix B: Physical Properties of 5CB.- References.- 6 Electrohydrodynamic Instabilities in Nematic Liquid Crystals.- 6.1 Introduction.- 6.2 Planar alignment: linear theory.- 6.3 Planar alignment: nonlinear theory.- 6.4 Homeotropic alignment.- 6.5 Concludingremarks.- References.- 7 Mesophase Growth.- 7.1 Introduction.- 7.2 The Mullins—Sekerka Instability.- 7.3 Directional Growth Experiments.- 7.4 Free-Growth Experiments.- 7.5 Prospects.- References.- 8 Viscous Fingering.- 8.1 Introduction.- 8.2 Theoretical Background.- 8.3 Experiments.- 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.- 9.5 Experimental Results.- 9.6 Discussion.- References.