Pattern Formation in Liquid Crystals: (Partially Ordered Systems)

This volume bridges two topics of considerable current interest: pattern formation in nonequilibrium phenomena and physics of liquid crystals, both active and diverse areas of research. Because liquid crystals form large-scale and regular patterns under the influence of a variety of applied fields they are fruitful materials to study the spontaneous formation and evolution of ordered and disordered patterns. The chapters, each by a noted researcher in the field, briefly summarize the fundamental work done in the 1960s but concentrate on reviewing results from the recent resurgence of interest in the field as well as indicating the direction of current work.

Table of Contents:
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.