内容

目次

1 Introduction.- 1.1 Liquid Crystal Phases.- 1.2 Solitons in Liquid Crystals.- References.- 2 Solitons and Field Induced Solitons in Liquid Crystals.- 2.1 Introduction.- 2.2 Solitons.- 2.2.1 Origin and Definition.- 2.2.2 A Brief History.- 2.3 Soliton Equations.- 2.3.1 Korteweg-deVries Equation.- 2.3.2 Nonlinear Schrödinger Equation.- 2.3.3 Sine-Gordon Equation.- 2.3.4 Fisher Equation.- 2.3.5 The Damped ?4Equation.- 2.3.6 Other Equations.- 2.4 Constructing Soliton Equations.- 2.5 Methods of Solving Soliton Equations.- 2.5.1 Inverse Scattering Method.- 2.5.2 Bäcklund Transformation.- 2.5.3 Hirota Method.- 2.5.4 Perturbation.- 2.5.5 Numerical Method.- 2.5.6 Experimental Simulation.- 2.6 Formation of Solitons.- 2.7 Magnetic Field Induced Solitons in Nematics.- 2.7.1 Early Works.- 2.7.2 Nematics Under Tilted Magnetic Fields.- 2.8 Electric Field Induced Solitons in Liquid Crystals.- 2.9 Conclusions.- References.- 3 Solitons in Shearing Liquid Crystals.- 3.1 Introduction.- 3.2 Steady Uniform Shear I: One-Dimensional Case.- 3.2.1 Equations of Motion.- 3.2.2 Classification of Solitons.- 3.2.3 Single Solitons.- 3.2.4 Multisolitons.- 3.2.5 Energy Dissipation.- 3.2.6 Transmitted Light Intensity.- 3.2.7 Flexoelectric Solitons.- 3.2.8 Spatiotemporal Distribution of Directors.- 3.2.9 Experimental Situation.- 3.3 Steady Uniform Shear II: Boundary Effects.- 3.3.1 Director Equation of Motion.- 3.3.2 Steady States.- 3.3.3 Numerical Soliton Solutions.- 3.3.4 Analytic Soliton Solutions.- 3.3.5 Relaxation Processes.- 3.4 Unsteady Uniform Shear.- 3.4.1 Multiple Scale Analysis.- 3.4.2 Perturbed Solitons.- 3.5 Steady Nonuniform Shear I: Linear Cell.- 3.5.1 Theory of Pressure Gradient Induced Solitons.- 3.5.2 Experimental Results in Linear Cells.- 3.5.3 Perturbed Solitons Under Spatially Varying Shear.- 3.6 Steady Nonuniform Shear II: Radial Cell.- 3.6.1 Torsional Shear Flow.- 3.6.2 Radial Poiseuille Flow.- 3.6.3 Experiments in Radial Cells.- 3.7 Conclusions.- References.- 4 Some Nonlinear Problems in Anisotropic Systems.- 4.1 Introduction.- 4.2 Nonlinear Aspects of Static Properties of Liquid Crystals.- 4.2.1 Nonlinearities Associated with the Freedericksz Transition.- 4.2.2 Escape into the Third Dimension.- 4.3 Nonlinear Macroscopic Dynamics of Liquid Crystals.- 4.3.1 Dynamics of Line Defects in Nematic Liquid Crystals.- 4.3.2 Moving Wall Fronts in Helielectric Liquid Crystals.- 4.3.3 An Exact Solitary Wave Solution for ?a< 0.- 4.3.4 Biological Significance of Chirality.- 4.3.5 Nonlinear Aspects of Liquid Crystals in Flow.- 4.4 Perspectives.- 4.5 Conclusions.- References.- 5 Solitary Waves in Ferroelectric Liquid Crystals.- 5.1 Introduction.- 5.2 Equations of Motion in One Dimension.- 5.2.1 Solving the Equation of Motion.- 5.3 Wave Fronts in Infinite Systems.- 5.3.1 Computer Simulations.- 5.3.2 Marginal Stability.- 5.3.3 Analytic Solution for the Metastable-Stable Case.- 5.3.4 Summary.- 5.4 Director Reorientation in Finite Domains with Fixed Boundaries.- 5.4.1 Thick Cells with a Helix.- 5.4.2 Thin Cells with Splay.- 5.4.3 Computer Simulations.- 5.5 Structures with Finite Interface Energies.- 5.5.1 Introduction.- 5.5.2 One-Dimensional Structures.- 5.5.3 Two-Dimensional Structures.- 5.6 Conclusions.- References.- 6 Frustrated Smectics.- 6.1 Introduction.- 6.2 The Physics of Polar Smectics.- 6.2.1 Intrinsic Incommensurability of Coexisting Modulations.- 6.2.2 Phenomenological Theory of Frustrated Smectics.- 6.2.3 Solitons in the Model of Frustrated Smectics.- 6.2.4 Connection with Experiments.- 6.3 Electric Properties of the Incommensurate Smectics.- 6.3.1 Intrinsic Ferroelectricity of Incommensurate Smectics.- 6.3.2 Distortion of the Modulated Smectic Structure by an Electric Field.- 6.3.3 Longitudinal Ferroelectricity.- 6.3.4 Conclusions.- 6.4 Escape from Incommensurability.- 6.4.1 Two-Dimensional Lockin of the Wavevectors.- 6.4.2 Theoretical Phase Diagrams with 2D Antiphases.- 6.4.3 Including Higher Order Harmonics in kx.- 6.5 Conclusions.- References.- 7 Soft Walls and Orientational Singularities in Two-Dimensional Liquid Crystal Films.- 7.1 Background.- 7.2 Experimental Techniques.- 7.3 Soft Tilt Director Walls in Ferroelectric Smectic C* Films.- 7.4 Characteristic Orientational Singularities in Tilted Hexatic Films.- 7.5 Concluding Remarks.- References.- 8 Charged Twist Walls in Nematic Liquid Crystals.- 8.1 Introduction.- 8.2 Experiment.- 8.3 Model.- 8.4 Conclusions.- References.- 9 Localized Instabilities in the Convection of Nematic Liquid Crystals.- 9.1 Introduction.- 9.2 Localized Instabilities in the Evolution to the Chaotic State.- 9.3 Theoretical Model: The Amplitude Equation.- 9.4 Convective Instabilities in Nematics Under A.C. Electric Fields.- 9.5 Sequence of Homogeneous Stationary States.- 9.6 Topology of Dislocations.- 9.7 Experimental Techniques.- 9.8 Nucleation of Dislocations in the Convective Rolls.- 9.9 Phase Propagation and Localization of a Convective Structure.- 9.10 Propagation of Solitary Rolls.- References.- 10 Solitons and Commensurate-Incommensurate Phase Transitions in Ferroelectric Smectics.- 10.1 Introduction.- 10.2 Condensation of Solitons.- 10.2.1 Soliton and Soliton Lattices of the Sine—Gordon Equation.- 10.2.2 Cholesteric-Nematic Phase Transition.- 10.2.3 Flexoelectric Instability of the Nematic Phase.- 10.3 The Chiral Smectic C—Smectic CPhase Transition.- 10.3.1 Chiral Smectic CPhase Under an Electric Field.- 10.3.2 Interaction Between Solitons.- 10.3.3 Multisolitons and Soliton Lattices.- 10.3.4 Phase Transition of Instability Type.- 10.3.5 Effect of Magnetic Field.- 10.4 Incommensurate and Rippled Phases Without Lifshitz Invariant.- 10.4.1 Rippled Phase.- 10.4.2 Phase Transitions Between Smectic APhases.- 10.5 Summary.- References.- Author Index.