Solitons in Liquid Crystals

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.