Global solution of nematic liquid crystals models

Global defect topology in nematic liquid crystals

We give the global homotopy classification of nematic textures for a general domain with weak anchoring boundary conditions and arbitrary defect set in terms of twisted cohomology, and give an explicit computation for the case of knotted and linked defects in [Formula: see text], showing that the distinct homotopy classes have a 1-1 correspondence with the first homology group of the branched d...

Models for biaxial nematic liquid crystals

Nematic Liquid Crystals: Defects

There are two types of defects in the uniaxial nematic F phase: line defects (disclinations) and point defects (hedgehogs and boojums). These are reviewed at three levels: (i) experimental observations; (ii) topological classification; and (iii) curvature elasticity. The reader is referred to the textbooks on liquid crystals (Chandrasekhar 1992, de Gennes and Prost 1993), defects (Kltman 1983),...

Defects in Nematic Liquid Crystals

Defects in liquid crystals are discontinuities in order parameter. In nematic liquid crystals (NLC) two types of stable defects exist: disclination lines and point defects. Defects formation depends on isotropic to nematic phase transition while their stability depends strongly on confining surface properties, surface geometry and presence of external field. Classical Frank’s model of director ...

Kickback in Nematic Liquid Crystals

We describe a nonlocal linear partial differential equation arising in the analysis of dynamics of a nematic liquid crystal. We confirm that it accounts for the kickback phenomenon by decoupling the director dynamics from the flow. We also analyse some of the mathematical properties of the decoupled director equation.