We model nematic liquid crystals using the Landau-de Gennes continuum theory, where equilibrium configurations are solutions of complex boundary-value problems of systems of coupled nonlinear partial differential equations. We analyse and present the exotic defect structures in model geometries with different boundary conditions and material properties. We study three-dimensional wells with tangent
boundary conditions on the lateral surfaces, and two physically relevant boundary conditions on the top and bottom surfaces, and prove the existence of the globally minimizing Well Order Reconstruction Solution for small geometries. This work is corroborated by an exhaustive numerical study of three-dimensional wells with square and rectangular cross-sections, where we have looked at the effects of geometrical anisotropy and anchoring. We then consider a two-term elastic energy density in the Landau-de Gennes free energy to investigate the role of elastic anisotropy in different asymptotic limits, focusing on two-dimensional square wells with tangent boundary conditions. We then model ferronematics in two-dimensional polygonal wells, tailoring multistability of the equilibrium profiles, and presenting new exotic states with interior domain walls and nematic point defects. Lastly, we study the nematic-isotropic phase transition for a fourth-order thermotropic bulk potential in a stochastic setting, where certain material-dependent parameters are assumed to follow a non-Gaussian probability distribution.
|Date of Award||19 Jan 2022|
- University Of Strathclyde
|Sponsors||University of Strathclyde|
|Supervisor||Apala Majumdar (Supervisor) & David Greenhalgh (Supervisor)|