This thesis uses multiscale computational modelling to find the fundamental principles that govern defects forming during the operation of new electro-optical devices and the processing of spider silk fibers. The generalized approach developed in this thesis bridges engineering devices and biological processes based on liquid crystalline materials. / Three types of defects are encountered: inversion walls, lines and points. Inversion wall defects are found in the electro-optical device when a nematic thin film undergoes a temperature-induced surface anchoring transition. Point defects naturally occur in the tubular extrusion duct of spiders, while line defects present close topological connections with point defects and are widespread in many high-performance industrial fibers. Three models are used in this thesis and their usage is dependent on the characteristics of the defects studied. / In the case of inversion wall defects, computational modelling is used to verify, complement and analyze experimental measurements made with fluorescence confocal polarizing microscopy by our collaborator at the Georgia Institute of Technology. The various simulation results agree and explain very well experimental observations and provide a thorough understanding of the wall defects behavior. A computational technique is developed to enable the precise determination of the interaction between the liquid crystal and the device substrate. Understanding the behavior of wall defects and estimating interfacial properties are indispensable to the development and optimization of the electro-optical device as they affect properties like temperature of operation, switching voltages and response time. / Computational modelling is also used to investigate the behavior of nematic point defects confined in cylindrical cavities as observed along spiders' spinning apparatus, and to examined textural connections with other well know structures seen in industrial fibers. The various scenarios investigated include: interactions between point defects, topological transformations between point, line and ring defects as well as interactions between ring defects. The simulation results agree and complement previous investigations but also offer a new fundamental understanding on the nature and stability of defects in cylindrical cavities. Understanding the behavior of nematic point and line defects in cylindrical geometries is important as they play a fundamental role in the processing of natural and industrial high-performance fibers.

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Nematic liquid crystals are mesogenic materials that are popular working materials for optical displays. There has been an increased interest in bistable liquid crystal devices which support two optically distinct stable equilibria. These devices typically exploit a complex geometry or anchoring conditions, which often induces defects in the equilibria. There remains a great deal to be understood about the structure of the defects and how they stabilize multiple equilibria in modern devices. This thesis focuses on four problems: the first three explore the effect of confinement and defects on nematic equilibria in simple geometries, with the aim of exploring multistability in these geometries; the fourth problem concerns the fine structure of point defects, essential for future modelling of nematic equilibria in more complex geometries. Firstly, we study nematic liquid crystals confined to two-dimensional rectangular wells using the Oseen-Frank theory. Secondly, we study equilibria within a semi-infinite rectangular domain with weak tangential anchoring on the surfaces. Thirdly, we study nematic equilibria within two-dimensional annuli. We derive explicit expressions for the director fields and free energies of equilibria within these geometries and discuss the stability of the predicted states. These three problems are motivated by the experimental work on colloidal nematic liquid crystals, which we interpret in the context of our results. Finally, we study the fine structure and stability of the radial hedgehog defect in the Landau-de Gennes theory with a sixth order bulk potential, relevant to the observability of global biaxial phases in a model with higher order potential terms.