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Structure of colloidal particles in anisotropic solvent with long-range orientational ordering, such as nematic liquid crystals, has attracted great attention in science and technology. The nematic director is distorted from its uniform orientation in the bulk due to anchoring on the surface of the colloidal particles. These elastic distortions create topological defects around the particles and induce long and short range anisotropic interactions between the particles. Depending on the anchoring type and the colloidal geometry, the particle-defect can induce a long-range dipolar-dipolar, quadrupolar-quadrupolar and/or dipolar-quadrupolar potential.Experimentally, the colloidal interactions... 

A liquid crystal is a state of matter composed of highly anisotropic building blocks. When liquid crystals are exposed to surfaces with given shapes and anchoring conditions, the orientation of their molecules gets spatially disordered and topological defects may form in the system. The interplay between liquid crystals and the geometry and topology of the colloidal particles has motivated extensive recent studies.In this thesis, we present the numerical modeling results for two faceted colloidal particles in a thermotropic nematic liquid crystal. To obtain the equilibrium nematic field with a finiteelement method, we numerically minimize the free energy of the system that based on the...