| The focus of this work is the theoretical modeling of nematic liquid crystals in nanoscale and microscale systems. Several studies have been performed investigating equilibrium defect structures in liquid crystal systems. Models have been successfully employed in the study of three-dimensional model biosensors, where defects traverse a sensor at high analyte coverage. The same theory has been extended to study micron scale particles in channels filled with nematic liquid crystals, showing that a minimization of defect volume forces the particles to settle near the side walls of channels.;Investigations of the flow behavior of liquid crystals are performed using a radial basis function collocation method. We present simulations of a cavity flow of liquid crystal, where the effects of the flow strength on the dynamics and final defect structures of the liquid crystal are discussed. We also simulate a two-dimensional thin film of liquid crystal with an initial state including two defects. As the film relaxes to a final uniform state, the stresses in the liquid crystal accelerate the relaxation of one defect and impede the relaxation of the other.;Next, we model mobile nanoscale colloids in liquid crystal channels. Depending upon the particle Ericksen number, the phase of the colloid, and the anchoring conditions, the defect surrounding the colloid behaves very differently. The flow can cause the defect to change from a Saturn ring to a hedgehog on the upstream side of the colloid, but that effect is only observed for solid nanoparticles. If the Saturn ring is oriented parallel to the direction of particle motion, the defect can separate to large distances from the particle. These theoretical results are compared with analogous molecular simulations, which provide good agreement.;Finally, we highlight work that is pending completion. We investigate the defect structures that arise within liquid crystal droplets, focusing on the effects of orientational preference at the droplet surface. We also introduce a system of multiple particles in a channel filled with liquid crystal, where the particles are moved by the flowing liquid crystal in an effort to investigate forced assembly of particles in liquid crystals on the nanoscale. |
