| Summary: | cylindrical symmetry of the core is broken and two defects of strength +1/2 may be resolved. We use molecular dynamics to study the ordering of a nematic liquid crystal around a spherical particle or droplet. We observe three defect structures for different particle sizes: a quadrupolar one with a ring defect surrounding the particle in the equatorial plane; a dipolar one with a satellite defect at the north or south pole; and a transitional, non-equatorial, ring defect. By studying density and order-parameter maps, we are able to examine behavior near the particle surface, and in the disclination core region, where the elastic theory is inapplicable. We present the results of molecular dynamics simulations of the topological defects that appear around an elongated colloidal particle. We also study the force and the torque on the particle suspended in the bulk of the nematic mesophase and modification of this torque when the particle is close to the cell substrate. In this thesis, we investigate several aspects of the behavior of confined liquid crystalline systems. We use different theoretical and computer simulation techniques, which are discussed briefly in the first two chapters. We then describe several essentially independent research topics. We propose a simple and reliable method to measure the liquid crystal surface anchoring strength by molecular simulation. The method is based on the measurement of the long-range fluctuation modes of the director in confined geometry. As an example, molecular simulations of a liquid crystal in slab geometry between parallel walls with homeotropic anchoring have been carried out using the Monte Carlo technique. By studying different slab thicknesses, we are able to calculate separately the position of the elastic boundary condition, and the extrapolation length. Then, combining molecular simulation, Onsager theory and the elastic description of nematic liquid crystals, we study the dependence of the nematic liquid crystal elastic constants and the polar surface anchoring coefficient on the value of the bulk order parameter. We continue with molecular simulations of a nematic liquid crystal confined in cylinder geometry with homeotropic anchoring. The core structure of a disclination line defect of strength +1 has been examined, and comparison made with various theoretical treatments, which are presented in a unified way. It is found that, on the timescales of the simulation, the
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