Langmuir films in the liquid-condensed phase and smectic-C films are examples of two-dimensional systems adequately described by a simple XY-model free energy with additional boundary terms. Video microscopy reveals interesting textures in these systems as well as complicated domain boundaries in the case of Langmuir films. Topological defects, both real and virtual, offer a simple explanation for many of these textures. We show that non-topological singularities also play a role in understanding some novel effects of fluctuations in these systems. Next we address the existence of non-trivial domain boundaries by appealing to the competing effects of elastic energy and an isotropic line tension for the domain boundary. For circular domains a first-order phase transition is found between states where the domain contains a defect and those in which it does not. For circular domains with and without a defect present we proceed to examine the stability of the shape of the domain and identify when instabilities arise as functions of the elastic parameters in our theory.
Source: Dissertation Abstracts International, Volume: 60-07, Section: B, page: 3339. Supervisor: Tom C. Lubensky. Thesis (Ph.D.)--University of Pennsylvania, 1999.