Mathematical Sciences: The Dynamics of Defects and Patterns in Nematic Liquid Crystals

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In this project the principal investigator will analyze models of nematic liquid crystals with variable degrees of orientation as a means of studying highly nonlinear material behavior such as the formation of structured domains and patterns. The approach will consist of an analytical part and an experimental part. On the analytical side the principal investigator will employ mathematical methods to describe the formation and evolution of banding structures, singularity lines and disclinations in the solutions of the system of parabolic partial differential equations that governs the behavior of the materials. On the experimental side the principal investigator and a graduate student will conduct actual experiments in the Fluid Dynamics Laboratory in the Mathematics Department at Penn State in order to discover some qualitative features of the coarsening processes of domain structures and the nature of the interaction between singularity lines. The project to be carried out by the principal investigator and a graduate student is an exciting interplay between analytical applied mathematics and experimental fluid dynamics. For the past few years the principal investigator has studied the systems of differential equations that govern the behavior of liquid crystals using mathematical tools. She plans now to combine this analytical work with experimental studies of the phenomena modelled by the equations. The research will have relevance to improving the industrial processing of anisotropic polymeric materials.