Mathematical Sciences: Mathematical Analysis of Problems in Liquid Crystals

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9310733 Gartland The investigator undertakes the mathematical and numerical analysis of problems related to the science of liquid crystal materials. He continues interdisciplinary work with the Glenn H. Brown Liquid Crystal Institute (LCI) at Kent State University. The primary focus of the project is on three areas: (1) numerical minimization of the Landau-deGennes free energy for liquid crystals (which involves tensor order parameters, finite-element analysis, large-sparse optimization, and numerical bifurcation), (2) automatic code generation for the finite-element analysis of problems in liquid crystals (using modern computer science technology from the area of symbolic and numeric computing), and (3) numerical analysis and modeling of the optics of display devices (involving the solution of Maxwell's equations in nonhomogeneous birefringent media). The study of liquid crystals is an area of materials science that is rapidly growing in importance, driven primarily by commercial applications in the display industry: watch or calculator displays, notebook computer screens, high-definition flat-panel TV screens, etc. The Liquid Crystal Institute at Kent State has a strong international reputation. It is the only academically-based institute devoted solely to research on liquid crystals, and it is the locus of the NSF Science and Technology Center on "Advanced Liquid Crystalline Optical Materials" (ALCOM). The investigator's research project contributes to this activity in an interdisciplinary environment involving physics and chemistry in addition to mathematics and computer science. He performs numerical simulations on current problems of interest to the theoreticians and experimentalists in the LCI. He brings to bear state-of-the-art techniques from modern numerical analysis and scientific computing to complement theory and experiment. Investigators in the LCI are at their limits, using sophisticated experimental techniques, in probing the stru cture of liquid crystals in the very small (submicron) size containments in certain display technologies currently under development. Also, the numerical simulation of the optical properties of complicated liquid crystal devices (of the types mentioned above) is in a rather primitive state of development. The project's numerical work plays an important role in these areas. ***