This grant supports ongoing research in the area of numerical modeling of basic and applied problems that arise in the physics of liquid crystals. The work is interdisciplinary in nature, involving collaborations with physicists in the Liquid Crystal Institute at Kent State University as well as with computer scientists and applied and computational mathematicians at Kent, Purdue University, and the Courant Institute. The emphases of the work will be in three project areas: (1) numerical modeling of equilibrium orientational properties of confined liquid crystal materials, (2) developing and utilizing modern CS problem-solving environments (for rapid prototyping of such numerical codes and packages), and (3) numerical modeling of the interaction between a laser beam and the liquid-crystal medium through which it is propagating (to investigate and validate modeling and asymptotic analyses performed on such a system by a group at Courant). Liquid Crystals are materials capable of existing in states (call "mesophases") in between solids and liquids. They enjoy properties of both. They are fluid; yet their molecules tend to orient themselves in certain preferred ways (depending on inter-molecular forces, geometry, conditions at boundaries, external applied electric or magnetic fields, and the like). They have significant commercial importance because of applications in the display industry. Modern liquid crystal devices (with microscopic geometry and interfering neighboring effects) now require considerable two- and three-dimensional numerical modeling for analysis and design. The proposed work will contribute to the advancement of the general state of the art for this type of scientific computing while numerically modeling specific systems of current interest.
