Numerical Modeling of Problems in Liquid Crystals

该基金支持在液晶物理中出现的基础和应用问题的数值模拟领域进行的研究。这项工作本质上是跨学科的，包括与肯特州立大学液晶研究所的物理学家以及肯特、普渡大学和Courant研究所的计算机科学家、应用和计算数学家的合作。工作的重点将放在三个项目领域：(1)受限液晶材料平衡取向特性的数值模拟，(2)开发和利用现代CS问题解决环境（用于此类数值代码和包的快速原型设计），以及(3)激光与传播的液晶介质之间相互作用的数值模拟（调查和验证由Courant的一个小组对此类系统进行的建模和渐近分析）。液晶是一种能够以介于固体和液体之间的状态（称为“中间相”）存在的材料。两者兼而有之。它们是流动的；然而，它们的分子倾向于以某些优选的方式（取决于分子间的作用力、几何形状、边界条件、外部施加的电场或磁场等）自我定向。由于在显示行业中的应用，它们具有重要的商业意义。现代液晶器件（具有微观几何和干涉邻近效应）现在需要大量的二维和三维数值模拟来进行分析和设计。提出的工作将有助于提高这种类型的科学计算的一般艺术状态，同时对当前感兴趣的特定系统进行数值建模。

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.