Numerical Modeling of Problems in Liquid Crystals

该补助金支持正在进行的研究领域， 液晶物理中出现的基本和应用问题的数值模拟。 这项工作是跨学科的 在自然界中，包括与液体物理学家的合作， 肯特州立大学水晶研究所以及与 计算机科学家、应用数学家和计算数学家 在肯特，普渡大学，和柯朗研究所。 的 工作的重点将在三个项目领域：（1）数字 平衡取向性质的模拟 液晶材料，（2）开发和利用现代CS解决问题的环境（用于这种数字的快速原型制作）， 代码和软件包），以及（3）相互作用的数值模拟 在激光束和它所通过的液晶介质之间 正在传播（调查和验证建模和渐近 由Courant的一个小组在这样的系统上进行的分析）。 液晶是一种能够以不同状态存在的材料 (call“中间相”）。 他们享受 两者的属性。 它们是流体，但它们的分子倾向于 以某些首选方式定位自己（取决于 分子间力，几何形状，边界条件， 外部施加的电场或磁场等）。 由于其应用范围广， 在显示器行业。 现代液晶器件（具有 微观几何和干扰邻近效应）现在 需要大量的二维和三维数值模拟 用于分析和设计。 拟议的工作将有助于推进这一类型的一般国家的艺术 科学计算的同时， 当前感兴趣的系统。

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.