Numerical Modeling of Problems in Liquid Crystals

这笔赠款支持液晶物理学中出现的基本和应用问题的数值模拟领域正在进行的研究。这项工作本质上是跨学科的，涉及与肯特州立大学液晶研究所的物理学家以及肯特大学、普渡大学和库兰特研究所的计算机科学家以及应用和计算数学家的合作。这项工作的重点将集中在三个项目领域：(1)受限液晶材料的平衡取向性质的数值模拟，(2)开发和利用现代CS问题求解环境(用于此类数字代码和组件的快速原型)，以及(3)激光与其传播通过的液晶介质之间的相互作用的数值模拟(以调查和验证由Courant的一个小组对此类系统进行的建模和渐近分析)。液晶是能够以固体和液体之间的状态(称为“中间相”)存在的材料。他们同时享受着这两种特性。它们是流动的；但它们的分子倾向于以某些首选的方式定向(取决于分子间力、几何形状、边界条件、外加电场或磁场等)。由于它们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(具有微观几何结构和干扰邻近效应)现在需要相当多的二维和三维数值模拟来进行分析和设计。拟议的工作将有助于提高这种类型的科学计算的一般技术水平，同时对当前感兴趣的特定系统进行数字建模。

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.