Mathematical Sciences: Mathematical Analysis of Problems in Liquid Crystals

数学科学：液晶问题的数学分析

• 批准号: 9310733
• 负责人: Eugene Gartland
• 金额: $ 4.2万
• 依托单位: Kent State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-15 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9310733&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analysis; Problems; Liquid

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. ***

小行星9310733 该研究员承担与液晶材料科学相关的问题的数学和数值分析。 他继续与格伦H跨学科的工作。 肯特州立大学的布朗液晶研究所（LCI）。 该项目的主要重点是三个领域：（1）液晶的Landau-deGennes自由能的数值最小化（涉及张量序参数、有限元分析、大稀疏优化和数值分叉），（2）液晶问题有限元分析程序的自动生成（使用来自符号和数值计算领域的现代计算机科学技术），以及（3）显示设备的光学的数值分析和建模（涉及非均匀双折射介质中的麦克斯韦方程的解）。 液晶的研究是材料科学的一个领域，其重要性正在迅速增长，主要是由显示器行业的商业应用驱动：手表或计算器显示器，笔记本电脑屏幕，高清平板电视屏幕等。 它是唯一一个专门致力于液晶研究的学术机构，也是美国国家科学基金会“先进液晶光学材料”科学技术中心（ALCOM）的所在地。调查员的研究项目有助于在涉及物理和化学以及数学和计算机科学的跨学科环境中开展这一活动。 他对LCI中的理论家和实验学家感兴趣的当前问题进行数值模拟。 他带来承担国家的最先进的技术，从现代数值分析和科学计算，以补充理论和实验。在LCI的研究人员是在他们的极限，使用先进的实验技术，在探测液晶的结构在非常小的（亚微米）尺寸的容器在某些显示技术目前正在开发中。 此外，复杂的液晶器件（上述类型）的光学特性的数值模拟是在一个相当原始的发展状态。 该项目的数字工作在这些领域发挥了重要作用。 ***