Mathematical Sciences: Mathematical Analysis of Problems in Liquid Crystals

9310733加特兰研究者承担与液晶材料科学有关的问题的数学和数值分析。他继续在肯特州立大学Glenn H. Brown液晶研究所（LCI）从事跨学科工作。该项目的主要重点是三个方面：(1)液晶朗多-德热纳自由能的数值最小化（涉及张量阶参数、有限元分析、大稀疏优化和数值分分叉）；(2)液晶问题有限元分析的自动代码生成（利用符号和数值计算领域的现代计算机科学技术）；(3)显示器件光学的数值分析和建模（涉及非均匀双折射介质中麦克斯韦方程组的求解）。液晶研究是材料科学的一个领域，其重要性正在迅速增长，主要是由显示行业的商业应用驱动的：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。肯特州立大学液晶研究所在国际上享有很高的声誉。它是唯一一个专门从事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”（ALCOM）科学技术中心的所在地。除了数学和计算机科学之外，研究者的研究项目还在涉及物理和化学的跨学科环境中为这项活动做出了贡献。他对LCI的理论家和实验家感兴趣的当前问题进行了数值模拟。他从现代数值分析和科学计算中引入了最先进的技术来补充理论和实验。LCI的研究人员使用复杂的实验技术来探测目前正在开发的某些显示技术中非常小（亚微米）尺寸容器中的液晶结构，这是他们的极限。此外，复杂液晶器件（上述类型）光学性质的数值模拟还处于相当原始的发展状态。该项目的数值工作在这些方面发挥着重要作用。＊＊＊

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. ***