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Mathematical Sciences: The Dynamics of Defects and Patterns in Nematic Liquid Crystals

数学科学：向列液晶缺陷和模式的动力学

基本信息

批准号：
9109765
负责人：
Maria-Carme Calderer
金额：
$ 2.95万
依托单位：
Pennsylvania State Univ University Park
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
1991
资助国家：
美国
起止时间：
1991-07-01 至 1992-12-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9109765&HistoricalAwards=false
关键词：
Mathematical Sciences Dynamics Defects Patterns

项目摘要

In this project the principal investigator will analyze models of nematic liquid crystals with variable degrees of orientation as a means of studying highly nonlinear material behavior such as the formation of structured domains and patterns. The approach will consist of an analytical part and an experimental part. On the analytical side the principal investigator will employ mathematical methods to describe the formation and evolution of banding structures, singularity lines and disclinations in the solutions of the system of parabolic partial differential equations that governs the behavior of the materials. On the experimental side the principal investigator and a graduate student will conduct actual experiments in the Fluid Dynamics Laboratory in the Mathematics Department at Penn State in order to discover some qualitative features of the coarsening processes of domain structures and the nature of the interaction between singularity lines. The project to be carried out by the principal investigator and a graduate student is an exciting interplay between analytical applied mathematics and experimental fluid dynamics. For the past few years the principal investigator has studied the systems of differential equations that govern the behavior of liquid crystals using mathematical tools. She plans now to combine this analytical work with experimental studies of the phenomena modelled by the equations. The research will have relevance to improving the industrial processing of anisotropic polymeric materials.

在这个项目中，首席研究员将分析具有不同取向程度的向列液晶模型，作为研究高度非线性材料行为的一种手段，如结构域和图案的形成。该方法将由分析部分和实验部分组成。在分析方面，首席研究员将采用数学方法来描述控制材料行为的抛物型偏微分方程系统解中的带状结构、奇点线和偏差的形成和演变。在实验方面，首席研究员和一名研究生将在宾夕法尼亚州立大学数学系的流体动力学实验室进行实际实验，以发现域结构粗化过程的一些定性特征和奇点线之间相互作用的本质。该项目将由首席研究员和一名研究生进行，是分析应用数学和实验流体动力学之间令人兴奋的相互作用。在过去的几年里，首席研究员一直在使用数学工具研究控制液晶行为的微分方程系统。她现在计划将这项分析工作与由方程式模拟的现象的实验研究结合起来。本研究对提高各向异性高分子材料的工业加工具有重要意义。