Equilibrium Liquid Crystal Configurations: Energetics, Singularities and Applications

平衡液晶构型：能量学、奇点和应用

• 批准号: EP/E010288/1
• 负责人: John Ball
• 金额: $ 40.39万
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2006
• 资助国家: 英国
• 起止时间: 2006 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FE010288%2F1
• 关键词: Equilibrium; Liquid; Crystal; Configurations; Energetics

The research concerns the mathematical description of liquid crystals, an intermediate state of matter between solids and liquids. Liquid crystals are of technological importance because they are the working material of many electronic displays. A uniaxial nematic liquid crystal consists of rod-like molecules which at each point tend to align in a particular direction, like matches in a matchbox. This direction can be influenced by electric fields. The direction is determined by solving the governing partial differential equations that describe the mechanics of the liquid crystal. These equations depend in particular on the form that is assumed for the energy density of the liquid crystal. The proposal has various aims. The first is to examine when an arrow can be consistently assigned to the preferred direction. Such an arrow is not physical, since the molecules can be inverted end-to-end without changing their mechanical properties. However the existence of such an arrow is assumed in some widely-used theories, and we will study how the predictions of such theories compare to other theories in which no such arrow is assigned. The second aim is to investigate whether forms of the energy density different from those usually used could help to describe the behaviour of liquid crystals at defects, that is at points where the alignment direction is not uniquely defined. Related to this is the question of how the energy density can be determined experimentally. The third aim is to study when the equations have equilibrium solutions, in the context of theories which do not assign an unphysical arrow to the preferred direction, and whether these solutions have defects. Finally we will apply our work to the study of prototype new display devices, such as the Post Aligned Bistable Nematic (PABN) Device being developed at Hewlett-Packard laboratories.

该研究涉及液晶的数学描述，液晶是固体和液体之间的中间状态。液晶具有重要的技术意义，因为它们是许多电子显示器的工作材料。单轴双折射液晶由棒状分子组成，这些分子在每一点上都倾向于在特定的方向上排列，就像火柴盒中的火柴一样。这个方向可以受到电场的影响。通过求解描述液晶力学的偏微分方程来确定方向。这些方程尤其取决于为液晶的能量密度假定的形式。该提案有各种目的。第一个是检查何时可以将箭头一致地分配给首选方向。这样的箭头不是物理的，因为分子可以首尾颠倒而不改变它们的机械性质。然而，在一些广泛使用的理论中假设存在这样一个箭头，我们将研究这些理论的预测如何与其他没有指定这样一个箭头的理论进行比较。第二个目的是调查是否形式的能量密度不同于通常使用的那些可以帮助描述的行为的液晶缺陷，即在点的排列方向是不是唯一定义。与此相关的问题是如何通过实验确定能量密度。第三个目的是研究方程在没有指定非物理箭头指向首选方向的理论背景下何时有平衡解，以及这些解是否有缺陷。最后，我们将把我们的工作应用到新的显示器件的原型研究中，例如惠普实验室正在开发的后对准双稳态向列（PABN）器件。

项目成果

Orientable and non‐orientable director fields for liquid crystals

• DOI: 10.1002/pamm.200700489
• 发表时间: 2007-12
• 期刊: PAMM
• 作者: J. Ball;A. Zarnescu

Orientability and Energy Minimization in Liquid Crystal Models

• DOI: 10.1007/s00205-011-0421-3
• 发表时间: 2010-09
• 期刊: Archive for Rational Mechanics and Analysis
• 影响因子: 2.5
• 作者: J. Ball;A. Zarnescu

On uniqueness for time harmonic anisotropic Maxwell's equations with piecewise regular coefficients

分段正则系数时调和各向异性麦克斯韦方程组的唯一性

• DOI: 10.48550/arxiv.1201.2006
• 发表时间: 2012
• 作者: Ball J

On one dimensional inverse problems arising from polarimetric measurements of nematic liquid crystals

向列液晶偏振测量引起的一维逆问题

• DOI: 10.48550/arxiv.1304.2147
• 发表时间: 2013
• 作者: Capdeboscq Y

Partial regularity and smooth topology-preserving approximations of rough domains

粗糙域的部分正则性和光滑拓扑保持近似

• DOI: 10.1007/s00526-016-1092-6
• 发表时间: 2017
• 期刊: Calculus of Variations and Partial Differential Equations
• 影响因子: 2.1
• 作者: Ball J