Numerical Methods for Large Scale Liquid Crystal Director Models and Analysis of Electric-Field-Induced Instabilities

大规模液晶导向器模型的数值方法和电场引起的不稳定性分析

• 批准号: 1211597
• 负责人: Eugene Gartland
• 金额: $ 18.02万
• 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: 2012
• 资助国家: 美国
• 起止时间: 2012-07-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1211597&HistoricalAwards=false
• 关键词: Numerical; Methods; Large; Scale; Liquid

The research supported by this award is concerned with the analysis and numerical modeling of problems that arise in the basic and applied physics of liquid crystals. Specifically, this award will support research in two interrelated areas: (1) development of more efficient numerical methods for characterizing the equilibrium orientational properties of liquid crystals in the large-scale regime (three space dimensions) and (2) refined analysis of the nature of the coupling between liquid crystal orientational order and electric fields. The most commonly used models for liquid crystals at experimental and device scales are macroscopic continuum director models, which model local average orientation in terms of a unit-length vector field (the "director field"). The principal investigator will use techniques from numerical linear algebra and numerical optimization (saddle point problems, nullspace methods, reduced Hessian methods, preconditioning) to develop efficient solvers that deal effectively with the pointwise unit-length constraint associated with discretizations of such models, for which current approaches are inadequate in large-scale settings. Most liquid crystal devices and experiments utilize electric fields to control liquid crystal order, and the interaction between liquid crystal orientation and local electric field poses both numerical and analytical challenges (due to coupled equilibrium equations, free energies failing to be positive definite, and anomalous behavior of instability thresholds). The principal investigator will develop a variationally based, unified stability framework capable of providing computable local stability criteria for numerical solutions (in the discretized setting) and also capable of explaining anomalous instability thresholds (in the continuum setting).Liquid crystal materials exist in a complex fluid phase that exhibits orientational order of molecular axes at the microscopic level, just like a crystal. Virtually all of their material properties are anisotropic, that is, they are direction dependent (unlike ordinary liquids which look and behave the same in all directions). The orientational properties can therefore be coupled to a variety of external fields (electromagnetic, optical, temperature gradients, acoustic waves, etc.). The well-known use of liquid crystals in optical displays makes use of this behavior. However, the special properties of these materials make them useful in a much wider range of technological applications, including also drug delivery systems, soft actuators, biosensors, and others. Scientific computing is widely used in this area to optimize the performance of devices, to analyze experiments, and to validate the theory that is used to describe such devices. This award will support the development of advanced computational techniques for the numerical exploration of equilibrium orientational properties of large, complicated, modern liquid crystal systems associated with realistic devices and experiments, especially those involving coupled electric fields. Special attention is given to the nature of the coupling between the liquid crystal order and an applied electric field and to electric-field-induced instabilities of orientational order, which underlie the functioning of most devices and for which a deeper understanding is needed. The research will be carried out in collaboration with interdisciplinary and international partners, and it will impact applications and technologies using liquid crystals through improved performance analysis tools and techniques for interpreting experiments. The impact is expected to extend to the numerical modeling of ferromagnetic materials such as magnetic films used in hard drives, where models with similar features arise.

该奖项支持的研究涉及液晶基础和应用物理中出现的问题的分析和数值建模。 具体而言，该奖项将支持两个相互关联的领域的研究：（1）开发更有效的数值方法，用于表征大规模区域（三维空间）中液晶的平衡取向特性;（2）精细分析液晶取向顺序和电场之间的耦合性质。 在实验和设备尺度上最常用的液晶模型是宏观连续指向矢模型，其根据单位长度矢量场（“指向矢场”）对局部平均取向进行建模。主要研究者将使用数值线性代数和数值优化（鞍点问题，零空间方法，减少Hessian方法，预处理）的技术来开发有效的求解器，有效地处理与这种模型的离散化相关的逐点单位长度约束，目前的方法在大规模设置中是不够的。 大多数液晶器件和实验利用电场来控制液晶有序性，并且液晶取向和局部电场之间的相互作用提出了数值和分析挑战（由于耦合平衡方程、自由能不能是正定的以及不稳定阈值的异常行为）。主要研究者将开发一个基于变分的，统一的稳定性框架，能够为数值解提供可计算的局部稳定性标准（在离散设置），也能够解释异常的不稳定阈值（在连续设置）。液晶材料存在于一个复杂的流体相，在微观水平上表现出分子轴的取向顺序，就像晶体一样。 实际上，它们所有的材料性质都是各向异性的，也就是说，它们是方向相关的（不像普通液体在所有方向上看起来和行为都一样）。 因此，取向特性可以与各种外部场（电磁场、光场、温度梯度场、声波等）相耦合。液晶在光学显示器中的众所周知的用途利用了这种行为。然而，这些材料的特殊性质使它们在更广泛的技术应用中有用，包括药物输送系统，软致动器，生物传感器等。 科学计算在这一领域被广泛用于优化设备的性能、分析实验以及验证用于描述此类设备的理论。 该奖项将支持先进的计算技术的发展，用于与现实设备和实验相关的大型，复杂，现代液晶系统的平衡取向特性的数值探索，特别是那些涉及耦合电场的系统。 特别注意的是液晶顺序和施加的电场之间的耦合的性质和电场诱导的取向顺序的不稳定性，这是大多数设备的功能，并需要更深入的了解。 该研究将与跨学科和国际合作伙伴合作开展，并将通过改进性能分析工具和解释实验的技术来影响使用液晶的应用和技术。 这种影响预计将扩展到铁磁材料的数值建模，例如硬盘驱动器中使用的磁性薄膜，其中出现了具有类似特征的模型。