Modeling, Computation, and Analysis of Complex Liquid Crystal Systems and Transitions

复杂液晶系统和转变的建模、计算和分析

• 批准号: 0608670
• 负责人: Eugene Gartland
• 金额: $ 23.79万
• 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: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0608670&HistoricalAwards=false
• 关键词: Modeling; Computation; Analysis; Complex; Liquid

GartlandDMS-0608670 The investigator carries out numerical modeling of problemsin two important new areas of the physics of liquid crystals: (1)mean-field theories for phases of biaxial and bent-coreliquid-crystal materials, and (2) numerical solution ofmacroscopic models for the dynamics and statics of point defectsin liquid-crystal systems (in the absence or presence of fluidflow). The investigator uses techniques from modern numericalbifurcation analysis together with the theories of singularitiesand bifurcations in the presence of symmetry to study the fullbifurcation and phase behavior of recent mean-field models forbiaxial materials, along with models that he and collaboratorsare developing for the important new class of bent-corematerials. The investigator adapts and extends methods fromcomputational fluids with moving and deforming bodies ("movingoverset grid methods") to provide effective techniques toaccurately model challenging problems involving the dynamics andstatics of point defects in macroscopic liquid-crystal directormodels, with application to surprising recent physicalexperiments on defect-pair annihilation in capillaries filledwith a liquid-crystal material. Liquid crystals are complex fluids that possess partialmolecular orientational order. They can be used to controllight, and this feature underlies many of their significanttechnological applications. In recent years, new liquid-crystalmolecules have been synthesized that exhibit certain specialphases. These new phases are termed "biaxial," because they havesecondary ordering properties in addition to those of the morecommon "uniaxial" materials. The liquid-crystal community hashigh hopes for potential new applications of these new materials. The theoretical and experimental study of biaxial liquid crystalsis at a relatively early stage. In this project the investigatoranalyzes a mathematical model for such materials thatcharacterizes the bulk equilibrium state of the system andassociated transitions, as a function of control parameters suchas temperature. This study requires both mathematical andnumerical techniques. In addition, the investigator andcollaborators develop new models for the special sub-class of"bent core" liquid crystals, which are of high current interest. The merits of this work are two-fold: (1) validation of themodels and (2) the development of predictive tools to aid in thedesign of experiments and in the identification of parameterranges for technological applications. The second main topic ofthe project concerns the numerical modeling of the dynamics ofdefects in liquid crystals (isolated singularities in the fieldsthat characterize the orientational properties of the medium). Defects are ubiquitous in liquid-crystal systems, and they causeconsiderable difficulty both from mathematical and numericalpoints of view. The investigator and co-workers apply numericalprocedures from other areas of computational fluid dynamics, bothto model numerically a target problem involving the annihilationof a pair of point defects in a capillary tube filled with liquidcrystal and to compare these numerical results to recentlypublished experimental data. These techniques (new to the areaof liquid crystals) should open the door to a number of othernumerical-modeling problems involving defects that havepreviously been hampered by unphysical numerical artifacts.

GartlandDMS-0608670 研究者在液晶物理学的两个重要的新领域中进行问题的数值模拟：（1）双轴和双芯液晶材料相的平均场理论，以及（2）点缺陷液晶系统的动态和静态的宏观模型的数值解（在没有或存在流体流动的情况下）。 研究者使用现代数值分叉分析技术，结合对称性条件下的奇点和分叉理论，研究双轴材料的最新平均场模型的全分叉和相位行为，沿着他和合作者正在为重要的新一类核芯材料开发的模型。 研究人员调整和扩展的方法从计算流体与移动和变形机构（“movingoverset网格方法”），以提供有效的技术，以准确地模拟具有挑战性的问题，涉及宏观液晶directormodels点缺陷的动态和静态，与应用程序令人惊讶的最近的物理实验缺陷对湮灭在充满液晶材料的毛细管。 液晶是具有部分分子取向有序性的复杂流体。 它们可以用来控制光线，这一特性是它们许多重要技术应用的基础。 近年来，新的液晶分子已被合成，表现出某些特殊的酶。 这些新相被称为“双轴”，因为它们除了具有那些更常见的“单轴”材料的有序性外，还具有其他的有序性。 液晶社区对这些新材料的潜在新应用寄予厚望。双轴液晶的理论和实验研究还处于相对较早的阶段。 在这个项目中，分析器分析了这种材料的数学模型，该模型描述了系统的整体平衡状态和相关的转变，作为控制参数（如温度）的函数。 这项研究需要数学和数值技术。 此外，研究人员和合作者开发了新的模型的特殊子类的“弯曲核心”液晶，这是目前的高度兴趣。这项工作的优点有两个方面：（1）验证模型和（2）开发预测工具，以帮助设计实验和确定技术应用的参数范围。 该项目的第二个主要课题是关于液晶缺陷动力学的数值模拟（表征介质取向特性的场孤立奇点）。缺陷在液晶系统中是普遍存在的，从数学和数值的观点来看，它们都造成了相当大的困难。 研究人员和同事应用numericalprocedures从其他领域的计算流体动力学，bothto数字模型的目标问题，涉及annihilationof一对点缺陷的毛细管充满liquidcrystal和比较这些数值结果recentlypublished实验数据。 这些技术（液晶领域的新技术）应该为许多其他数值模拟问题打开大门，这些问题涉及以前被非物理数值伪影阻碍的缺陷。