Analysis of Defects in Soft Matter Systems

今天为高科技应用设计的许多材料都是在微米或纳米尺度上设计的。 这些材料在外加电场或边界处理中的物理行为仍在通过实验和模拟来研究。 这一领域的一个重要挑战是，这些材料的小尺度结构不可避免地包含缺陷，使其响应更加复杂。 物理学家已经提出了数学模型来解释这种行为。 重要的是要调查这些模型中的解决方案的性质，以更好地了解他们的结构下的外部影响，以获得更大的可预测性，他们的行为，并开发有效的应用程序。 这就是这个项目的目标。 该项目包括研究生的培训和参与。研究人员和他的同事研究软物质系统中缺陷的形成，包括液晶材料和层状超导体。 物理学家使用矢量场和标量或张量值序参数来描述这些材料的稳定状态，这些序参数使自由能最小化。 外部影响下的图案形成，以及缺陷和其他拓扑特性，研究使用变分法和非线性偏微分方程与自由能。 在双折射液晶中，Landau-de Gennes和Maier-Saupe Q张量模型构成了研究的基础。 特别令人感兴趣的是在弹性消失的极限下得到的构形的性质。 几何的影响，如平面或弯曲，厚或薄的液晶材料，被认为是。 在层状高温超导体中，劳伦斯-多尼亚克模型是这项研究的基础。 研究了缺陷的性质和溶液在不同强度和取向的外加磁场中的行为。 上述工作包括研究生的培训和参与。

Many materials designed for high-tech applications today are engineered at the micro or nano scale. The physics of how these materials behave in applied electric fields or boundary treatments is still being worked out through experiments and simulations. An important challenge in this area is that the small-scale structure of these materials inevitably contains defects that make their responses even more complex. Physicists have proposed mathematical models to explain this behavior. It is important to investigate the nature of solutions in these models to better understand their structure under outside influences, to obtain greater predictability of their behavior, and to develop effective applications for them. That is the goal of this project. The project includes the training and participation of graduate students. The investigator and his colleagues study the formation of defects in soft matter systems, including liquid crystal materials and layered superconductors. Physicists describe stable states of these materials using vector fields and scalar or tensor-valued order parameters that minimize a free energy. Pattern formations under external influences, as well as defects and other topological characteristics, are studied using the calculus of variations and nonlinear partial differential equations associated with the free energy. In nematic liquid crystals, the Landau-de Gennes and Maier-Saupe Q-tensor models form the basis of the investigation. Of special interest is the nature of configurations obtained in the limit of vanishing elasticity. Geometric influences, such as flat or curved, thick or thin liquid crystal materials, are considered. In layered high-temperature superconductors, the Lawrence-Doniach model is the basis for this investigation. The nature of defects and behavior of solutions in applied magnetic fields of various intensities and orientations is investigated. The above work includes the training and participation of graduate students.