Analysis of Defects in Soft Matter Systems

今天，许多为高科技应用而设计的材料都是在微纳米尺度上设计的。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，这些材料的小规模结构不可避免地包含缺陷，使它们的反应更加复杂。物理学家提出了数学模型来解释这种行为。重要的是研究这些模型中解的性质，以便更好地理解它们在外部影响下的结构，获得它们的行为的更大的可预测性，并为它们开发有效的应用。这就是这个项目的目标。该项目包括研究生的培训和参与。研究者和他的同事们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。物理学家用矢量场和最小化自由能的标量或张量值序参数来描述这些材料的稳定状态。利用变分法和与自由能相关的非线性偏微分方程，研究了外部影响下的图案形成，以及缺陷和其他拓扑特征。在向列液晶中，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极限下得到的构形的性质。几何影响，如平面或弯曲，厚或薄的液晶材料，被考虑。在层状高温超导体中，Lawrence-Doniach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养和参与。

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.