Vorticity driven dynamics in orientationally ordered systems

液晶(LCS)是取向有序的流体。在更广泛的意义上，LCS可以被认为是具有取向有序性的软物质，是一类新兴的复杂流体。有许多实验表明液晶中有有趣的流动现象。我们专注于其中的两个，在这些地方，涡度由外部来源驱动，产生物质流动。在Janossy效应中，液晶主体中的染料分子在光激发下充当分子马达的转子，并产生涡旋和随后的流动。在横山-田部实验中，朗缪尔单分子膜中的手性分子在水蒸气的横流作用下旋转并产生流动。这一奖项将支持旨在理解这种现象的工作，在这种现象中，局部力矩基本上作为涡度的点源，引起宏观旋转平移和流动。这项工作将通过涉及应用数学和物理的跨学科合作进行，目标是开发一个合理的数学模型，能够预测流动起关键作用的定向有序系统的动力学行为；并建立稳健的计算工具，捕捉流动和微观结构之间相互作用的基本特征。我们提出的数学模型有两个重要组成部分。首先，它使用全取向概率密度函数，而不是它的几个矩来表征取向顺序。其次，在模型中考虑了流动动力学。众所周知，非均质流动在形成瞬时微观结构中起着重要的作用，因此取向状态必须与宏观流场相耦合。这将为其他复杂软物质系统的研究和设计奠定基础，在这些软物质系统中，流动和局部涡度起着重要作用。一个新的方面是通过应用数学和物理在这个项目上的合作来探索研究生同伴指导的有效性。在快速发展的材料科学领域，复杂流体正在成为一类日益重要的材料。它们能够在对刺激的反应中表现出非常广泛的行为，导致了广泛的应用。这种丰富的响应性源于复杂的内部结构使之成为可能的物理过程。今天，复杂的流体范围从液晶到微纳胶体、病毒悬浮液和活性生物流体。其中许多系统的一个关键组成部分是成分的取向顺序。方向顺序和平移之间的耦合可能会导致非凡和意想不到的行为；这包括橡胶激光和光驱动塑料马达。该奖项将支持旨在理解这种现象的工作，目的是建立描述和帮助理解和利用负责机制的计算工具。拟议工作的更广泛影响是，所开发的工具在设计光响应性软物质、用于变形光学的超材料和生物运输战略方面对更大的社区有用。其中包括对研究生阶段科学和数学教育的贡献。参加该项目的两名研究生，一名是应用数学专业的，一名是化学物理的，将获得这项多方面工作的各个方面的专业知识，并将从与研究团队更资深的成员和彼此的互动中受益。将积极努力鼓励妇女和任职人数不足的群体成员参与这一项目。

Liquid Crystals (LCs) are orientationally ordered fluids. In a broader sense, LCs can be thought of as soft matter with orientational order, an emerging class of complex fluids. There are many experiments which show interesting flow phenomena in liquid crystals. We focus on two of these, where vorticity, driven by external sources, creates material flow. In the Janossy effect, dye molecules under photoexcitation in a liquid crystal host act as rotors of molecular motors, and generate vorticity and subsequent flow. In the Yokoyama-Tabe experiment, chiral molecules in a Langmuir monolayer are caused, by a transverse current of water vapor, to rotate and give rise to flow. This award will support work aimed at understanding such phenomena, where local torques, acting essentially as point sources of vorticity, give rise to macroscropic translation and flow. The work will be carried out through an interdisciplinary collaboration involving applied mathematics and physics, with the goal of developing a sound mathematical model which is capable of predicting the dynamical behavior of orientationally ordered systems where flow plays an essential role; and building robust computational tools that will capture the essential features of the interplay between flow and microstructure. The mathematical model we propose has two important components. First, it is the use of the full orientational probability density function, rather than a few of its moments to characterize orientational order. Second, the flow dynamics is included in the model. It is known that inhomogeneous flows play important roles in forming transient microstructures, thus the orientational state must be coupled with the macroscopic flow field. This will lay the framework for the study and design of other complex soft matter systems where flow and local vorticity play important roles. A novel aspect is the exploration of the effectiveness of peer mentoring by graduate students from applied mathematics and physics collaborating on this project. In the rapidly advancing field of materials science, complex fluids are emerging as an increasingly important class of materials. They are capable of exhibiting a remarkably broad range of behavior in response to excitations, leading to a wide variety of applications. This rich responsivity originates in physical processes which are made possible by complex internal structure. Complex fluids range today from liquid crystals to micro- and nanocolloids, virus suspensions and active biofluids. A key component of many of these systems is orientational order of the constituents. Remarkable and unexpected behavior can result from the coupling between orientational order and translation; this includes rubber lasers and light driven plastic motors. This award will support work aimed at understanding such phenomena, with the goal of building computational tools to describe and to help to understand and utilize the responsible mechanisms. The broader impacts of the proposed work are the usefulness of the developed tools to the larger community in the design of photo-responsive soft matter, metamaterials for transformation optics and strategies for biological transport. They include contributions to science and mathematics education at the graduate level. The two graduate students, one in applied mathematics and one in chemical physics, participating in this project will gain expertise in various aspects of this multifaceted work and will benefit from interactions with more senior members of the research team and each other. A vigorous effort will be made to encourage the participation of women and members of underrepresented groups in this project.