标题： 极性液晶在演化表面上的流体动力学相互作用 显示英文标题

标题： Hydrodynamic interactions in polar liquid crystals on evolving surfaces

摘要： 我们考虑被动和主动极性液晶流动的推导和数值解，其分子取向在演化曲面上受到切向锚定作用。 底层的被动模型是一个简化的表面Ericksen-Leslie模型，它是通过适当的边界条件对相应的三维方程进行薄层极限推导得到的。 考虑了有限元离散化，并研究了流体动力学对该模型在各种静态和演化表面上拓扑结构、几何特性和缺陷动力学相互作用的影响。 此外，我们还考虑了一个主动模型。 我们提出了一个主动极性粘性凝胶的表面公式，并以环面为例展示了基本曲率对拓扑缺陷位置的影响。 显示英文摘要

摘要： We consider the derivation and numerical solution of the flow of passive and active polar liquid crystals, whose molecular orientation is subjected to a tangential anchoring on an evolving curved surface. The underlying passive model is a simplified surface Ericksen-Leslie model, which is derived as a thin-film limit of the corresponding three-dimensional equations with appropriate boundary conditions. A finite element discretization is considered and the effect of hydrodynamics on the interplay of topology, geometric properties and defect dynamics is studied for this model on various stationary and evolving surfaces. Additionally, we consider an active model. We propose a surface formulation for an active polar viscous gel and exemplarily demonstrate the effect of the underlying curvature on the location of topological defects on a torus.