标题： 在 evolving surfaces 上的 Beris-Edwards 模型：拉格朗日-D'Alembert 方法 显示英文标题

标题： Beris-Edwards Models on Evolving Surfaces: A Lagrange-D'Alembert Approach

摘要： 利用拉格朗日－达朗贝尔原理，我们发展了热力学一致的表面伯利斯－爱德华兹模型。 这些模型耦合了粘性不可伸长的表面流与Landau-de Gennes-Helfrich能量，并考虑了表面Q-张量场和表面的同时松弛，同时将表面流体力学纳入考虑范围。 我们研究了不同的表述方式：一种是一般模型，包含三维表面Q-张量动力学以及通过拉格朗日乘子引入的可能约束；另一种是表面一致模型，具有表面Q-张量场的切向锚定以及可能的附加约束。 除了对表面Q-张量的不同处理方法（这引入了与表面几何特性不同耦合机制）外，我们还考虑了不同的时间导数，以解释表面向列体的不同物理意义。 我们将所推导出的模型与简化情况下的已有模型进行对比，并比较不同表述方式在数值实现方面的差异，同时提及这些模型在生物学中的潜在应用。 显示英文摘要

摘要： Using the Lagrange-D'Alembert principle we develop thermodynamically consistent surface Beris-Edwards models. These models couple viscous inextensible surface flow with a Landau-de Gennes-Helfrich energy and consider the simultaneous relaxation of the surface Q-tensor field and the surface, by taking hydrodynamics of the surface into account. We consider different formulations, a general model with three-dimensional surface Q-tensor dynamics and possible constraints incorporated by Lagrange multipliers and a surface conforming model with tangential anchoring of the surface Q-tensor field and possible additional constraints. In addition to different treatments of the surface Q-tensor, which introduces different coupling mechanisms with the geometric properties of the surface, we also consider different time derivatives to account for different physical interpretations of surface nematics. We relate the derived models to established models in simplified situations, compare the different formulations with respect to numerical realizations and mention potential applications in biology.