Nitschke Ingo, Reuther Sebastian, Voigt Axel
Institute of Scientific Computing, TU Dresden, 01062 Dresden, Germany.
Center for Systems Biology Dresden (CSBD), Pfotenhauerstraße 108, 01307 Dresden, Germany.
Proc Math Phys Eng Sci. 2020 Sep;476(2241):20200313. doi: 10.1098/rspa.2020.0313. Epub 2020 Sep 2.
Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk-free energies of the liquid crystal with geometric properties of the surface. We derive a thermodynamically consistent Landau-de Gennes-Helfrich model which considers the simultaneous relaxation of the -tensor field and the surface. The resulting system of tensor-valued surface partial differential equation and geometric evolution laws is numerically solved to tackle the rich dynamics of this system and to compute the resulting equilibrium shape. The results strongly depend on the intrinsic and extrinsic curvature contributions and lead to unexpected asymmetric shapes.
分子被限制在曲面切丛上的液晶呈现出有趣的现象，这些现象源于液晶的弹性自由能和体自由能与表面几何性质的紧密耦合。我们推导了一个热力学自洽的朗道 - 德热纳 - 赫尔弗里希模型，该模型考虑了张量场和表面的同时弛豫。对由此产生的张量值表面偏微分方程和几何演化定律系统进行数值求解，以处理该系统丰富的动力学并计算最终的平衡形状。结果强烈依赖于内在和外在曲率贡献，并导致意想不到的不对称形状。
