Nitschke Ingo, Nestler Michael, Praetorius Simon, Löwen Hartmut, Voigt Axel
Institut für Wissenschaftliches Rechnen, Technische Universität Dresden, 01062 Dresden, Germany.
Institut für Theoretische Physik II - Soft Matter, Heinrich-Heine- Universität Düsseldorf, 40225 Düsseldorf, Germany.
Proc Math Phys Eng Sci. 2018 Jun;474(2214):20170686. doi: 10.1098/rspa.2017.0686. Epub 2018 Jun 20.
We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the limiting process, we observe a continuous transition where the normal and tangential parts of the Q-tensor decouple and various intrinsic and extrinsic contributions emerge. The main properties of the thin film model, like uniaxiality and parameter phase space, are preserved in the limiting process. For the derived surface Landau-de Gennes model, we consider an -gradient flow. The resulting tensor-valued surface partial differential equation is numerically solved to demonstrate realizations of the tight coupling of elastic and bulk free energy with geometric properties.
我们考虑朗道-德热纳Q张量模型的薄膜极限情况。在极限过程中，我们观察到一种连续转变，其中Q张量的法向和切向部分解耦，各种本征和非本征贡献出现。薄膜模型的主要性质，如单轴性和参数相空间，在极限过程中得以保留。对于导出的表面朗道-德热纳模型，我们考虑一种 -梯度流。对由此产生的张量值表面偏微分方程进行数值求解，以证明弹性和体自由能与几何性质紧密耦合的各种实例。
