论文标题
四面体框架字段通过约束的三阶对称张量
Tetrahedral frame fields via constrained third order symmetric tensors
论文作者
论文摘要
四面体框架场在某些类别的列液晶和沮丧的培养基中具有应用。我们考虑在边界框架中包含边界正常向量的三个维域中构建四面体框架场的问题。为此，我们确定给定的四面体框架与在特定非线性约束下的对称，无可接触式三阶张量之间的同构。然后，我们定义了Ginzburg-Landau型功能，该功能会惩罚相关的非线性约束。使用梯度下降，一个人检索一个全球定义的限制张量。然后，可以通过在这项工作中开发的确定性最大化方法从该张量中回收四面体框架。所得的数值生成的框架字段在一个尺寸丝的外部平滑，这些丝网丝在三个连接处连接在一起。
Tetrahedral frame fields have applications to certain classes of nematic liquid crystals and frustrated media. We consider the problem of constructing a tetrahedral frame field in three dimensional domains in which the boundary normal vector is included in the frame on the boundary. To do this we identify an isomorphism between a given tetrahedral frame and a symmetric, traceless third order tensor under a particular nonlinear constraint. We then define a Ginzburg-Landau-type functional which penalizes the associated nonlinear constraint. Using gradient descent, one retrieves a globally defined limiting tensor outside of a singular set. The tetrahedral frame can then be recovered from this tensor by a determinant maximization method, developed in this work. The resulting numerically generated frame fields are smooth outside of one dimensional filaments that join together at triple junctions.
