Tetrahedral Frame Fields via Constrained Third-Order Symmetric Tensors

Tetrahedral frame fields have applications to certain classes of nematic liquid crystals and frustrated media. We consider the problem constructing a tetrahedral field in three dimensional domains which boundary normal vector is included on boundary. To do this we identify an isomorphism between given symmetric, traceless third order tensor under particular nonlinear constraint. then define Ginzburg-Landau-type functional penalizes associated Using gradient descent, one retrieves globally defined limiting outside singular set. The can be recovered from by determinant maximization method, developed work. resulting numerically generated are smooth filaments that join together at triple junctions.