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arXiv · 2210.00575

Tetrahedral frame fields via constrained third order symmetric tensors

Dmitry Golovaty·Matthias Kurzke·Jose Alberto Montero·Daniel Spirn
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Abstract

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.

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Dmitry Golovaty, Matthias Kurzke, Jose Alberto Montero, Daniel Spirn. 2022-10-02. Tetrahedral frame fields via constrained third order symmetric tensors. https://doi.org/10.1007/s00332-023-09898-x

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