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Tetrahedral frame fields via constrained third order symmetric tensors

Golovaty, Dmitry; Kurzke, Matthias; Montero, Jose Alberto; Spirn, Daniel


Dmitry Golovaty

Jose Alberto Montero

Daniel Spirn


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.


Golovaty, D., Kurzke, M., Montero, J. A., & Spirn, D. (in press). Tetrahedral frame fields via constrained third order symmetric tensors. Journal of Nonlinear Science,

Journal Article Type Article
Acceptance Date Feb 15, 2023
Deposit Date Mar 3, 2023
Print ISSN 0938-8974
Electronic ISSN 1432-1467
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Public URL
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