Tetrahedral frame fields via constrained third order symmetric tensors

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

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.

Citation

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: https://nottingham-repository.worktribe.com/output/17945368
• Publisher URL: https://www.springer.com/journal/332