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Tetrahedral Frame Fields via Constrained Third-Order Symmetric Tensors

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

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Authors

Dmitry Golovaty

Jose Alberto Montero

Daniel Spirn



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.

Journal Article Type Article
Acceptance Date Feb 15, 2023
Online Publication Date Mar 31, 2023
Publication Date 2023-06
Deposit Date Mar 3, 2023
Publicly Available Date Apr 1, 2024
Journal Journal of Nonlinear Science
Print ISSN 0938-8974
Electronic ISSN 1432-1467
Publisher Springer Science and Business Media LLC
Peer Reviewed Peer Reviewed
Volume 33
Issue 3
Article Number 48
DOI https://doi.org/10.1007/s00332-023-09898-x
Keywords Tetrahedral frame · Third-order tensor · Liquid crystal · Ginzburg-Landau functional
Public URL https://nottingham-repository.worktribe.com/output/17945368
Publisher URL https://link.springer.com/article/10.1007/s00332-023-09898-x
Additional Information Received: 4 October 2022; Accepted: 15 February 2023; First Online: 31 March 2023; : ; : The authors declare that they have no conflict of interests.

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