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Tetrahedral Frame Fields via Constrained Third-Order Symmetric Tensors

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

Tetrahedral Frame Fields via Constrained Third-Order Symmetric Tensors Thumbnail


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.

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
Keywords Tetrahedral frame · Third-order tensor · Liquid crystal · Ginzburg-Landau functional
Public URL
Publisher URL
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.


2210.00575 (22.5 Mb)

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