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.
Original language | English (US) |
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Article number | 48 |
Journal | Journal of Nonlinear Science |
Volume | 33 |
Issue number | 3 |
DOIs | |
State | Published - Jun 2023 |
Bibliographical note
Funding Information:DG was supported in part by the NSF grant DMS-2106551. DS was supported in part by the NSF grant DMS-2009352. The authors would like to thank the IMA where the project was initiated.
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Ginzburg-Landau functional
- Liquid crystal
- Tetrahedral frame
- Third-order tensor