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Intrinsic geometry and director reconstruction for three-dimensional liquid crystals

Pollard, Joseph; Alexander, Gareth P

Intrinsic geometry and director reconstruction for three-dimensional liquid crystals Thumbnail


Authors

Joseph Pollard

Gareth P Alexander



Abstract

We give a description of the intrinsic geometry of elastic distortions in three-dimensional nematic liquid crystals and establish necessary and sufficient conditions for a set of functions to represent these distortions by describing how they couple to the curvature tensor. We demonstrate that, in contrast to the situation in two dimensions, the first-order gradients of the director alone are not sufficient for full reconstruction of the director field from its intrinsic geometry: it is necessary to provide additional information about the second-order director gradients. We describe several different methods by which the director field may be reconstructed from its intrinsic geometry. Finally, we discuss the coupling between individual distortions and curvature from the perspective of Lie algebras and groups and describe homogeneous spaces on which pure modes of distortion can be realised.

Citation

Pollard, J., & Alexander, G. P. (2021). Intrinsic geometry and director reconstruction for three-dimensional liquid crystals. New Journal of Physics, 23(6), Article 063006. https://doi.org/10.1088/1367-2630/abfdf4

Journal Article Type Article
Acceptance Date May 4, 2021
Online Publication Date Jun 3, 2021
Publication Date 2021-06
Deposit Date Sep 8, 2021
Publicly Available Date Sep 8, 2021
Journal New Journal of Physics
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 23
Issue 6
Article Number 063006
DOI https://doi.org/10.1088/1367-2630/abfdf4

Files

Published Journal Article (Advance online version) (1.8 Mb)
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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
Advance online version Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.







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