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Intrinsic geometry and director reconstruction for three-dimensional liquid crystals
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Pollard, Joseph and Alexander, Gareth P. (2021) Intrinsic geometry and director reconstruction for three-dimensional liquid crystals. New Journal of Physics, 23 (6). 063006. doi:10.1088/1367-2630/abfdf4 ISSN 1367-2630.
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Official URL: https://doi.org/10.1088/1367-2630/abfdf4
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.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QC Physics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Physics | |||||||||
SWORD Depositor: | Library Publications Router | |||||||||
Library of Congress Subject Headings (LCSH): | Liquid crystals , Soft condensed matter , Statistical physics | |||||||||
Journal or Publication Title: | New Journal of Physics | |||||||||
Publisher: | IOP Publishing | |||||||||
ISSN: | 1367-2630 | |||||||||
Official Date: | 3 June 2021 | |||||||||
Dates: |
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Volume: | 23 | |||||||||
Number: | 6 | |||||||||
Article Number: | 063006 | |||||||||
DOI: | 10.1088/1367-2630/abfdf4 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||
Copyright Holders: | © 2021 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft | |||||||||
Date of first compliant deposit: | 9 June 2021 | |||||||||
Date of first compliant Open Access: | 11 June 2021 | |||||||||
RIOXX Funder/Project Grant: |
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