Lee, Y;
(2022)
Micropolar continua as projective space of Skyrmions.
Philosophical Magazine
, 102
(1)
pp. 26-59.
10.1080/14786435.2021.1984605.
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Abstract
Micropolar continua are shown to be the generalisation of nematic liquid crystals through perspectives of order parameters, topological and geometrical considerations. Micropolar continua and nematic liquid crystals are recognised as antipodals of S^{3} and S^{2} in projective geometry. We show that position-dependent rotational axial fields in kinematic micropolar continua can be considered as solutions of anisotropic Higgs fields, characterised by integers N. We emphasise that the identical integers N are topological invariants through homotopy classifications based on defects of order parameters and a finite energy requirement. Magnetic monopoles and Skyrmions are investigated based on the theories of defects of continua in Riemann–Cartan manifolds.
| Type: | Article |
|---|---|
| Title: | Micropolar continua as projective space of Skyrmions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1080/14786435.2021.1984605 |
| Publisher version: | https://doi.org/10.1080/14786435.2021.1984605 |
| Language: | English |
| Additional information: | Copyright © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | Conserved current, topological invariance, homotopy, Cosserat continuum, Skyrmion |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10136828 |
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