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Global defect topology in nematic liquid crystals
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Machon, Thomas and Alexander, Gareth P. (2016) Global defect topology in nematic liquid crystals. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472 (2191). doi:10.1098/rspa.2016.0265 ISSN 1364-5021.
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Official URL: http://dx.doi.org/10.1098/rspa.2016.0265
Abstract
We give the global homotopy classification of nematic textures for a general domain with weak anchoring boundary conditions and arbitrary defect set in terms of twisted cohomology, and give an explicit computation for the case of knotted and linked defects in ℝ3, showing that the distinct homotopy classes have a 1–1 correspondence with the first homology group of the branched double cover, branched over the disclination loops. We show further that the subset of those classes corresponding to elements of order 2 in this group has representatives that are planar and characterize the obstruction for other classes in terms of merons. The planar textures are a feature of the global defect topology that is not reflected in any local characterization. Finally, we describe how the global classification relates to recent experiments on nematic droplets and how elements of order 4 relate to the presence of τ lines in cholesterics.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QC Physics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Physics | ||||||||
| Library of Congress Subject Headings (LCSH): | Liquid crystals, Topological defects (Physics) , Knot theory | ||||||||
| Journal or Publication Title: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | ||||||||
| Publisher: | The Royal Society Publishing | ||||||||
| ISSN: | 1364-5021 | ||||||||
| Official Date: | 6 July 2016 | ||||||||
| Dates: |
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| Volume: | 472 | ||||||||
| Number: | 2191 | ||||||||
| DOI: | 10.1098/rspa.2016.0265 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 7 July 2016 | ||||||||
| Date of first compliant Open Access: | 8 July 2016 | ||||||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), University of Warwick Chancellor's Scholarship, University of Warwick Institute of Advanced Study Scholarship | ||||||||
| Grant number: | A.MACX.0002, EP/N007883/1 (EPSRC) |
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