Tangent unit-vector fields: Nonabelian homotopy invariants and the Dirichlet energy

Handle URI:
http://hdl.handle.net/10754/599864
Title:
Tangent unit-vector fields: Nonabelian homotopy invariants and the Dirichlet energy
Authors:
Majumdar, Apala; Robbins, J.M.; Zyskin, Maxim
Abstract:
Let O be a closed geodesic polygon in S2. Maps from O into S2 are said to satisfy tangent boundary conditions if the edges of O are mapped into the geodesics which contain them. Taking O to be an octant of S2, we evaluate the infimum Dirichlet energy, E (H), for continuous tangent maps of arbitrary homotopy type H. The expression for E (H) involves a topological invariant - the spelling length - associated with the (nonabelian) fundamental group of the n-times punctured two-sphere, π1 (S2 - {s1, ..., sn}, *). These results have applications for the theoretical modelling of nematic liquid crystal devices. To cite this article: A. Majumdar et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2009 Académie des sciences.
Citation:
Majumdar A, Robbins JM, Zyskin M (2009) Tangent unit-vector fields: Nonabelian homotopy invariants and the Dirichlet energy. Comptes Rendus Mathematique 347: 1159–1164. Available: http://dx.doi.org/10.1016/j.crma.2009.09.002.
Publisher:
Elsevier BV
Journal:
Comptes Rendus Mathematique
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Oct-2009
DOI:
10.1016/j.crma.2009.09.002
Type:
Article
ISSN:
1631-073X
Sponsors:
A.M. is supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) to the Oxford Centre for Collaborative Applied Mathematics (OCCAM). We thank Ulrike Tillmann for stimulating discussions and we thank Cameron Hall for help with the French summary.
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Full metadata record

DC FieldValue Language
dc.contributor.authorMajumdar, Apalaen
dc.contributor.authorRobbins, J.M.en
dc.contributor.authorZyskin, Maximen
dc.date.accessioned2016-02-28T06:31:11Zen
dc.date.available2016-02-28T06:31:11Zen
dc.date.issued2009-10en
dc.identifier.citationMajumdar A, Robbins JM, Zyskin M (2009) Tangent unit-vector fields: Nonabelian homotopy invariants and the Dirichlet energy. Comptes Rendus Mathematique 347: 1159–1164. Available: http://dx.doi.org/10.1016/j.crma.2009.09.002.en
dc.identifier.issn1631-073Xen
dc.identifier.doi10.1016/j.crma.2009.09.002en
dc.identifier.urihttp://hdl.handle.net/10754/599864en
dc.description.abstractLet O be a closed geodesic polygon in S2. Maps from O into S2 are said to satisfy tangent boundary conditions if the edges of O are mapped into the geodesics which contain them. Taking O to be an octant of S2, we evaluate the infimum Dirichlet energy, E (H), for continuous tangent maps of arbitrary homotopy type H. The expression for E (H) involves a topological invariant - the spelling length - associated with the (nonabelian) fundamental group of the n-times punctured two-sphere, π1 (S2 - {s1, ..., sn}, *). These results have applications for the theoretical modelling of nematic liquid crystal devices. To cite this article: A. Majumdar et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2009 Académie des sciences.en
dc.description.sponsorshipA.M. is supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) to the Oxford Centre for Collaborative Applied Mathematics (OCCAM). We thank Ulrike Tillmann for stimulating discussions and we thank Cameron Hall for help with the French summary.en
dc.publisherElsevier BVen
dc.titleTangent unit-vector fields: Nonabelian homotopy invariants and the Dirichlet energyen
dc.typeArticleen
dc.identifier.journalComptes Rendus Mathematiqueen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionUniversity of Bristol, Bristol, United Kingdomen
dc.contributor.institutionDepartment of Mathematics, Brownsville, TX 78520, United Statesen
kaust.grant.numberKUK-C1-013-04en
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