dc.contributor.author
Chillingworth, David
dc.contributor.author
Forest, M. Gregory
dc.contributor.author
Lauterbach, Reiner
dc.contributor.author
Wulff, Claudia
dc.date.accessioned
2021-11-18T08:54:49Z
dc.date.available
2021-11-18T08:54:49Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/32756
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-32482
dc.description.abstract
We use geometric methods of equivariant dynamical systems to address a long-standing open problem in the theory of nematic liquid crystals, namely a proof of the existence and asymptotic stability of kayaking periodic orbits in response to steady shear flow. These are orbits for which the principal axis of orientation of the molecular field (the director) rotates out of the plane of shear and around the vorticity axis. With a small parameter attached to the symmetric part of the velocity gradient, the problem can be viewed as a symmetry-breaking bifurcation from an orbit of the rotation group SO(3) that contains both logrolling (equilibrium) and tumbling (periodic rotation of the director within the plane of shear) regimes as well as a continuum of neutrally stable kayaking orbits. The results turn out to require expansion to second order in the perturbation parameter.
en
dc.format.extent
59 Seiten
dc.rights.uri
https://creativecommons.org/licenses/by/4.0/
dc.subject
nematic liquid crystals
en
dc.subject
kayaking periodic orbits
en
dc.subject
steady shear flow
en
dc.subject.ddc
500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik
dc.title
Existence and Stability of Kayaking Orbits for Nematic Liquid Crystals in Simple Shear Flow
dc.type
Wissenschaftlicher Artikel
dcterms.bibliographicCitation.doi
10.1007/s00205-021-01703-x
dcterms.bibliographicCitation.journaltitle
Archive for Rational Mechanics and Analysis
dcterms.bibliographicCitation.number
2
dcterms.bibliographicCitation.pagestart
1229
dcterms.bibliographicCitation.pageend
1287
dcterms.bibliographicCitation.volume
242
dcterms.bibliographicCitation.url
https://doi.org/10.1007/s00205-021-01703-x
refubium.affiliation
Mathematik und Informatik
refubium.affiliation.other
Institut für Mathematik
refubium.resourceType.isindependentpub
no
dcterms.accessRights.openaire
open access
dcterms.isPartOf.eissn
1432-0673
refubium.resourceType.provider
WoS-Alert