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dc.contributor.authorChillingworth, D.R.J.
dc.date.accessioned2016-06-13T13:33:50Z
dc.date.available2016-06-13T13:33:50Z
dc.date.issued2015-12-31
dc.identifier.issn0951-7715
dc.identifier.urihttp://hdl.handle.net/20.500.11824/243
dc.description.abstractWe describe a general mean field model for the free energy function for a homogeneous medium of mutually interacting molecules, based on the formalism for a biaxial nematic liquid crystal set out by Katriel et al (1986) in an influential paper in Liquid Crystals 1 and subsequently called the KKLS formalism. The free energy is expressed as the sum of an entropy term and an interaction (Hamiltonian) term. Using the language of group representation theory we identify the order parameters as averaged components of a linear transformation, and characterize the full symmetry group of the entropy term in the liquid crystal context as a wreath product SO(3) Z2. The symmetry-breaking role of the Hamiltonian, pointed out by Katriel et al, is here made explicit in terms of centre manifold reduction at bifurcation from isotropy. We use tools and methods of equivariant singularity theory to reduce the bifurcation study to that of a D3-invariant function on R2, ubiquitous in liquid crystal theory, and to describe the 'universal' bifurcation geometry in terms of the superposition of a familiar swallowtail surface controlling uniaxial equilibria and another less familiar surface controlling biaxial equilibria. In principle this provides a template for all nematic liquid crystal phase transitions close to isotropy, although further work is needed to identify the absolute minima that are the critical points representing stable phases.
dc.formatapplication/pdf
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectbiaxial nematic
dc.subjectbifurcation
dc.subjectfree energy
dc.subjectliquid crystal
dc.subjectsymmetry
dc.titleCritical points and symmetries of a free energy function for biaxial nematic liquid crystals
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1088/0951-7715/28/5/1483
dc.relation.publisherversionhttp://iopscience.iop.org/article/10.1088/0951-7715/28/5/1483/meta
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleNonlinearityen_US


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