title: Singular values, nematic disclinations, and emergent biaxiality.
abstract: Both uniaxial and biaxial nematic liquid crystals are defined by orientational ordering of their building blocks. While uniaxial nematics only orient the long molecular axis, biaxial order implies local order along three axes. As the natural degree of biaxiality and the associated frame that can be extracted from the tensorial description of the nematic order vanishes in the uniaxial phase, we extend the nematic director to a full biaxial frame by making use of a singular value decomposition of the gradient of the director field instead. The degrees of freedom are unveiled in the form of quasidefects and the similarities and differences between the uniaxial and biaxial phase are analyzed by applying the algebraic rules of the quaternion group to the uniaxial phase.
authors.affiliation: Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104, USA.
authors.forename: Simon
authors.initials: S
authors.lastname: Čopar
authors.forename: Mark R
authors.initials: MR
authors.lastname: Dennis
authors.forename: Randall D
authors.initials: RD
authors.lastname: Kamien
authors.forename: Slobodan
authors.initials: S
authors.lastname: Žumer
mesh_terms: D016880:Anisotropy; D003198:Computer Simulation; D050866:Liquid Crystals / Q000737:chemistry*; D008956:Models, Chemical; D008958:Models, Molecular; D008968:Molecular Conformation; D044367:Phase Transition