title: Symmetry breaking of nematic umbilical defects through an amplitude equation.
abstract: The existence, stability properties, and bifurcation diagram of the nematic umbilical defects is studied. Close to the Fréedericksz transition of nematic liquid crystals with negative anisotropic dielectric constant and homeotropic anchoring, an anisotropic Ginzburg-Landau equation for the amplitude of the tilt of the director away from the vertical axis is derived by taking the three-dimensional (3D) to 2D limit of the Frank-Oseen model. The anisotropic Ginzburg-Landau equation allows us to reveal the mechanism of symmetry breaking of nematic umbilical defects. The positive defect is fully characterized as a function of the anisotropy, while the negative defect is characterized perturbatively. Numerical simulations show quite good agreement with the analytical results.
authors.affiliation: Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile.
authors.forename: Marcel G
authors.initials: MG
authors.lastname: Clerc
authors.affiliation: Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile.
authors.forename: Estefania
authors.initials: E
authors.lastname: Vidal-Henriquez
authors.affiliation: Departamento de Ingeniería Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile.
authors.forename: Juan Diego
authors.initials: JD
authors.lastname: Davila
authors.affiliation: Departamento de Ingeniería Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile.
authors.forename: Michał
authors.initials: M
authors.lastname: Kowalczyk
mesh_terms: D016880:Anisotropy; D017097:Electric Impedance; D050866:Liquid Crystals