Related Experiment Video
Updated: Apr 25, 2026

Author Spotlight: Non-Contact Measurement of Tissue Mechanics in Live Chick Embryos Using Brillouin Microscopy
Published on: November 10, 2023
Symmetry breaking of nematic umbilical defects through an amplitude equation
Marcel G Clerc1, Estefania Vidal-Henriquez1, Juan Diego Davila2
1Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile.
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.
Related Concept Videos
Symmetry in Maxwell's Equations
Unsymmetric Bending - Angle of Neutral Axis
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal...
Unsymmetric Bending
Deformations in a Symmetric Member in Bending
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
Plastic Deformations of Members with a Single Plane of Symmetry
General Case of Eccentric Axial Loading
Consider a member subjected to equal and opposite forces that are applied along a line that does not coincide with the member's neutral axis. In unsymmetrical...

