Bifurcation analysis in a frustrated nematic cell

DOI10.1007/s00332-014-9216-7zbMath1316.76009arXiv1310.6920OpenAlexW3099462234MaRDI QIDQ484452

Xavier Lamy

Publication date: 7 January 2015

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.6920

zbMATH Keywords

minimizerEuler-Lagrange equationeigenvalue exchange solutionLandau-de Gennes reduced free energy

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Liquid crystals (76A15) Hydrodynamic stability (76E99)

Related Items (18)

Nematic Liquid Crystals in a Rectangular Confinement: Solution Landscape, and Bifurcation ⋮ Minimizers of the Landau-de Gennes energy around a spherical colloid particle ⋮ Entire vortex solutions of negative degree for the anisotropic Ginzburg-Landau system ⋮ Harmonic maps with prescribed degrees on the boundary of an annulus and bifurcation of catenoids ⋮ One-Dimensional Ferronematics in a Channel: Order Reconstruction, Bifurcations, and Multistability ⋮ Revisiting the Two-Dimensional Defect-Free Azimuthal Nematic Equilibrium on an Annulus ⋮ Uniaxial symmetry in nematic liquid crystals ⋮ A Multifaceted Study of Nematic Order Reconstruction in Microfluidic Channels ⋮ The radial hedgehog solution in the Landau-de Gennes theory: effects of the bulk potentials ⋮ Order Reconstruction for Nematics on Squares and Hexagons: A Landau--de Gennes Study ⋮ Surface, size and topological effects for some nematic equilibria on rectangular domains ⋮ A Reduced Study for Nematic Equilibria on Two-Dimensional Polygons ⋮ Saturn ring defect around a spherical particle immersed in a nematic liquid crystal ⋮ On the covergence of minimizers of singular perturbation functionals ⋮ Global Uniform Estimate for the Modulus of Two-Dimensional Ginzburg-Landau Vortexless Solutions with Asymptotically Infinite Boundary Energy ⋮ Order Reconstruction for Nematics on Squares with Isotropic Inclusions: A Landau--De Gennes Study ⋮ Pattern formation for nematic liquid crystals -- modelling, analysis, and applications ⋮ Singular perturbation of manifold-valued maps with anisotropic energy

Cites Work

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• Orientability and energy minimization in liquid crystal models
• On minimizers of a Landau-de Gennes energy functional on planar domains
• The principle of symmetric criticality
• Landau-De Gennes theory of nematic liquid crystals: the Oseen-Frank limit and beyond
• A boundary-value problem for nematic liquid crystals with a variable degree of orientation
• Bifurcation, perturbation of simple eigenvalues, and linearized stability
• Analysis of nematic liquid crystals with disclination lines
• Bifurcation from simple eigenvalues
• On compound vortices in a two-component Ginzburg--Landau functional
• Biaxiality in the asymptotic analysis of a 2D Landau−de Gennes model for liquid crystals
• Ginzburg-Landau vortices

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