A Reduced Study for Nematic Equilibria on Two-Dimensional Polygons

DOI10.1137/19M1293156zbMath1446.35204arXiv1910.05740OpenAlexW3104446286MaRDI QIDQ3298137

Lei Zhang, Apala Majumdar, Yucen Han

Publication date: 21 July 2020

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.05740

zbMATH Keywords

defectsbifurcation diagramspolygonsLandau-de Gennesring solutions

Mathematics Subject Classification ID

Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Liquid crystals (76A15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Variational methods for second-order elliptic equations (35J20) Bifurcations in context of PDEs (35B32) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) PDEs in connection with statistical mechanics (35Q82)

Related Items (9)

Parameter dependent finite element analysis for ferronematics solutions ⋮ Hierarchies of critical points of a Landau-de Gennes free energy on three-dimensional cuboids ⋮ Modelling and computation of liquid crystals ⋮ Nematic Liquid Crystals in a Rectangular Confinement: Solution Landscape, and Bifurcation ⋮ A Multifaceted Study of Nematic Order Reconstruction in Microfluidic Channels ⋮ Surface, size and topological effects for some nematic equilibria on rectangular domains ⋮ Solution landscape of a reduced Landau–de Gennes model on a hexagon ⋮ Pattern formation for nematic liquid crystals -- modelling, analysis, and applications ⋮ Multistability for a reduced nematic liquid crystal model in the exterior of 2D polygons

Uses Software

• Schwarz-Christoffel
• FEniCS
• SC Toolbox
• SyFi

Cites Work

• Instability of point defects in a two-dimensional nematic liquid crystal model
• Bifurcation analysis in a frustrated nematic cell
• Morphological characterization of the diblock copolymer problem with topological computation
• Automated solution of differential equations by the finite element method. The FEniCS book
• Dimension reduction for the Landau-de Gennes model in planar nematic thin films
• Landau-De Gennes theory of nematic liquid crystals: the Oseen-Frank limit and beyond
• Asymptotics for the minimization of a Ginzburg-Landau functional
• Parallel transport and defects on nematic shells
• Transition pathways between defect patterns in confined nematic liquid crystals
• Order reconstruction patterns in nematic liquid crystal wells
• Order Reconstruction for Nematics on Squares and Hexagons: A Landau--de Gennes Study
• Schwarz-Christoffel Mapping
• Surface, size and topological effects for some nematic equilibria on rectangular domains
• Order Reconstruction for Nematics on Squares with Isotropic Inclusions: A Landau--De Gennes Study
• High-Index Optimization-Based Shrinking Dimer Method for Finding High-Index Saddle Points
• On the Disclination Lines of Nematic Liquid Crystals
• Ginzburg-Landau vortices
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