Pattern formation for nematic liquid crystals -- modelling, analysis, and applications

DOI10.1007/978-3-031-04496-0_18zbMath1500.76002arXiv2107.14236OpenAlexW4312766200MaRDI QIDQ2080570

Publication date: 9 October 2022

Full work available at URL: https://arxiv.org/abs/2107.14236

regularity Euler-Lagrange equations asymptotic limit solution multiplicity energy-minimizing solution non-energy-minimizing solution two-dimensional Landau-de Gennes theory

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Variational methods applied to problems in fluid mechanics (76M30) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Liquid crystals (76A15) Research exposition (monographs, survey articles) pertaining to fluid mechanics (76-02)

Uses Software

FEniCS
SyFi

Cites Work

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Bifurcation analysis in a frustrated nematic cell
Automated solution of differential equations by the finite element method. The FEniCS book
Liquid crystals with variable degree of orientation
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
Transition pathways between defect patterns in confined nematic liquid crystals
Error analysis of Nitsche's and discontinuous Galerkin methods of a reduced Landau-de Gennes problem
Analysis of nematic liquid crystals with disclination lines
Order reconstruction patterns in nematic liquid crystal wells
Order Reconstruction for Nematics on Squares and Hexagons: A Landau--de Gennes Study
A Reduced Study for Nematic Equilibria on Two-Dimensional Polygons
Equilibrium order parameters of nematic liquid crystals in the Landau-de Gennes theory
Solution landscape of a reduced Landau–de Gennes model on a hexagon
Discontinuous Galerkin finite element methods for the Landau–de Gennes minimization problem of liquid crystals
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
Ginzburg-Landau vortices
An explicit finite difference scheme over hexagonal tessellation

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