Nematic Liquid Crystals in a Rectangular Confinement: Solution Landscape, and Bifurcation

DOI10.1137/21M1447404zbMath1500.35244arXiv2109.10318OpenAlexW4306406294MaRDI QIDQ5044542

Lei Zhang, Baoming Shi, Yucen Han

Publication date: 1 November 2022

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

Full work available at URL: https://arxiv.org/abs/2109.10318

zbMATH Keywords

bifurcationnematic liquid crystalssaddle pointLandau-de Gennes modelsolution landscape

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Liquid crystals (76A15) Optimality conditions for minimax problems (49K35) Bifurcations in context of PDEs (35B32) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Dynamical systems in numerical analysis (37N30) Numerical problems in dynamical systems (65P99) Integro-partial differential equations (35R09)

Related Items (4)

Hierarchies of critical points of a Landau-de Gennes free energy on three-dimensional cuboids ⋮ Discretization and index-robust error analysis for constrained high-index saddle dynamics on the high-dimensional sphere ⋮ A model-free shrinking-dimer saddle dynamics for finding saddle point and solution landscape ⋮ Energy landscape analysis for two-phase multi-component NVT flash systems by using ETD type high-index saddle dynamics

Cites Work

• Bifurcation analysis in a frustrated nematic cell
• A mesh adaptivity scheme on the Landau-de Gennes functional minimization case in 3D, and its driving efficiency
• Landau-De Gennes theory of nematic liquid crystals: the Oseen-Frank limit and beyond
• Dimension reduction for the Landau-de Gennes model on curved nematic thin films
• Solution landscape of the Onsager model identifies non-axisymmetric critical points
• Transition pathways between defect patterns in confined nematic liquid crystals
• Axial symmetry and classification of stationary solutions of Doi-Onsager equation on the sphere with Maier-Saupe potential
• 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
• Solution landscape of a reduced Landau–de Gennes model on a hexagon
• Surface, size and topological effects for some nematic equilibria on rectangular domains
• High-Index Optimization-Based Shrinking Dimer Method for Finding High-Index Saddle Points
• On the Disclination Lines of Nematic Liquid Crystals
• Modelling and computation of liquid crystals

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