Order Reconstruction for Nematics on Squares with Isotropic Inclusions: A Landau--De Gennes Study

DOI10.1137/17M1179820zbMath1473.35568arXiv1803.02597WikidataQ127495170 ScholiaQ127495170MaRDI QIDQ5231220

Apala Majumdar, YiWei Wang, Giacomo Canevari

Publication date: 26 August 2019

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

Full work available at URL: https://arxiv.org/abs/1803.02597

zbMATH Keywords

Landau-de Gennesorder reconstructionisotropic inclusionsnumerical deflation techniques

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Liquid crystals (76A15) Variational methods for second-order elliptic equations (35J20) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) PDEs in connection with statistical mechanics (35Q82)

Related Items (14)

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 ⋮ Polydispersity and surface energy strength in nematic colloids ⋮ Placement of an Obstacle for Optimizing the Fundamental Eigenvalue of Divergence Form Elliptic Operators ⋮ One-Dimensional Ferronematics in a Channel: Order Reconstruction, Bifurcations, and Multistability ⋮ A Multifaceted Study of Nematic Order Reconstruction in Microfluidic Channels ⋮ Design of effective bulk potentials for nematic liquid crystals via colloidal homogenisation ⋮ Surface, size and topological effects for some nematic equilibria on rectangular domains ⋮ A Reduced Study for Nematic Equilibria on Two-Dimensional Polygons ⋮ A Variational Lagrangian Scheme for a Phase-Field Model: A Discrete Energetic Variational Approach ⋮ Error analysis of Nitsche's and discontinuous Galerkin methods of a reduced Landau-de Gennes problem ⋮ Pattern formation for nematic liquid crystals -- modelling, analysis, and applications ⋮ Cubic microlattices embedded in nematic liquid crystals: a Landau-de Gennes study

Cites Work

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• Dimension Reduction for the Landau--de Gennes Model: The Vanishing Nematic Correlation Length Limit
• Deflation Techniques for Finding Distinct Solutions of Nonlinear Partial Differential Equations

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