The Well Order Reconstruction Solution for three dimensional wells in the Landau-de Gennes theory

Giacomo Canevari, Joseph Harris, Apala Majumdar, Yiwei Wang

Research output: Contribution to journalArticle

Abstract

We study nematic equilibria on three-dimensional square wells, with emphasis on Well Order Reconstruction Solutions (WORS) as a function of the well size, characterized by , and the well height denoted by . The WORS are distinctive equilibria reported in Kralj and Majumdar (2014) for square domains, without taking the third dimension into account, which have two mutually perpendicular defect lines running along the square diagonals, intersecting at the square centre. We prove the existence of WORS on three-dimensional wells for arbitrary well heights, with (i) natural boundary conditions and (ii) realistic surface energies on the top and bottom well surfaces, along with Dirichlet conditions on the lateral surfaces. Moreover, the WORS is globally stable for small enough in both cases and unstable as increases. We numerically compute novel mixed 3D solutions for large and followed by a numerical investigation of the effects of surface anchoring on the WORS, exemplifying the relevance of the WORS solution in a 3D context.
Original languageEnglish
Article number103342
Number of pages14
JournalInternational Journal of Nonlinear Mechanics
Volume119
Early online date2 Nov 2019
DOIs
Publication statusE-pub ahead of print - 2 Nov 2019

Fingerprint

Three-dimensional
Dirichlet conditions
Surface Energy
Numerical Investigation
Perpendicular
Lateral
Defects
Unstable
Boundary conditions
Line
Arbitrary

Keywords

  • nematics
  • Landau–de Gennes theory
  • Well Order Reconstruction Solution
  • three-dimensional analysis
  • surface anchoring

Cite this

Canevari, Giacomo ; Harris, Joseph ; Majumdar, Apala ; Wang, Yiwei. / The Well Order Reconstruction Solution for three dimensional wells in the Landau-de Gennes theory. In: International Journal of Nonlinear Mechanics. 2020 ; Vol. 119.
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The Well Order Reconstruction Solution for three dimensional wells in the Landau-de Gennes theory. / Canevari, Giacomo; Harris, Joseph; Majumdar, Apala; Wang, Yiwei.

In: International Journal of Nonlinear Mechanics, Vol. 119, 103342, 31.03.2020.

Research output: Contribution to journalArticle

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AU - Canevari, Giacomo

AU - Harris, Joseph

AU - Majumdar, Apala

AU - Wang, Yiwei

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KW - nematics

KW - Landau–de Gennes theory

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