A reduced Landau-de Gennes study for nematic equilibria in three-dimensional prisms

Yucen Han, Baoming Shi, Lei Zhang, Apala Majumdar

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We model nematic liquid crystal configurations inside three-dimensional prisms, with a polygonal crosssection and Dirichlet boundary conditions on all prism surfaces. We work in a reduced Landau-de Gennes framework, and the Dirichlet conditions on the top and bottom surfaces are special in the sense, that they are critical points of the reduced Landau-de Gennes energy on the polygonal cross-section. The choice of the boundary conditions allows us to make a direct correspondence between the three-dimensional Landau-de Gennes critical points and pathways on the two-dimensional Landau-de Gennes solution landscape on the polygonal cross-section. We explore this concept by means of asymptotic analysis and numerical examples, with emphasis on a cuboid and a hexagonal prism, focusing on three-dimensional multistability tailored by two-dimensional solution landscapes.
Original languageEnglish
Pages (from-to)645-676
Number of pages32
JournalIMA Journal of Applied Mathematics
Issue number5
Early online date8 Nov 2023
Publication statusPublished - 1 Dec 2023


  • nematic liquid crystals
  • prism
  • equilibria
  • two-dimensional pathway


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