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Existence of surface smectic states of liquid crystals

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  • Søren Fournais
  • Ayman Kachmar, Lebanese University
  • ,
  • Xing Bin Pan, East China Normal University

The Landau–de Gennes model of liquid crystals is a functional acting on wave functions (order parameters) and vector fields (director fields). In a specific asymptotic limit of the physical parameters, we construct critical points such that the wave function (order parameter) is localized near the boundary of the domain, and we determine a sharp localization of the boundary region where the wave function concentrates. Furthermore, we compute the asymptotics of the energy of such critical points along with a boundary energy that may serve in localizing the director field. In physical terms, our results prove the existence of a surface smectic state.

Original languageEnglish
JournalJournal of Functional Analysis
Volume274
Issue3
Pages (from-to)900-958
Number of pages59
ISSN0022-1236
DOIs
Publication statusPublished - 1 Feb 2018

    Research areas

  • Ginzburg–Landau functional, Landau–de Gennes functional, Surface smectic states, Surface superconductivity

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