Lifting ordered surfaces: ellipsoidal nematic shells

Leonid V. Mirantsev, André M. Sonnet, Epifanio G. Virga

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Abstract

When a material surface is functionalized so as to acquire some type of order,
functionalization of which soft condensed matter systems have recently provided many interesting examples, the modeller faces an alternative. Either the order is described on the curved, physical surface where it belongs, or it is described on a flat surface that is unrolled as pre-image of the physical surface under a suitable height function. This paper applies a general method that pursues the latter avenue by lifting whatever order tensor is deemed appropriate from a flat to a curved surface. We specialize this method to nematic shells, for which it also provides a simple, but perhaps convincing interpretation of the outcomes of some molecular-dynamics experiments on ellipsoidal shells.
Original languageEnglish
Article number012701
Number of pages12
JournalPhysical Review E
Volume98
Early online date20 Jul 2018
DOIs
Publication statusE-pub ahead of print - 20 Jul 2018

Keywords

  • condensed matter
  • lifting
  • ellipsoidal shells
  • ordered material surfaces
  • lifting tensor

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