Octupolar tensors for liquid crystals

Yannan Chen, Liqun Qi, Epifanio G. Virga

Research output: Journal article publicationJournal articleAcademic researchpeer-review

13 Citations (Scopus)

Abstract

A third-rank three-dimensional symmetric traceless tensor, called the octupolar tensor, has been introduced to study tetrahedratic nematic phases in liquid crystals. The octupolar potential, a scalar-valued function generated on the unit sphere by that tensor, should ideally have four maxima (on the vertices of a tetrahedron), but it was recently found to possess an equally generic variant with three maxima instead of four. It was also shown that the irreducible admissible region for the octupolar tensor in a three-dimensional parameter space is bounded by a dome-shaped surface, beneath which is a separatrix surface connecting the two generic octupolar states. The latter surface, which was obtained through numerical continuation, may be physically interpreted as marking a possible intra-octupolar transition. In this paper, by using the resultant theory of algebraic geometry and the E-characteristic polynomial of spectral theory of tensors, we give a closed-form, algebraic expression for both the dome-shaped surface and the separatrix surface. This turns the envisaged intra-octupolar transition into a quantitative, possibly observable prediction.
Original languageEnglish
Article number025206
JournalJournal of Physics A: Mathematical and Theoretical
Volume51
Issue number2
DOIs
Publication statusPublished - 12 Jan 2018

Keywords

  • Liquid crystals
  • Octupolar order tensors
  • Resultants

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this