Diffusive transport in two-dimensional nematics

Ibrahim Fatkullin, Valeriy Slastikov

Research output: Contribution to journalReview articlepeer-review

Abstract

We discuss a dynamical theory for nematic liquid crystals describing the stage of evolution in which the hydrodynamic fluid motion has already equilibrated and the subsequent evolution proceeds via diffusive motion of the orientational degrees of freedom. This diffusion induces a slow motion of singularities of the order parameter field. Using asymptotic methods for gradient flows, we establish a relation between the Doi-Smoluchowski kinetic equation and vortex dynamics in two-dimensional systems. We also discuss moment closures for the kinetic equation and Landau-de Gennes-type free energy dissipation.

Original languageEnglish (US)
Pages (from-to)323-340
Number of pages18
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume8
Issue number2
DOIs
StatePublished - Apr 1 2015

Keywords

  • Diffusive transport
  • Doi-Smoluchowski
  • Liquid crystals
  • Nematics
  • Vortex motion

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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