Diffusive transport in two-dimensional nematics

Ibrahim Fatkullin; Valeriy Slastikov

doi:10.3934/dcdss.2015.8.323

Article Contents

2015, Volume 8, Issue 2: 323-340. Doi: 10.3934/dcdss.2015.8.323

This issue Previous Article Conley's theorem for dispersive systems Next Article Structure formation in sheared polymer-rod nanocomposites

Diffusive transport in two-dimensional nematics

Ibrahim Fatkullin^1, and
Valeriy Slastikov^2,

1.
Department of Mathematics, University of Arizona, Tucson, AZ 85721
2.
Department of Mathematics, University of Bristol, Bristol BS8 1TW

Received: June 2013

Revised: November 2013

Published: April 2015

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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.

Keywords:

Mathematics Subject Classification: Primary: 76A15, 82B21, 82D30; Secondary: 35Q82, 35R09.

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