Diffusive transport in two-dimensional nematics

Ibrahim Fatkullin; Valeriy Slastikov

doi:10.3934/dcdss.2015.8.323

Diffusive transport in two-dimensional nematics

Ibrahim Fatkullin^*, Valeriy Slastikov

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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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.

Original language	English
Pages (from-to)	323-340
Number of pages	18
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	8
Issue number	2
Early online date	1 Jul 2014
DOIs	https://doi.org/10.3934/dcdss.2015.8.323
Publication status	Published - 1 Apr 2015

Keywords

Diffusive transport
Doi-Smoluchowski
Liquid crystals
Nematics
Vortex motion

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10.3934/dcdss.2015.8.323

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AB - 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.

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JF - Discrete and Continuous Dynamical Systems - Series S

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Diffusive transport in two-dimensional nematics

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Mathematical analysis of domain wall motion in nanowires.

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Diffusive transport in two-dimensional nematics

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Mathematical analysis of domain wall motion in nanowires.

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