Diffusive transport in two-dimensional nematics

Ibrahim Fatkullin, Valeriy Slastikov

Research output: Contribution to journalArticle

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

Fingerprint

Kinetic Equation
Kinetics
Motion
Nematic liquid crystals
Moment Closure
Free energy
Vortex Dynamics
Smoluchowski Equation
Energy dissipation
Vortex flow
Gradient Flow
Hydrodynamics
Asymptotic Methods
Two-dimensional Systems
Nematic Liquid Crystal
Energy Dissipation
Order Parameter
Fluids
Free Energy
Degree of freedom

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

Diffusive transport in two-dimensional nematics. / Fatkullin, Ibrahim; Slastikov, Valeriy.

In: Discrete and Continuous Dynamical Systems - Series S, Vol. 8, No. 2, 01.04.2015, p. 323-340.

Research output: Contribution to journalArticle

@article{2be62d4c0c46425d98d33cea23fb0618,
title = "Diffusive transport in two-dimensional nematics",
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 = "Diffusive transport, Doi-Smoluchowski, Liquid crystals, Nematics, Vortex motion",
author = "Ibrahim Fatkullin and Valeriy Slastikov",
year = "2015",
month = "4",
day = "1",
doi = "10.3934/dcdss.2015.8.323",
language = "English (US)",
volume = "8",
pages = "323--340",
journal = "Discrete and Continuous Dynamical Systems - Series S",
issn = "1937-1632",
publisher = "American Institute of Mathematical Sciences",
number = "2",

}

TY - JOUR

T1 - Diffusive transport in two-dimensional nematics

AU - Fatkullin, Ibrahim

AU - Slastikov, Valeriy

PY - 2015/4/1

Y1 - 2015/4/1

N2 - 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.

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.

KW - Diffusive transport

KW - Doi-Smoluchowski

KW - Liquid crystals

KW - Nematics

KW - Vortex motion

UR - http://www.scopus.com/inward/record.url?scp=84907416434&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907416434&partnerID=8YFLogxK

U2 - 10.3934/dcdss.2015.8.323

DO - 10.3934/dcdss.2015.8.323

M3 - Article

VL - 8

SP - 323

EP - 340

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

SN - 1937-1632

IS - 2

ER -