Half-Integer Point Defects in the Q-Tensor Theory of Nematic Liquid Crystals

G. Di Fratta; J. M. Robbins; V. Slastikov; A. Zarnescu

doi:10.1007/s00332-015-9271-8

Half-Integer Point Defects in the Q-Tensor Theory of Nematic Liquid Crystals

G. Di Fratta^*
, J. M. Robbins
, V. Slastikov
, A. Zarnescu

^*Corresponding author for this work

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

32 Citations (Scopus)

435 Downloads (Pure)

Abstract

We investigate prototypical profiles of point defects in two-dimensional liquid crystals within the framework of Landau–de Gennes theory. Using boundary conditions characteristic of defects of index k/2, we find a critical point of the Landau–de Gennes energy that is characterised by a system of ordinary differential equations. In the deep nematic regime, b² small, we prove that this critical point is the unique global minimiser of the Landau–de Gennes energy. For the case b² = 0, we investigate in greater detail the regime of vanishing elastic constant L → 0, where we obtain three explicit point defect profiles, including the global minimiser.

Original language	English
Pages (from-to)	121-140
Number of pages	20
Journal	Journal of Nonlinear Science
Volume	26
Issue number	1
Early online date	25 Aug 2015
DOIs	https://doi.org/10.1007/s00332-015-9271-8
Publication status	Published - Feb 2016

Keywords

Liquid crystal defects
Nonlinear elliptic PDE system
Singular ODE system
Stability
Vortex

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10.1007/s00332-015-9271-8

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title = "Half-Integer Point Defects in the Q-Tensor Theory of Nematic Liquid Crystals",

abstract = "We investigate prototypical profiles of point defects in two-dimensional liquid crystals within the framework of Landau–de Gennes theory. Using boundary conditions characteristic of defects of index k/2, we find a critical point of the Landau–de Gennes energy that is characterised by a system of ordinary differential equations. In the deep nematic regime, b2 small, we prove that this critical point is the unique global minimiser of the Landau–de Gennes energy. For the case b2 = 0, we investigate in greater detail the regime of vanishing elastic constant L → 0, where we obtain three explicit point defect profiles, including the global minimiser.",

keywords = "Liquid crystal defects, Nonlinear elliptic PDE system, Singular ODE system, Stability, Vortex",

author = "\{Di Fratta\}, G. and Robbins, \{J. M.\} and V. Slastikov and A. Zarnescu",

year = "2016",

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language = "English",

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journal = "Journal of Nonlinear Science",

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T1 - Half-Integer Point Defects in the Q-Tensor Theory of Nematic Liquid Crystals

AU - Di Fratta, G.

AU - Robbins, J. M.

AU - Slastikov, V.

AU - Zarnescu, A.

PY - 2016/2

Y1 - 2016/2

N2 - We investigate prototypical profiles of point defects in two-dimensional liquid crystals within the framework of Landau–de Gennes theory. Using boundary conditions characteristic of defects of index k/2, we find a critical point of the Landau–de Gennes energy that is characterised by a system of ordinary differential equations. In the deep nematic regime, b2 small, we prove that this critical point is the unique global minimiser of the Landau–de Gennes energy. For the case b2 = 0, we investigate in greater detail the regime of vanishing elastic constant L → 0, where we obtain three explicit point defect profiles, including the global minimiser.

AB - We investigate prototypical profiles of point defects in two-dimensional liquid crystals within the framework of Landau–de Gennes theory. Using boundary conditions characteristic of defects of index k/2, we find a critical point of the Landau–de Gennes energy that is characterised by a system of ordinary differential equations. In the deep nematic regime, b2 small, we prove that this critical point is the unique global minimiser of the Landau–de Gennes energy. For the case b2 = 0, we investigate in greater detail the regime of vanishing elastic constant L → 0, where we obtain three explicit point defect profiles, including the global minimiser.

KW - Liquid crystal defects

KW - Nonlinear elliptic PDE system

KW - Singular ODE system

KW - Stability

KW - Vortex

UR - https://www.scopus.com/pages/publications/84939817851

U2 - 10.1007/s00332-015-9271-8

DO - 10.1007/s00332-015-9271-8

M3 - Article (Academic Journal)

SN - 0938-8974

VL - 26

SP - 121

EP - 140

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

IS - 1

ER -

Half-Integer Point Defects in the Q-Tensor Theory of Nematic Liquid Crystals

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Mathematical analysis of domain wall motion in nanowires.

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Half-Integer Point Defects in the Q-Tensor Theory of Nematic Liquid Crystals

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