Symmetry of uniaxial global Landau-de Gennes minimizers in the theory of nematic liquid crystals

Duvan Henao, Apala Majumdar

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We extend the recent radial symmetry results by Pisante [J. Funct. Anal., 260 (2011), pp. 892--905] and Millot and Pisante [J. Eur. Math. Soc. $($JEMS$)$, 12 (2010), pp. 1069--1096] (who show that the equivariant solutions are the only entire solutions of the three-dimensional Ginzburg--Landau equations in superconductivity theory) to the Landau--de Gennes framework in the theory of nematic liquid crystals. In the low temperature limit, we obtain a characterization of global Landau--de Gennes minimizers, in the restricted class of uniaxial tensors, in terms of the well-known radial-hedgehog solution. We use this characterization to prove that global Landau--de Gennes minimizers cannot be purely uniaxial for sufficiently low temperatures.
Original languageEnglish
Pages (from-to)3217–3241
Number of pages25
JournalSIAM Journal on Mathematical Analysis (SIMA)
Volume44
Issue number5
DOIs
Publication statusPublished - 10 Sep 2012

Fingerprint

Nematic Liquid Crystal
Minimizer
Radial Symmetry
Symmetry
Entire Solution
Radial Solutions
Ginzburg-Landau Equation
Superconductivity
Equivariant
Tensor
Three-dimensional
Framework
Class

Keywords

  • liquid crystals
  • Landau--de Gennes
  • Ginzburg--Landau
  • low-temperature limit
  • radial symmetry
  • radial hedgehog
  • uniaxiality
  • biaxiality
  • instability
  • asymptotic analysis

Cite this

Henao, Duvan ; Majumdar, Apala. / Symmetry of uniaxial global Landau-de Gennes minimizers in the theory of nematic liquid crystals. In: SIAM Journal on Mathematical Analysis (SIMA). 2012 ; Vol. 44, No. 5. pp. 3217–3241.
@article{e47aeaed9d8f407db372cecdab8e4dc1,
title = "Symmetry of uniaxial global Landau-de Gennes minimizers in the theory of nematic liquid crystals",
abstract = "We extend the recent radial symmetry results by Pisante [J. Funct. Anal., 260 (2011), pp. 892--905] and Millot and Pisante [J. Eur. Math. Soc. $($JEMS$)$, 12 (2010), pp. 1069--1096] (who show that the equivariant solutions are the only entire solutions of the three-dimensional Ginzburg--Landau equations in superconductivity theory) to the Landau--de Gennes framework in the theory of nematic liquid crystals. In the low temperature limit, we obtain a characterization of global Landau--de Gennes minimizers, in the restricted class of uniaxial tensors, in terms of the well-known radial-hedgehog solution. We use this characterization to prove that global Landau--de Gennes minimizers cannot be purely uniaxial for sufficiently low temperatures.",
keywords = "liquid crystals, Landau--de Gennes, Ginzburg--Landau, low-temperature limit, radial symmetry, radial hedgehog, uniaxiality, biaxiality, instability, asymptotic analysis",
author = "Duvan Henao and Apala Majumdar",
year = "2012",
month = "9",
day = "10",
doi = "10.1137/110856861",
language = "English",
volume = "44",
pages = "3217–3241",
number = "5",

}

Henao, D & Majumdar, A 2012, 'Symmetry of uniaxial global Landau-de Gennes minimizers in the theory of nematic liquid crystals', SIAM Journal on Mathematical Analysis (SIMA), vol. 44, no. 5, pp. 3217–3241. https://doi.org/10.1137/110856861

Symmetry of uniaxial global Landau-de Gennes minimizers in the theory of nematic liquid crystals. / Henao, Duvan; Majumdar, Apala.

In: SIAM Journal on Mathematical Analysis (SIMA), Vol. 44, No. 5, 10.09.2012, p. 3217–3241.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Symmetry of uniaxial global Landau-de Gennes minimizers in the theory of nematic liquid crystals

AU - Henao, Duvan

AU - Majumdar, Apala

PY - 2012/9/10

Y1 - 2012/9/10

N2 - We extend the recent radial symmetry results by Pisante [J. Funct. Anal., 260 (2011), pp. 892--905] and Millot and Pisante [J. Eur. Math. Soc. $($JEMS$)$, 12 (2010), pp. 1069--1096] (who show that the equivariant solutions are the only entire solutions of the three-dimensional Ginzburg--Landau equations in superconductivity theory) to the Landau--de Gennes framework in the theory of nematic liquid crystals. In the low temperature limit, we obtain a characterization of global Landau--de Gennes minimizers, in the restricted class of uniaxial tensors, in terms of the well-known radial-hedgehog solution. We use this characterization to prove that global Landau--de Gennes minimizers cannot be purely uniaxial for sufficiently low temperatures.

AB - We extend the recent radial symmetry results by Pisante [J. Funct. Anal., 260 (2011), pp. 892--905] and Millot and Pisante [J. Eur. Math. Soc. $($JEMS$)$, 12 (2010), pp. 1069--1096] (who show that the equivariant solutions are the only entire solutions of the three-dimensional Ginzburg--Landau equations in superconductivity theory) to the Landau--de Gennes framework in the theory of nematic liquid crystals. In the low temperature limit, we obtain a characterization of global Landau--de Gennes minimizers, in the restricted class of uniaxial tensors, in terms of the well-known radial-hedgehog solution. We use this characterization to prove that global Landau--de Gennes minimizers cannot be purely uniaxial for sufficiently low temperatures.

KW - liquid crystals

KW - Landau--de Gennes

KW - Ginzburg--Landau

KW - low-temperature limit

KW - radial symmetry

KW - radial hedgehog

KW - uniaxiality

KW - biaxiality

KW - instability

KW - asymptotic analysis

U2 - 10.1137/110856861

DO - 10.1137/110856861

M3 - Article

VL - 44

SP - 3217

EP - 3241

IS - 5

ER -