Magnetic field-induced instabilities in liquid crystals

Fanghua Lin; Xing Bin Pan

doi:10.1137/050638643

Magnetic field-induced instabilities in liquid crystals

Fanghua Lin, Xing Bin Pan

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We use the Landau-de Gennes model to investigate the magnetic field-induced instabilities in liquid crystals. In particular, we examine the change of weak and strong stabilities in the pure smectic states and in the pure nematic states. Motivated by de Gennes' discovery on the analogies between liquid crystals and superconductors, we introduce critical magnetic fields H _s and H_sh. The pure smectic states lose their global minimality (strong stability) at H_s and lose their local minimality (weak stability) at H_sh.. We also examine the change of stability in the pure nematic states. We show in the case of equal elastic coefficients that a liquid crystal in a sufficiently strong magnetic field will not be in a pure nematic state, which exhibits a significant difference between the Landau-de Gennes model for liquid crystals and the Ginzburg-Landau model for superconductivity.

Original language	English (US)
Pages (from-to)	1588-1612
Number of pages	25
Journal	SIAM Journal on Mathematical Analysis
Volume	38
Issue number	5
DOIs	https://doi.org/10.1137/050638643
State	Published - 2006

Keywords

Critical magnetic field
Landau-de Gennes model
Liquid crystal
Phase transition

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/050638643

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AU - Lin, Fanghua

AU - Pan, Xing Bin

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AB - We use the Landau-de Gennes model to investigate the magnetic field-induced instabilities in liquid crystals. In particular, we examine the change of weak and strong stabilities in the pure smectic states and in the pure nematic states. Motivated by de Gennes' discovery on the analogies between liquid crystals and superconductors, we introduce critical magnetic fields H s and Hsh. The pure smectic states lose their global minimality (strong stability) at Hs and lose their local minimality (weak stability) at Hsh.. We also examine the change of stability in the pure nematic states. We show in the case of equal elastic coefficients that a liquid crystal in a sufficiently strong magnetic field will not be in a pure nematic state, which exhibits a significant difference between the Landau-de Gennes model for liquid crystals and the Ginzburg-Landau model for superconductivity.

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