Magnetic field-induced instabilities in liquid crystals

Fanghua Lin, Xing Bin Pan

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1588-1612
Number of pages25
JournalSIAM Journal on Mathematical Analysis
Issue number5
StatePublished - 2006


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

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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