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Volume 25, Issue 3
The Freedericksz Transition and the Asymptotic Behavior in Nematic Liquid Crystals

Junichi Aramaki

J. Part. Diff. Eq., 25 (2012), pp. 276-294.

Published online: 2012-09

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  • Abstract

We consider the stability of a specific nematic liquid crystal configuration under an applied magnetic field. We show that for some specific configuration there exist two critical values H_n and H_{sh} of applied magnetic field. When the intensity of the magnetic field is smaller than H_n, the configuration of the energy is only global minimizer, when the intensity is between H_n and H_{sh}, the configuration is not global minimizer, but is weakly stable, and when the intensity is larger than H_{sh}, the configuration is instable. Moreover, we also examine the asymptotic behavior of the global minimizer as the intensity tends to the infinity.

  • Keywords

Freedricksz transition variational problem liquid crystals Landau-de Gennes functional

  • AMS Subject Headings

82D30, 35A15, 58E50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

aramaki@mail.dendai.ac.jp (Junichi Aramaki)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-25-276, author = {Junichi and Aramaki and aramaki@mail.dendai.ac.jp and 12138 and Division of Science, Faculty of Science and Engineering, Tokyo Denki University, Hatoyama-machi, Saitama, 350-0394, Japan and Junichi Aramaki}, title = {The Freedericksz Transition and the Asymptotic Behavior in Nematic Liquid Crystals}, journal = {Journal of Partial Differential Equations}, year = {2012}, volume = {25}, number = {3}, pages = {276--294}, abstract = {

We consider the stability of a specific nematic liquid crystal configuration under an applied magnetic field. We show that for some specific configuration there exist two critical values H_n and H_{sh} of applied magnetic field. When the intensity of the magnetic field is smaller than H_n, the configuration of the energy is only global minimizer, when the intensity is between H_n and H_{sh}, the configuration is not global minimizer, but is weakly stable, and when the intensity is larger than H_{sh}, the configuration is instable. Moreover, we also examine the asymptotic behavior of the global minimizer as the intensity tends to the infinity.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v25.n3.5}, url = {http://global-sci.org/intro/article_detail/jpde/5187.html} }
TY - JOUR T1 - The Freedericksz Transition and the Asymptotic Behavior in Nematic Liquid Crystals AU - Aramaki , Junichi JO - Journal of Partial Differential Equations VL - 3 SP - 276 EP - 294 PY - 2012 DA - 2012/09 SN - 25 DO - http://doi.org/10.4208/jpde.v25.n3.5 UR - https://global-sci.org/intro/article_detail/jpde/5187.html KW - Freedricksz transition KW - variational problem KW - liquid crystals KW - Landau-de Gennes functional AB -

We consider the stability of a specific nematic liquid crystal configuration under an applied magnetic field. We show that for some specific configuration there exist two critical values H_n and H_{sh} of applied magnetic field. When the intensity of the magnetic field is smaller than H_n, the configuration of the energy is only global minimizer, when the intensity is between H_n and H_{sh}, the configuration is not global minimizer, but is weakly stable, and when the intensity is larger than H_{sh}, the configuration is instable. Moreover, we also examine the asymptotic behavior of the global minimizer as the intensity tends to the infinity.

Junichi Aramaki. (2019). The Freedericksz Transition and the Asymptotic Behavior in Nematic Liquid Crystals. Journal of Partial Differential Equations. 25 (3). 276-294. doi:10.4208/jpde.v25.n3.5
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