Open AccessMagnetic field-induced stability of a specific configuration and the asymptotic behavior of minimizers in nematic liquid crystals
Author(s) -
Junichi Aramaki
Publication year - 2013
Publication title -
turkish journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.454
H-Index - 27
eISSN - 1303-6149
pISSN - 1300-0098
DOI - 10.3906/mat-1206-43
Subject(s) - liquid crystal , intensity (physics) , mathematics , magnetic field , infinity , boundary (topology) , anchoring , field (mathematics) , energy (signal processing) , boundary value problem , stability (learning theory) , mathematical analysis , field intensity , condensed matter physics , physics , pure mathematics , quantum mechanics , nuclear magnetic resonance , statistics , structural engineering , machine learning , computer science , engineering
We consider the stability of a specic nematic liquid crystal conguration under an applied magnetic eld. We impose the strong anchoring condition, and we allow the boundary data to be nonconstant and also the applied eld to be nonconstant. Thus, we shall extend the results of Lin and Pan in 2007. We show that for some specic conguration there exist 2 critical values Hn and Hsh of applied magnetic eld. When the intensity of the magnetic eld is smaller than Hn, the conguration of the energy is only a global minimizer, when the intensity is between Hn and Hsh, the conguration is not a global minimizer, but is weakly stable, and when the intensity is larger than Hsh, the conguration is not weakly stable. Moreover, we also examine the behavior of minimal values of energy and the asymptotic behavior of the global minimizer as the intensity tends to innity. eld-induced stability, variational problem, nematic liquid crystal
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom