Magnetic field-induced stability of a specific configuration and the asymptotic behavior of minimizers in nematic liquid crystals

Junichi ARAMAKI

Makale detayları

Magnetic field-induced stability of a specific configuration and the asymptotic behavior of minimizers in nematic liquid crystals

Yazarlar:

Junichi ARAMAKI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2013 Vol.37 Issue 6, pp.1001-1021

Belge Tipi:

Makale

Yayın Tarihi:

5/2013

Belge Dili:

Türkçe

Document ID (Org No.):

2000747484

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

We consider the stability of a specific nematic liquid crystal configuration under an applied magnetic field.  We impose the strong anchoring condition, and we allow the boundary data to be nonconstant and also the applied field to be nonconstant.  Thus, we shall extend the results of Lin and Pan in 2007.  We show that for some specific configuration there exist 2 critical values Hn and Hsh of applied magnetic field.  When the intensity of the magnetic field is smaller than Hn, the configuration of the energy is only a global minimizer, when the intensity is between Hn and Hsh, the configuration is not a global minimizer, but is weakly stable, and when the intensity is larger than Hsh, the configuration 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 infinity.

 

We consider the stability of a specific nematic liquid crystal configuration under an applied magnetic field.  We impose the strong anchoring condition, and we allow the boundary data to be nonconstant and also the applied field to be nonconstant.  Thus, we shall extend the results of Lin and Pan in 2007.  We show that for some specific configuration there exist 2 critical values Hn and Hsh of applied magnetic field.  When the intensity of the magnetic field is smaller than Hn, the configuration of the energy is only a global minimizer, when the intensity is between Hn and Hsh, the configuration is not a global minimizer, but is weakly stable, and when the intensity is larger than Hsh, the configuration 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 infinity.

Makale detayları

Magnetic field-induced stability of a specific configuration and the asymptotic behavior of minimizers in nematic liquid crystals

Yazarlar:

Junichi ARAMAKI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2013 Vol.37 Issue 6, pp.1001-1021

Belge Tipi:

Makale

Yayın Tarihi:

5/2013

Belge Dili:

Türkçe

Document ID (Org No.):

2000747484

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Magnetic field-induced stability

variational problem

nematic liquid crystal

Sayı

Makale detayları

Magnetic field-induced stability of a specific configuration and the asymptotic behavior of minimizers in nematic liquid crystals

Yazarlar: Junichi ARAMAKI

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2013 Vol.37 Issue 6, pp.1001-1021

Belge Tipi: Makale

Yayın Tarihi: 5/2013

Belge Dili: Türkçe

Document ID (Org No.): 2000747484

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Magnetic field-induced stability

variational problem

nematic liquid crystal

Sayı

Yazarlar:

Junichi ARAMAKI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2013 Vol.37 Issue 6, pp.1001-1021

Belge Tipi:

Makale

Yayın Tarihi:

5/2013

Belge Dili:

Türkçe

Document ID (Org No.):

2000747484

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098