Liquid crystal defects in the Landau-de Gennes theory in two dimensions - Beyond the one-constant approximation

Kitavtsev G., Robbins J., Slastikov V., Zarnescu A.

Mathematical Models and Methods in Applied Sciences, cilt.26, sa.14, ss.2769-2808, 2016 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 26 Sayı: 14
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1142/s0218202516500664
  • Dergi Adı: Mathematical Models and Methods in Applied Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2769-2808
  • Anahtar Kelimeler: k -radially symmetric solutions, Liquid crystals, minimisers, Q -tensors
  • Orta Doğu Teknik Üniversitesi Kuzey Kıbrıs Kampüsü Adresli: Hayır

Özet

We consider the two-dimensional (2D) Landau-de Gennes energy with several elastic constants, subject to general k-radially symmetric boundary conditions. We show that for generic elastic constants the critical points consistent with the symmetry of the boundary conditions exist only in the case k = 2. In this case we identify three types of radial profiles: with two, three of full five components and numerically investigate their minimality and stability depending on suitable parametres. We also numerically study the stability properties of the critical points of the Landau-de Gennes energy and capture the intricate dependence of various qualitative features of these solutions on the elastic constants and the physical regimes of the liquid crystal system.