Abstract
We study equilibrium liquid crystal configurations in three-dimensional geometries, within the continuum Landau-de Gennes theory. We obtain explicit bounds for the equilibrium scalar order parameters in terms of the temperature and material-dependent constants. We explicitly quantify the temperature regimes where the Landau-de Gennes predictions match and the temperature regimes where the Landau-de Gennes predictions do not match the probabilistic second-moment definition of the Q-tensor order parameter. The regime of agreement may be interpreted as the regime of validity of the Landau-de Gennes theory since the Landau-de Gennes theory predicts large values of the equilibrium scalar order parameters – larger than unity, in the low-temperature regime. We discuss a modified Landau-de Gennes energy functional which yields physically realistic values of the equilibrium scalar order parameters in all temperature regimes.
Original language | English |
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Pages (from-to) | 181-203 |
Number of pages | 23 |
Journal | European Journal of Applied Mathematics |
Volume | 21 |
Issue number | 2 |
Early online date | 25 Feb 2010 |
DOIs | |
Publication status | Published - 30 Apr 2010 |
Keywords
- nematic liquid crystals
- order parameters
- equilibrium configurations
- Landau–De Gennes theory