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arXiv · 1403.2566

Half-integer point defects in the $Q$-tensor theory of nematic liquid crystals

G. Di Fratta·JM Robbins·V. Slastikov·A. Zarnescu
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Abstract

We investigate prototypical profiles of point defects in two dimensional liquid crystals within the framework of Landau-de Gennes theory. Using boundary conditions characteristic of defects of index $k/2$, we find a critical point of the Landau-de Gennes energy that is characterised by a system of ordinary differential equations. In the deep nematic regime, $b^2$ small, we prove that this critical point is the unique global minimiser of the Landau-de Gennes energy. We investigate in greater detail the regime of vanishing elastic constant $L \to 0$, where we obtain three explicit point defect profiles, including the global minimiser.

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G. Di Fratta, JM Robbins, V. Slastikov, A. Zarnescu. 2014-03-11. Half-integer point defects in the $Q$-tensor theory of nematic liquid crystals. https://doi.org/10.1007/s00332-015-9271-8

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