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Springer Verlag, Journal of Nonlinear Science, 1(26), p. 121-140

DOI: 10.1007/s00332-015-9271-8

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

Journal article published in 2014 by G. Di Fratta ORCID, Jm M. Robbins, V. Slastikov, A. Zarnescu
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This paper is available in a repository.

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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, (Formula presented.) small, we prove that this critical point is the unique global minimiser of the Landau–de Gennes energy. For the case (Formula presented.), we investigate in greater detail the regime of vanishing elastic constant (Formula presented.), where we obtain three explicit point defect profiles, including the global minimiser.