Orientability and energy minimization in liquid crystal models

Ball, John M and Zarnescu, Arghir (2011) Orientability and energy minimization in liquid crystal models. Archive for Rational Mechanics and Analysis, 202 (2). pp. 493-535. ISSN 0003-9527

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Uniaxial nematic liquid crystals are modelled in the Oseen–Frank theory through a unit vector field n. This theory has the apparent drawback that it does not respect the head-to-tail symmetry in which n should be equivalent to −n. This symmetry is preserved in the constrained Landau–de Gennes theory that works with the tensor Q=snn−31Id . We study the differences and the overlaps between the two theories. These depend on the regularity class used as well as on the topology of the underlying domain. We show that for simply-connected domains and in the natural energy class W 1,2 the two theories coincide, but otherwise there can be differences between the two theories, which we identify. In the case of planar domains with holes and various boundary conditions, for the simplest form of the energy functional, we completely characterise the instances in which the predictions of the constrained Landau–de Gennes theory differ from those of the Oseen–Frank theory.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Arghir Zarnescu
Date Deposited: 06 Feb 2012 18:50
Last Modified: 03 Oct 2012 15:28
URI: http://sro.sussex.ac.uk/id/eprint/18552
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