Function spaces for liquid crystals

Abstract

We consider the relationship between three continuum liquid crystal theories: Oseen-Frank, Ericksen and Landau-de Gennes. It is known that the function space is an important part of the mathematical model and by considering various function space choices for the order parameters $s$, $\mathbf{n}$, and $\mathbf{Q}$, we establish connections between the variational formulations of these theories. We use these results to derive a version of the Oseen-Frank theory using special functions of bounded variation. This proposed model can describe both orientable and non-orientable defects. Finally we study a number of frustrated nematic and cholesteric liquid crystal systems and show that the model predicts the existence of point and surface discontinuities in the director.

References in corpus (1)

• Global minimisers of cholesteric liquid crystal systems

Cited by in corpus (11)

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• Lifting of ${\mathbb{RP}}^{d-1}$-valued maps in $BV$ and applications to uniaxial $Q$-tensors. With an appendix on an intrinsic $BV$-energy for manifold-valued maps
• $\Gamma$-convergence of a mean-field model of a chiral doped nematic liquid crystal to the Oseen-Frank description of cholesterics
• Discontinuous order parameters in liquid crystal theories
• The $\mathbf{Q}$-tensor Model with Uniaxial Constraint