Coupling of nematic in-plane orientational ordering and equilibrium shapes of closed flexible nematic shells

We study the interplay between equilibrium shapes and the in-plane nematic orientational ordering of closed axially symmetric flexible shells with attached curved rod-like nematic molecules. The local geometry and order at the mesoscopic level of such nematic shells are described by the curvature field and nematic order parameter field of the nematic shell. Our model could describe diverse 2D curved manifolds exhibiting an in-plane nematic-type orientational order. Prototypical examples are nematic LC shells23,24 and biological membranes3,4,6,10,11,13,14.

The local curvature of the flexible…

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