# A conservation law for liquid crystal defects on manifolds

@article{Pim2021ACL, title={A conservation law for liquid crystal defects on manifolds}, author={Aaron Pim}, journal={arXiv: Analysis of PDEs}, year={2021} }

The analysis of nematics shells has recently become of great importance, with novel applications ranging from the creation of colloidal materials using DNA strands, to inventing contact lenses capable of changing their dioptre. In this piece, we analyse the orientation of a thin nematic film on the surface of a smooth manifold, specifically the strength of point defects located on the surface and the boundary.
We model the orientation by a unit vector field which is orthogonal to the surface…

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Multistability for a Reduced Landau--de Gennes Model in the Exterior of 2D Polygons

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We presents a systematic study of nematic equlibria in an unbounded domain, with a twodimensional regular polygonal hole with K edges in a reduced Landau–de Gennes framework. This complements our…

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