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Nematic braids: Effects of chirality and confinement

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Nematic disclinations can form stable braids when they are stabilized by a confining geometry, chirality, or by interplay of both effects. These are stable or metastable topologically diverse defect structures in the nematic ordering field. Based on the synergy of our theoretical and numerical, approaches we are able to characterize geometries and properties of disclination loops forming braids by winding numbers, lengths, knot or link types, and self-linking numbers. We focus our attention to selected nematic braids of the lowest complexity: knotted 2D colloidal crystals, opal structures permeated by nematics, and knots in cholesteic drops. With this overview I would like to show how topology and geometry enables the assembling of complex soft materials. [1] S. ?opar and S. umer, Nematic Braids: Topological Invariants and Rewiring of Disclinations, Phys. Rev. Lett. 106, 177801 (2011). [2] S. ?opar, and S. umer, Quaternions and hybrid nematic disclinations, Proc. R. Soc. A 469 , 1471 (2013). [3] U. Tkalec, M. Ravnik, S. ?opar, S. umer and I. Muevi?, Reconfigurable Knots and Links in Chiral Nematic Colloids, Science 333, 62 (2011). [4] S. ?opar, N. A. Clark, M. Ravnik and S. umer, Elementary building blocks of nematic disclination networks in densely packed 3D colloidal lattices, Soft Matter, DOI : 10.1039/C3SM50475A (2013).

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