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Abstract: Smectic orders on curved substrates can be described by differential forms ofrank one 1-forms, whose geometric meaning is the differential of the localphase field of density modulation. The exterior derivative of 1-form is thelocal dislocation density. Elastic deformations are described by superpositionof exact differential forms. Applying this formalism to study smectic order ontorus as well as on sphere, we find that both systems exhibit manytopologically distinct low energy states, that can be characterized by twointeger topological charges. The total number of low energy states scales asthe square root of the substrate area. For smectic on a sphere, we also explorethe motion of disclinations as possible low energy excitations, as well as itstopological implications.



Author: Xiangjun Xing Syracuse University

Source: https://arxiv.org/



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