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arXiv · 2211.11051

A free discontinuity model for smectic thin films

John M. Ball·Giacomo Canevari·Bianca Stroffolini
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Abstract

We attempt to describe surface defects in smectic A thin films by formulating a free discontinuity problem - that is, a variational problem in which the order parameter is allowed to have jump discontinuities on some (unknown) set. The free energy functional contains an interfacial energy which penalizes dislocations of the smectic layers at the jump. We discuss mathematical issues related to the existence of minimizers and provide examples of minimizers in some simplified settings.

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John M. Ball, Giacomo Canevari, Bianca Stroffolini. 2022-11-20. A free discontinuity model for smectic thin films. https://arxiv.org/abs/2211.11051

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