2022•arXiv (Cornell University)Open access

A free discontinuity model for smectic thin films

John Macleod Ball, Giacomo Canevari, Bianca Stroffolini

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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Key concepts: Classification of discontinuities, Discontinuity (linguistics), Jump, Free surface, Energy (signal processing), Surface energy, Set (abstract data type), Order (exchange)