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 penalises dislocations of the smectic layers at the jump. We discuss mathematical issues related to the existence of minimisers and provide examples of minimisers in some simplified settings.[Graphics].

A free discontinuity model for smectic thin films

Canevari, G;
2023-01-01

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 penalises dislocations of the smectic layers at the jump. We discuss mathematical issues related to the existence of minimisers and provide examples of minimisers in some simplified settings.[Graphics].
2023
Smectic liquid crystals
surface defects
special functions of bounded variation
BV ellipticity
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1095966
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