A free discontinuity model for smectic thin films
John M. Ball, Giacomo Canevari, Bianca Stroffolini
TL;DR
This paper models surface defects in smectic A thin films using a free discontinuity variational approach, incorporating interfacial energy to penalize layer dislocations, and discusses mathematical existence of minimizers.
Contribution
It introduces a novel free discontinuity model for smectic thin films, addressing the mathematical existence of minimizers and providing simplified examples.
Findings
Existence of minimizers discussed
Interfacial energy penalizes dislocations
Examples of minimizers provided
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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Taxonomy
TopicsFluid Dynamics and Thin Films · Textile materials and evaluations · Advanced Numerical Analysis Techniques