A free discontinuity model for smectic thin films

2022/11/20 by J. M. Ball, Ball, John M., Giacomo Canevari +3 · 1 citation
Engineering · Materials Science · #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Thin Films #Soft Condensed Matter (cond-mat.soft) #Textile materials and evaluations

paper · pdf · doi:10.48550/arxiv.2211.11051

openalex publication_date 2022/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Superlinear free-discontinuity models: relaxation and phase field approximation

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