A note on the homogenization of incommensurate thin films

2022/12/21 by Anello, Irene, Braides, Andrea, Caragiulo, Fabrizio
#35B27 #49J45 #74Q05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2212.11189

Abstract

Dimension-reduction homogenization results for thin films have been obtained under hypotheses of periodicity or almost-periodicity of the energies in the directions of the mid-plane of the film. In this note we consider thin films, obtained as sections of a periodic medium with a mid-plane that may be incommensurate; that is, not containing periods other than 0. A geometric almost-periodicity argument similar to the cut-and-project argument used for quasicrystals allows to prove a general homogenization result.

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