Published Paper (on line)

Inserted: 22 dec 2022
Last Updated: 23 may 2023

Journal: Math. Meth. Appl. Sci.
Year: 2023
Doi: 10.1002/mma.9418

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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• Incommensurate thin films