Accepted Paper

Inserted: 9 feb 2021
Last Updated: 11 oct 2022

Journal: Calc. Var. PDE
Year: 2022
Doi: 10.1007/s00526-022-02318-0

Abstract:

We prove discrete-to-continuum convergence of interaction energies defined on lattices in the Euclidean space (with interactions beyond nearest neighbours) to a crystalline perimeter, and we discuss the possible Wulff shapes obtainable in this way. Exploiting the "multigrid construction" of quasiperiodic tilings (which is an extension of De Bruijn's "pentagrid" construction of Penrose tilings) we adapt the same techniques to also find the macroscopical homogenized perimeter when we microscopically rescale a given quasiperiodic tiling.