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Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings
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Del Nin, Giacomo and Petrache, Mircea (2022) Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings. Calculus of Variations and Partial Differential Equations, 61 . 226. doi:10.1007/s00526-022-02318-0 ISSN 0944-2669.
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WRAP-Continuum-limits-of-discrete-isoperimetric-problems-and-Wulff-shapes-in-lattices-and-quasicrystal-tilings-Del-Nin-2022.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (848Kb) | Preview |
Official URL: https://link.springer.com/article/10.1007/s00526-0...
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.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Geometric measure theory, Continuum (Mathematics), Convergence, Calculus of variations, Lattice theory, Quasicrystals | |||||||||
| Journal or Publication Title: | Calculus of Variations and Partial Differential Equations | |||||||||
| Publisher: | Springer | |||||||||
| ISSN: | 0944-2669 | |||||||||
| Official Date: | 11 October 2022 | |||||||||
| Dates: |
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| Volume: | 61 | |||||||||
| Number of Pages: | 44 | |||||||||
| Article Number: | 226 | |||||||||
| DOI: | 10.1007/s00526-022-02318-0 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Date of first compliant deposit: | 11 October 2022 | |||||||||
| Date of first compliant Open Access: | 11 October 2022 | |||||||||
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