Abstract
AbstractWe 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.
Funder
European Research Council
Chilean Fondecyt Iniciación
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference52 articles.
1. Alicandro, R., Gelli, M.S.: Local and nonlocal continuum limits of Ising-type energies for spin systems. SIAM J. Math. Anal. 48(2), 895–931 (2016)
2. Althoff, M.: On computing the Minkowski difference of zonotopes. arXiv preprint arXiv:1512.02794 (2015)
3. Ambrosio, L., Fusco, N., Pallara, D.: Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York (2000)
4. Au Yeung, Y., Friesecke, G., Schmidt, B.: Minimizing atomic configurations of short range pair potentials in two dimensions: crystallization in the Wulff shape. Calc. Var. Part. Differ. Equ. 44(1–2), 81–100 (2012)
5. Bétermin, L., De Luca, L., Petrache, M.: Crystallization to the square lattice for a two-body potential. Arch. Ration. Mech. Anal. 240(2), 987–1053 (2021)
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献