Comptes Rendus
Calculus of Variations
Homogenization of Penrose tilings
[Homogénéisation d'un pavage de Penrose]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 697-700.

On démontre un théorème d'homogénéisation pour des énergies qui suivent la géométrie d'un pavage apériodique de Penrose. Nos résultats, applicables à des géométries quasicristallines générales, sont obtenus en démontrant que les densités d'énergie correspondantes sont W1 – et donc Besicovitch – quasi-périodiques, de sort que l'on peut appliquer les théorèmes d'homogénéisation de Braides, 1986.

A homogenization theorem is proved for energies which follow the geometry of an a-periodic Penrose tiling. The result is obtained by proving that the corresponding energy densities are W1-almost periodic and hence also Besicovitch almost periodic, so that existing general homogenization theorems can be applied (Braides, 1986). The method applies to general quasicrystalline geometries.

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DOI : 10.1016/j.crma.2009.03.019

Andrea Braides 1 ; Giuseppe Riey 2 ; Margherita Solci 3

1 Dipartimento di Matematica, Università di Roma Tor Vergata, via della ricerca scientifica 1, 00133 Roma, Italy
2 Dipartimento di Matematica, Università della Calabria, via P. Bucci, 87036 Arcavacata di Rende (CS), Italy
3 DAP, Università di Sassari, piazza Duomo 6, 07041 Alghero (SS), Italy
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Andrea Braides; Giuseppe Riey; Margherita Solci. Homogenization of Penrose tilings. Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 697-700. doi : 10.1016/j.crma.2009.03.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.03.019/

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