Homogenization of Penrose tilings

Andrea Braides; Giuseppe Riey; Margherita Solci

doi:10.1016/j.crma.2009.03.019

Calculus of Variations

Homogenization of Penrose tilings
[Homogénéisation d'un pavage de Penrose]

Présenté par : Philippe G. Ciarlet

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

Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 697-700.

Résumé
Abstract

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 $W^{1}$ – 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 $W^{1}$ -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.

Reçu le : 2009-03-10
Accepté le : 2009-03-20
Publié le : 2009-04-21

DOI : 10.1016/j.crma.2009.03.019

Affiliations des auteurs :

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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     author = {Andrea Braides and Giuseppe Riey and Margherita Solci},
     title = {Homogenization of {Penrose} tilings},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {697--700},
     publisher = {Elsevier},
     volume = {347},
     number = {11-12},
     year = {2009},
     doi = {10.1016/j.crma.2009.03.019},
     language = {en},
}

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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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Cité par

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