Comptes Rendus
Calculus of Variations
Homogenization of Penrose tilings
Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 697-700.

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.

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.

Published online:
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
     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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AU  - Giuseppe Riey
AU  - Margherita Solci
TI  - Homogenization of Penrose tilings
JO  - Comptes Rendus. Mathématique
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EP  - 700
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PB  - Elsevier
DO  - 10.1016/j.crma.2009.03.019
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%J Comptes Rendus. Mathématique
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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.

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