Calculus of Variations and Geometric Measure Theory

A. Braides - M. Solci

Interfacial energies on Penrose lattices

created by braidesa on 26 Oct 2009
modified on 01 Jul 2011


Published Paper

Inserted: 26 oct 2009
Last Updated: 1 jul 2011

Journal: Math. Mod. Meth. Appl. Sci. (M3AS)
Volume: 21
Pages: 1193-1210
Year: 2011


Penrose lattices are discrete sets of the plane (which are also subsets of a regular Bravais lattice), whose underlying tassellations of the plane by rhomboidal tiles with angles multiple of $\pi/5$ (with vertices the points of the Penrose lattice itself) are a prototype of quasicrystalline a-periodic structures.

In this paper we consider ``discrete'' energies directly defined on a Penrose lattice and examine their overall behaviour via a $\Gamma$-convergence approach. Such a treatment combines homogenization issues and a passage from discrete systems to continuous variational problems.

Keywords: Homogenization, Discrete energies, surface energy, Penrose lattice