Modulation functions for quasicrystals

Abstract

Modulation functions (MFs) are introduced for detailed descriptions of quasicrystals. As an example, the MFs for scalar properties, like the occupation probability, in dihedral quasicrystals are demonstrated. They are a linear combination of products of Chebyshev polynomials fulfilling the conditions imposed by the site symmetry and are orthogonal within polygonal occupation domains.