Discrete quasiperiodic sets with predefined local structure

Details Discrete quasiperiodic sets with predefined local structure Discrete quasiperiodic sets with predefined local structure

2004-05-10

arxiv.org/abs/math-ph/0405027v2

Journal of Geometry and Physics 56 (2006) 2415-2428

Physics

Mathematical Physics

This is the revised version (19 pages, 3 figures) of a paper submitted to Journal of Geometry and Physics. Software for genera

Scientific paper

10.1016/j.geomphys.2005.12.008

Model sets play a fundamental role in structure analysis of quasicrystals. The diffraction diagram of a quasicrystal admits as symmetry group a finite group G, and there is a G-cluster C (union of orbits of G) such that the quasicrystal can be regarded as a quasiperiodic packing of interpenetrating copies of C. We present an algorithm which leads from any G-cluster C directly to a multi-component model set Q such that the arithmetic neighbours of any point x belonging to Q are distributed on the sites of the translated copy x+C of C. Our mathematical algorithm may be useful in quasicrystal physics.

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