Discrete quasiperiodic sets with predefined local structure
Abstract
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.
Keywords
Cite
@article{arxiv.math-ph/0405027,
title = {Discrete quasiperiodic sets with predefined local structure},
author = {Nicolae Cotfas},
journal= {arXiv preprint arXiv:math-ph/0405027},
year = {2007}
}
Comments
This is the revised version (19 pages, 3 figures) of a paper submitted to Journal of Geometry and Physics. Software for generating quasiperiodic discrete sets available at http://fpcm5.fizica.unibuc.ro/~ncotfas