Coverings of Discrete Quasiperiodic Sets - Theory and Applications to Quasicrystals

Coverings are efficient ways to exhaust Euclidean N-space with congruent geometric objects. Discrete quasiperiodic systems are exemplified by the atomic structure of quasicrystals. The subject of coverings of discrete quasiperiodic sets emerged in 1995. The theory of these coverings provides a new and fascinating perspective of order down to the atomic level. The authors develop concepts related to quasiperiodic coverings and describe results. Specific systems in 2 and 3 dimensions are described with many illustrations. The atomic positions in quasicrystals are analyzed.

List of contents

Covering of Discrete Quasiperiodic Sets: Concepts and Theory.- Covering Clusters in Icosahedral Quasicrystals.- Generation of Quasiperiodic Order by Maximal Cluster Covering.- Voronoi and Delone Clusters in Dual Quasiperiodic Tilings.- The Efficiency of Delone Coverings of the Canonical Tilings ? *(a4) and ? *(d6).- Lines and Planes in 2- and 3-Dimensional Quasicrystals.- Thermally-Induced Tile Rearrangements in Decagonal Quasicrystals - Superlattice Ordering and Phason Fluctuation.- Tilings and Coverings of Quasicrystal Surfaces.

Summary

Coverings are efficient ways to exhaust Euclidean N-space with congruent geometric objects. Discrete quasiperiodic systems are exemplified by the atomic structure of quasicrystals. The subject of coverings of discrete quasiperiodic sets emerged in 1995. The theory of these coverings provides a new and fascinating perspective of order down to the atomic level. The authors develop concepts related to quasiperiodic coverings and describe results. Specific systems in 2 and 3 dimensions are described with many illustrations. The atomic positions in quasicrystals are analyzed.

Product details

• Assisted by: Pete Kramer (Editor), Peter Kramer (Editor), Papadopolos (Editor), Papadopolos (Editor), Zorka Papadopolos (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 11.10.2010
• EAN: 9783642077494
• ISBN: 978-3-642-07749-4
• No. of pages: 273
• Illustrations: XV, 273 p.
• Series: Springer Tracts in Modern Physics; Springer Tracts in Modern Physics; Springer Tracts in Modern Physics. Ergebnisse der exakten Naturwissenschaften
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Electricity, magnetism, optics; Werkstoffprüfung, C, Gruppen und Gruppentheorie, Group Theory, Crystallography and Scattering Methods, Physics and Astronomy, Crystallography, Phase Transitions and Multiphase Systems, Phase transitions (Statistical physics), Groups & group theory, Group Theory and Generalizations