Coverings of Discrete Quasiperiodic Sets: Theory and Applications to Quasicrystals / Edition 1

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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.

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Product Details

  • ISBN-13: 9783540432418
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 9/18/2002
  • Series: Springer Tracts in Modern Physics Series, #180
  • Edition description: 2003
  • Edition number: 1
  • Pages: 273
  • Product dimensions: 6.34 (w) x 9.48 (h) x 0.81 (d)

Table of Contents

1 Covering of Discrete Quasiperiodic Sets: Concepts and Theory 1
2 Covering Clusters in Icosahedral Quasicrystals 23
3 Generation of Quasiperiodic Order by Maximal Cluster Covering 63
4 Voronoi and Delone Clusters in Dual Quasiperiodic Tilings 97
5 The Efficiency of Delone Coverings of the Canonical Tilings T[superscript (A[subscript 4])] and T[superscript (D[subscript 6])] 165
6 Lines and Planes in 2- and 3-Dimensional Quasicrystals 185
7 Thermally-Induced Tile Rearrangements in Decagonal Quasicrystals - Superlattice Ordering and Phason Fluctuation 227
8 Tilings and Coverings of Quasicrystal Surfaces 257
Index 269
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