By Peter Kramer, Zorka Papadopolos
ISBN-10: 3540432418
ISBN-13: 9783540432418
During this updated evaluation and advisor to most up-to-date literature, the specialist authors enhance suggestions relating to quasiperiodic coverings and describe effects. The textual content describes particular platforms in 2 and three dimensions with many illustrations, and analyzes the atomic positions in quasicrystals.
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Additional info for Coverings of Discrete Quasiperiodic Sets (Springer Tracts in Modern Physics)
Example text
The intersection of two or more convex polyhedra is a (possibly empty) convex polyhedron. If C and C are polyhedra of this kind then we construct the union of their bounding planes P = P ∪ P = p1 , . . , pn , p1 , . . , pn . The intersection C = C ∪ C is then calculated by reducing the sequence of planes P as explained above: first obtain the vertices of C from P and then obtain the bounding planes from the set of vertices. The calculation of intersections may be shortened if for each convex polyhedron we compute a bounding box, recorded together with the sets of planes and vertices.
Verger-Gaugry, R. Currat (World Scientific, Singapore 1998), pp. 39–45 16 54. K. W. Urban: “From tilings to coverings”. Nature 396, 14–15 (1998) 16 55. A. Weiss: “On shelling icosahedral quasicrystals”. In: Directions in Mathematical Quasicrystals, ed. by M. Baake, R. V. Moody, (CRM Monograph Series, Vol. 13, American Mathematical Society, Providence 2000), pp. 161–176 15 56. J. M. Wills: “Spheres and sausages, crystals and catastrophes – and a joint packing theory”. Math. Intelligencer 20, 16–21 (1998) 1, 2 2 Covering Clusters in Icosahedral Quasicrystals Michel Duneau and Denis Gratias Summary.
G¨ ahler, P. -R. Trebin, K. Urban (Mater. Sci. Eng. A 294–296; Elsevier Science, Amsterdam 2000) pp. 192–198 16 1 Covering of Discrete Quasiperiodic Sets: Concepts and Theory 19 9. V. Elser: “Random tiling structure of icosahedral quasicrystals”. Phil. Mag. B 73, 641–656 (1996) 16 10. F. -C. Jeong: “Quasicrystalline ground states without matching rules”. J. Phys. A 28, 1807–1815 (1995) 15 11. F. G¨ ahler: “Cluster coverings: a powerful ordering principle for quasicrystals”. In: Proceedings of the 6th International Conference on Quasicrystals, Tokyo 1997, ed.
Coverings of Discrete Quasiperiodic Sets (Springer Tracts in Modern Physics) by Peter Kramer, Zorka Papadopolos
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