Averaged coordination numbers of planar aperiodic tilings

Baake M, Grimm U (2006)
In: Proceedings of the 9th International Conference on Quasicrystals, 22–26 May 2005. PHILOSOPHICAL MAGAZINE, 86(3-5). TAYLOR & FRANCIS LTD: 567-572.

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Autor*in
Baake, MichaelUniBi; Grimm, Uwe
Abstract / Bemerkung
We consider averaged shelling and coordination numbers of aperiodic tilings. Shelling numbers count the vertices on radial shells around a vertex. Coordination numbers, in turn, count the vertices on coordination shells of a vertex, defined via the graph distance given by the tiling. For the Ammann-Beenker tiling, we find that coordination shells consist of complete shelling orbits, which enables us to calculate averaged coordination numbers for rather large distances explicitly. The relation to topological invariants of tilings is briefly discussed.
Erscheinungsjahr
2006
Titel des Konferenzbandes
Proceedings of the 9th International Conference on Quasicrystals, 22–26 May 2005
forms.conference.field.series_title_volume.series_title.label
PHILOSOPHICAL MAGAZINE
Band
86
Ausgabe
3-5
Seite(n)
567-572
Konferenz
9th International Conference on Quasicrystals
Konferenzort
Ames, Iowa, USA
Konferenzdatum
2005-05-22 – 2005-05-26
ISSN
1478-6435
Page URI
https://pub.uni-bielefeld.de/record/1600868

Zitieren

Baake M, Grimm U. Averaged coordination numbers of planar aperiodic tilings. In: Proceedings of the 9th International Conference on Quasicrystals, 22–26 May 2005. PHILOSOPHICAL MAGAZINE. Vol 86. TAYLOR & FRANCIS LTD; 2006: 567-572.
Baake, M., & Grimm, U. (2006). Averaged coordination numbers of planar aperiodic tilings. Proceedings of the 9th International Conference on Quasicrystals, 22–26 May 2005, PHILOSOPHICAL MAGAZINE, 86, 567-572. TAYLOR & FRANCIS LTD. https://doi.org/10.1080/14786430500269022
Baake, M., and Grimm, U. (2006). “Averaged coordination numbers of planar aperiodic tilings” in Proceedings of the 9th International Conference on Quasicrystals, 22–26 May 2005 PHILOSOPHICAL MAGAZINE, vol. 86, (TAYLOR & FRANCIS LTD), 567-572.
Baake, M., & Grimm, U., 2006. Averaged coordination numbers of planar aperiodic tilings. In Proceedings of the 9th International Conference on Quasicrystals, 22–26 May 2005. PHILOSOPHICAL MAGAZINE. no.86 TAYLOR & FRANCIS LTD, pp. 567-572.
M. Baake and U. Grimm, “Averaged coordination numbers of planar aperiodic tilings”, Proceedings of the 9th International Conference on Quasicrystals, 22–26 May 2005, PHILOSOPHICAL MAGAZINE, vol. 86, TAYLOR & FRANCIS LTD, 2006, pp.567-572.
Baake, M., Grimm, U.: Averaged coordination numbers of planar aperiodic tilings. Proceedings of the 9th International Conference on Quasicrystals, 22–26 May 2005. PHILOSOPHICAL MAGAZINE. 86, p. 567-572. TAYLOR & FRANCIS LTD (2006).
Baake, Michael, and Grimm, Uwe. “Averaged coordination numbers of planar aperiodic tilings”. Proceedings of the 9th International Conference on Quasicrystals, 22–26 May 2005. TAYLOR & FRANCIS LTD, 2006.Vol. 86. PHILOSOPHICAL MAGAZINE. 567-572.

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