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Parallelogram Frameworks and Flexible Quasicrystals

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Parallelogram Frameworks and Flexible Quasicrystals. / Power, Stephen.
In: Mathematical Proceedings of the Royal Irish Academy, Vol. 121A, No. 1, 31.08.2021, p. 9-31.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Power, S 2021, 'Parallelogram Frameworks and Flexible Quasicrystals', Mathematical Proceedings of the Royal Irish Academy, vol. 121A, no. 1, pp. 9-31. https://doi.org/10.1353/mpr.2021.0000

APA

Power, S. (2021). Parallelogram Frameworks and Flexible Quasicrystals. Mathematical Proceedings of the Royal Irish Academy, 121A(1), 9-31. https://doi.org/10.1353/mpr.2021.0000

Vancouver

Power S. Parallelogram Frameworks and Flexible Quasicrystals. Mathematical Proceedings of the Royal Irish Academy. 2021 Aug 31;121A(1):9-31. doi: 10.1353/mpr.2021.0000

Author

Power, Stephen. / Parallelogram Frameworks and Flexible Quasicrystals. In: Mathematical Proceedings of the Royal Irish Academy. 2021 ; Vol. 121A, No. 1. pp. 9-31.

Bibtex

@article{7790c5291e3f4fbb9f5ba92adeb6cf59,
title = "Parallelogram Frameworks and Flexible Quasicrystals",
abstract = "The first-order flex space of the bar-joint framework $\G_P$ of a parallelogram tiling $P$ is determined in terms of an explicit free basis. Applications are given to braced parallelogram frameworks and to quasicrystal frameworks associated with multigrids in the sense of de Bruijn and Beenker. In particular we characterise rigid bracing patterns, identify quasicrystal frameworks with finite dimensional flex spaces, and define a zero mode spectrum.",
keywords = "quasicrystal, bar-joint framework, rigidity",
author = "Stephen Power",
year = "2021",
month = aug,
day = "31",
doi = "10.1353/mpr.2021.0000",
language = "English",
volume = "121A",
pages = "9--31",
journal = "Mathematical Proceedings of the Royal Irish Academy",
issn = "1393-7197",
publisher = "Royal Irish Academy",
number = "1",

}

RIS

TY - JOUR

T1 - Parallelogram Frameworks and Flexible Quasicrystals

AU - Power, Stephen

PY - 2021/8/31

Y1 - 2021/8/31

N2 - The first-order flex space of the bar-joint framework $\G_P$ of a parallelogram tiling $P$ is determined in terms of an explicit free basis. Applications are given to braced parallelogram frameworks and to quasicrystal frameworks associated with multigrids in the sense of de Bruijn and Beenker. In particular we characterise rigid bracing patterns, identify quasicrystal frameworks with finite dimensional flex spaces, and define a zero mode spectrum.

AB - The first-order flex space of the bar-joint framework $\G_P$ of a parallelogram tiling $P$ is determined in terms of an explicit free basis. Applications are given to braced parallelogram frameworks and to quasicrystal frameworks associated with multigrids in the sense of de Bruijn and Beenker. In particular we characterise rigid bracing patterns, identify quasicrystal frameworks with finite dimensional flex spaces, and define a zero mode spectrum.

KW - quasicrystal

KW - bar-joint framework

KW - rigidity

U2 - 10.1353/mpr.2021.0000

DO - 10.1353/mpr.2021.0000

M3 - Journal article

VL - 121A

SP - 9

EP - 31

JO - Mathematical Proceedings of the Royal Irish Academy

JF - Mathematical Proceedings of the Royal Irish Academy

SN - 1393-7197

IS - 1

ER -