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    Rights statement: https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/crystal-flex-bases-and-the-rum-spectrum/23137CE9EF898E08B027719FB6B35F46 The definitive version of this article has been published in the Journal, Proceedings of the Edinburgh Mathematical Society, 64 (4), pp 735-761 2021, © 2021 Cambridge University Press.

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Crystal flex bases and the RUM spectrum

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Crystal flex bases and the RUM spectrum. / Badri, Ghada; Kitson, Derek; Power, Stephen.
In: Proceedings of the Edinburgh Mathematical Society, Vol. 64, No. 4, 24.11.2021, p. 735-761.

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

Harvard

Badri, G, Kitson, D & Power, S 2021, 'Crystal flex bases and the RUM spectrum', Proceedings of the Edinburgh Mathematical Society, vol. 64, no. 4, pp. 735-761. https://doi.org/10.1017/s0013091521000389

APA

Badri, G., Kitson, D., & Power, S. (2021). Crystal flex bases and the RUM spectrum. Proceedings of the Edinburgh Mathematical Society, 64(4), 735-761. Advance online publication. https://doi.org/10.1017/s0013091521000389

Vancouver

Badri G, Kitson D, Power S. Crystal flex bases and the RUM spectrum. Proceedings of the Edinburgh Mathematical Society. 2021 Nov 24;64(4):735-761. Epub 2021 Nov 24. doi: 10.1017/s0013091521000389

Author

Badri, Ghada ; Kitson, Derek ; Power, Stephen. / Crystal flex bases and the RUM spectrum. In: Proceedings of the Edinburgh Mathematical Society. 2021 ; Vol. 64, No. 4. pp. 735-761.

Bibtex

@article{994fa3316cbe40acbabb39ad63a6b81c,
title = "Crystal flex bases and the RUM spectrum",
abstract = "A theory of infinite spanning sets and bases is developed for the first order flex space of an infinite bar-joint framework, together with space group symmetric versions for a crystallographic bar-joint framework $\C$. The existence of crystal flex basis for $\C$ is shown to be closely related to the spectral analysis of the rigid unit mode (RUM) spectrum of $\C$ and an associated \emph{geometric flex spectrum}. Additionally, infinite spanning sets and bases are computed for a range of fundamental crystallographic bar-joint frameworks, including the honeycomb (graphene) framework, the octahedron (perovskite) framework and the 2D and 3D kagome frameworks. ",
keywords = "periodic frameworks, rigid unit modes",
author = "Ghada Badri and Derek Kitson and Stephen Power",
note = "https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/crystal-flex-bases-and-the-rum-spectrum/23137CE9EF898E08B027719FB6B35F46 The definitive version of this article has been published in the Journal, Proceedings of the Edinburgh Mathematical Society, 64 (4), pp 735-761 2021, {\textcopyright} 2021 Cambridge University Press. ",
year = "2021",
month = nov,
day = "24",
doi = "10.1017/s0013091521000389",
language = "English",
volume = "64",
pages = "735--761",
journal = "Proceedings of the Edinburgh Mathematical Society",
issn = "0013-0915",
publisher = "Cambridge University Press",
number = "4",

}

RIS

TY - JOUR

T1 - Crystal flex bases and the RUM spectrum

AU - Badri, Ghada

AU - Kitson, Derek

AU - Power, Stephen

N1 - https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/crystal-flex-bases-and-the-rum-spectrum/23137CE9EF898E08B027719FB6B35F46 The definitive version of this article has been published in the Journal, Proceedings of the Edinburgh Mathematical Society, 64 (4), pp 735-761 2021, © 2021 Cambridge University Press.

PY - 2021/11/24

Y1 - 2021/11/24

N2 - A theory of infinite spanning sets and bases is developed for the first order flex space of an infinite bar-joint framework, together with space group symmetric versions for a crystallographic bar-joint framework $\C$. The existence of crystal flex basis for $\C$ is shown to be closely related to the spectral analysis of the rigid unit mode (RUM) spectrum of $\C$ and an associated \emph{geometric flex spectrum}. Additionally, infinite spanning sets and bases are computed for a range of fundamental crystallographic bar-joint frameworks, including the honeycomb (graphene) framework, the octahedron (perovskite) framework and the 2D and 3D kagome frameworks.

AB - A theory of infinite spanning sets and bases is developed for the first order flex space of an infinite bar-joint framework, together with space group symmetric versions for a crystallographic bar-joint framework $\C$. The existence of crystal flex basis for $\C$ is shown to be closely related to the spectral analysis of the rigid unit mode (RUM) spectrum of $\C$ and an associated \emph{geometric flex spectrum}. Additionally, infinite spanning sets and bases are computed for a range of fundamental crystallographic bar-joint frameworks, including the honeycomb (graphene) framework, the octahedron (perovskite) framework and the 2D and 3D kagome frameworks.

KW - periodic frameworks

KW - rigid unit modes

U2 - 10.1017/s0013091521000389

DO - 10.1017/s0013091521000389

M3 - Journal article

VL - 64

SP - 735

EP - 761

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 4

ER -