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  • BKPbases - PEMS_submission

    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.

    Accepted author manuscript, 347 KB, PDF document

    Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

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Crystal flex bases and the RUM spectrum

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

E-pub ahead of print
<mark>Journal publication date</mark>24/11/2021
<mark>Journal</mark>Proceedings of the Edinburgh Mathematical Society
Issue number4
Volume64
Number of pages27
Pages (from-to)735-761
Publication StatusE-pub ahead of print
Early online date24/11/21
<mark>Original language</mark>English

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.

Bibliographic 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, © 2021 Cambridge University Press.