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  • BKPbases - PEMS_submission

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    Accepted author manuscript, 347 KB, PDF document

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Crystal flex bases and the RUM spectrum

Research output: Contribution to journalJournal articlepeer-review

<mark>Journal publication date</mark>31/05/2021
<mark>Journal</mark>Proceedings of the Edinburgh Mathematical Society
Publication StatusAccepted/In press
<mark>Original language</mark>English


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.