Home > Research > Publications & Outputs > Crystal flex bases and the RUM spectrum

Electronic data

  • BKPbases - PEMS_submission

    Rights statement: 6m

    Accepted author manuscript, 347 KB, PDF document

    Embargo ends: 1/01/50

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

View graph of relations

Crystal flex bases and the RUM spectrum

Research output: Contribution to journalJournal articlepeer-review

Forthcoming
<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

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.