Crystal flex bases and the RUM spectrum

Power, Stephen and Kitson, Derek and Badri, Ghada (2021) Crystal flex bases and the RUM spectrum. Proceedings of the Edinburgh Mathematical Society. ISSN 0013-0915 (In Press)

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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.

Item Type:
Journal Article
Journal or Publication Title:
Proceedings of the Edinburgh Mathematical Society
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
155627
Deposited By:
Deposited On:
02 Jun 2021 09:25
Refereed?:
Yes
Published?:
In Press
Last Modified:
05 Jun 2021 05:51