• DOI:10.1017/S0013091521000389
• Corpus ID: 119167472

Crystal flex bases and the RUM spectrum

@article{Badri2018CrystalFB,
  title={Crystal flex bases and the RUM spectrum},
  author={Ghada Badri and Derek Kitson and S. C. Power},
  journal={Proceedings of the Edinburgh Mathematical Society},
  year={2018},
  volume={64},
  pages={735 - 761}
}

• G. Badri, D. Kitson, S. C. Power
• Published 2 July 2018
• Mathematics
• Proceedings of the Edinburgh Mathematical Society

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 ${{\mathcal {C}}}$. The existence of a crystal flex basis for ${{\mathcal {C}}}$ is shown to be closely related to the spectral analysis of the rigid unit mode (RUM) spectrum of ${{\mathcal {C}}}$ and an associated 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.