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The Rigid Unit Mode spectrum for symmetric frameworks by Kastis, Eleftherios; Kitson, Derek is a scholarly article available to read on EtoBox.

What is The Rigid Unit Mode spectrum for symmetric frameworks about?

We establish several fundamental properties of the Rigid Unit Mode (RUM) spectrum for symmetric frameworks with a discrete abelian symmetry group and arbitrary linear constraints. In particular, we identify a nonempty subset of the RUM spectrum which derives from the joint eigenvalues of generators for the linear part of the symmetry group. These joint eigenvalues give rise to $\chi$-symmetric flexes which span the space of translations for the framework. We show that the RUM spectrum is a union of Bohr-Fourier spectra arising from twisted almost-periodic flexes of the framework. We also characterise frameworks for which every almost periodic flex is a translation.

Author

Kastis, Eleftherios; Kitson, Derek

Published

2025

Language

EN