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} }
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…
One Citation
Linear zero mode spectra for quasicrystals
- MathematicsJournal of Mathematical Analysis and Applications
- 2022
References
SHOWING 1-10 OF 22 REFERENCES
The first-order flexibility of a crystal framework
- Mathematics
- 2018
Four sets of necessary and sufficient conditions are obtained for the first-order rigidity of a crystallographic bond-node framework $\C$ in $\bR^d$. In particular, an extremal rank characterisation…
The Almost Periodic Rigidity of Crystallographic Bar-Joint Frameworks
- MathematicsSymmetry
- 2014
The almost periodic infinitesimal flexes of C are characterised in terms of a matrix-valued function, ΦC(z), on the d-torus, Td, determined by a full rank translation symmetry group and an associated motif of joints and bars.
Infinite bar-joint frameworks, crystals and operator theory
- Mathematics
- 2011
A theory of fl exibility and rigidity is developed for general infinite bar-joint frameworks (G; p). Determinations of nondeformability through vanishing flexibility are obtained as well as…
The Rigidity of Infinite Graphs
- MathematicsDiscret. Comput. Geom.
- 2018
A rigidity theory is developed for countably infinite simple graphs and analogous results are obtained for the classical non-Euclidean $$\ell ^q$$ℓq norms.
Exotic distributions of rigid unit modes in the reciprocal spaces of framework aluminosilicates
- Physics
- 2007
Until recently it was assumed that rigid unit modes, defined as the zero-frequency solutions to the dynamical equations for an infinite framework of rigid corner-linked tetrahedra, were confined to a…
Rigid unit modes in framework silicates
- PhysicsMineralogical Magazine
- 1995
Abstract We describe a model for framework silicates in which the SiO4 (and AlO4) tetrahedra are treated as perfectly rigid and freely jointed. From this model we are able to identify low-energy…
Bulk-Edge Correspondence for Two-Dimensional Topological Insulators
- Physics
- 2013
Topological insulators can be characterized alternatively in terms of bulk or edge properties. We prove the equivalence between the two descriptions for two-dimensional solids in the single-particle…
Rigidity and symmetry
- Mathematics
- 2014
Volumes of Polytopes in Spaces of Constant Curvature (N. Abrosimov, A. Mednykh).- Cubic Cayley Graphs and Snarks (H. Ademir, K. Kutnar, D. Marusic).- Local, Dimensional and Universal Rigidities: A…
Algebraic spectral synthesis and crystal rigidity
- MathematicsJournal of Pure and Applied Algebra
- 2019