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Linear zero mode spectra for quasicrystals
- Publication Year :
- 2021
-
Abstract
- A converse is given to the well-known fact that a hyperplane localised zero mode of a crystallographic bar-joint framework gives rise to a line or lines in the zero mode (RUM) spectrum. These connections motivate definitions of linear zero mode spectra, for an aperiodic bar-joint framework $G$, that are based on relatively dense sets of linearly localised flexes. For a Delone framework in the plane the limit spectrum ${\bf L}_{lim}(G, a)$ is defined in this way, as a subset of the reciprocal space for a reference basis $a$ of the ambient space. A smaller spectrum, the slippage spectrum ${\bf L}_{slip}(G, a)$, is also defined. In the case of the quasicrystal parallelogram frameworks associated with regular multi-grids, in the sense of de Bruijn and Beenker, these spectra coincide and are determined in terms of the geometry of $G$.<br />Comment: 21 pages, 4 figures. Some minor corrections and a notation adjustment have been made
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2111.06136
- Document Type :
- Working Paper