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Symmetry 2014, 6(2), 308-328; doi:10.3390/sym6020308
Article

The Almost Periodic Rigidity of Crystallographic Bar-Joint Frameworks

,
*  and
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK
* Author to whom correspondence should be addressed.
Received: 25 February 2014 / Revised: 11 April 2014 / Accepted: 15 April 2014 / Published: 24 April 2014
(This article belongs to the Special Issue Rigidity and Symmetry)

Abstract

A crystallographic bar-joint framework, C in Rd, is shown to be almost periodically infinitesimally rigid if and only if it is strictly periodically infinitesimally rigid and the rigid unit mode (RUM) spectrum, Ω (C), is a singleton. Moreover, 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.
Keywords: crystal framework; infinitesimal rigidity; almost periodic functions crystal framework; infinitesimal rigidity; almost periodic functions
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Badri, G.; Kitson, D.; Power, S.C. The Almost Periodic Rigidity of Crystallographic Bar-Joint Frameworks. Symmetry 2014, 6, 308-328.

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