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Crystal frameworks, symmetry and affinely periodic flexes

Power, Stephen (2014) Crystal frameworks, symmetry and affinely periodic flexes. New York Journal of Mathematics, 20. pp. 665-693. ISSN 1076-9803

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    Abstract

    Symmetry equations are obtained for the rigidity matrices associated with various forms of infinitesimal flexibility for an idealised bond-node crystal framework C in Rd. These equations are used to derive symmetry-adapted Maxwell-Calladine counting formulae for periodic self-stresses and affinely periodic infinitesimal mechanisms. The symmetry equations also lead to general Fowler-Guest formulae connecting the character lists of subrepresentations of the crystallographic space and point groups which are associated with bonds, nodes, stresses, flexes and rigid motions. A new derivation is also given for the Borcea-Streinu rigidity matrix and the correspondence between its nullspace and the space of affinely periodic infinitesimal flexes.

    Item Type: Article
    Journal or Publication Title: New York Journal of Mathematics
    Uncontrolled Keywords: Periodic bar-joint framework ; symmetry ; affine flex
    Subjects:
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 70172
    Deposited By: ep_importer_pure
    Deposited On: 05 Aug 2014 09:24
    Refereed?: Yes
    Published?: Published
    Last Modified: 23 Oct 2017 04:00
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/70172

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