Rights statement: c 2014 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).
Final published version, 617 KB, PDF document
Available under license: CC BY
Research output: Contribution to Journal/Magazine › Journal article › peer-review
The almost periodic rigidity of crystallographic bar-joint frameworks. / Badri, Ghada; Kitson, Derek; Power, Stephen.
In: Symmetry, Vol. 6, No. 2, 24.04.2014, p. 308-328.Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - The almost periodic rigidity of crystallographic bar-joint frameworks
AU - Badri, Ghada
AU - Kitson, Derek
AU - Power, Stephen
N1 - c 2014 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/). Special Issue on "Rigidity and Symmetry". Guest Editor: Dr. Bernd Schulze, Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster, LA1 4YF, UK
PY - 2014/4/24
Y1 - 2014/4/24
N2 - A crystallographic bar-joint framework C 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 is a singleton. Moreover the almost periodic infinitesimal flexes of C are characterised in terms of a matrix-valued function on the d-torus determined by a full rank translation symmetry group and an associated motif of joints and bars.
AB - A crystallographic bar-joint framework C 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 is a singleton. Moreover the almost periodic infinitesimal flexes of C are characterised in terms of a matrix-valued function on the d-torus determined by a full rank translation symmetry group and an associated motif of joints and bars.
KW - crystal framework
KW - infinitesimal rigidity
KW - almost periodic functions
U2 - 10.3390/sym6020308
DO - 10.3390/sym6020308
M3 - Journal article
VL - 6
SP - 308
EP - 328
JO - Symmetry
JF - Symmetry
SN - 2073-8994
IS - 2
ER -