Frameworks With Crystallographic Symmetry

Authors

Ciprian Borcea, Rider University
Ileana Streinu, Smith CollegeFollow

Document Type

Article

Publication Date

12-30-2013

Publication Title

Philosophical Transactions A: Mathematical, Physical and Engineering Sciences

Abstract

Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in R^d. It is shown that natural parametrizations provide affine section descriptions for families of frameworks with a specified graph and symmetry. A simple geometric setting for diaplacive phase transitions is obtained. Upper bounds are derived for the number of realizations of minimally rigid periodic graphs.

Volume

372

Issue

2008

DOI

dx.doi.org/10.1098/rsta.2012.0143

ISSN

1471-2962

Comments

Author’s submitted manuscript.

Recommended Citation

Borcea, Ciprian and Streinu, Ileana, "Frameworks With Crystallographic Symmetry" (2013). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/9