Realizations of Isostatic Material Frameworks
Abstract
This paper studies the set of equivalent realizations of isostatic frameworks in two dimensions, and algorithms for finding all such realizations. We show that an isostatic framework has an even number of equivalent realizations that preserve edge lengths and connectivity. We enumerate the complete set of equivalent realizations for a toy framework with pinned boundary in two dimensions and study the impact of boundary length on the emergence of these realizations. To ameliorate the computational complexity of finding a solution to a large multivariate quadratic system corresponding to the constraints; alternative methods - based on constraint reduction and distance-based covering map or Cayley parameterization of the search space - are presented. The application of these methods is studied on atomic clusters, a model two-dimensional glasses, and jamming.
Keywords
Cite
@article{arxiv.2102.06295,
title = {Realizations of Isostatic Material Frameworks},
author = {Mahdi Sadjadi and Varda F. Hagh and Mingyu Kang and Meera Sitharam and Robert Connelly and Steven J. Gortler and Louis Theran and Miranda Holmes-Cerfon and M. F. Thorpe},
journal= {arXiv preprint arXiv:2102.06295},
year = {2021}
}
Comments
16 pages, 21 figures, submitted to Physica Status Solidi (b)