Realizations of Isostatic Material Frameworks. Issue 9 (8th March 2021)

• Record Type: Journal Article
• Authors: Sadjadi, Mahdi; Hagh, Varda F.; Kang, Mingyu; Sitharam, Meera; Connelly, Robert; Gortler, Steven J.; Theran, Louis; Holmes-Cerfon, Miranda; Thorpe, Michael F.
• Is Part Of: Physica status solidi. Volume 258:Issue 9(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-03-08
• Subjects: glasses -- isostatic -- jamming -- networks -- tunneling; Solid state physics -- Periodicals; Solids -- Periodicals; Atomic structure -- Periodicals; 530.41
• DOI: 10.1002/pssb.202000555
• Languages: English
• ISSNs: 0370-1972

Abstract

Abstract : This article studies the set of equivalent realizations of isostatic frameworks and algorithms for finding all such realizations. It is shown that an isostatic framework has an even number of equivalent realizations that preserve edge lengths and connectivity. The complete set of equivalent realizations for a toy framework with pinned boundary in two dimensions is enumerated and the impact of boundary length on the emergence of these realizations is studied. 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 of 2D glasses and jamming. Abstract : In a multidisciplinary collaboration, the authors show that an isostatic framework has an even number of equivalent realizations that preserve edge lengths and connectivity. New methods, based on constraint reduction and distance‐based covering, are presented and applied to atomic clusters, a model of 2D glasses and jamming.