Anchored boundary conditions for locally isostatic networks

Theran, Louis and Nixon, Anthony Keith and Ross, Elissa and Sadjadi, Mahdi and Servatius, Brigitte and Thorpe, Mike (2015) Anchored boundary conditions for locally isostatic networks. Physical Review E, 92 (5). ISSN 1539-3755

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Abstract

Finite pieces of locally isostatic networks have a large number of floppy modes because of missing constraints at the surface. Here we show that by imposing suitable boundary conditions at the surface, the network can be rendered {\it{effectively isostatic}}. We refer to these as {\it{anchored boundary conditions}}. An important example is formed by a two-dimensional network of corner sharing triangles, which is the focus of this paper. Another way of rendering such networks isostatic, is by adding an external wire along which all unpinned vertices can slide ({\it{sliding boundary conditions}}). This approach also allows for the incorporation of boundaries associated with internal {\it{holes}} and complex sample geometries, which are illustrated with examples. The recent synthesis of bilayers of vitreous silica has provided impetus for this work. Experimental results from the imaging of finite pieces at the atomic level needs such boundary conditions, if the observed structure is to be computer-refined so that the interior atoms have the perception of being in an infinite isostatic environment.

Item Type:
Journal Article
Journal or Publication Title:
Physical Review E
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/3100/3104
Subjects:
ID Code:
76914
Deposited By:
Deposited On:
27 Nov 2015 11:58
Refereed?:
Yes
Published?:
Published
Last Modified:
29 Nov 2020 03:05