Anchored boundary conditions for locally isostatic networks

Louis Theran, Anthony Nixon, Elissa Ross, Mahdi Sadjadi, Brigitte Servatius, Michael Thorpe

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 effectively isostatic. We refer to these as 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 (sliding boundary conditions). This approach also allows for the incorporation of boundaries associated with internal 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 need 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.

Original languageEnglish (US)
Article number053306
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume92
Issue number5
DOIs
StatePublished - Nov 30 2015
Externally publishedYes

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boundary conditions
Boundary conditions
Impetus
Silica
chutes
triangles
Rendering
sliding
Triangle
Sharing
apexes
Interior
Imaging
wire
Synthesis
silicon dioxide
Internal
Experimental Results
synthesis
geometry

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Anchored boundary conditions for locally isostatic networks. / Theran, Louis; Nixon, Anthony; Ross, Elissa; Sadjadi, Mahdi; Servatius, Brigitte; Thorpe, Michael.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 92, No. 5, 053306, 30.11.2015.

Research output: Contribution to journalArticle

Theran, Louis ; Nixon, Anthony ; Ross, Elissa ; Sadjadi, Mahdi ; Servatius, Brigitte ; Thorpe, Michael. / Anchored boundary conditions for locally isostatic networks. In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2015 ; Vol. 92, No. 5.
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