Anchored boundary conditions for locally isostatic networks

Research output: Contribution to journalArticleScientificpeer-review

Details

Original languageEnglish
Article number053306
Number of pages9
JournalPhysical Review E
Volume92
Issue number5
Publication statusPublished - 30 Nov 2015
MoE publication typeA1 Journal article-refereed

Researchers

  • Louis Theran
  • Anthony Nixon
  • Elissa Ross
  • Mahdi Sadjadi
  • Brigitte Servatius
  • M. F. Thorpe

Research units

  • Lancaster University
  • Arizona State University
  • Worcester Polytechnic Institute
  • University of Oxford
  • Fields Institute for Research in the Mathematical Sciences
  • MESH Consultants

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.

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