TY - JOUR

T1 - Anchored boundary conditions for locally isostatic networks

AU - Theran, Louis

AU - Nixon, Anthony Keith

AU - Ross, Elissa

AU - Sadjadi, Mahdi

AU - Servatius, Brigitte

AU - Thorpe, Mike

PY - 2015/11/30

Y1 - 2015/11/30

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevE.92.053306

DO - 10.1103/PhysRevE.92.053306

M3 - Journal article

VL - 92

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 5

M1 - 053306

ER -