### 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 language | English (US) |
---|---|

Article number | 053306 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 92 |

Issue number | 5 |

DOIs | |

State | Published - Nov 30 2015 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*92*(5), [053306]. https://doi.org/10.1103/PhysRevE.92.053306

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

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 92, no. 5, 053306. https://doi.org/10.1103/PhysRevE.92.053306

}

TY - JOUR

T1 - Anchored boundary conditions for locally isostatic networks

AU - Theran, Louis

AU - Nixon, Anthony

AU - Ross, Elissa

AU - Sadjadi, Mahdi

AU - Servatius, Brigitte

AU - Thorpe, Michael

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 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.

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 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.

UR - http://www.scopus.com/inward/record.url?scp=84949267346&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84949267346&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.92.053306

DO - 10.1103/PhysRevE.92.053306

M3 - Article

AN - SCOPUS:84949267346

VL - 92

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 5

M1 - 053306

ER -