title: Anchored boundary conditions for locally isostatic networks.
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.
authors.affiliation: Aalto Science Institute and Department of Computer Science, Aalto University, Post Office Box 15500, 00076 Aalto, Finland.
authors.forename: Louis
authors.initials: L
authors.lastname: Theran
authors.affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England, United Kingdom.
authors.forename: Anthony
authors.initials: A
authors.lastname: Nixon
authors.affiliation: MESH Consultants, Inc., Fields Institute for Research in the Mathematical Sciences, 222 College Street, Toronto, Ontario, Canada M5T 3J1.
authors.forename: Elissa
authors.initials: E
authors.lastname: Ross
authors.affiliation: Department of Physics, Arizona State University, Tempe, Arizona 85287-1504, USA.
authors.forename: Mahdi
authors.initials: M
authors.lastname: Sadjadi
authors.affiliation: Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, Massachusetts 01609, USA.
authors.forename: Brigitte
authors.initials: B
authors.lastname: Servatius
authors.affiliation: Department of Physics, Arizona State University, Tempe, Arizona 85287-1504, USA and Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, England, United Kingdom.
authors.forename: M F
authors.initials: MF
authors.lastname: Thorpe