@article {2015,
title = {Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires},
number = {SISSA;04/2015/MATE},
year = {2015},
institution = {SISSA},
abstract = {In the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of Γ-convergence techniques. Nearest neighbours are identified by employing the notions of Voronoi diagrams and Delaunay
triangulations. The scaling of the nanowire is done in such a way that we perform
not only a continuum limit but a dimension reduction simultaneously. The main part of
the proof is a discrete geometric rigidity result that we announced in an earlier work and
show here in detail for a variety of three-dimensional lattices. We perform the passage
from discrete to continuum twice: once for a system that compensates a lattice mismatch between two parts of the heterogeneous nanowire without defects and once for a system that creates dislocations. It turns out that we can verify the experimentally observed fact that the nanowires show dislocations when the radius of the specimen is large},
url = {http://urania.sissa.it/xmlui/handle/1963/7494},
author = {Giuliano Lazzaroni and Mariapia Palombaro and Anja Schlomerkemper}
}