%0 Report
%D 2015
%T Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires
%A Giuliano Lazzaroni
%A Mariapia Palombaro
%A Anja Schlomerkemper
%X 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
%I SISSA
%G en
%U http://urania.sissa.it/xmlui/handle/1963/7494
%1 7623
%$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-01-30T07:54:33Z
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