%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 No. of bitstreams: 1 LaPaSc-3dim.pdf: 249836 bytes, checksum: 8b8edddc952b9a4a084c1c0c85514051 (MD5)