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Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires

Show simple item record Lazzaroni, Giuliano Palombaro, Mariapia Schlomerkemper, Anja 2015-01-30T07:54:55Z 2015-01-30T07:54:55Z 2015-01
dc.description.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 en_US
dc.language.iso en en_US
dc.publisher SISSA en_US
dc.relation.ispartofseries SISSA;04/2015/MATE
dc.subject Nonlinear elasticity en_US
dc.subject Discrete to continuum en_US
dc.subject Dimension reduction en_US
dc.subject Rod theory en_US
dc.subject Geometric rigidity en_US
dc.subject Non-interpenetration en_US
dc.subject Gamma-convergence en_US
dc.subject Crystals en_US
dc.subject Dislocations en_US
dc.subject Heterostructures en_US
dc.title Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires en_US
dc.type Preprint en_US

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