Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires
| dc.contributor.author | Lazzaroni, Giuliano | |
| dc.contributor.author | Palombaro, Mariapia | |
| dc.contributor.author | Schlomerkemper, Anja | |
| dc.date.accessioned | 2015-01-30T07:54:55Z | |
| dc.date.available | 2015-01-30T07:54:55Z | |
| dc.date.issued | 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.identifier.uri | https://openscience.sissa.it/handle/1963/7494 | |
| 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 |