On the effect of interactions beyond nearest neighbours on non-convex lattice systems

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dc.contributor.areaMathematicsen_US
dc.contributor.authorAlicandro, Roberto
dc.contributor.authorLazzaroni, Giuliano
dc.contributor.authorPalombaro, Mariapia
dc.date.accessioned2017-01-16T12:38:57Z
dc.date.available2017-01-16T12:38:57Z
dc.date.issued2017-01
dc.description.abstractWe analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation.en_US
dc.identifier.urihttps://openscience.sissa.it/handle/1963/35268
dc.language.isoenen_US
dc.miur.area1en_US
dc.relation.ispartofseriesSISSA;57/2016/MATE
dc.subjectNonlinear elasticityen_US
dc.subjectDiscrete to continuumen_US
dc.subjectGeometric rigidityen_US
dc.subjectNext-to-nearest neighboursen_US
dc.subjectGamma-convergenceen_US
dc.titleOn the effect of interactions beyond nearest neighbours on non-convex lattice systemsen_US
dc.typePreprinten_US
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