TY - RPRT
T1 - On the effect of interactions beyond nearest neighbours on non-convex lattice systems
Y1 - 2017
A1 - Roberto Alicandro
A1 - Giuliano Lazzaroni
A1 - Mariapia Palombaro
AB - We 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.
UR - http://urania.sissa.it/xmlui/handle/1963/35268
U1 - 35574
U2 - Mathematics
U4 - 1
ER -