A-L-P-2016-surface-scaling_FINAL-Accepted.pdf (239.01 kB)
On the effect of interactions beyond nearest neighbours on non-convex lattice systems
journal contribution
posted on 2023-06-09, 05:20 authored by Roberto Alicandro, Giuliano Lazzaroni, Mariapia PalombaroWe 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.
History
Publication status
- Published
File Version
- Accepted version
Journal
Calculus of Variations and Partial Differential EquationsISSN
0944-2669Publisher
Springer VerlagExternal DOI
Issue
2Volume
56Article number
a42Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Analysis and Partial Differential Equations Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes