University of Sussex
Browse
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

Download (239.01 kB)
journal contribution
posted on 2023-06-09, 05:20 authored by Roberto Alicandro, Giuliano Lazzaroni, Mariapia Palombaro
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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Calculus of Variations and Partial Differential Equations

ISSN

0944-2669

Publisher

Springer Verlag

Issue

2

Volume

56

Article number

a42

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Analysis and Partial Differential Equations Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2017-03-01

First Open Access (FOA) Date

2018-03-18

First Compliant Deposit (FCD) Date

2017-03-01

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC