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

Alicandro, Roberto, Lazzaroni, Giuliano and Palombaro, Mariapia (2017) On the effect of interactions beyond nearest neighbours on non-convex lattice systems. Calculus of Variations and Partial Differential Equations, 56 (2). a42. ISSN 0944-2669

[img] PDF - Accepted Version
Restricted to SRO admin only until 18 March 2018.

Download (244kB)

Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Analysis and Partial Differential Equations Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Richard Chambers
Date Deposited: 01 Mar 2017 09:32
Last Modified: 28 Mar 2017 23:41
URI: http://sro.sussex.ac.uk/id/eprint/66948

View download statistics for this item

📧 Request an update