Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interactions beyond nearest neighbours and rigidity of discrete
  energies: a compactness result and an application to dimension reduction   We analyse the rigidity of 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 surface-scaled energy and we give bounds on its
possible Gamma-limit.
  In the second part of the paper we follow the approach developed in the first
part to study a discrete model for (possibly heterogeneous) nanowires. In the
heterogeneous case, by applying the compactness result shown in the first part
of the paper, we obtain an estimate on the minimal energy spent to match
different equilibria. This gives insight into the nucleation of dislocations in
epitaxially grown heterostructured nanowires.

8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio