Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Microscopic validation of a variational model of epitaxially strained
  crystalline film   A discrete-to-continuum analysis for free-boundary problems related to
crystalline films deposited on substrates is performed by $\Gamma$-convergence.
The discrete model here introduced is characterized by an energy with two
contributions, the surface and the elastic-bulk energy, and it is formally
justified starting from atomistic interactions. The surface energy counts
missing bonds at the film and substrate boundaries, while the elastic energy
models the fact that for film atoms there is a preferred interatomic distance
different from the preferred interatomic distance for substrate atoms. In the
regime of small mismatches between the film and the substrate optimal lattices,
a discrete rigidity estimate is established by regrouping the elastic energy in
triangular-cell energies and by locally applying rigidity estimates from the
literature. This is crucial to establish pre-compactness for sequences with
equibounded energy and to prove that the limiting deformation is one single
rigid motion. By properly matching the convergence scaling of the different
terms in the discrete energy, both surface and elastic contributions appear
also in the resulting continuum limit in agreement (and in a form consistent)
with literature models. Thus, the analysis performed here is a microscopical
justifications of such models.

5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
3
The categories of this paper are: physics
9
The categories of this paper are: nlin