Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Neumann sieve problem and dimensional reduction: a multiscale
  approach   We perform a multiscale analysis for the elastic energy of a $n$-dimensional
bilayer thin film of thickness $2\delta$ whose layers are connected through an
$\epsilon$-periodically distributed contact zone. Describing the contact zone
as a union of $(n-1)$-dimensional balls of radius $r\ll \epsilon$ (the holes of
the sieve) and assuming that $\delta \ll \epsilon$, we show that the asymptotic
memory of the sieve (as $\epsilon \to 0$) is witnessed by the presence of an
extra interfacial energy term. Moreover we find three different limit behaviors
(or regimes) depending on the mutual vanishing rate of $\delta$ and $r$. We
also give an explicit nonlinear capacitary-type formula for the interfacial
energy density in each regime.

16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio