Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogenization of high-contrast Mumford-Shah energies   We prove a homogenization result for Mumford-Shah-type energies associated to
a brittle composite material with weak inclusions distributed periodically at a
scale ${\varepsilon}>0$. The matrix and the inclusions in the material have the
same elastic moduli but very different toughness moduli, with the ratio of the
toughness modulus in the matrix and in the inclusions being
$1/\beta_{\varepsilon}$, with $\beta_{\varepsilon}>0$ small. We show that the
high-contrast behaviour of the composite leads to the emergence of interesting
effects in the limit: The volume and surface energy densities interact by
$\Gamma$-convergence, and the limit volume energy is not a quadratic form in
the critical scaling $\beta_{\varepsilon} = {\varepsilon}$, unlike the
${\varepsilon}$-energies, and unlike the extremal limit cases.

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The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph