Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singular kernels, multiscale decomposition of microstructure, and
  dislocation models   We consider a model for dislocations in crystals introduced by Koslowski,
Cuiti\~no and Ortiz, which includes elastic interactions via a singular kernel
behaving as the $H^{1/2}$ norm of the slip. We obtain a sharp-interface limit
of the model within the framework of $\Gamma$-convergence. From an analytical
point of view, our functional is a vector-valued generalization of the one
studied by Alberti, Bouchitt\'e and Seppecher to which their rearrangement
argument no longer applies. Instead we show that the microstructure must be
approximately one-dimensional on most length scales and exploit this property
to derive a sharp lower bound.

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The categories of this paper are: hep-ph
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga