Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of Ginzburg-Landau functionals in 3-d superconductivity   In this paper we consider the asymptotic behavior of the Ginzburg- Landau
model for superconductivity in 3-d, in various energy regimes. We rigorously
derive, through an analysis via {\Gamma}-convergence, a reduced model for the
vortex density, and we deduce a curvature equation for the vortex lines. In a
companion paper, we describe further applications to superconductivity and
superfluidity, such as general expressions for the first critical magnetic
field H_{c1}, and the critical angular velocity of rotating Bose-Einstein
condensates.

11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ