Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exploration of stable and unstable vortex patterns in a superconductor
  under a magnetic disc   The stable and unstable solutions of a square 2D extreme type-II
superconductor are studied in the field of a magnetic disc. We use a
preconditioned Newton-Krylov solver to find the solutions and use numerical
continuation to track the solutions as the field strength varies. For a disc
with a small radius, we have identified generic scenarios through which the
state loses and regains its stability.

22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat