Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Energy dependence of a vortex line length near a zigzag of pinning
  centers
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con