Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Collective vortex rectification effects in films with a periodic pinning
  array
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga