Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy Barriers for Flux Lines in 3 Dimensions   I determine the scaling behavior of the free energy barriers encountered by a
flux line in moving through a three-dimensional random potential. A combination
of numerical simulations and analytic arguments suggest that these barriers
scale with the length of the line in the same way as the fluctuation in the
free energy.

22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math