Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thomson problem in one dimension: minimal energy configurations of $N$
  charges on a curve   We have studied the configurations of minimal energy of $N$ charges on a
curve on the plane, interacting with a repulsive potential $V_{ij} =
1/r_{ij}^s$, with $s \geq 1$ and $i,j=1,\dots, N$. Among the examples
considered are ellipses of different eccentricity, a straight wire and a
cardioid. We have found that, for some geometries, multiple minima are present,
as well as points of unstable equilibrium. For the case of the cardioid, we
observe that the presence of the cusp has a dramatic effect on the distribution
of the charges, in the limit $N \gg 1$.

2
The categories of this paper are: math
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg