Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Why charges go to the surface: a generalized Thomson problem   We study a generalization of a Thomson problem of n particles confined to a
sphere and interacting by a 1/r^g potential. It is found that for g \le 1 the
electrostatic repulsion expels all the charges to the surface of the sphere.
However for g>1 and n>n_c(g) occupation of the bulk becomes energetically
favorable. It is curious to note that the Coulomb law lies exactly on the
interface between these two regimes.

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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: q-fin