Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mesoscopic Superconducting Cylinders: Phase Transitions, Phase Diagrams
  and Magnetization   Superconducting state in mesoscopic cylinder placed in the external magnetic
field is analyzed at general de Gennes boundary condition for the order
parameter. The lower and the surface critical fields of the cylinder are
calculated at different values of de Gennes "extrapolation length" $b$. For the
case of standard boundary condition (corresponding to $b\to \infty $) we use a
variational method to calculate the phase transitions between different
superconducting states. Based on the trial function for the order parameter, we
find an approximate solutions to the Ginzburg-Landau equations for the
Meissner, the single-vortex, and the giant-vortex states. The magnetization
curves of thin cylinders are calculated.

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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph