Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Individual and Multi Vortex Pinning in Systems with Periodic Pinning
  Arrays   We examine multi and individual vortex pinning in thin superconductors with
periodic pinning arrays. For multi-vortex pinning we observe peaks in the
critical current of equal magnitude at every matching field, while for
individual vortex pinning we observe a sharp drop in the critical current after
the first matching field in agreement with experiments. We examine the scaling
of the critical current at commensurate and incommensurate fields for varied
pinning strength and show that the depinning force at incommensurate fields
decreases faster than at the commensurate fields.

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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: bayes-an