Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The magneto-rotational instability near threshold: spatio-temporal
  amplitude equation and saturation   We show, by means of a perturbative weakly nonlinear analysis, that the
axisymmetric magneto-rotational instability (MRI) in a magnetic Taylor-Couette
(mTC) flow in a thin-gap gives rise, for very small magnetic Prandtl numbers
(P_m), to a real Ginzburg-Landau equation for the disturbance amplitude. The
saturation amplitude A_s is found to scale in this regime as P^\delta, with
1/2<\delta<2/3 (depending on the boundary conditions adopted). The asymptotic
results are shown to comply with numerical calculations performed by using a
spectral code. They suggest that the transport due to the nonlinearly developed
MRI may be vanishingly small for P_m << 1.

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The categories of this paper are: econ
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: eess
3
The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
1
The categories of this paper are: cs
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The categories of this paper are: q-fin