Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resonant Excitation of Disk Oscillations in Deformed Disks VII:
  Stability Criterion in MHD Systems   In a disk with an oscillatory deformation from an axisymmetric state with
frequency $\omega_{\rm D}$ and azimuthal wavenumber $m_{\rm D}$, a set of two
normal mode oscillations with frequency and azimuthal wavenumber being
($\omega_1$, $m_1$) and ($\omega_2$, $m_2$) resonantly couple through the disk
deformation, when the resonant conditions ($\omega_1+\omega_2+\omega_{\rm D}=0$
and $m_1+m_2+m_{\rm D}=0$) are satisfied. In the case of hydrodynamical disks,
the resonance amplifies the set of the oscillations if
$(E_1/\omega_1)(E_2/\omega_2)>0$ (Kato 2013b), where $E_1$ and $E_2$ are wave
energies of the two oscillations with $\omega_1$ and $\omega_2$, respectively.
In this paper we show that this instability criterion is still valid even when
the oscillations are ideal MHD ones in magnetized disks, if the displacements
associated with the oscillations vanish on the boundary of the system.

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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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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: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: stat