Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An example of anti-dynamo conformal Arnold metric   A 3D metric conformally related to Arnold cat fast dynamo metric:
${ds_{A}}^{2}=e^{-{\lambda}z}dp^{2}+e^{{\lambda}z}dq^{2}+dz^{2}$ is shown to
present a behaviour of non-dynamos where the magnetic field exponentially decay
in time. The Riemann-Christoffel connection and Riemann curvature tensor for
the Arnold and its conformal counterpart are computed. The curvature decay as
z-coordinates increases without bounds. Some of the Riemann curvature
components such as $R_{pzpz}$ also undergoes dissipation while component
$R_{qzqz}$ increases without bounds. The remaining curvature component
$R_{pqpq}$ is constant on the torus surface. The Riemann curvature invariant
$K^{2}=R_{ijkl}R^{ijkl}$ is found to be 0.155 for the ${\lambda}=0.75$. A
simple solution of Killing equations for Arnold metric yields a stretch Killing
vector along one direction and compressed along other direction in order that
the modulus of the Killing vector is not constant along the flow. The flow is
shown to be untwisted. The stability of the two metrics are found by examining
the sign of their curvature tensor components.

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The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg