Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scaling Laws for Dynamic Solar Loops   The scaling laws which relate the peak temperature $T_M$ and volumetric
heating rate $E_H$ to the pressure $P$ and length $L$ for static coronal loops
were established over 40 years ago; they have proved to be of immense value in
a wide range of studies. Here we extend these scaling laws to {\it dynamic}
loops, where enthalpy flux becomes important to the energy balance, and study
impulsive heating/filling characterized by upward enthalpy flows. We show that
for collision-dominated thermal conduction, the functional dependencies of the
scaling laws are the same as for the static case, when the radiative losses
scale as $T^{-1/2}$, but with a different constant of proportionality that
depends on the Mach number $M$ of the flow. The dependence on the Mach number
is such that the scaling laws for low to moderate Mach number flows are almost
indistinguishable from the static case. When thermal conduction is limited by
turbulent processes, however, the much weaker dependence of the scattering mean
free path (and hence thermal conduction coefficient) on temperature leads to a
limiting Mach number for return enthalpy fluxes driven by thermal conduction
between the corona and chromosphere.

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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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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: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: math
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat