Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy density balance during shock wave implosion in water   Analytical modeling of the evolution of cylindrical and spherical shock waves
(shocks) during an implosion in water is presented for an intermediate range of
convergence radii. Up to now this range is determined only in experiments
observations as a range of implosion radii which are already far from the
piston influence, but yet not described by well-known self-similar solutions.
The model is based on an analysis of the change in pressure and kinetic energy
density, as well as on the corresponding fluxes of internal and kinetic energy
densities behind the shock front. It shows that the spatial evolution of the
shock velocity strongly depends on the initial compression, the adiabatic index
of water, and the geometry of convergence. The model also explains the
transition to a rapid like self-similar increase in the shock velocity at only
a certain radius of the shock that is observed in experiments. The dependence
of the threshold radius, where the shock implosion follows the power law (quasi
self-similarity), on the initial compression is determined. It is stated that
in the entire range of the shock radii the internal and kinetic energy density
fluxes are equal, which is in agreement with known experimental data.

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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom