Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical laws and self-similarity of vortex rings emitted from a
  localized vortex tangle in superfluid ${}^4$He   We numerically simulated quantum turbulence in superfluid $^4$He to
investigate the emission of vortex rings from a localized vortex tangle.
Turbulence is characterized by some universal statistical laws. Although there
are a lot of studies on statistical laws in bulk quantum turbulence, studies in
inhomogeneous or localized turbulence is scarce. We first investigate the
statistical laws of localized quantum turbulence, referring to two statistical
laws deduced from the vibrating wire experiments in [Yano $et$ $al.$, J. Low
Temp. Phys. $\bf{196}$, $184\ (2019)$]. The first law is the Poisson process
for the detection of vortex rings; the vortex tangle emits vortex rings with
frequencies depending on their sizes. The second law is the power law between
the frequency and the size of the emitted vortex rings, showing the
self-similarity of the tangle. To study these statistical laws numerically, we
developed a system similar to experiments. First, we generate a localized
statistically steady vortex tangle by injecting vortex rings from two opposite
sides and causing collisions. We investigated the conditions that aid the
formation of the tangles and the anisotropy of the emission of vortex rings
from the tangle. Second, from the data on emitted rings, we reconstruct the two
statistical laws. Results from our numerical investigations are consistent with
the known self-similarity of emitted vortex rings and localized tangles.

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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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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: adap-org
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The categories of this paper are: math
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci