Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical Simulation of Vortex Crystals and Merging in N-Point Vortex
  Systems with Circular Boundary   In two-dimensional (2D) inviscid incompressible flow, low background
vorticity distribution accelerates intense vortices (clumps) to merge each
other and to array in the symmetric pattern which is called ``vortex
crystals''; they are observed in the experiments on pure electron plasma and
the simulations of Euler fluid. Vortex merger is thought to be a result of
negative ``temperature'' introduced by L. Onsager. Slight difference in the
initial distribution from this leads to ``vortex crystals''. We study these
phenomena by examining N-point vortex systems governed by the Hamilton
equations of motion. First, we study a three-point vortex system without
background distribution. It is known that a N-point vortex system with boundary
exhibits chaotic behavior for N\geq 3. In order to investigate the properties
of the phase space structure of this three-point vortex system with circular
boundary, we examine the Poincar\'e plot of this system. Then we show that
topology of the Poincar\'e plot of this system drastically changes when the
parameters, which are concerned with the sign of ``temperature'', are varied.
Next, we introduce a formula for energy spectrum of a N-point vortex system
with circular boundary. Further, carrying out numerical computation, we
reproduce a vortex crystal and a vortex merger in a few hundred point vortices
system. We confirm that the energy of vortices is transferred from the clumps
to the background in the course of vortex crystallization. In the vortex
merging process, we numerically calculate the energy spectrum introduced above
and confirm that it behaves as k^{-\alpha},(\alpha\approx 2.2-2.8) at the
region 10^0<k<10^1 after the merging.

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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph