Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The hydrodynamic singular vortex on the sphere and the Dirac monopole   An exact correspondence is established between mathematical description of
the single "elementary vortex" (EV)velocity on the sphere
(Zermelo,1902;Bogomolov,1977) and the Dirac magnetic monopole (DMM) vector
potential (Dirac, 1931). Similar analogy with DMM was noted only for the
vortices in quantum fluid He-3A (Blaha,1976;Volovik,Mineev,1976). Singular EV
on a sphere is usually considered using compensating vortex field, uniformly
distributed over the sphere. It is necessary to meet the Gauss-Kelvin theorem
with zero integral vorticity over the sphere. However since Bogomolov
(1977)(see also Dritshel,Boatto,2015)uniform vorticity impact on dynamics is
neglected when only the velocity field of singular EV is taken into account. It
is not true because the hydrodynamic equations do not allow existence of a
solution in the form of an isolated EV but allow solutions in the form of the
antipodal EV pairs. It is also suggested the possibility of DMM existence only
in the form of the point magnetic dipoles, consisting of two DMM with different
signs of the magnetic charge.

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The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph