Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multipole Vortex Blob (MVB): Symplectic Geometry and Dynamics   Vortex blob methods are typically characterized by a regularization length
scale, below which the dynamics are trivial for isolated blobs. In this article
we observe that the dynamics need not be trivial if one is willing to consider
distributional derivatives of Dirac delta functionals as valid vorticity
distributions. More specifically, a new singular vortex theory is presented for
regularized Euler fluid equations of ideal incompressible flow in the plane. We
determine the conditions under which such regularized Euler fluid equations may
admit vorticity singularities which are stronger than delta functions, e.g.,
derivatives of delta functions. We also describe the symplectic geometry
associated to these augmented vortex structures and we characterize the
dynamics as Hamiltonian. Applications to the design of numerical methods
similar to vortex blob methods are also discussed. Such findings illuminate the
rich dynamics which occur below the regularization length scale and enlighten
our perspective on the potential for regularized fluid models to capture
multiscale phenomena.

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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom