Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Incompressible active phases at an interface. I. Formulation and
  axisymmetric odd flows   Inspired by the recent realization of a 2D chiral fluid as an active
monolayer droplet moving atop a 3D Stokesian fluid, we formulate mathematically
its free-boundary dynamics. The surface droplet is described as a general 2D
linear, incompressible, and isotropic fluid, having a viscous shear stress, an
active chiral driving stress, and a Hall stress allowed by the lack of
time-reversal symmetry. The droplet interacts with itself through its driven
internal mechanics and by driving flows in the underlying 3D Stokes phase. We
pose the dynamics as the solution to a singular integral-differential equation,
over the droplet surface, using the mapping from surface stress to surface
velocity for the 3D Stokes equations. Specializing to the case of axisymmetric
droplets, exact representations for the chiral surface flow are given in terms
of solutions to a singular integral equation, solved using both analytical and
numerical techniques. For a disc-shaped monolayer, we additionally employ a
semi-analytical solution that hinges on an orthogonal basis of Bessel functions
and allows for efficient computation of the monolayer velocity field, which
ranges from a nearly solid-body rotation to a unidirectional edge current
depending on the subphase depth and the Saffman-Delbruck length. Except in the
near-wall limit, these solutions have divergent surface shear stresses at
droplet boundaries, a signature of systems with codimension one domains
embedded in a three-dimensional medium. We further investigate the effect of a
Hall viscosity, which couples radial and transverse surface velocity
components, on the dynamics of a closing cavity.

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The categories of this paper are: hep-ph
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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: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg