Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Surface homogenization of an array of Helmholtz resonators for a
  viscoacoustic model using two-scale convergence   We derive the weak limit of a linear viscoacoustic model in an acoustic liner
that is a chamber connected to a periodic repetition of elongated chambers --
the Helmholtz resonators. As model we consider the time-harmonic and linearized
compressible Navier-Stokes equations for the acoustic velocity and pressure.
Following the approach in Schmidt et al., J. Math. Ind 8:15, 2018 for the
viscoacoustic transmission problem of multiperforated plates the viscosity is
scaled as $\delta^{4}$ with the period $\delta$ of the array of chambers and
the size of the necks as well as the wall thickness like $\delta^2$ such that
the viscous boundary layers are of the order of the size of the necks. Applying
the method of two-scale convergence we obtain with a stability assumption in
the limit $\delta \to 0$ that the acoustic pressure fulfills the Helmholz
equation with impedance boundary conditions. These boundary conditions depend
on the frequency, the length of the resonators and through the effective
Rayleigh conductivity -- that can be computed numerically -- on the shape of
their necks. We compare the limit model to semi-analytical models in the
literature.

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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph