Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Acoustic scattering by cascades with complex boundary conditions:
  compliance, porosity and impedance   We present a solution for the scattered field caused by an incident wave
interacting with an infinite cascade of blades with complex boundary
conditions. This extends previous studies by allowing the blades to be
compliant, porous or satisfying a generalised impedance condition. Beginning
with the convected wave equation, we employ Fourier transforms to obtain an
integral equation amenable to the Wiener--Hopf method. This Wiener--Hopf system
is solved using a method that avoids the factorisation of matrix functions. The
Fourier transform is inverted to obtain an expression for the acoustic
potential function that is valid throughout the entire domain. We observe that
the principal effect of complex boundary conditions is to perturb the zeros of
the Wiener--Hopf kernel, which correspond to the duct modes in the inter-blade
region. We focus efforts on understanding the role of porosity, and present a
range of results on sound transmission and generation. The behaviour of the
duct modes is discussed in detail in order to explain the physical mechanisms
behind the associated noise reductions. In particular, we show that cut-on duct
modes do not exist for arbitrary porosity coefficients. Conversely, the
acoustic modes are unchanged by modifications to the boundary conditions.
Consequently, we observe that even modest values of porosity can result in
reductions in the sound power level of $5$ dB for the first mode and $20$ dB
for the second mode. The solution is essentially analytic (the only numerical
requirements are matrix inversion and root finding) and is therefore extremely
rapid to compute.

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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th