Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spatial transient behavior in waveguides with lossy impedance boundary
  conditions   Attenuation in acoustic waveguides with lossy impedance boundary conditions
are associated with non-Hermitian and non-normal operators. This subject has
been extensively studied in fundamental and engineering research, and it has
been traditionally assumed that the attenuation behavior of total sound power
can be totally captured by considering the decay of each transverse mode
individually. One of the classical tools in this context is the Cremer optimum
concept that aims to maximize the attenuation of the least attenuated mode.
However, a typical sound field may be a superposition of a large number of
transverse modes which are nonorthogonal, and the individual mode attenuation
may have little to do with the total sound power attenuation. By using singular
value decomposition, we link the least attenuated total sound power to the
maximum singular value of the non-normal propagator. The behaviors of the least
attenuated total sound power depend only on the lossy boundary conditions and
frequency, but are independent of sources. The sound may be almost non-decaying
along the waveguide transition region for any lossy impedance boundary
conditions although all modes attenuate exponentially. This spatial transient
appears particularly strongly if the impedance is close to an exceptional point
of the propagator, at which a pair of adjacent modes achieve maximum
attenuation predicted by Cremer optimum concept. These results are confirmed
using non-modal numerical calculations and a two-by-two toy model.

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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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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: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: math