Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric Perturbation Theory and Acoustic Boundary Condition Dynamics   Geometric perturbation theory is universal. A typical example is provided by
the 3D wave equation, widely used in acoustics. We face vibrating eardrums as a
binaural auditory input stemming from an external sound source. In the setup of
internally coupled ears (ICE), which are present in more than half of the
land-living vertebrates, the two tympana are coupled by an internal air-filled
cavity, whose geometry determines the acoustic properties of the ICE system.
The eardrums themselves are described by a 2-dimensional, damped, wave equation
and are part of the spatial boundary conditions of the three-dimensional
Laplacian belonging to the wave equation in the internal cavity that couples
and internally drives the eardrums. In animals with ICE the resulting signal is
the superposition of external sound arriving at both eardrums and the internal
pressure coupling them. This is also the typical setup for geometric
perturbation theory. In the context of ICE it boils down to acoustic
boundary-condition dynamics (ABCD) for the coupled dynamical system of eardrums
and internal cavity. In acoustics the deviations from equilibrium are extremely
small (nm). Perturbation theory is therefore natural and shown to be
appropriate. In doing so, we use a time-dependent perturbation theory \`a la
Dirac in the context of Duhamel's principle. The relaxation dynamics of the
tympanic-membrane system, which neuronal information processing stems from, is
explicitly obtained in first order. Furthermore, both the initial and the
quasi-stationary asymptotic state are derived and analyzed. Finally, we set the
general stage for geometric perturbation theory where (d-1)-dimensional
manifolds as subsets of the boundary of a d-dimensional domain are driven by
their own dynamics with the domain pressure $p$ and an external source term as
input, at the same time constituting time-dependent boundary conditions for
$p$.

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The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
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The categories of this paper are: cs
4
The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph