Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric Perturbation Theory for a Class of Fiber Bundles   A systematic study of small, time-dependent, perturbations to geometric
wave-equation domains is hardly existent. Acoustic enclosures are typical
examples featuring locally reacting surfaces that respond to a pressure
gradient or a pressure difference, alter the enclosure's volume and, hence, the
boundary conditions, and do so locally through their vibrations. Accordingly,
the Laplace-Beltrami operator in the acoustic wave equation lives in a
temporally varying domain depending on the displacement of the locally reacting
surface from equilibrium. The resulting partial differential equations feature
nonlinearities and are coupled though the time-dependent boundary conditions.
The solution to the afore-mentioned problem, as presented here, integrates
techniques from differential geometry, functional analysis, and physics. The
appropriate space is shown to be a (perturbation) fiber bundle. In the context
of a systematic perturbation theory, the solution to the dynamical problem is
obtained from a combination of semigroup techniques for operator evolution
equations and metric perturbation theory as used in AdS/CFT. Duhamel's
principle then yields a time-dependent perturbation theory, called geometric
perturbation theory. It is analogous to, though different from, both Dirac's
time-dependent perturbation theory and the Magnus expansion. Specifically, the
formalism demonstrates that the stationary-domain approximation for vibrational
acoustics only introduces a small error. Analytic simplifications methods are
derived in the framework of the piston approximation. Globally reacting
surfaces (so-called pistons) replace the formerly locally reacting surfaces and
reduce the number of independent variables in the underlying partial
differential equations. In this way, a straightforwardly applicable formalism
is derived for scalar wave equations on time-varying domains.

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The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
1
The categories of this paper are: cs
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The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat