Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Number of Transition Frequencies of a System Containing an Arbitrary
  Number of Gas Bubbles   ``Transition frequencies'' of a system containing an arbitrary number of
bubbles levitated in a liquid are discussed. Using a linear coupled-oscillator
model, it is shown theoretically that when the system contains $N$ bubbles of
different sizes, each bubble has $2N - 1$ (or less) transition frequencies
which make the phase difference between an external sound and a bubble's
pulsation $\pi / 2$. Furthermore, we discuss a discrepancy appearing between
the present result regarding the transition frequencies and existing ones for
the resonance frequencies in a two-bubble case, and show that the transition
frequency, defined as above, and the resonance frequency have a different
physical meaning when $N \ge 2$, while they are consistent for $N = 1$.

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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: bayes-an
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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: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex