Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Localized Breathing Modes in Granular Crystals with Defects   We investigate nonlinear localized modes at light-mass impurities in a
one-dimensional, strongly-compressed chain of beads under Hertzian contacts.
Focusing on the case of one or two such "defects", we analyze the problem's
linear limit to identify the system eigenfrequencies and the linear defect
modes. We then examine the bifurcation of nonlinear defect modes from their
linear counterparts and study their linear stability in detail. We identify
intriguing differences between the case of impurities in contact and ones that
are not in contact. We find that the former bears similarities to the single
defect case, whereas the latter features symmetry-breaking bifurcations with
interesting static and dynamic implications.

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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: math
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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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: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con