Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: In-Plane Breathing and Shear Modes in Low-Dimensional Nanostructures   We use continuum elasticity theory to revise scaling laws for radial
breathing-like and shear-like vibration modes in quasi-2D nanostructures
including finite-width nanoribbons and finite-size thin circular discs. Such
modes can be observed spectroscopically in corresponding nanostructures of
graphene and phosphorene and can be determined numerically by atomistic <i> ab
initio</i> density functional theory and classical force-field calculation. The
revised scaling laws differ from previously used expressions, some of which
display an unphysical asymptotic behavior. Apart from model assumptions
describing the effect of edge termination, the continuum scaling laws have no
adjustable parameters and display correct asymptotic behavior. These scaling
laws yield excellent agreement with experimental and numerical results for
vibration frequencies in both isotropic and anisotropic structures as well as
useful expressions for the frequency dependence on structure size and edge
termination.

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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
2
The categories of this paper are: math
21
The categories of this paper are: adap-org