Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Granular impact and the critical packing state   Impact dynamics during collisions of spheres with granular media reveal a
pronounced and non-trivial dependence on volume fraction \phi. Post impact
crater morphology identifies the critical packing state \phi_{cps}, where
sheared grains neither dilate nor consolidate, and indicates an associated
change in spatial response. Current phenomenological models fail to capture the
observed impact force for most \phi; only near \phi_{cps} is force separable
into additive terms linear in depth and quadratic in velocity. At fixed depth
the quadratic drag coefficient decreases (increases) with depth for \phi <
\phi_{cps} (\phi > \phi_{cps}). At fixed low velocity, depth dependence of
force shows a Janssen-type exponential response with a length scale that
decreases with increasing \phi; and is nearly constant for \phi > \phi_{cps}.

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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
18
The categories of this paper are: econ