Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trapping in dendrimers and regular hyperbranched polymers   Dendrimers and regular hyperbranched polymers are two classic families of
macromolecules, which can be modeled by Cayley trees and Vicsek fractals,
respectively. In this paper, we study the trapping problem in Cayley trees and
Vicsek fractals with different underlying geometries, focusing on a particular
case with a perfect trap located at the central node. For both networks, we
derive the exact analytic formulas in terms of the network size for the average
trapping time (ATT)---the average of node-to-trap mean first-passage time over
the whole networks. The obtained closed-form solutions show that for both
Cayley trees and Vicsek fractals, the ATT display quite different scalings with
various system sizes, which implies that the underlying structure plays a key
role on the efficiency of trapping in polymer networks. Moreover, the
dissimilar scalings of ATT may allow to differentiate readily between
dendrimers and hyperbranched polymers.

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The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
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The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
1
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: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
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The categories of this paper are: eess