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Anomalous behavior of trapping in extended dendrimers with a perfect trap | | Zhongzhi Zhang
; Huan Li
; Yuhao Yi
; | | Date: |
3 Aug 2015 | | Abstract: | Compact and extended dendrimers are two important classes of dendritic
polymers. The impact of the underlying structure of compact dendrimers on
dynamical processes has been much studied, yet the relation between the
dynamical and structural properties of extended dendrimers remains not well
understood. In this paper, we study the trapping problem in extended dendrimers
with generation-dependent segment lengths, which is different from that of
compact dendrimers where the length of the linear segments is fixed. We first
consider a particular case that the deep trap is located at the central node,
and derive an exact formula for the average trapping time (ATT) defined as the
average of the source-to-trap mean first passage time over all starting points.
Then, using the obtained result we deduce a closed-form expression for the ATT
to an arbitrary trap node, based on which we further obtain an explicit
solution to the ATT corresponding to the trapping issue with the trap uniformly
distributed in the polymer systems. We show that the trap location has a
substantial influence on the trapping efficiency measured by the ATT, which
increases with the shortest distance from the trap to the central node, a
phenomenon similar to that for compact dendrimers. In contrast to this
resemblance, the leading terms of ATTs for the three trapping problems differ
drastically between extended and compact dendrimers, with the trapping
processes in the extended dendrimers being less efficient than in compact
dendrimers. | | Source: | arXiv, 1508.0374 | | Services: | Forum | Review | PDF | Favorites | |
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