Trapping in dendrimers and regular hyperbranched polymers

Wu, Bin; Lin, Yandan; Zhang, Zhongzhi; Chen, Guanrong

doi:10.1063/1.4737635

Cited by 63 publications

(69 citation statements)

References 57 publications

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“…(14) in Ref. [44] about PMFPT of Cayley tree, we have the leading asymptotic term of ATT with trap located in central node in C g…”

Section: Average Trapping Time On Husimi Cactusmentioning

confidence: 97%

“…As a representative network, dendrimer (also called Cayley tree) [30][31][32][33][34] has extensive applications in different fields, including medicinal and diagnosis [35,36], drug delivery system [37,38], light harvesting [39,40] and electronic applications [41]. Random walks on dendrimer have been widely studied [42][43][44][45]. During the transport processes, the excitations are usually located on the chromophores of dendrimer or the segments connecting the chromophores [46].…”

Section: Introductionmentioning

confidence: 99%

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Mean first passage time for random walk on dual structure of dendrimer

Guan

Zhou

2014

Physica A: Statistical Mechanics and its Applications

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“…(14) in Ref. [44] about PMFPT of Cayley tree, we have the leading asymptotic term of ATT with trap located in central node in C g…”

Section: Average Trapping Time On Husimi Cactusmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Mean first passage time for random walk on dual structure of dendrimer

Guan

Zhou

2014

Physica A: Statistical Mechanics and its Applications

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“…During the past years significant efforts have been devoted to trapping issue in diverse networked a) Electronic mail: zhangzz@fudan.edu.cn; http://www.researcherid.com/rid/G-5522-2011 systems with particular structural properties, such as square-planar lattices and cubic lattices 19,20 , Sierpinski gasket 21,22 and Sierpinski tower 23 , T −shape fractal and its extensions [24][25][26][27][28][29] , dendrimers [30][31][32][33] , hyperbranched polymers 32,33 , non-fractal [34][35][36] and fractal scale-free networks [37][38][39] . These works showed that topological properties crucially affect the trapping efficiency measured by ATT, which can display superlinear, linear, sublinear, logarithmical and other dependence on the system size, depending on network structure.…”

Section: Introductionmentioning

confidence: 99%

Random walks in unweighted and weighted modular scale-free networks with a perfect trap

Yang

Zhang

2013

The Journal of Chemical Physics

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Designing optimal structure favorable to diffusion and effectively controlling the trapping process are crucial in the study of trapping problem-random walks with a single trap. In this paper, we study the trapping problem occurring on unweighted and weighted networks, respectively. The networks under consideration display the striking scale-free, small-world, and modular properties, as observed in diverse real-world systems. For binary networks, we concentrate on three cases of trapping problems with the trap located at a peripheral node, a neighbor of the root with the least connectivity, and a farthest node, respectively. For weighted networks with edge weights controlled by a parameter, we also study three trapping problems, in which the trap is placed separately at the root, a neighbor of the root with the least degree, and a farthest node. For all the trapping problems, we obtain the analytical formulas for the average trapping time (ATT) measuring the efficiency of the trapping process, as well as the leading scaling of ATT. We show that for all the trapping problems in the binary networks with a trap located at different nodes, the dominating scalings of ATT reach the possible minimum scalings, implying that the networks have optimal structure that is advantageous to efficient trapping. Furthermore, we show that for trapping in the weighted networks, the ATT is controlled by the weight parameter, through modifying which, the ATT can behave superlinealy, linearly, sublinearly, or logarithmically with the system size. This work could help improving the design of systems with efficient trapping process and offers new insight into control of trapping in complex systems.

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“…In Refs. [42][43][44][45] , MFPT from any node to the central node, as well as the ATT to the center, were deduced. These a) Electronic mail: zhangzz@fudan.edu.cn; http://www.researcherid.com/rid/G-5522-2011 works unveiled the effect of structure on the MFPT and ATT to the central node.…”

Section: Introductionmentioning

confidence: 99%

Maximal entropy random walk improves efficiency of trapping in dendrimers

Peng

Zhang

2014

The Journal of Chemical Physics

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We use maximal entropy random walk (MERW) to study the trapping problem in dendrimers modeled by Cayley trees with a deep trap fixed at the central node. We derive an explicit expression for the mean first passage time from any node to the trap, as well as an exact formula for the average trapping time (ATT), which is the average of the source-to-trap mean first passage time over all non-trap starting nodes. Based on the obtained closed-form solution for ATT, we further deduce an upper bound for the leading behavior of ATT, which is the fourth power of ln N , where N is the system size. This upper bound is much smaller than the ATT of trapping depicted by unbiased random walk in Cayley trees, the leading scaling of which is a linear function of N . These results show that MERW can substantially enhance the efficiency of trapping performed in dendrimers.

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Trapping in dendrimers and regular hyperbranched polymers

Cited by 63 publications

References 57 publications

Mean first passage time for random walk on dual structure of dendrimer

Mean first passage time for random walk on dual structure of dendrimer

Random walks in unweighted and weighted modular scale-free networks with a perfect trap

Maximal entropy random walk improves efficiency of trapping in dendrimers

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