Random walks on the Apollonian network with a single trap

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dc.creatorZhang, Zhongzhi
dc.creatorGuan, Jihong
dc.creatorXie, Wenlei
dc.creatorQi, Yi
dc.creatorZhou, Shuigeng
dc.date2009-03-17
dc.date.accessioned2026-07-07T13:06:17Z
dc.date.available2026-07-07T13:06:17Z
dc.descriptionExplicit determination of the mean first-passage time (MFPT) for trapping problem on complex media is a theoretical challenge. In this paper, we study random walks on the Apollonian network with a trap fixed at a given hub node (i.e. node with the highest degree), which are simultaneously scale-free and small-world. We obtain the precise analytic expression for the MFPT that is confirmed by direct numerical calculations. In the large system size limit, the MFPT approximately grows as a power-law function of the number of nodes, with the exponent much less than 1, which is significantly different from the scaling for some regular networks or fractals, such as regular lattices, Sierpinski fractals, T-graph, and complete graphs. The Apollonian network is the most efficient configuration for transport by diffusion among all previously studied structure.
dc.descriptionDefinitive version accepted for publication in EPL (Europhysics Letters)
dc.identifierhttps://arxiv.org/abs/0903.2887
dc.identifierhttp://arxiv.org/abs/0903.2887
dc.identifierEurophysics Letters 86 (2009) 10006
dc.identifierdoi:10.1209/0295-5075/86/10006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227733
dc.subjectStatistical Mechanics
dc.titleRandom walks on the Apollonian network with a single trap
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