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The average trapping time on a half Sierpinski Gasket

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  • Wu, Bo
  • Zhang, Zhizhuo

Abstract

Random walks and diffusion on fractal structures often occur in various physical situations. In this paper, we focus on a particular fractal, a half Sierpinski Gasket (HSG), which is the left half of Sierpinski Gasket (SG) based on the vertical cutting of symmetry axis. We study the average trapping time (ATT) on HSG. ATT is the mean of the first-passage time of a random walker starting from any site on the network to a trap(a perfect absorber). It characteristics the diffusion efficiency of different networks. According to the structural properties of HSG, we derive the analytic expression of the ATT (〈T^〉t) on the tth generation HSG(t), which is 〈T^〉t=3t·5t+1+3·5t+1−16·3t−2t3t+1+2t+1. The result indicates that the diffusion efficiency of HSG is not affected much compared with SG at large scale.

Suggested Citation

  • Wu, Bo & Zhang, Zhizhuo, 2020. "The average trapping time on a half Sierpinski Gasket," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306573
    DOI: 10.1016/j.chaos.2020.110261
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    References listed on IDEAS

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    1. Dai, Meifeng & Dai, Changxi & Ju, Tingting & Shen, Junjie & Sun, Yu & Su, Weiyi, 2019. "Mean first-passage times for two biased walks on the weighted rose networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 268-278.
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    Cited by:

    1. Hu, Zhongren & Wu, Bo, 2023. "The average shortest distance of three colored substitution networks," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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