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The average weighted receiving time with weight-dependent walk on a family of double-weighted polymer networks

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  • Fei Zhang

    (Institute of Orthopaedics, The Third Hospital of Hebei Medical University, ShijiaZhuang, Hebei 050051, P. R. China†Key Laboratory of Biomechanics of Hebei Province, Shijiazhuang, Hebei 050051, P. R. China)

  • Dandan Ye

    (Institute of Orthopaedics, The Third Hospital of Hebei Medical University, ShijiaZhuang, Hebei 050051, P. R. China†Key Laboratory of Biomechanics of Hebei Province, Shijiazhuang, Hebei 050051, P. R. China)

  • Changling Han

    (Institute of Orthopaedics, The Third Hospital of Hebei Medical University, ShijiaZhuang, Hebei 050051, P. R. China†Key Laboratory of Biomechanics of Hebei Province, Shijiazhuang, Hebei 050051, P. R. China)

  • Wei Chen

    (Institute of Orthopaedics, The Third Hospital of Hebei Medical University, ShijiaZhuang, Hebei 050051, P. R. China†Key Laboratory of Biomechanics of Hebei Province, Shijiazhuang, Hebei 050051, P. R. China)

  • Yingze Zhang

    (Institute of Orthopaedics, The Third Hospital of Hebei Medical University, ShijiaZhuang, Hebei 050051, P. R. China†Key Laboratory of Biomechanics of Hebei Province, Shijiazhuang, Hebei 050051, P. R. China‡Chinese Academy of Engineering, Beijing 100088, P. R. China)

Abstract

In this paper, a family of the double-weighted polymer networks is introduced depending on the number of copies f and two weight factors w,r. The double-weights represent the selected weights and the consumed weights, respectively. Denote by wijS the selected weight connecting the nodes i and j, and denote by wijC the consumed weight connecting the nodes i and j. Let wijS be related to the weight factor w, and let wijC be related to the weight factors r. Assuming that the walker, at each step, starting from its current node, moves to any of its neighbors with probability proportional to the selected weight of edge linking them. The weighted time for two adjacency nodes is the consumed weight connecting the two nodes. The average weighted receiving time (AWRT) is defined on the double-weighted polymer networks. Our results show that in large network, the leading behaviors of AWRT for the double-weighted polymer networks follow distinct scalings, with the trapping efficiency associated with the network size Ng, the number of copies f, and two weight factors w,r. We also found that the scalings of the AWRT with weight-dependent walk in double-weighted polymer networks is due to the use of the weight-dependent walk and the weighted time. The dominant reason is the range of each weight factor. To investigate the reason of the scalings, the AWRT for four cases are discussed.

Suggested Citation

  • Fei Zhang & Dandan Ye & Changling Han & Wei Chen & Yingze Zhang, 2019. "The average weighted receiving time with weight-dependent walk on a family of double-weighted polymer networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 30(08), pages 1-18, August.
    • Handle: RePEc:wsi:ijmpcx:v:30:y:2019:i:08:n:s0129183119500633
    DOI: 10.1142/S0129183119500633
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    References listed on IDEAS

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