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Statistical dynamics of early river networks

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  • Wang, Xu-Ming
  • Wang, Peng
  • Zhang, Ping
  • Hao, Rui
  • Huo, Jie

Abstract

Based on local erosion rule and fluctuations in rainfall, geology and parameters of a river channel, a generalized Langevin equation is proposed to describe the random prolongation of a river channel. This equation is transformed into the Fokker–Plank equation to follow the early evolution of a river network and the variation of probability distribution of channel lengths. The general solution of the equation is in the product form of two terms. One term is in power form and the other is in exponent form. This distribution shows a complete history of a river network evolving from its infancy to “adulthood”). The infancy is characterized by the Gaussian distribution of the channel lengths, while the adulthood is marked by a power law distribution of the channel lengths. The variation of the distribution from the Gaussian to the power law displays a gradual developing progress of the river network. The distribution of basin areas is obtained by means of Hack’s law. These provide us with new understandings towards river networks.

Suggested Citation

  • Wang, Xu-Ming & Wang, Peng & Zhang, Ping & Hao, Rui & Huo, Jie, 2012. "Statistical dynamics of early river networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(19), pages 4497-4505.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:19:p:4497-4505
    DOI: 10.1016/j.physa.2012.04.029
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    References listed on IDEAS

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    1. Wang, Xu-Ming & Hao, Rui & Huo, Jie & Zhang, Jin-Feng, 2008. "Modeling sediment transport in river networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(25), pages 6421-6430.
    2. Chang, Hui & Su, Bei-Bei & Zhou, Yue-Ping & He, Da-Ren, 2007. "Assortativity and act degree distribution of some collaboration networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 687-702.
    3. Barabási, A.L & Jeong, H & Néda, Z & Ravasz, E & Schubert, A & Vicsek, T, 2002. "Evolution of the social network of scientific collaborations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 590-614.
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    Cited by:

    1. Huo, Jie & Wang, Xu-Ming & Zhao, Ning & Hao, Rui, 2016. "Statistical characteristics of dynamics for population migration driven by the economic interests," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 123-134.

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