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Fractional Calculus and Applied Analysis

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Volume 22, Issue 6


An investigation on continuous time random walk model for bedload transport

ZhiPeng Li
  • State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, College of Mechanics and Materials, Hohai University Nanjing, Jiangsu, 210098, China
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ HongGuang Sun
  • Corresponding author
  • State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, College of Mechanics and Materials, Hohai University Nanjing, Jiangsu, 210098, China
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Renat T. Sibatov
Published Online: 2019-12-31 | DOI: https://doi.org/10.1515/fca-2019-0077


Bedload particles in the armoring layer may experience a multi-scale effect and multiple mass transfer rates between mobile and immobile domains. Anomalous transport behaviors and retarded space evolution plume cannot be described by the normal diffusion equation. In this paper, we apply the continuous time random walk model with different distributions of waiting times to capture bedload transport behavior under different conditions. Experimental data indicate that fluctuations of diffusive rates for bedload transport can be captured by the truncated power law (TPL). The retarded plume evolution can be well characterized by an exponential distribution of waiting times and advection-diffusion equation with a retarded kernel. The heavy-tailed snapshots of bedload transport are interpreted in terms of mobile and immobile states.

MSC 2010: Primary 60G50; Secondary 82C41; 82C31; 60G22; 82C70; 82C80

Key Words and Phrases: bedload transport; continuous time random walk (CTRW); waiting time distribution; anomalous transport; mobile-immobile domains

This paper is dedicated to the memory of the late Professor Wen Chen


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About the article

Received: 2019-07-15

Published Online: 2019-12-31

Published in Print: 2019-12-18

Citation Information: Fractional Calculus and Applied Analysis, Volume 22, Issue 6, Pages 1480–1501, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2019-0077.

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