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Networks and Heterogeneous Media

2009, Volume 4, Issue 4: 731-753. doi: 10.3934/nhm.2009.4.731
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A non-Markovian model of rill erosion

  • 1.
    Mathematics Department, Princeton University, 304 Fine Hall, Washington Rd., Princeton, NJ 08544
  • 2.
    National Center for Atmospheric Research, 1850 Table Mesa Dr., Boulder, CO 80305
  • Received: 01 February 2009 Revised: 01 July 2009

  • Primary: 60K35, 82D99; Secondary: 60G09.

  • We introduce a new model for rill erosion. We start with a network similar to that in the Discrete Web [7, 11] and instantiate a dynamics which makes the process highly non-Markovian. The behavior of nodes in the streams is similar to the behavior of Polya urns with time-dependent input. In this paper we use a combination of rigorous arguments and simulation results to show that the model exhibits many properties of rill erosion; in particular, nodes which are deeper in the network tend to switch less quickly.

    Citation: Michael Damron, C. L. Winter. A non-Markovian model of rill erosion[J]. Networks and Heterogeneous Media, 2009, 4(4): 731-753. doi: 10.3934/nhm.2009.4.731

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  • We introduce a new model for rill erosion. We start with a network similar to that in the Discrete Web [7, 11] and instantiate a dynamics which makes the process highly non-Markovian. The behavior of nodes in the streams is similar to the behavior of Polya urns with time-dependent input. In this paper we use a combination of rigorous arguments and simulation results to show that the model exhibits many properties of rill erosion; in particular, nodes which are deeper in the network tend to switch less quickly.


  • This article has been cited by:

    1. Dan Jenkins, Superdiffusive and subdiffusive exceptional times in the dynamical discrete web, 2015, 125, 03044149, 3373, 10.1016/j.spa.2015.05.003
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  • © 2009 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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