A non-Markovian model of rill erosion

Michael Damron; C. L. Winter; Michael Damron; C. L. Winter

doi:10.3934/nhm.2009.4.731

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

Michael Damron ^{1
,},
C. L. Winter ^{2
,}

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.
- erosion,
- rill erosion; Pólya urn; exchangeability; dynamical discrete web
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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Abstract

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.
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