December  2009, 4(4): 731-753. doi: 10.3934/nhm.2009.4.731

A non-Markovian model of rill erosion

1. 

Mathematics Department, Princeton University, 304 Fine Hall, Washington Rd., Princeton, NJ 08544, United States

2. 

National Center for Atmospheric Research, 1850 Table Mesa Dr., Boulder, CO 80305, United States

Received  February 2009 Revised  July 2009 Published  October 2009

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. Networks & Heterogeneous Media, 2009, 4 (4) : 731-753. doi: 10.3934/nhm.2009.4.731
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