# American Institute of Mathematical Sciences

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