A non-Markovian model of rill erosion

Michael Damron; C. L. Winter

doi:10.3934/nhm.2009.4.731

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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, and
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: January 31, 2009

Revised: June 30, 2009

Published: November 2009

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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.

Keywords:

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

Mathematics Subject Classification: Primary: 60K35, 82D99; Secondary: 60G09.

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