A non-Markovian model of rill erosion

Details A non-Markovian model of rill erosion A non-Markovian model of rill erosion

2008-10-08

arxiv.org/abs/0810.1483v2

Networks and Heterogeneous Media 2009, Vol. 4, No. 4, 731-753.

Mathematics

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26 pages, 9 figures, reference added, acknowledgments added

Scientific paper

We introduce a new model for rill erosion. We start with a network similar to that in the Discrete Web 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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