Article Contents
Article Contents

# A non-Markovian model of rill erosion

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

 Citation: