April 10, 2009: Michael Damron, CIMS
A non-Markovian model of rill erosion
This talk will focus on the probabilistic aspects of a recently introduced model for rill erosion. We begin 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. 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. This is joint work with C. L. Winter (NCAR and Arizona).
* see arXiv:0704:2706 and arXiv:math/0702542