Two dimensional self-organized transitions for propagation in random media

A simple so-called dynamic epidemic model, for the evolution of an advancing interface through a two-dimensional medium containing mobile impurities is investigated. A short range repulsion between the front and the impurities leads to an aggregation process along the front, and to trapping of aggregates. The pattern of trapped impurities is found to be self-organized. The critical concentration of impurity for growth blocking on a square lattice is 0..56. The kinetics of this self-organization is analyzed and discussed.