Granular flow modelled by Brownian particles

Granular flows through pipes show interesting phenomena, e.g. clogging and density waves, 1/f-noise. These things are fairly good studied by computer-experiments, but there is a lack in theoretical and analytical consideration. We introduce a simple "minimal" model describing such a flow of granular particles and examine the stability of an initially homogeneous system against perturbations. In order to define the collisions between the granular particles we use two different approaches. For both, the simple and the more advanced collision definition, the model shows the qualitative same behaviour.