  This is the final version of the author's diploma thesis written at the
Humboldt University of Berlin in 1995. The topic is the flow of granular
material in narrow vertical pipes, driven by the gravity, that is described by
Langevin equations. Neglecting the interactions, we can solve the resulting
Fokker-Planck equation for the homogeneous case. The consideration of inelastic
collisions leads to a Boltzmann equation. Assuming local equilibrium, the
hydrodynamic equations lead to the extension of the Langevin equation formalism
for the inhomogeneous case. For certain parameter ranges, our formalism can
also be used to describe traffic flows. We applied stability analyses to the
hydrodynamic equations and found critical densities for the occurrence of
particle clustering. We used numerical simulations of the Langevin equations to
verify our homogeneous solution as well as the critical densities.
