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This is the final version of the author's diploma thesis written at theHumboldt University of Berlin in 1995. The topic is the flow of granularmaterial in narrow vertical pipes, driven by the gravity, that is described byLangevin equations. Neglecting the interactions, we can solve the resultingFokker-Planck equation for the homogeneous case. The consideration of inelasticcollisions leads to a Boltzmann equation. Assuming local equilibrium, thehydrodynamic equations lead to the extension of the Langevin equation formalismfor the inhomogeneous case. For certain parameter ranges, our formalism canalso be used to describe traffic flows. We applied stability analyses to thehydrodynamic equations and found critical densities for the occurrence ofparticle clustering. We used numerical simulations of the Langevin equations toverify our homogeneous solution as well as the critical densities.

Theoretische Modellierung granularer Stroeme in duennen Roehren mit Langevin-Gleichungen