Density waves and 1/fdensity fluctuations in granular flow

We simulate granular flow in a narrow pipe with a lattice-gas automaton model. We find that the density in the system is characterized by two features. One is that spontaneous density waves propagate through the system with well-defined shapes and velocities. The other is that density waves are distributed so as to make the power spectra of density fluctuations vary as 1/${\mathit{f}}^{\mathrm{\alpha }}$ noise. Three important parameters make these features observable; they are energy dissipation, average density, and the roughness of the pipe walls.