Density waves of granular flow in a pipe using lattice gas automata

Density waves of granular flow in a pipe using lattice gas automata Gongwen Peng and Hans J. Herrmann HLRZ, KFA J\"ulich, D--52425 J\"ulich, Germany We use a lattice gas automaton modelling the formation of density waves of granular flow through a vertical pipe. It is found that both the dissipation and the roughness of walls of the pipe are essential to the emergence of density waves. The density waves can only be observed when the average density of the system is in a certain range. The power spectra of density fluctuations in one region in the pipe follow, apart from a sharp peak corresponding to the density wave, a power law spectrum $1/f^\alpha$ with $\alpha$ close to $4/3$. PACS numbers: 47.50.+d, 47.20.-k, 46.10.+z, 47.55.Kf