A Stochastic Description of Transition Between Granular Flow States

Two-dimensional granular flow in a channel with small exit is studied by molecular dynamics simulations.We firstly define a key area near the exit,which is considered to be the choke area of the system.Then we observe thetime variation of the local packing fraction and flow rate in this area for several fixed inflow rate,and find that thesequantities change abruptly when the transition from dilute flow state to dense flow state happens.A relationship betweenthe local flow rate and the local packing fraction in the key area is also given.The relationship is a continuous functionunder the fixed particle number condition,and has the characteristic that the flow rate has a maximum at a moderatepacking fraction and the packing fraction is terminated at a high value with negative slope.By use of the relationship,the properties of the flow states under the fixed inflow rate condition are discussed in detail,and the discontinuities andthe complex time variation behavior observed in the preexisting works are naturally explained by a stochastic process.