A model of dissipative granular gas: the limit case of complete inelasticity of grain-grain collision

Also, for sake of simplicity, we consider a piston that moves according to a saw tooth motion of period T , amplitude b. The piston first moves toward the interior with speed Vp ≈ b/T , then return very quickly with speed V2 >> Vp ≈ b/T to its original position. We do not consider balls with speed v > V2, so that ball collision with the piston coming backward does not exist.