The Bethe ansatz method and an iterative procedure based on detailed balanc
e arc used to obtain exact results for an asymmetric avalanche process on a
ring. The average velocity of particle flow, upsilon, is derived as a func
tion of the toppling probabilities and the density of particles, rho. As rh
o increases, the system shows a transition from intermittent to continuous
flow, and upsilon diverges at a critical point rho (c) with exponent alpha.
The exact phase diagram of the transition is obtained and alpha is found t
o depend on the toppling rules.