Velocity of front propagation in 1-dimensional autocatalytic reactions

We study a discrete model of the irreversible autocatalytic reaction A + B -> 2A in one dimension. Looking at the dynamics of propagation, we find that in the low-concentration limit the average velocity of propagation approaches v = theta/2, where theta is the concentration, and, in the high concentration limit, we nd the velocity approaches v = 1 - e-theta/2.