COAGULATION REACTION IN A ONE-DIMENSIONAL GAS

An extension of previous work on the ballistic annihilation reaction A + A --> 0 to the coagulation reaction A + A --> A is presented. Three possible velocities c (with probability p), - c (with probability q), and zero are considered. While the long-time behavior is controlled by moving particles when p = q, it is controlled by the stationary particles when p not-equal q. The comparison of the coagulation reaction with the annihilation reaction shows that the long-time results are essentially the same except for a rescaling of the time. In addition, the time dependences of the decay in the ballistic coagulation reaction when p = q and the diffusion-limited coagulation reaction are also identical, but for different physical reasons. The reason for this becomes transparent by rederiving the ballistic coagulation results using a random-walk formalism, which can perhaps be generalized to more complicated ballistic reactions.