KINETICS OF BALLISTICALLY-CONTROLLED REACTIONS

We investigate the kinetics of generic single-species reaction process es when the reactants move ballistically, namely ballistic annihilatio n, A + A --> 0, and a ballistic aggregation process which mimics traff ic flow on a single-lane roadway. For ballistic annihilation, dimensio nal analysis shows that the concentration and root means square veloci ty decay as c similar to l(-alpha) and upsilon similar to l(-beta), re spectively, with alpha + beta = 1 in any spatial dimension. Analysis o f the Boltzmann equation for the evolution of the velocity distributio n predicts alpha = (2 + 2 mu)/(3 + 2 mu) and beta = 1/(3 + 2 mu) for a n initial velocity distribution P(upsilon,t=0) similar to upsilon(mu) as upsilon --> 0. New phenomena associated with discrete initial veloc ity distributions and with mixed ballistic and diffusive reactant moti on are also discussed. In the aggregation process, each ''car'' moves at its initial velocity until the preceding car or cluster is overtake n after which the incident car assumes the velocity of the cluster whi ch it has just joined. For P-0(upsilon) similar to upsilon(mu) as upsi lon --> 0, the average cluster size grows as n similar to t((mu+1)/(mu +2)) and the average velocity decays as upsilon similar to t(-1/(mu+2) ). We also derive an asymptotic expression for the joint distribution function for the cluster mass and velocity.