STEADY-STATE OF IMPERFECT ANNIHILATION AND COAGULATION REACTIONS

We study the coagulation (A + A --> A) and annihilation (A + A --> O) reactions with input probability epsilon and reaction probability p in a one-dimensional lattice. In the steady state we find two different behaviours for the density of nearest-neighbour occupied sites Gamma against the density of particles rho. These behaviours correspond to the diffusion-limited regime (rho --> O) and to the reaction-limited regime (rho similar to 1). Using a scaling ansatz for Gamma against rho we derive an approximation for rho as a function of epsilon and rho that agrees well with Monte Carlo numerical results.