The Trapping Reaction with Mobile and Reacting Traps

We study the trapping reaction $A+B\to B$ in the case where both species of particle are mobile, and the traps themselves are annihilating $B+B\to 0$ or coagulating $B+B\to B$. We allow for a mixed trap reaction, with probability $p$ of annihilation and $1-p$ of coagulation, for the general case of unequal diffusion constants and variable trapping rate. We develop a computational technique that enables determination of the full probability distribution of the $A$ particles for a particular realization of the $B$ particles, which provides highly accurate measures for the $A$ particle density and correlations. The $A$ particle density is found to exhibit power law decay in all cases with a nontrivial decay exponent, and the $A$ particle correlations exhibit scaling with an anomolous dimension. Our results are compared with various exact solutions, Schmoluchowski theory, and renormalization group predictions in applicable limits.