Trapping reactions for mobile particles and a trap in the laboratory frame

We have used a stochastic model to obtain the exact spatial particle density profile for the trapping process A+B-->B in a one-dimensional lattice with a single trap, as seen from the laboratory frame. We obtain the profile for either perfect or imperfect reactions when A particles are immobile, but only for perfect absorption in the general case where both particles are mobile with different diffusivities. This profile is found to be similar to that seen from the reference system attached to the trap, the most noticeable difference being near the origin.