Trapping of Brownian particles by random spheres of different radii

We analyze the survival of a Brownian particle moving among randomly distributed spherical traps of two different radii. All of the results known in the case of identical traps, the mean-field Smoluchowski solution, the lowest order correction of this solution, the cumulant expansion, and the long-time behavior, are generalized to the case of two types of traps. Our approach is readily extended to deal with trapping spheres having more than two different radii. (C) 2001 American Institute of Physics.