Trapping of Brownian particles by random spheres of different radii

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