We study a one-dimensional system with a single trap initially located at t
he origin, and many random-walkers initially uniformly distributed througho
ut the infinite or the semi-infinite space. For a mobile imperfect trap, we
study the spatiotemporal properties of the system, such as the trapping ra
te, the particle distribution and the segregation around the trap, all as a
function of the diffusivities of both the trap and the walkers. (C) 2000 E
lsevier Science B.V. All rights reserved.