  We consider a repulsion actuator located in an $n$-sided convex environment
full of point particles. When the actuator is activated, all the particles move
away from the actuator. We study the problem of gathering all the particles to
a point. We give an $O(n^2)$ time algorithm to compute all the actuator
locations that gather the particles to one point with one activation, and an
$O(n)$ time algorithm to find a single such actuator location if one exists. We
then provide an $O(n)$ time algorithm to place the optimal number of actuators
whose sequential activation results in the gathering of the particles when such
a placement exists.
