  We show how a gradient in the motility properties of non-interacting
point-like active particles can cause a pressure gradient that pushes a large
inert object. We calculate the force on an object inside a system of active
particles with position dependent motion parameters, in one and two dimensions,
and show that a modified Archimedes' principle is satisfied. We characterize
the system, both in terms of the model parameters and in terms of
experimentally measurable quantities: the spatial profiles of the density,
velocity and pressure. This theoretical analysis is motivated by recent
experiments, which showed that the nucleus of a mouse oocyte (immature egg
cell) moves from the cortex to the center due to a gradient of activity of
vesicles propelled by molecular motors; it more generally applies to artificial
systems of controlled localized activity.
