Extracting work from gradients in active motion

We study how the active motion of particles can cause a pressure gradient on a large inert object that moves it to a target position. This 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 pressure gradient exerted by the active motion of vesicles. We calculate the force on a symmetric inert object inside a system of active particles with position dependent motion parameters, in one and two dimensions. We characterize a system where such a force exists, both in terms of the model parameters and in terms of measurable quantities: the density, velocity and pressure profiles.