  The swimming of cells, far from any boundary, can arise in the absence of
long-range liquid-crystalline order within the cytoplasm, but simple models of
this effect are lacking. Here we present a two-dimensional model of droplet
self-propulsion involving two scalar fields, representing the cytoplasm and a
contractile cortex. An active stress results from coupling between these
fields; self-propulsion results when rotational symmetry is spontaneously
broken. The swimming speed is predicted, and shown numerically, to vary
linearly with the activity parameter and with the droplet area fraction. The
model exhibits a Crowley-like instability for an array of active droplets.
