Elasticity mediated attraction between active polar particles

We investigate in experiments and simulations the interaction between a pair of motile granular rods moving through a dense monolayer of beads. Vibration of the supporting surface provides the energy source for motility. Above a critical value of the bead area fraction we find that the rods reorient in such as way as to be drawn towards each other. We present a theory for this active attraction based on the forcing imposed by the motile rods on the crystalline medium of beads, and the action of the medium on the rod orientation. Our theoretically calculated the displacement field around a single rod compares favourably with measurements in simulations. We also discuss the segregation instability for the case of many rods.