Why walking is easier than pointing: Hydrodynamics of dry active matter

Abstract

Although human beings have known about the phenomenon of "flocking"- that is, the coherent movement of large numbers of creatures (flocks of birds, schools of fish, herds of woolly mammoths, etc.)- since prehistoric times, it is only in the last two decades that we have begun to truly understand this phenomenon. In particular, the surprising fact that a very large collection of organisms in two dimensions cannot all {\it point} in the same direction, but can quite easily {\it move} in the same direction, can now be explained. In these lectures, I'll review one of the principle theoretical tools that made this possible: hydrodynamics. My intention is both to elucidate flocking- or, to use the specific technical mouthful, "polar ordered dry active fluids"-, and to use flocking as an illustration of how to use the hydrodynamic approach on new and unfamiliar systems.