The mechanics of active matter: Broken-symmetry hydrodynamics of motile particles and granular layers

This articles reviews briefly our recent theoretical results on order, fluctuations and flow in collections of self-driven particles, in suspension or on a solid surface. The theoretical approach we have developed applies not only to collections of organisms such as schools of fish or collectively swimming bacteria, but also to motor-microtubule extracts with ATP and, most surprisingly, to agitated monolayers of orientable granular particles. We contrast the behaviour of these active systems with that of thermal equilibrium systems with the same symmetry. As an illustration of the role of activity we show that active smectics in three dimensions show true long-range order, unlike their thermal equilibrium counterparts.