This is a series of four lectures presented at the 2015 Enrico Fermi summer
school in Varenna. The aim of the lectures is to give an introduction to the
hydrodynamics of active matter concentrating on low Reynolds number examples
such as cells and molecular motors. Lecture 1 introduces the hydrodynamics of
single active particles, covering the Stokes equation and the Scallop Theorem,
and stressing the link between autonomous activity and the dipolar symmetry of
the far flow field. In lecture 2 I discuss applications of this mathematics to
the behaviour of microswimmers at surfaces and in external flows, and describe
our current understanding of how swimmers stir the surrounding fluid. Lecture 3
concentrates on the collective behaviour of active particles, modelled as an
active nematic. I write down the equations of motion and motivate the form of
the active stress. The resulting hydrodynamic instability leads to a state
termed active turbulence characterised by strong jets and vortices in the flow
field and the continual creation and annihilation of pairs of topological
defects. Lecture 4 compares simulations of active turbulence to experiments on
suspensions of microtubules and molecular motors. I introduce lyotropic active
nematics and discuss active anchoring at interfaces.Comment: Lecture Notes, 2015 Enrico Fermi Summer School on Soft Matter
Self-Assembly, Vienn