||Nonlinear dynamics and rheology of biologically active fluids
We present recent results for the flow and dynamics of a broad category of complex "biologically active" fluids that are taken far from equilibrium by an activity inherent within their own bulk. Examples include swarms of self-propelled bacteria or protozoa; and the viscoelastic matrix of the biological cell in which molecular motors at cross-links between polymeric strands render the network as a whole capable of mechanical motion (in cell division or amoebic crawling, for example). In these fluids each mesoscopic substructure (bacterium/motor) individually consumes energy and so can actively propel itself: ``swimming'' through the suspending fluid, or ``marching'' along a neighbouring cytoskeletal filament. Their collective dynamics is thus inherently far from equilibrium, even without any externally applied driving. We focus particularly on emergent phenomena that include hydrodynamic instabilities in which an initially quiescent fluid gives way to shear banded or turbulently swirling flow patterns, as seen experimentally.