Complex spontaneous flows and concentration banding in active polar films.

We study the dynamical properties of active polar liquid crystalline films. Like active nematic films, active polar films undergo a dynamical transition to spontaneously flowing steady states. Spontaneous flow in polar fluids is, however, always accompanied by strong concentration inhomogeneities or "banding" not seen in nematics. In addition, a spectacular property unique to polar active films is their ability to generate spontaneously oscillating and banded flows even at low activity. The oscillatory flows become increasingly complicated for strong polarity.