the interaction is of course crucial in controlling the properties of the ordered state. Apolar active particles generally experience apolar interactions and the resulting ordered state has the symmetry of equilibrium nematic liquid crystals. The broken orientational symmetry identifies a direction ${\bf \hat{n}}$, but the ordered state is invariant for ${\bf \hat{n}}\rightarrow -{\bf \hat{n}}$. The properties of these *active nematic* fluids have been studied by several authors [@Simha2002; @Ramaswamy2003]. SP and polar particles may experience either polar interactions, i.e., ones that tend to align particles head to head and tail to tail, or interactions that are apolar, i.e, align particles regardless of their polarity. A well studied example of polar particles with polar interactions is provided by Vicsek-type models [@Vicsek1995; @Gregoire2004]. This class of active systems can order in polar states, characterized by a nonzero vector order parameter and mean motion, and will be referred to as *active polar* fluids.

![ Top - active particles of various microscopic symmetry: (a) Polar active particles with head/tail asymmetry resulting in polar interactions, as studied in [@Vicsek1995; @Gregoire2004], (b) Apolar active particles, as studied in [@Simha2002; @Ramaswamy2003], (c) Sels-propelled particles, with physical head-tail symmetry, resulting in apolar interactions. Bottom - ordered macroscopic states 