Active nematics on a substrate: giant number fluctuations and long-time   tails
  We construct the equations of motion for the coupled dynamics of order parameter and concentration for the nematic phase of driven particles on a solid surface, and show that they imply (i) giant number fluctuations, with a standard deviation proportional to the mean and (ii) long-time tails $\sim t^{-d/2}$ in the autocorrelation of the particle velocities in $d$ dimensions despite the absence of a hydrodynamic velocity field. Our predictions can be tested in experiments on aggregates of amoeboid cells as well as on layers of agitated granular matter. 
Sriram Ramaswamy, R. Aditi Simha and John Toner