Active nematics on a substrate: Giant number fluctuations and long-time tails

@article{Ramaswamy2002ActiveNO,
  title={Active nematics on a substrate: Giant number fluctuations and long-time tails},
  author={Sriram Ramaswamy and R. Aditi Simha and John Toner},
  journal={EPL},
  year={2002},
  volume={62},
  pages={196-202}
}
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 in dimension d = 2 of primary relevance to experiment, and ii) long-time tails $\sim t^{-d/2}$in the autocorrelation of the particle velocities despite the absence of a hydrodynamic velocity field. Our predictions can be tested in… 
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Banding, excitability and chaos in active nematic suspensions

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The mechanics of active matter: Broken-symmetry hydrodynamics of motile particles and granular layers

Swimmer Suspensions on Substrates: Anomalous Stability and Long-Range Order.

It is shown that, depending on the sign of a single parameter, a state with polar orientational order is anomalously stable (or anomalously unstable), with a nonzero relaxation rate for angular fluctuations, not parallel to the ordering direction, at zero wave number.
...

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