fact this instability, although not discussed before in the literature for overdamped active nematic, occurs in all active fluids of nematic symmetry, both for shakers and self-propelled particles. It arises from the density dependence of the parameter $\alpha(r\rho)$ that controls the mean-field transition and the fact that in active systems $\rho$ is not tuned from the outside, as in equilibrium, but is itself a dynamical variable convected by the order parameter.

The hydrodynamic equations of self-propelled nematics given in Eqs.  (or Eqs.  in the dimensionless form studied here) contain many new active terms that arise from modifications of the two-body interaction due to self propulsion. These equations have also been derived by us for a specific microscopic model of self-propelled hard rods [@Baskaran2008a; @Baskaran2010], although the low order closure of the kinetic theory used in that work only gives terms up to quadratic in the hydrodynamic fields. Self-propelled nematics also exhibit both the curvature induced instability discussed in section \[subsec:curvature\] and the banding instability discussed in section \[subsec:self-reg\]. Both are of course modified at finite Peclet number due to additional convective contributions to the underlying mechanisms the details of which will be discussed elsewhere. In addition, self-propulsion yields a novel 