identify two classes of such fluids, depending on the properties of the individual active units. Active nematics consist of shaker particles that are themselves apolar. Self-propelled nematics are collections of particles that are physically head-tail symmetric (such as SP rods), but where a microscopic dynamical polarity is induced by self-propulsion . Although both systems form ordered states of nematic symmetry, their dynamical behavior is qualitatively different, as seen in recent simulations [@Peruani2006; @Ginelli2010; @Yang2010].

The hydrodynamic equations of active nematics have the form given in Eqs. [2]{}. We have shown that the same equations are also obtained by considering SP particles and neglecting the effect of self-propulsion on the interaction between active units, suggesting that the active nematic may be considered the zero Peclet number $\overline{v}$ limit of self-propelled nematic. In this case the only active term is the curvature current proportional to ${\cal D}_Q$ in Eq. . This non equilibrium coupling of orientation and flow induces instabilities of the ordered state that have been studied before in the literature [@Simha2002; @Ramaswamy2003; @Baskaran2008] and are also summarized in section. \[subsec:curvature\]. The curvature current is also key in controlling the banding instability arising from dynamical self-regulation discussed in section \[subsec:self-reg\]. In 