density $\rho _{c}$ on the magnitude of self-propulsion speed. In this simplified form, the dynamics of the system is characterized by two central parameters: the mean density $\rho _{0}$ of active nematogens and the self-propulsion velocity $\overline{
v}=v_0/\sqrt{D_rD_0}$, which is effectively the Peclet number for this flow. The other parameters $\gamma$, $\lambda$, $\overline{D}_Q$, $\overline{D}_\rho$ and $\overline{D}_s$ are in general functions of $\rho _{0}$ and $\overline{v}$, although we will treat them here as independent parameters and simply fix their values.

Linear Dynamics and Emergent Structures {#sec:emergent}
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The dynamics of self propelled rod-like particles with steric repulsion has been studied extensively by numerical simulation of microscopic models [@Mishra2006; @Chate2006; @Yang2010; @Sam2012]. This work has revealed a rich variety of emergent structures, including bands of high density regions where the particles are ordered along the direction of the band, lane formation, migrating defect structures and low Reynolds number turbulence. Here we examine the minimal continuum model of self-propelled nematic given by Eqs.  to identify the generic dynamical mechanisms responsible for the emergence of these structures. As mentioned above, there are three important mechanisms for dynamical instabilities and parttern formation in these systems. To unfold the role of each of these mechanisms in 