energy-momentum conserving interactions. As shown in Fig. (\[Fig1.1\]), the angular momentum transfer due to the linear momentum from self-propulsion for a collision between two rods scales as $\omega \sim \cos \left(
\theta _{1}-\theta _{2}\right) \sin \left( \theta _{1}-\theta _{2}\right) $. If the rods are nearly aligned head to head (as in Fig \[Fig1.1\].a), the effect of this angular momentum is to turn the rods towards each other, while if they are nearly aligned head to tail as in Fig \[Fig1.1\].b, the collision turns both rods in the same direction, leaving their relative angle unchanged. This mechanism effectively promotes head-to-head alignment. Since collisions among such nearly aligned nematogens will dominate the dynamics in the nematic state, the nematic order effectively induces polar order.

Self-propelled Nematic Hydrodynamics {#subsec:sp_nematic}
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The fact that interactions among self-propelled nematogens tend to induce polar order is reflected in the hydrodynamic description by a number of new nonlinear terms that couple $\bm\tau$ and ${\bf Q}$, with coefficients that vanish in the limit $v_0=0$. The continuum equations for a self-propelled nematic that incorporate the above physics are given by

$$\begin{gathered}
\label{3.1}
\partial _{t}\rho +v_{0}\nabla \cdot \bm{\tau }=D
\nabla ^{2}\rho +\mathcal{D}_{Q}\nabla \nabla :\mathbf{Q}\\
%
\partial _{t}\bm{\tau }+D_r\bm{\tau }+\gamma_1{\bf Q}{\bf 