is an important point as it stresses that the qualitative differences between active and self-propelled nematic that have been observed in simulations must arise entirely from the dependence of the interaction on self propulsion $v_0$.

Momentum-conserving interaction of self-propelled nematogens {#subsec:interaction}
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As shown in Ref. [@Baskaran2008a] and supported by simulations of self-propelled hard rods [@Peruani2006; @Ginelli2010; @Yang2010], self-propulsion does modify the repulsive interaction in a qualitative way. This modification results in local build-up of polarization in the nematic state, making it necessary to retain the dynamics of polarization density in the continuum model.

![ Illustration of momentum conserving collisions among self propelled particles. It can readily be shown that two rods as shown in (a), coming in with only their self-replenishing velocities, will acquire opposite angular momenta $\bm\omega _{1}\sim {\bf \hat{z}} \ell v_{0}\left[{\bf \hat{z}}\cdot\left( \mathbf{\hat{u}}\right]%
_{1}\times \mathbf{\hat{u}}_{2}\right) $ and $\bm\omega _{2}\sim-{\bf \hat{z}} \ell
v_{0} \left(
\mathbf{\hat{u}}_{1}\cdot \mathbf{\hat{u}}_{2}\right)\left[{\bf \hat{z}}\cdot\left( \mathbf{\hat{u}}_{1}\times \mathbf{\hat{u}}_{2}\right)\right] $, where the vectors are defined in the image and in  [@Baskaran2010]. The collision will therefore induce rotations as indicated, promoting alignment of the two rods. On the other hand, two nearly antialigned rods as in (b) acquire angular momenta of the same sign, inducing rotation of both rods 