of broken symmetry, i.e., $\mathbf{k}=k\mathbf{\hat{x}}$. The relevant coupled fluctuations in this case are $\delta \rho $, $\tau _{x}$ and $
\delta Q_{xx}$. For simplicity, we consider the regime of large Peclet number $\overline{v}$, where the linear dynamics is controlled by Euler order terms and neglect terms quadratic in the gradients, with the result $$\begin{gathered}
\partial _{t}\delta \rho _{\mathbf{k}}+ik\overline{v}\tau _{x,\mathbf{k}}=0
\label{7.1} \\
\partial _{t}\tau _{x,\mathbf{k}}+\gamma _{e}\tau _{x,\mathbf{k}}=-ik%
\overline{v}\delta Q_{xx,\mathbf{k}}-ik\frac{\overline{v}}{2}\delta \rho _{%
\mathbf{k}}  \label{7.2} \\
\partial _{t}\delta Q_{xx,\mathbf{k}}-\frac{\alpha _{0}}{2}\delta Q_{xx,%
\mathbf{k}}=ik\left( \overline{v}+\frac{\lambda }{2}Q_{0}\right) \tau _{x,%
\mathbf{k}}+\frac{\alpha ^{\prime }}{2}Q_{0}\delta \rho _{\mathbf{k}}
\label{7.3}\end{gathered}$$where $\gamma _{e}=1+\frac{\gamma }{2}Q_{0}^{2}-\frac{\gamma }{2}Q_{0}$. As discussed earlier and highlighted in Fig. \[Fig1.1\], the anisotropy of small angle collisions in the nematic state enhances polar order by suppressing the decay rate of $\tau _{x,\mathbf{k}}$ from its bare value of $
1$ (in units of $D_{r}^{-1}$) to $\gamma _{e}$. The dispersion relations of the hydrodynamic modes associated with Eqs.  are easily calculated at small wavevectors. Clearly, if $\gamma _{e}\leq 0$, In addition, as a consequence of this built up of polar order, the diffusive mode associated with the density fluctuations (i.e., the only truly hydrodynamic mode in these considerations), given by $$s_{x}(k)=-k^{2}\frac{\overline{v}^{2}}{2\gamma _{e}}\left( 1+\frac{%
2\alpha ^{\prime }}{\sqrt{\alpha _{0}\beta }}\right)   \label{8}$$ becomes unstable. In 