$\overline{v}$, $\lambda $ and $\gamma $, deep in the nematic phase. In this case, the long-wavelength dynamics is controlled by hydrodynamic modes associated with fluctuations in the density and the director $\mathbf{\hat{n}}$. This case has been considered in the literature already and is summarized here for completeness  [@Simha2002a; @Ramaswamy2003; @Baskaran2008]. For our choice of coordinates to linear order we have $\delta Q_{{xx}}=-\delta Q_{yy}=0$ and $\delta Q_{xy}=\delta
Q_{yx}=Q_{0}\delta \hat{n}\left( \mathbf{r},t\right) $. Neglecting polarization fluctuations that decay on microscopic time scales, the linearized equations are given by

$$\begin{gathered}
\partial _{t}\delta \rho _{\mathbf{k}}=-k^{2}\delta \rho _{\mathbf{k}}-Q_{0}%
\overline{D}k^{2}\sin 2\theta \delta \hat{n}_{\mathbf{k}}\;,  \label{5.1} \\
\partial _{t}\delta \hat{n}_{\mathbf{k}}=-\frac{\overline{D}_\rho k^2}{2Q_{0}}\sin 2\theta
\delta \rho _{\mathbf{k}}+\left[ \overline{D}_{s}+\cos 2\theta \right]
k^{2}\delta \hat{n}_{\mathbf{k}}\;,  \label{5.2}\end{gathered}$$

where $\theta $ is the angle between $\mathbf{k}$ and the direction of broken symmetry ($x$). If $\theta=0,\pi$, the two equations are decoupled and the modes are diffusive and stable. For general $\theta$ one of the hydrodynamic modes becomes unstable for $\overline{D}\overline{D}_\rho\sin^{2} 2\theta >2(\overline{D}_{s}+\cos 2\theta)$. This can be satisfied provided $\overline{D}_Q\overline{D}_\rho>2D_{s}$, i.e., the curvature driven fluxes exceed the restoring effects of diffusion. This instability has been discussed in detail elsewhere [@Baskaran2008].

Induced Polar Order  {#subsec:polar}
--------------------

Finally, we examine the effect of fluctuations with spatial variations along the direction 