--- trunk/ripple2/ripple.tex 2006/11/09 14:41:45 3075 +++ trunk/ripple2/ripple.tex 2006/12/26 21:50:50 3091 @@ -420,6 +420,19 @@ A second, more accurate, and simpler method for estima estimated by measuring peak-to-trough distances in $h(q_{\mathrm{rip}})$ itself. +\begin{figure}[ht] +\centering +\caption{Contours of the height-dipole correlation function as a function +of the dot product between the dipole ($\hat{\mu}$) and inter-dipole +separation vector ($\hat{r}$) and the distance ($r$) between the dipoles. +Perfect height correlation (contours approaching 1) are present in the +ordered phase when the two dipoles are in the same head-to-tail line. +Anti-correlation (contours below 0) is only seen when the inter-dipole +vector is perpendicular to the dipoles. } +\includegraphics[width=\linewidth]{height-dipole-correlation.pdf} +\label{fig:CrossCorrelation} +\end{figure} + A second, more accurate, and simpler method for estimating ripple shape is to extract the wavelength and height information directly from the largest non-thermal peak in the undulation spectrum. For