deletions | additions       diff --git a/subsubsection_Delta_Variance_The_Delta__.tex b/subsubsection_Delta_Variance_The_Delta__.tex  index ab75f1a..d009a81 100644  --- a/subsubsection_Delta_Variance_The_Delta__.tex  +++ b/subsubsection_Delta_Variance_The_Delta__.tex 
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\subsubsection{$\Delta$-Variance}  The $\Delta$-variance is a filtered average over the Fourier power spectrum \citep{sutzki98}. It has been used to characterize the structure distribution and turbulent power spectra of molecular cloud maps. The revised method presented by Ossenkopf et al. (2008b,a) takes into account noise variation and provides a means to discriminate between small-scale map structure and noise. We adopt this method for our analysis (K16). We generate a series of Mexican hat wavelets that vary in width. We approximate the wavelets as the difference between two Gaussians with a diameter ratio of 1.5. For each output, we weight the integrated intensity map by its inverse variance, convolve it with a Mexican hat wavelet, and calculate the $\Delta$-variance in Fourier space. Figure 9 shows the $\Delta$-variance as a function of wavelet width, which is by convention denoted as the ``lag" \citep{sutzki98}. Similar to the Fourier statistics discussed previously, we find a common horizontal offset between the case with feedback and the purely turbulent case. The $\Delta$-variance curve of T2t0 also declines more at scales near 0.1 arcminutes than the curve for output W2T2t2. {\bf what might this mean? Need In noisy observations, the $\Delta$-variance increases towards small lags, indicating enhanced structure. Here, the difference between the curves indicates that the wind output has slightly more structure on smaller scales, probably caused by the wind shells, which have a thickness of $\sim$ pixels (0.1 pc). However, the $\Delta$-variance of W1T20.2 does not exhibit any break, which would indicate a preferred structure scale. In fact, it more directly resembles a pure power low than the non-wind $\Delta$-variance curve. Ossenkopf et al. (2008b) also found a smooth power-law $\Delta$-variance for rho Ophiuchus, even though clump-finding on the same map produced a mass distribution with a break \citep{motte98}. This suggests that the $\Delta-$variance statistic as applied to integrated intensity maps is not especially sensitive  to revisit earlier literature.} feedback signatures.