deletions | additions       diff --git a/subsubsection_Wavelet_Transform_The_Wavelet__.tex b/subsubsection_Wavelet_Transform_The_Wavelet__.tex  index d6b5f3e..2f0af9f 100644  --- a/subsubsection_Wavelet_Transform_The_Wavelet__.tex  +++ b/subsubsection_Wavelet_Transform_The_Wavelet__.tex 
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\subsubsection{Wavelet Transform}  The Wavelet Transform is transforms offer  an alternative data decomposition to Fourier transforms for studying itermittancy and nonlinear scale coupling. Wavelet transforms have been utilized to study MHD and plasma turbulence for more than two decades \citep{forge15}. They are less frequently applied in studies of astrophysical turbulence, although the first application of the wavelet transform was presented by \cite{gill90} of $^{13}$CO molecular emission of L1551. We define the wavelet transform as the  average value of the positive regions of a convolved image (Koch et al., 2015) (direct quote, is the citation ok?); (K16);  it is essentially an intensity average computed over a range of size scales. We convolve the integrated intensity maps of the outputs with a Mexican hat kernel, a process similar to that of the $\Delta$-variance technique described in \S3.2.4. Figure 10 shows the wavelet transforms transform  for all scales. K15 fits the fiducial outputs. Following K16, we fit  a portion of the transform to a power-law, based on where the range is informed by  the results of Gill & Henriksen (1990). {\bf it looks like the whole thing is fitted here.} here - or is the fit plotted for all data points instead of the fit range?}  Although the resultant slopes are similar, output T2t0, the purely turbulent model, diverges more from power-law behavior than output W1T2t0.2. We also note that the wavelet transforms are higher for output W1T2t0.2 than than T2t0, which is consistent with the increased molecular excitation produced by the higher density and temperature in the wind shells. While the shape of the Wavelet transform may provide insight into underlying turbulent properties, neither the offset nor the slope appear to exhibit sufficiently different behavior to serve as a diagnostic for embedded feedback. Indeed, the first astrophysical application of the Wavelet transform by \cite{gill90} compared the wavelet transform both ``on" and ``off" the outflow region of L1551; however, they found little difference in slope between the two regions. Their data did exhibit a turnover around $log(a) \sim -0.6$, which they postulated was a transition between two competing physical processes. The turnover here is more subtle, but it occurs in a similar point in both outputs, so it more likely represents edge effects. Given the similarity between the two curves, we tentatively conclude that this formulation of wavelet analysis is not a good indicator of feedback.  (Eric, {\bf Eric,  do you define the Mexican Hat Wavelet here differently than you define it in the Delta Variance section?) section?}