deletions | additions       diff --git a/subsection_Fourier_Statistics_VCA_VCS__.tex b/subsection_Fourier_Statistics_VCA_VCS__.tex  index e27e8cd..30c40da 100644  --- a/subsection_Fourier_Statistics_VCA_VCS__.tex  +++ b/subsection_Fourier_Statistics_VCA_VCS__.tex 
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\subsection{Fourier Statistics} VCA/VCS, delta variance, MVC, SPS/Bicoherence, wavelet %Just %SSRO Just  use the +Text to create a new separated text box for each category (here \subsubsection{}) into it. \subsubsection{Velocity Channel Analysis and Velocity Coordinate Spectrum} \label{VCA}  %SSRO Note power spectra - lower case; to cite text add label as \label{VCA} and then add (e.g., \ref{VCA}) in the text  Velocity Channel Analysis (VCA) and Velocity Coordinate Spectrum (VCS) are techniques that isolate how fluctuations in velocity contribute to differences between spectral cubes (cite Authorea text?). cubes.  VCA yields (wc?) produces  a 1D Power Spectrum power spectrum  as a function of spatial frequency, while VCS yields a 1D Power Spectrum power spectrum  as a function of velocity-channel frequency (frequency equivalent of velocity). For runs W1T2t0.2 and W2T2t0, we compute the three-dimensional Power Spectrum power spectrum  (of their Fourier transforms). To obtain the VCA, we calculate a one-dimensional Power power  spectrum by integrating the 3D Power Spectrum power spectrum  over the velocity channels, channels  and then radially averaging over the two-dimensional spatial frequencies. A portion (look back when you get a chance to see what this portion physically is) of the now 1-D Power Spectrum 1D power spectrum  is then fit to a power law. We derive the VCS from different integration techniques. We reduce each 3-D Power Spectrum 3D power spectrum  to one dimension by averaging over the spatial frequencies. The VCS yields two distinct power laws that correspond to certain (different?) simulation (cloud?) parameters driving gas motion at different scales. The fit at larger scales describes bulk gas velocity-dominated motion; the fit at smaller scales describes gas density-dominated motions (Chepurnov and Lazarian 2009). To quanity quantity  the VCS, we fit the 1D power spectrum to the segmented linear model used Koch et al. (2015) (or cite the paper describing the model?). We Figures 5 and 6  show the VCA and VCS power law fits for runs W1T2t0.2 and W2T2t0 in Figures 5 and 6. W2T2t0.  VCA generates similarly sloped power laws for our Power Spectra, both runs,  but there isalso  a constant horizontal offset between them. At offset. This implies that at  all spatial scales,we find that  run W1T2t0.2, our run with feedback, generates has  more energy than that of run W2T2t0, our run without feedback. The VCS also shows a horizontal offset between our runs, the two curves,  confirming that there is more power in  velocities at all scales generate more energy in the case  with feedback than without it. feedback.  We also note a difference in both VCS power-law fits, and, more apparent, importantly,  the break point between the two fits. Our {\bf the breakpoint: what it means and how it is determined needs to be described. The specific position and how this corresponds to a spatial or velocity scale needs to be noted: e.g. box size ~ 1 = 5pc, so k=0.1 = 0.5 pc; velocity range = +/-20 km/s, so k=0.1 is ~ 2 km/s. }  The  run without feedback (our purely turbulent run? Go back and denotes everything like this?) appears to be more affected have a larger range over which it is dominated  bychanges in bulk gas  velocity than it fluctuations ($k\simeq 1-0.05$). The velocity-dominated regime  is smaller  for changes in gas density. For our the  run with feedback, this appears to be less drastic, as feedback ($k\simeq 1-0.1$), such that  changes in gas density affect a greater portion of thecloud  structure in the cloud emission.%  (here than in the other run...trying to be grammatically correct with comparisons while including sentence variation--not sure if this sentance is grammatically correct). %SSRO Good job. made some small edits to address content.