Ryan Boyden edited subsection_Fourier_Statistics_All_Fourier__.tex  almost 8 years ago

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\subsection{Fourier Statistics} statistics}  All Fourier statistic color plots are shown in Fig ???. Unlike the Intensity statistics, the Fourier Statistics statistics  do not share a common behavior, and their color plots appear more heterogeneous. As a whole, we note various sensitivities to changes in stellar mass-loss rates, magnetic field strength, and time evolution. The Delta-Variance and Wavelet transform color plots closely resemble those of the intensity statistics, as their greatest sensitivities correspond to changes in stellar-mass loss rates. The Delta-Variance's strong wind comparisons also appear slightly impacted by magnetic field strength, as seen in their distance magnitudes. The Wavelet transform displays a similar trend that is further augmented by time evolution. %In fact, the Delta-variance exhibits a hierarchical structure/trend in wind model pairings similar to that of the Kurtosis and Skewness. For the Wavelet transform, we note a different hierarchical structure, one closer linked to magnetic fields. As we compare our strong wind models to different turbulent clouds, the distances vary, and often decrease if weaker winds are also considered. When comparing turbulent runs with weaker wind models, the Delta-Variance shows small responses, but the Wavelet Transform appears slightly sensitive.  The VCS statistic demonstrates strong, roughly equal sensitivities to both stellar mass-loss rates and magnetic field strength. As its color-plot shows, distances solely quantifying changes in stellar mass-loss rates tend to resemble those explicitly comparing changes in magnetic field. In fact, some of our the  largest distances involve T4, the run with the strongest magnetic field. We also note large distances between our two the  turbulent clouds T1 and T2 in the presence of strong winds. These clouds have the same magnetic field strength, indicating that the VCS is sensitive to the initial turbulence conditions. We also find the SPS to be sensitive to allof our  simulation parameters, but unlike the VCS, it's sensitivities are not structured. (This makes it a difficult statistic to utilize?) For purely turbulent runs, we find the Bicoherence to exhibit a binary behavior, similar to that of the Cramer statistic. While it usually yields equal distances for all simulation pairs, the statistic produces a range of values for comparisons involving purely turbulent runs. T3t0 and T4t0 appear to be relatively similar, and different from all other simulations. And, although the distances for pairs (W3T2t0.1, T3t0) and (W2T4t0.1, T4t0) appear to be different, the distance between runs W3T2t0.1 and W2T4t0.1 is found to be similar. %still waiting for HPC to fix python issue, so I can't test out the new distance metric just yet.  Out of all of our the  statistics, the VCA demonstrates the weakest sensitivity towards magnetic field strength. The behavior of its color-plot suggests an insensitivity to turbulent structure, as distances only change with wind model and evolution time. This allows the VCA to clearly detect changes in stellar mass-loss rates. The color plot shows the distances for strong wind models to be different from those of all other models. But as time evolves, the weak wind distances more closely resemble the strong wind distances. This trend is clear because of the magnetic field's weak impact on the statistic. Despite the various degrees of sensitivities, many of the Fourier statistics fail to produce distinct visual differences corresponding to feedback. As discussed in section 3.2, the most common difference is horizontal offset/power spectra/characteristic energy scale, which is relatively minor (in taking observations?). The VCS does produce distinct responses, but its color plot suggests sensitivities to parameters other than stellar mass-loss rates.