Ryan Boyden edited subsection_Fourier_statistics_All_Fourier__.tex  almost 8 years ago

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\subsection{Fourier statistics}  All Fourier statistic color plots are shown in Fig ???. Unlike the Intensity statistics, the Fourier 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. evolutionary time.  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 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 the largest distances involve T4, the run with the strongest magnetic field. We also note large distances between 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 all simulation parameters, but unlike the VCS, it's sensitivities are not structured.  We find the Bicoherence to exhibit strong sensitivities to stellar mass-loss rates, magnetic field strength, and time evolution. evolutionary time.  As time evolves, wind models do become more alike, but they remain largely different from turbulent models. Turbulent models also appear relatively similar to each other. %The observed trend deviates from those of previously considered Intensity statistics, but still %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.