Editing Appendix/Ramblings/ToHadleyAndImamura (section)

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Figure 3 displays, for various values of the polytropic index, <math>~0.0 \le n\le 5.0</math>, the radial structure of the Blaes85 <math>~m=2</math> eigenfunction for a slim PP-torus having <math>~\beta = 0.18</math>.  More specifically, for each frame of the animation, the figure displays as a function of the dimensionless radial coordinate, <math>~x</math>, (left panel) the behavior of
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'''Left:'''&nbsp; &nbsp; <math>~\sqrt{\mathcal{A}_\mathrm{Blaes}^2 + \mathcal{B}_\mathrm{Blaes}^2}</math>
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on a semi-log plot; and (right panel) the "constant phase locus,"
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'''Right:'''&nbsp; &nbsp; <math>~\frac{1}{2} \tan^{-1} \biggl[ \frac{\mathcal{A}_\mathrm{Blaes}}{\mathcal{B}_\mathrm{Blaes}} \biggr] - \theta \, .</math>
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<font size="+1"><b>Figure 3:</b></font> &nbsp; The Blaes85 Analytic Eigenfunction
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[[File:Blaes85Analytic.gif|600px|Amp and Phase from Blaes (1985)]]
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CAPTION: &nbsp; Radial dependence of the (left) amplitude and (right) "constant phase locus" of the Blaes85 analytic eigenfunction, for various values of the polytropic Index, <math>~n</math>, as indicated in the bottom-right corner of the left panel.
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