Editing Appendix/Ramblings/PatrickMotl (section)

====Assume a Mean-Molecular-Weight Ratio of Unity====
If we continue to examine equilibrium models that have <math>~\mu_e/\mu_c = 1</math>, is there a value of the interface radius, <math>~\xi_i</math>, for which the entropy step-function disappears and above which the step function flips?  The answer appears to be, "Yes."  It occurs along the equilibrium sequence where the normalized specific entropy has the same value in the core and as in the envelope.  That is, it occurs when,
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<tr><td align="center">'''Figure 3'''</td></tr>
<tr><td align="center"><math>~\gamma_c = 6/5</math> &nbsp; &nbsp; and &nbsp; &nbsp;  <math>~\gamma_e = 2</math><br />&nbsp;<br />[[File:Entropy02Annotated.png|250px|Entropy distribution]]</td></tr></table>
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<math>~
\ln \biggl[ \biggl( 1 + \frac{\xi_i^2}{3}\biggr)^2 \biggr]_\mathrm{smooth} 
</math>
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<math>~=</math>
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<math>~5\ln(5)</math>
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<math>~
\Rightarrow ~~~ \biggl( 1 + \frac{\xi_i^2}{3}\biggr)_\mathrm{smooth} 
</math>
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<math>~=</math>
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<math>~5^{5 / 2}</math>
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<math>~
\Rightarrow ~~~ [\xi_i ]_\mathrm{smooth}
</math>
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<math>~=</math>
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<math>~\biggl[3 \biggl(5^{5 / 2} - 1 \biggr)\biggr]^{1 / 2} \approx 12.83375</math> &hellip;
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<font color="red">'''Prediction:'''</font> &nbsp; Any initial model with <math>~\mu_e/\mu_c = 1</math> and <math>~\xi_i > [\xi_i]_\mathrm{smooth}</math> will be stable against convection, but will be globally dynamically unstable.