https://selfgravitatingfluids.education/JETohline/index.php?action=history&feed=atom&title=SSC%2FIndex SSC/Index - Revision history 2026-04-24T08:31:58Z Revision history for this page on the wiki MediaWiki 1.43.1 https://selfgravitatingfluids.education/JETohline/index.php?title=SSC/Index&diff=317&oldid=prev Joel2: Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Spherically Symmetric Configurations (SSC) Index= ==Detailed Force Balance== <ol type="A"> <li> <font color="orange">SGF Menu Tile:</font> &nbsp; One-Dimensional PGEs<br /> SGF link: &nbsp; '''SSCpt1/PGE''' &nbsp; &nbsp; <math>\leftarrow</math> &nbsp; <font color="red">backup: "Chapters" B001</font><br /> File Headline: &nbsp; PGE for Spherically Symmetric Configurations<br /> (old) VisTrails link: &nbs..." 2023-12-16T23:41:04Z <p>Created page with &quot;__FORCETOC__ &lt;!-- __NOTOC__ will force TOC off --&gt; =Spherically Symmetric Configurations (SSC) Index= ==Detailed Force Balance== &lt;ol type=&quot;A&quot;&gt; &lt;li&gt; &lt;font color=&quot;orange&quot;&gt;SGF Menu Tile:&lt;/font&gt;   <a href="/JETohline/index.php/SSCpt1/PGE" title="SSCpt1/PGE">One-Dimensional PGEs</a>&lt;br /&gt; SGF link:   &#039;&#039;&#039;SSCpt1/PGE&#039;&#039;&#039;     &lt;math&gt;\leftarrow&lt;/math&gt;   &lt;font color=&quot;red&quot;&gt;backup: &quot;Chapters&quot; B001&lt;/font&gt;&lt;br /&gt; File Headline:   PGE for Spherically Symmetric Configurations&lt;br /&gt; (old) VisTrails link: &amp;nbs...&quot;</p> <p><b>New page</b></p><div>__FORCETOC__ <br /> &lt;!-- __NOTOC__ will force TOC off --&gt;<br /> <br /> =Spherically Symmetric Configurations (SSC) Index=<br /> ==Detailed Force Balance==<br /> &lt;ol type=&quot;A&quot;&gt;<br /> &lt;li&gt;<br /> &lt;font color=&quot;orange&quot;&gt;SGF Menu Tile:&lt;/font&gt; &amp;nbsp; [[SSCpt1/PGE|One-Dimensional PGEs]]&lt;br /&gt;<br /> SGF link: &amp;nbsp; &#039;&#039;&#039;SSCpt1/PGE&#039;&#039;&#039; &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Chapters&quot; B001&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; PGE for Spherically Symmetric Configurations&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SphericallySymmetricConfigurations/PGE User:Tohline/SphericallySymmetricConfigurations/PGE]<br /> &lt;ol&gt;<br /> &lt;li&gt;<br /> SGF link: &amp;nbsp; &#039;&#039;&#039;SSCpt2/SolutionStrategies&#039;&#039;&#039; &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Chapters&quot; C002&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; Spherically Symmetric Configurations (Part II)&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies]<br /> &lt;/li&gt;<br /> <br /> &lt;li&gt;<br /> SGF link: &amp;nbsp; &#039;&#039;&#039;SSCpt2/Stability&#039;&#039;&#039;&lt;br /&gt;<br /> File Headline: &amp;nbsp; Spherically Symmetric Configurations (Stability - Part II)&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SSC/Perturbations User:Tohline/SSC/Perturbations]<br /> &lt;/li&gt;<br /> &lt;/ol&gt;<br /> &lt;/li&gt;<br /> &lt;li&gt;<br /> &lt;font color=&quot;orange&quot;&gt;SGF Menu Tile:&lt;/font&gt; &amp;nbsp; [[SSCpt2/IntroductorySummary|Hydrostatic Balance Equation]]&lt;br /&gt;<br /> SGF link: &amp;nbsp; &#039;&#039;&#039;SSCpt2/IntroductorySummary&#039;&#039;&#039; &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Chapters&quot; C001&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; Hydrostatic Balance Equation&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SphericallySymmetricConfigurations/IntroductorySummary#Applications User:Tohline/SphericallySymmetricConfigurations/IntroductorySummary]<br /> &lt;/li&gt;<br /> &lt;/ol&gt;<br /> <br /> ==Free Energy &amp;amp; Virial Analysis==<br /> &lt;ol type=&quot;A&quot;&gt;<br /> &lt;li&gt;<br /> &lt;font color=&quot;orange&quot;&gt;SGF Menu Tile:&lt;/font&gt; &amp;nbsp; [[VE|Global Energy Considerations]]&lt;br /&gt;<br /> SGF link: &amp;nbsp; &#039;&#039;&#039;VE&#039;&#039;&#039; &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Chapters&quot; A006&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; Global Energy Considerations&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/VE#Global_Energy_Considerations User:Tohline/VE]<br /> &lt;ol&gt;<br /> &lt;li&gt;<br /> SGF link: &amp;nbsp; [[PGE/RotatingFrame|&#039;&#039;&#039;PGE/RotatingFrame&#039;&#039;&#039;]] &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Ramblings&quot; L007&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; Rotating Reference Frame&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/PGE/RotatingFrame User:Tohline/PGE/RotatingFrame]<br /> &lt;/li&gt;<br /> &lt;/ol&gt;<br /> &lt;/li&gt;<br /> <br /> &lt;li&gt;<br /> &lt;font color=&quot;orange&quot;&gt;SGF Menu Tile:&lt;/font&gt; &amp;nbsp; [[SSCpt1/Virial|Free-Energy of Spherical Systems]]&lt;br /&gt;<br /> SGF link: &amp;nbsp; &#039;&#039;&#039;SSCpt1/Virial&#039;&#039;&#039; &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Chapters&quot; B006&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; Virial Equilibrium of Spherically Symmetric Configurations&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SphericallySymmetricConfigurations/Virial User:Tohline/SphericallySymmetricConfigurations/Virial]<br /> &lt;ol&gt;<br /> &lt;li&gt;<br /> SGF link: &amp;nbsp; [[SSC/Virial/Polytropes|&#039;&#039;&#039;SSC/Virial/Polytropes&#039;&#039;&#039;]] &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Ramblings&quot; U006&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; Virial Equilibrium of Adiabatic Spheres&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SSC/Virial/Polytropes User:Tohline/SSC/Virial/Polytropes]<br /> &lt;/li&gt;<br /> <br /> &lt;li&gt;<br /> SGF link: &amp;nbsp; [[SSC/BipolytropeGeneralizationVersion2|&#039;&#039;&#039;SSC/BipolytropeGeneralizationVersion2&#039;&#039;&#039;]] &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Ramblings&quot; V012&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; Bipolytrope Generalization&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SSC/BipolytropeGeneralization_Version2 User:Tohline/SSC/BipolytropeGeneralization_Version2]<br /> &lt;/li&gt;<br /> <br /> &lt;li&gt;<br /> SGF link: &amp;nbsp; [[AxisymmetricConfigurations/SolutionStrategies|&#039;&#039;&#039;AxisymmetricConfigurations/SolutionStrategies&#039;&#039;&#039;]] &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Chapters&quot; G003&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; Axisymmetric Configurations (Solution Strategies)&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/AxisymmetricConfigurations/SolutionStrategies User:Tohline/AxisymmetricConfigurations/SolutionStrategies]&lt;br /&gt;<br /> &lt;font color=&quot;darkgreen&quot;&gt;NOTE: This chapter contains &quot;Simple Rotation Profiles&quot;&lt;/font&gt;<br /> &lt;/li&gt;<br /> <br /> &lt;li&gt;<br /> SGF link: &amp;nbsp; [[SSC/Structure/PolytropesEmbedded|&#039;&#039;&#039;SSC/Structure/PolytropesEmbedded&#039;&#039;&#039;]] &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Chapters&quot; C016&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; Embedded Polytropic Spheres&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SSC/Structure/PolytropesEmbedded User:Tohline/SSC/Structure/PolytropesEmbedded]<br /> &lt;/li&gt;<br /> <br /> &lt;li&gt;<br /> SGF link: &amp;nbsp; [[SSC/Structure/Polytropes|&#039;&#039;&#039;SSC/Structure/Polytropes&#039;&#039;&#039;]] &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Chapters&quot; C008&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; Polytropic Spheres&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SSC/Structure/Polytropes User:Tohline/SSC/Structure/Polytropes]<br /> &lt;/li&gt;<br /> <br /> &lt;li&gt;<br /> SGF link: &amp;nbsp; [[SSC/Virial/PolytropesSummary|&#039;&#039;&#039;SSC/Virial/PolytropesSummary&#039;&#039;&#039;]] &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Ramblings&quot; U007&lt;/font&gt;&amp;nbsp; [needs lots of updated links!]&lt;br /&gt;<br /> File Headline: &amp;nbsp; Virial Equilibrium of Adiabatic Spheres (Summary)&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SSC/Virial/PolytropesSummary User:Tohline/SSC/Virial/PolytropesSummary]<br /> &lt;/li&gt;<br /> <br /> &lt;li&gt;<br /> SGF link: &amp;nbsp; [[SSC/Structure/BiPolytropes/Analytic51|&#039;&#039;&#039;SSC/Structure/BiPolytropes/Analytic51&#039;&#039;&#039;]] &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Chapters&quot; C025&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; BiPolytrope with n&lt;sub&gt;c&lt;/sub&gt; = 5 and n&lt;sub&gt;e&lt;/sub&gt; = 1&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SSC/Structure/BiPolytropes/Analytic51 User:Tohline/SSC/Structure/BiPolytropes/Analytic51]<br /> &lt;/li&gt;<br /> <br /> &lt;li&gt;<br /> SGF link: &amp;nbsp; [[SSC/Virial/Isothermal|&#039;&#039;&#039;SSC/Virial/Isothermal&#039;&#039;&#039;]] &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Ramblings&quot; U008&lt;/font&gt;&amp;nbsp; [needs lots of updated links!]&lt;br /&gt;<br /> File Headline: &amp;nbsp; Virial Equilibrium of Isothermal Spheres&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SSC/Virial/Isothermal User:Tohline/SSC/Virial/Isothermal]<br /> &lt;/li&gt;<br /> <br /> &lt;li&gt;<br /> SGF link: &amp;nbsp; [[SSC/Structure/LimitingMasses|&#039;&#039;&#039;SSC/Structure/LimitingMasses&#039;&#039;&#039;]] &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Chapters&quot; C023&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; Mass Upper Limits&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SSC/Structure/LimitingMasses User:Tohline/SSC/Structure/LimitingMasses]<br /> &lt;/li&gt;<br /> &lt;/ol&gt;<br /> &lt;/li&gt;<br /> <br /> &lt;li&gt;<br /> &lt;font color=&quot;orange&quot;&gt;SGF Menu Tile:&lt;/font&gt; &amp;nbsp; [[SSCpt1/Virial/FormFactors|Structural Form Factors]]&lt;br /&gt;<br /> SGF link: &amp;nbsp; &#039;&#039;&#039;SSCpt1/Virial/FormFactors&#039;&#039;&#039; &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Chapters&quot; B005&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; Structural Form Factors&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SSC/Virial/FormFactors User:Tohline/SSC/Virial/FormFactors]<br /> &lt;ol&gt;<br /> &lt;li&gt;SGF link: &amp;nbsp; [[SSC/Structure/PolytropesEmbedded|&#039;&#039;&#039;SSC/Structure/PolytropesEmbedded&#039;&#039;&#039;]]&lt;/li&gt;<br /> <br /> &lt;li&gt;<br /> SGF link: &amp;nbsp; [[SSC/Virial/PolytropesEmbedded/SecondEffortAgain|&#039;&#039;&#039;SSC/Virial/PolytropesEmbedded/SecondEffortAgain&#039;&#039;&#039;]] &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Ramblings&quot; V001f&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; Virial Equilibrium of Adiabatic Spheres (Summary)&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SSC/Virial/PolytropesEmbedded/SecondEffortAgain User:Tohline/SSC/Virial/PolytropesEmbedded/SecondEffortAgain]<br /> &lt;/li&gt;<br /> <br /> &lt;li&gt;SGF link: &amp;nbsp; [[SSC/Structure/Polytropes|&#039;&#039;&#039;SSC/Structure/Polytropes&#039;&#039;&#039;]]&lt;br /&gt;&lt;/li&gt;<br /> <br /> &lt;li&gt;<br /> SGF link: &amp;nbsp; [[SSC/Virial/PolytropesEmbedded/FirstEffortAgain|&#039;&#039;&#039;SSC/Virial/PolytropesEmbedded/FirstEffortAgain&#039;&#039;&#039;]] &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Ramblings&quot; V001e&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; Virial Equilibrium of Adiabatic Spheres&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SSC/Virial/PolytropesEmbedded/FirstEffortAgain User:Tohline/SSC/Virial/PolytropesEmbedded/FirstEffortAgain]<br /> &lt;/li&gt;<br /> <br /> &lt;li&gt;SGF link: &amp;nbsp; [[SSC/Virial/PolytropesSummary|&#039;&#039;&#039;SSC/Virial/PolytropesSummary&#039;&#039;&#039;]]&lt;/li&gt;<br /> &lt;li&gt;SGF link: &amp;nbsp; [[SSC/Structure/BiPolytropes/Analytic51|&#039;&#039;&#039;SSC/Structure/BiPolytropes/Analytic51&#039;&#039;&#039;]]&lt;/li&gt;<br /> &lt;/ol&gt;<br /> &lt;/li&gt;<br /> <br /> &lt;li&gt;<br /> &lt;font color=&quot;orange&quot;&gt;SGF Menu Tile:&lt;/font&gt; &amp;nbsp; File:FreeNRGpressureRadiusIsothermal.png; [[SSCpt1/Virial/PolytropesEmbeddedOutline|Whitworth&#039;s (1981) Isothermal Free-Energy Surface]]&lt;br /&gt;<br /> SGF link: &amp;nbsp; &#039;&#039;&#039;SSCpt1/Virial/PolytropesEmbeddedOutline&#039;&#039;&#039; &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Chapters&quot; B004&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; Virial Equilibrium of Embedded Polytropic Spheres&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SSC/Virial/PolytropesEmbeddedOutline User:Tohline/SSC/Virial/PolytropesEmbeddedOutline]<br /> &lt;ol&gt;<br /> &lt;li&gt;SGF link: &amp;nbsp; [[SSC/Virial/PolytropesEmbedded/SecondEffortAgain|&#039;&#039;&#039;SSC/Virial/PolytropesEmbedded/SecondEffortAgain&#039;&#039;&#039;]]&lt;/li&gt;<br /> <br /> &lt;li&gt;<br /> SGF link: &amp;nbsp; [[SSC/Structure/PolytropesASIDE1|&#039;&#039;&#039;SSC/Structure/PolytropesASIDE1&#039;&#039;&#039;]] &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Ramblings&quot; V007&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; ASIDE: Whitworth&#039;s Scaling&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SSC/Structure/PolytropesASIDE1 User:Tohline/SSC/Structure/PolytropesASIDE1]<br /> &lt;/li&gt;<br /> &lt;li&gt;SGF link: &amp;nbsp; [[SSC/Virial/PolytropesEmbedded/FirstEffortAgain|&#039;&#039;&#039;SSC/Virial/PolytropesEmbedded/FirstEffortAgain&#039;&#039;&#039;]]&lt;/li&gt;<br /> <br /> &lt;li&gt;SGF link: &amp;nbsp; [[SSC/Virial/Polytropes|&#039;&#039;&#039;SSC/Virial/Polytropes&#039;&#039;&#039;]]&lt;/li&gt;<br /> &lt;li&gt;SGF link: &amp;nbsp; [[SSC/Structure/PolytropesEmbedded|&#039;&#039;&#039;SSC/Structure/PolytropesEmbedded&#039;&#039;&#039;]]&lt;/li&gt;<br /> &lt;li&gt;SGF link: &amp;nbsp; [[SSC/Virial/PolytropesSummary|&#039;&#039;&#039;SSC/Virial/PolytropesSummary&#039;&#039;&#039;]]&lt;/li&gt;<br /> &lt;/ol&gt;<br /> &lt;/li&gt;<br /> <br /> &lt;li&gt;<br /> &lt;font color=&quot;orange&quot;&gt;SGF Menu Tile:&lt;/font&gt; &amp;nbsp; [[Appendix/Ramblings/TurningPoints|Turning Points (Broader Context)]]&lt;br /&gt;<br /> SGF link: &amp;nbsp; &#039;&#039;&#039;Appendix/Ramblings/TurningPoints&#039;&#039;&#039; &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Chapters&quot; C019&lt;/font&gt;&lt;br /&gt;<br /> File Headline: &amp;nbsp; Turning Points (VisTrails Headline = Instabilities Associated with Equilibrium Sequence Turning Points)&lt;br /&gt;<br /> (old) VisTrails link: &amp;nbsp; [https://www.vistrails.org/index.php/User:Tohline/SSC/FreeEnergy/Equilibrium_Sequence_Instabilities User:Tohline/SSC/FreeEnergy/Equilibrium_Sequence_Instabilities] &amp;nbsp; &amp;nbsp; &lt;math&gt;\leftarrow&lt;/math&gt; &amp;nbsp; this &#039;&#039;raw&#039;&#039; VisTrails version &amp;nbsp; &lt;font color=&quot;red&quot;&gt;backup: &quot;Chapters&quot; C019b&lt;/font&gt;<br /> &lt;/li&gt;<br /> &lt;/ol&gt;<br /> <br /> <br /> {{ SGFfooter }}</div> Joel2