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(Index to Free-Energy Analyses: Begin detailing index)
(Index to Free-Energy Analyses)
 
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   <li><font size="+1">&#x2460;</font> &nbsp;[[User:Tohline/SSC/VirialEquilibrium/UniformDensity#Uniform-Density_Sphere|SSC VirialEquilibrium UniformDensity (Isolated)]]</li>
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  <li><font size="+1">&#x24EA;</font> &nbsp;[[User:Tohline/SphericallySymmetricConfigurations/Virial#Virial_Equilibrium_of_Spherically_Symmetric_Configurations|SphericallySymmetricConfigurations Virial]] (Introduction)</li>
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   <li><font size="+1">&#x2461;</font> &nbsp;[[User:Tohline/SSC/VirialEquilibrium/UniformDensity#Adiabatic_Evolution_of_Pressure-truncated_Sphere|SSC VirialEquilibrium UniformDensity (Embedded)]]</li>
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   <li><font size="+1">&#x2460;</font> &amp; <font size="+1">&#x2461;</font> &nbsp;[[User:Tohline/SSC/VirialEquilibrium/UniformDensity#Uniform-Density_Sphere|SSC VirialEquilibrium UniformDensity]] (Isolated and Embedded)</li>
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   <li><font size="+1">&#x2462;</font> &nbsp;[[User:Tohline/SSC/Virial/Polytropes#Isolated_Nonrotating_Adiabatic_Configuration|SSC Virial Polytropes (Isolated)]]</li>
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  <li><font size="+1">&#x2462;</font> &nbsp;[[User:Tohline/SSC/Virial/Polytropes#Isolated_Nonrotating_Adiabatic_Configuration|SSC Virial Polytropes]] (Isolated)</li>
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   <li><font size="+1">&#x2463;</font> &nbsp;[[User:Tohline/SSC/Virial/PolytropesEmbeddedOutline#Virial_Equilibrium_of_Embedded_Polytropic_Spheres|SSC Virial PolytropesEmbeddedOutline]] (w/ Movie)</li>
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  <li>[[User:Tohline/SSC/FreeEnergy/PolytropesEmbedded|Free Energy of Truncated Polytropes]] &nbsp; &nbsp; <math>~\Leftarrow</math> &nbsp; &nbsp; This chapter contains key summary expressions used in the PowerPoint presentation (see especially the "Summary" subsection)</li>
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   <li><font size="+1">&#x2464;</font> &amp; <font size="+1">&#x2465;</font> &nbsp;[[User:Tohline/SSC/Virial/Isothermal|SSC Virial Isothermal]] (Isolated and Bounded)</li>
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  <li><font size="+1">&#x2466;</font> &nbsp;[[User:Tohline/SSC/BipolytropeGeneralization_Version2#Bipolytrope_Generalization|SSC BipolytropeGeneralization_Version2]] (Overview)</li>
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  <li><font size="+1">&#x2467;</font> &nbsp;[[User:Tohline/SSC/Structure/BiPolytropes/FreeEnergy0_0#Free_Energy_of_BiPolytrope_with|SSC Structure BiPolytropes FreeEnergy0_0]] <math>~(n_c,n_e) = (0,0)</math></li>
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  <li><font size="+1">&#x2468;</font> &nbsp;[[User:Tohline/SSC/Structure/BiPolytropes/FreeEnergy5_1#Free_Energy_of_BiPolytrope_with|SSC Structure BiPolytropes FreeEnergy5_1]] <math>~(n_c,n_e) = (5,1)</math></li>
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<li>Two key graphical summaries:<ul>
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<li>[[User:Tohline/SSC/Virial/PolytropesEmbedded/SecondEffortAgain#Plotting_Concise_Mass-Radius_Relation|For Pressure-truncated Polytropes]]</li>
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<li>[[User:Tohline/SSC/Structure/BiPolytropes/Analytic5_1#Stability_Condition|For Bipolytropes with]] <math>~(n_e,n_c) = (5,1)</math></li>
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</ul>
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</li>
</ul>
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   </th>
   </th>
   <th align="center">
   <th align="center">
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<font color="black">Virial Equilibrium</font><br>([[User:Tohline/SphericallySymmetricConfigurations/Virial#Virial_Equilibrium_of_Spherically_Symmetric_Configurations|Introduction]])
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<font color="black">Virial Equilibrium</font><br>([[User:Tohline/SphericallySymmetricConfigurations/Virial#Virial_Equilibrium_of_Spherically_Symmetric_Configurations|Introduction]])<font size="+1">&#x24EA;</font>
   </th>
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   <td align="left">&nbsp;&nbsp;&nbsp;&nbsp;</td><td align="left">Embedded in an External Medium &hellip;</td>
   <td align="left">&nbsp;&nbsp;&nbsp;&nbsp;</td><td align="left">Embedded in an External Medium &hellip;</td>
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   <td align="center" width="25%">[[User:Tohline/SSC/Structure/PolytropesEmbedded#Embedded_Polytropic_Spheres|<font size="+2" color="green">&#x2713;</font>]]</td><td align="center" width="25%">[[User:Tohline/SSC/Virial/PolytropesEmbeddedOutline#Virial_Equilibrium_of_Embedded_Polytropic_Spheres|<font size="+2" color="green">&#x2713;</font>]]&nbsp; &nbsp;[[User:Tohline/SSC/Virial/PolytropesEmbeddedOutline#3DIsothermalSurface|<font size="+2">&#x1F3A6;</font>]]</td>
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   <td align="center" width="25%">[[User:Tohline/SSC/Structure/PolytropesEmbedded#Embedded_Polytropic_Spheres|<font size="+2" color="green">&#x2713;</font>]]</td><td align="center" width="25%">[[User:Tohline/SSC/Virial/PolytropesEmbeddedOutline#Virial_Equilibrium_of_Embedded_Polytropic_Spheres|<font size="+1">&#x2463;</font>]]&nbsp; &nbsp;[[User:Tohline/SSC/Virial/PolytropesEmbeddedOutline#3DIsothermalSurface|<font size="+2">&#x1F3A6;</font>]]</td>
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   <td align="left">&nbsp;&nbsp;&nbsp;&nbsp;</td><td align="left">Isolated &hellip;</td>
   <td align="left">&nbsp;&nbsp;&nbsp;&nbsp;</td><td align="left">Isolated &hellip;</td>
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   <td align="center" width="25%">[[User:Tohline/SSC/Structure/IsothermalSphere#Isothermal_Sphere|<font size="+2" color="green">&#x2713;</font>]]</td><td align="center" width="25%">[[User:Tohline/SSC/Virial/Isothermal|<font size="+2" color="green">&#x2713;</font>]]</td>
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   <td align="center" width="25%">[[User:Tohline/SSC/Structure/IsothermalSphere#Isothermal_Sphere|<font size="+2" color="green">&#x2713;</font>]]</td><td align="center" width="25%">[[User:Tohline/SSC/Virial/Isothermal#Isothermal_Evolutions|<font size="+1">&#x2464;</font>]]</td>
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   <td align="left">&nbsp;&nbsp;&nbsp;&nbsp;</td><td align="left">Embedded in an External Medium (Bonnor-Ebert Sphere) &hellip;</td>
   <td align="left">&nbsp;&nbsp;&nbsp;&nbsp;</td><td align="left">Embedded in an External Medium (Bonnor-Ebert Sphere) &hellip;</td>
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   <td align="center" width="25%">[[User:Tohline/SSC/Structure/BonnorEbert#Pressure-Bounded_Isothermal_Sphere|<font size="+2" color="green">&#x2713;</font>]]<td align="center" width="25%">[[User:Tohline/SphericallySymmetricConfigurations/Virial#Bounded_Isothermal|<font size="+2" color="green">&#x2713;</font>]]</td>
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   <td align="center" width="25%">[[User:Tohline/SSC/Structure/BonnorEbert#Pressure-Bounded_Isothermal_Sphere|<font size="+2" color="green">&#x2713;</font>]]<td align="center" width="25%">[[User:Tohline/SSC/Virial/Isothermal#Bounded_Isothermal|<font size="+1">&#x2465;</font>]]</td>
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   </td>
   </td>
   <td align="center" width="25%">[[User:Tohline/SSC/Structure/BiPolytropes#BiPolytropes|Overview]]</td>
   <td align="center" width="25%">[[User:Tohline/SSC/Structure/BiPolytropes#BiPolytropes|Overview]]</td>
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   <td align="center" width="25%">[[User:Tohline/SSC/BipolytropeGeneralization_Version2#Bipolytrope_Generalization|Overview]]</td>
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   <td align="center" width="25%">[[User:Tohline/SSC/BipolytropeGeneralization_Version2#Bipolytrope_Generalization|Overview]] <font size="+1">&#x2466;</font></td>
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   <td align="left">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</td><td align="left">Core-Envelope Structure with <math>~(n_c,n_e) = (0,0)</math> &hellip;</td>
   <td align="left">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</td><td align="left">Core-Envelope Structure with <math>~(n_c,n_e) = (0,0)</math> &hellip;</td>
   <td align="center" width="25%">[[User:Tohline/SSC/Structure/BiPolytropes/Analytic0_0#BiPolytrope_with_nc_.3D_0_and_ne_.3D_0|<font size="+2" color="green">&#x2713;</font>]]</td>
   <td align="center" width="25%">[[User:Tohline/SSC/Structure/BiPolytropes/Analytic0_0#BiPolytrope_with_nc_.3D_0_and_ne_.3D_0|<font size="+2" color="green">&#x2713;</font>]]</td>
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   <td align="center" width="25%">[[User:Tohline/SSC/Structure/BiPolytropes/FreeEnergy0_0#Free_Energy_of_BiPolytrope_with|<font size="+2" color="green">&#x2713;</font>]]</td>
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   <td align="center" width="25%">[[User:Tohline/SSC/Structure/BiPolytropes/FreeEnergy0_0#Free_Energy_of_BiPolytrope_with|<font size="+1">&#x2467;</font>]]</td>
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   <td align="left">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</td><td align="left">Core-Envelope Structure with <math>~(n_c,n_e) = (5,1)</math> &hellip;</td>
   <td align="left">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</td><td align="left">Core-Envelope Structure with <math>~(n_c,n_e) = (5,1)</math> &hellip;</td>
   <td align="center" width="25%">[[User:Tohline/SSC/Structure/BiPolytropes/Analytic5_1#BiPolytrope_with_nc_.3D_5_and_ne_.3D_1|<font size="+2" color="green">&#x2713;</font>]]</td>
   <td align="center" width="25%">[[User:Tohline/SSC/Structure/BiPolytropes/Analytic5_1#BiPolytrope_with_nc_.3D_5_and_ne_.3D_1|<font size="+2" color="green">&#x2713;</font>]]</td>
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   <td align="center" width="25%">[[User:Tohline/SSC/Structure/BiPolytropes/FreeEnergy5_1#Free_Energy_of_BiPolytrope_with|<font size="+2" color="green">&#x2713;</font>]]</td>
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   <td align="center" width="25%">[[User:Tohline/SSC/Structure/BiPolytropes/FreeEnergy5_1#Free_Energy_of_BiPolytrope_with|<font size="+1">&#x2468;</font>]]</td>
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<tr>

Current revision as of 18:11, 20 November 2016


Contents

Index to Free-Energy Analyses

I have put this index together in an effort to help me, first find, then keep track of all chapters that discuss the use of a free-energy expression and/or virial equilibrium constructs to analyze the structure and stability of spherically symmetric configurations.

Whitworth's (1981) Isothermal Free-Energy Surface
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First, let's explain what the topic is of each chapter that is currently (up to July 2016) in the template titled, LSU_HBook_SSC_Structure.



Solution Strategies:    

Detailed Force-Balance
(Introduction)

Virial Equilibrium
(Introduction)

Example Solutions:
  • Uniform-density sphere
        Isolated …
    Embedded in an External Medium …
  • Polytropes
    Isolated …
    Embedded in an External Medium …    🎦
  • Isothermal sphere
    Isolated …
    Embedded in an External Medium (Bonnor-Ebert Sphere) …
  • Zero-temperature White Dwarf — Overview
  • Power-law density distribution — Overview
  • Other Analytically Definable Models
  …  
  • BiPolytropes (also referred to as Composite Polytropes)
Overview Overview
        Core-Envelope Structure with ~(n_c,n_e) = (0,0)
        Core-Envelope Structure with ~(n_c,n_e) = (5,1)
        Core-Envelope Structure with ~(n_c,n_e) = (1,5)   …  
        Core-Envelope Structure with ~(n_c,n_e) = (\tfrac{3}{2},3)   …  


Whitworth's (1981) Isothermal Free-Energy Surface

© 2014 - 2021 by Joel E. Tohline
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Appendices: | Equations | Variables | References | Ramblings | Images | myphys.lsu | ADS |
Recommended citation:   Tohline, Joel E. (2021), The Structure, Stability, & Dynamics of Self-Gravitating Fluids, a (MediaWiki-based) Vistrails.org publication, https://www.vistrails.org/index.php/User:Tohline/citation

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