Template:LAWEsolutions: Difference between revisions

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Created page with "<table border="1" align="center" cellpadding="5"> <tr> <td align="center" colspan="2"><b>Isolated n = 1 Polytrope with γ<sub>g</sub> = 2</b></td> </tr> <tr> <td align="center" rowspan="2">250px|n = 1 Eigenvectors</td> <td align="left">Relevant Chapters <ul><li>Origin of Planetary Nebulae</li> <li>SSC/Structure/BiPolytropes/Analytic51Renormalize#Isolated_n_=_1_Polytrope|Isolate..."
 
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<tr>
   <td align="center" colspan="2"><b>Isolated n = 1 Polytrope with &gamma;<sub>g</sub> = 2</b></td>
   <td align="center" colspan="3"><b>Isolated n = 1 Polytrope</b></td>
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<tr>
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   <td align="center" rowspan="2">[[File:N1osc06.gif|250px|n = 1 Eigenvectors]]</td>
   <td align="center" rowspan="2"><math>\gamma_g = (n+1)/n = 2</math><br /><p><br /><p><br />[[File:N1osc06.gif|250px|n = 1 Eigenvectors]]</td>
   <td align="left">Relevant Chapters
  <td align="center" rowspan="2"><math>\gamma_g = \tfrac{5}{3}</math><br />[[File:OurImprovedSummary2.png|250px|n = 1 Eigenvectors]]</td>
<ul><li>[[Appendix/Ramblings/OriginOfPlanetaryNebulae#Polytropes|Origin of Planetary Nebulae]]</li>
   <td align="left">Key Reference(s):
<ul><li>{{ Chatterji51 }}</li></ul></td>
</tr>
 
<tr>
  <td align="left">Relevant Chapters:
<ul>
<li>[[SSC/Structure/BiPolytropes/Analytic51Renormalize#Isolated_n_=_1_Polytrope|Isolated n = 1 Polytrope]]</li>
<li>[[SSC/Structure/BiPolytropes/Analytic51Renormalize#Isolated_n_=_1_Polytrope|Isolated n = 1 Polytrope]]</li>
<li>[[Appendix/Ramblings/OriginOfPlanetaryNebulae#Polytropes|Origin of Planetary Nebulae]]</li>
</ul>
  </td>
</tr>
</table>
<table border="1" align="center" cellpadding="5">
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  <td align="center" colspan="2"><b>Isolated n = 3 Polytrope</b></td>
</tr>
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  <td align="center" rowspan="2"><math>\gamma_g = \tfrac{20}{13}</math><br />[[File:Schwarzschild1941movie.gif|250px|n = 3 Eigenvectors]]</td>
  <td align="left">Key Reference(s):
<ul><li>{{ Schwarzschild41 }}</li></ul></td>
</tr>
<tr>
  <td align="left">Relevant Chapters:
<ul>
<li>[[SSC/Stability/n3PolytropeLAWE#Radial_Oscillations_of_n_.3D_3_Polytropic_Spheres|Radial Oscillations of n = 3 Polytropic Spheres]]</li>
<li>[[Appendix/Ramblings/OriginOfPlanetaryNebulae#Isolated_n_=_3_Polytrope_with_γg_=_20/13|Origin of Planetary Nebulae]]</li>
</ul></td>
</tr>
</table>
<table border="1" align="center" cellpadding="5">
<tr>
  <td align="center" colspan="2"><b>Pressure-Truncated n = 5 Polytrope</b></td>
</tr>
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  <td align="center" rowspan="2"><math>\gamma_g = (n+1)/n = \tfrac{6}{5}</math><br />[[File:N5Truncated2.gif|250px|Truncated n = 5 Polytrope]]</td>
  <td align="left">Key Reference(s):
<ul><li>n/a</li></ul></td>
</tr>
<tr>
  <td align="left">Relevant Chapters:
<ul>
<li>[[SSC/Stability/n5PolytropeLAWE#Numerical_Integration_of_LAWE|Radial Oscillations of n = 5 Polytropic Spheres]]</li>
<li>[[Appendix/Ramblings/OriginOfPlanetaryNebulae#Pressure-Truncated_n_=_5_Polytrope_with_γg_=_6/5|Origin of Planetary Nebulae]]</li>
</ul></td>
</ul></td>
</tr>
</table>
<table border="1" align="center" cellpadding="5">
<tr>
  <td align="center" colspan="2"><b>Pressure-Truncated Isothermal (n = &infin;) Sphere</b></td>
</tr>
</tr>


<tr>
<tr>
   <td align="left">Key References:
  <td align="center" rowspan="2"><math>\gamma_g = 1</math><br />[[File:TaffVanHorn1974Harmonic.gif|250px|Truncated n = 5 Polytrope]]</td>
<ul><li>{{ Chatterji51 }}</li></ul></td>
   <td align="left">Key Reference(s):
<ul>
  <li>{{ Yabushita68 }}</li>
  <li>{{ TVH74 }}</li></ul>
</td>
</tr>
 
<tr>
  <td align="left">Relevant Chapters:
<ul>
<li>[[SSC/Stability/Isothermal#Previously_Published_Eigenvalues_and_Eigenfunctions|Radial Oscillations of Isothermal Spheres]]</li>
<li>[[Appendix/Ramblings/OriginOfPlanetaryNebulae#Pressure-Truncated_n_=_5_Polytrope_with_γg_=_6/5|Origin of Planetary Nebulae]]</li>
</ul>
</td>
</tr>
</tr>
</table>
</table>

Latest revision as of 18:18, 1 November 2023

Isolated n = 1 Polytrope
γg=(n+1)/n=2



n = 1 Eigenvectors

 γg=53
n = 1 Eigenvectors		 Key Reference(s):
Relevant Chapters:


Isolated n = 3 Polytrope
γg=2013
n = 3 Eigenvectors		 Key Reference(s):
Relevant Chapters:


Pressure-Truncated n = 5 Polytrope
γg=(n+1)/n=65
Truncated n = 5 Polytrope		 Key Reference(s):
  • n/a
Relevant Chapters:


Pressure-Truncated Isothermal (n = ∞) Sphere
γg=1
Truncated n = 5 Polytrope		 Key Reference(s):
Relevant Chapters:
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