Editing Apps/EriguchiHachisu/Models

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=Eriguchi, Hachisu, and their various Colleagues=

Following the completion of their respective doctoral dissertations, Yoshiharu Eriguchi and Izumi Hachisu embarked upon an extremely fertile research collaboration which, especially over the decade of the 1980s, transformed the international astrophysics community's understanding of the structure and stability of rotating, self-gravitating fluid configurations.  Others &#8212; including myself (J.E.T.) &#8212; were drawn into, and benefitted significantly from participation in, various ones of these collaborative research efforts. In what follows, we list and summarize the key results from a significant number of these "Eriguchi and Hachisu" collaborative publications.

Our list is broken into two broad topical categories: &nbsp; ''Principally Uniformly Rotating, Incompressible Configurations'' (polytropic index, <math>n=0</math>) and ''Principally Differentially Rotating, Compressible Configurations'' (polytropic index, <math>n>0</math>).  The efforts by both Eriguchi and Hachisu to extend our understanding of incompressible configurations beyond the Maclaurin spheroid sequence and the Jacobi/Dedekind sequence &#8212; more broadly, Riemann S-type ellipsoids &#8212; is summarized in [[#HE84c|HE84c]].

==Kickoff==

===Eriguchi78===
<div align="center">
{{ Eriguchi78figure }}<br />
(p. 515): &nbsp; <font color="red">"This paper is based on the author's dissertation, submitted to the University of Tokyo, in partial fulfillment of the requirements for the doctorate."</font>
</div>

===Hachisu82===
<div align="center">
{{ Hachisu82figure }}<br />
(p. 333): &nbsp; <font color="red">"This paper is based on the author's dissertation, submitted to the University of Tokyo, in partial fulfillment of the requirements for the doctorate."</font>
</div>

==Principally Uniformly Rotating, Incompressible Configurations==

===ES81===
<font color="darkgreen"><b>Concave Hamburger: One-Ring</b> (incompressible case)</font><br />&hellip; as categorized in {{ HE84c }}; also see [[#HE84c|HE84c]], below.
<div align="center">{{ ES81figure }}</div>
<table border="1" align="center" cellpadding="5">
<tr>
  <td align="center">[[File:ES81Table1.png|200px|ES81Table1]]</td>
  <td align="center">[[File:ES81Fig1.png|250px|ES81Fig1]]</td>
  <td align="center">[[File:ES81Fig2.png|150px|ES81Fig2]]</td>
</tr>
</table>


<table align="center" border="0" cellpadding="10">
<tr>
  <td align="center">
<font color="red">NOTE:</font>&nbsp; Results from an independent effort to construct models along this identical sequence appear in &hellip;<br />
{{ AKM2003figure }}
  </td>
  <td align="center" rowspan="2">
[[File:ES81andAKM2003oneRingB.png|200px|ES81 &amp; AKM2003 one-ring]]
  </td>
</tr>
<tr><td align="center">
<table border="1" align="center" cellpadding="10">
<tr>
  <td align="center">See Table 2 (p. 519) of<br />{{ AKM2003hereafter }}</td>
  <td align="center">See the curve labeled "(1)"<br />in Figure 2 (p. 517) of<br />{{ AKM2003hereafter }}</td>
  <td align="center">See Figure 6 (p. 520) of<br />{{ AKM2003hereafter }}</td>
</tr>
</table>

</td></tr></table>

===HES82===
<font color="darkgreen"><b>Concave Hamburger: One-Ring</b> (compressible, as well as, incompressible case)</font><br />&hellip; as categorized in {{ HE84c }}; also see [[#HE84c|HE84c]], below.
<div align="center">{{ HES82figure }}</div>
<table border="1" align="center" cellpadding="5">
<tr>
  <td align="center">[[File:HES82Table1.png|300px|HES82Table1]]</td>
  <td align="center">[[File:HES82Fig3.png|300px|HES82Fig3]]</td>
  <td align="center">[[File:HES82Hamburger.png|200px|HES82Hamburger]]</td>
</tr>
</table>


<font color="red">NOTE:</font> &nbsp; &nbsp; In this {{ HES82hereafter }} publication, the authors point out (with attending explanation) that some of the modeling results published earlier by {{ FESB-K80 }} are demonstratively wrong.

===EH82===
<font color="darkgreen"><b>Triangle: Square: Ammonite</b></font> and <font color="darkgreen"><b>Two-Ring</b> (pt. 1)</font><br />&hellip; as categorized in {{ HE84c }}; also see [[#HE84c|HE84c]]  
<div align="center">{{ EH82figure }}</div>
<table border="1" align="center" cellpadding="5">
<tr>
  <td align="center">[[File:EH82Fig2.png|200px|EH82Fig2]]</td>
  <td align="center">[[File:EH82Fig3.png|200px|EH82Fig3]]</td>
  <td align="center">[[File:EH82Fig4.png|200px|EH82Fig4]]</td>
</tr>
<tr>
  <td align="center" bgcolor="black">[[File:Q04D_triangleD.png|200px|See Saturn discussion]]</td>
  <td align="center" bgcolor="black">[[File:Q04D_squareD.png|200px|See Saturn discussion]]</td>
  <td align="center" bgcolor="black">[[File:Q04DcroppedD.png|200px|See Saturn discussion]]</td>
</tr>
<tr>
  <td align="left" colspan="3">
NOTE:  Color images copied from our separate discussion of [[Appendix/Ramblings/Saturn#Binary_Mass-Transfer|binary mass-transfer simulations]].
  </td>
</tr>
</table>


<table border="1" align="center" cellpadding="5">
<tr>
  <td align="center">[[File:EH82Table1.png|200px|EH82Table1]]</td>
  <td align="center">[[File:EH82Fig1.png|200px|EH82Fig1]]</td>
  <td align="center">[[File:EH82TableV.png|200px|EH82TableV]]</td>
  <td align="center">[[File:EH82Fig5.png|200px|EH82Fig5]]</td>
</tr>
</table>


<div align="center">
<font color="red">NOTE:</font>&nbsp; Results from an independent effort to construct models along this identical "two-ring" sequence appear in &hellip;<br />
{{ AKM2003figure }}
</div>
<table border="1" align="center" cellpadding="10">
<tr>
  <td align="center">n/a</td>
  <td align="center">See the curve labeled "(3)"<br />in Figure 2 (p. 517) of<br />{{ AKM2003hereafter }}</td>
  <td align="center">See Table 4 (p. 520) of<br />{{ AKM2003hereafter }}</td>
  <td align="center">See Figure 8 (p. 521) of<br />{{ AKM2003hereafter }}</td>
</tr>
</table>

===EHS82===
<font color="darkgreen"><b>Dumb-Bell: Pear-Shaped</b></font><br />&hellip; as categorized in {{ HE84c }}; also see [[#HE84c|HE84c]], below.
<div align="center">{{ EHS82figure }}</div>
<table border="1" align="center" cellpadding="5">
<tr>
  <td align="center">[[File:EHS82Fig1.png|200px|EHS82Fig1]]</td>
  <td align="center">[[File:EHS82Fig2.png|200px|EHS82Fig2]]</td>
  <td align="center">[[File:EHS82Fig3.png|200px|EHS82Fig3]]</td>
  <td align="center">[[File:EHS82Fig4.png|200px|EHS82Fig4]]</td>
</tr>
</table>

===EH83a===
<font color="darkgreen"><b>Two-Ring</b> (pt. 2)</font><br />&hellip; as categorized in {{ HE84c }}; also see [[#HE84c|HE84c]], below.
<div align="center">{{ EH83afigure }}</div>
<table border="1" align="center" cellpadding="5">
<tr>
  <td align="center">
    <table border="0" align="center" cellpadding="1"><tr>
      <td align="center">[[File:EH83aFig3.png|200px|EH83aFig3]]</td>
      <td align="center">[[File:EH83aCaption3.png|200px|EH83aCaption3]]</td>
    </tr></table>
  </td>
  <td align="center">
    <table border="0" align="center" cellpadding="1"><tr>
      <td align="center">[[File:EH83aFig2.png|100px|EH83aFig2]]</td>
      <td align="center">[[File:EH83aCaption2.png|200px|EH83aCaption2]]</td>
    </tr></table>
  </td>
</tr>
</table>

===EH83b===
<font color="darkgreen"><b>Multi-Body</b></font><br />&hellip; as categorized in {{ HE84c }}; also see [[#HE84c|HE84c]], below.
<div align="center">{{ EH83bfigure }}</div>
<table border="1" align="center" cellpadding="5">
<tr>
      <td align="center">[[File:EH83bFig3.png|300px|EH83bFig3]]</td>
      <td align="center">[[File:EH83bFig4.png|200px|EH83bFig4]]</td>
      <td align="center">[[File:EH83bFig2.png|150px|EH83bFig2]]</td>
</tr>
</table>

===HE84c===
<font color="darkgreen"><b>Summary</b></font>
<div align="center">{{ HE84cfigure }}</div>
<table border="1" align="center" cellpadding="5">
<tr>
  <td align="center">[[File:HE84cFig1.png|400px|HE84cFig1]]</td>
</tr>
<tr>
  <td align="center">[[File:HE84cFission.png|400px|HE84cFission]]

----

Also see our separate discussion of the [[ThreeDimensionalConfigurations/BinaryFission#Illustration|Fission Hypothesis]]</td>
</tr>
</table>
</li>
</ol>

===HE84===
<div align="center">{{ HE84figure }}</div>
<table border="1" align="center" cellpadding="5">
<tr>
  <td align="center">[[File:BifurcationPointsHE84.png|200px|BifurcationPointsHE84]]</td>
  <td align="center">[[File:HE84Table1.png|200px|HE84Table1]]</td>
</tr>
</table>
</li>
</ol>

===HE83===
<div align="center">{{ HE83figure }}</div>
<table border="1" align="center" cellpadding="5">
<tr>
  <td align="center">[[File:HE83Fig1.png|300px|HE83Fig1]]</td>
</tr>
</table>

===EH85===
<font color="darkgreen"><b>Differentially Rotating, "Maclaurin Toroid" Sequence</b></font><br />&hellip; extending the work of {{ MPT77 }}.
<div align="center">{{ EH85figure }}</div>
<table border="1" align="center" cellpadding="5">
<tr>
      <td align="center">[[File:EH85Fig1.png|200px|EH85Fig1]]</td>
      <td align="center">[[File:EH85Fig2.png|300px|EH85Fig2]]</td>
</tr>
</table>

==Principally Differentially Rotating, Compressible Configurations==

===Hachisu86a===

<div align="center">{{ Hachisu86afigure }}</div>
<table border="1" align="center" cellpadding="5">
<tr>
<td align="center" colspan="4">
Models having <font color="maroon"><b>[[AxisymmetricConfigurations/SolutionStrategies#SRPtable|Uniform Rotation]]</b></font> &#8212; &sect;II.c, Eq. (11), p. 481 
</td>
</tr>
<tr>
  <td align="center">[[File:Hachisu86aFig3.png|200px|Hachisu86aFig3]]</td>
  <td align="center">[[File:Hachisu86aTableI.png|200px|Hachisu86aTableI]]</td>
  <td align="center">[[File:Hachisu86aFig2.png|200px|Hachisu86aFig2]]</td>
  <td align="center">[[File:Hachisu86aFig4.png|200px|Hachisu86aFig4]]</td>
</tr>
<tr>
<td align="center" colspan="4">
Models having <font color="maroon"><b>[[AxisymmetricConfigurations/SolutionStrategies#SRPtable|Uniform <math>v_\varphi</math>]]</b></font> &#8212; &sect;II.c, Eq. (12), p. 481 
</td>
</tr>
<tr>
  <td align="center">[[File:Hachisu86aFig15vConstant.png|200px|Hachisu86aFig15vConstant]]</td>
  <td align="center">[[File:Hachisu86aTable2.png|200px|Hachisu86aTable2]]</td>
  <td align="center">
    [[File:Hachisu86aFig12Pt1.png|150px|Hachisu86aFig12Pt1]]
    [[File:Hachisu86aFig12Pt2.png|150px|Hachisu86aFig12Pt2]]
    [[File:Hachisu86aFig12Caption.png|150px|Hachisu86aFig12Caption]]
  </td>
  <td align="center">[[File:Hachisu86aFig16vConstant.png|200px|Hachisu86aFig16vConstant]]</td>
</tr>
<tr>
<td align="center" colspan="4">
Models having <font color="maroon"><b>[[AxisymmetricConfigurations/SolutionStrategies#SRPtable|j-constant rotation]]</b></font> &#8212; &sect;II.c, Eq. (13), p. 481 
</td>
</tr>
</table>

=See Also=
* [[Apps/MaclaurinSpheroids#Maclaurin_Spheroids_.28axisymmetric_structure.29|Properties of Maclaurin Spheroids]]
* [[Apps/MaclaurinSpheroids/GoogleBooks#Excerpts_from_A_Treatise_of_Fluxions|Excerpts from Maclaurin's (1742) ''A Treatise of Fluxions'']]
* [[ThreeDimensionalConfigurations/EFE_Energies#Properties_of_Homogeneous_Ellipsoids_.282.29|Properties of Homogeneous Ellipsoids]]


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