Difference between revisions of "User:Tohline/Appendix/Ramblings/RiemannB28C256"

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<tr>
<tr>
   <td align="center" rowspan="5">
   <td align="center" rowspan="6">
<b>Figure 1a</b><br />
<b>Figure 1a</b><br />&nbsp;<br />
[[File:EFE_STypeB28C256.png|325px|EFE Parameter Space]]
[[File:B28c256EFEdiagram02.png|325px|EFE Parameter Space]]
   </td>
   </td>
   <td align="center" rowspan="5" width="2%">
   <td align="center" rowspan="6" width="2%">
&nbsp;
&nbsp;
   </td>
   </td>
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<math>~\frac{b}{a} = 0.28</math>
<math>~\frac{b}{a} = 0.28</math>
   </td>
   </td>
   <td align="center" rowspan="5" width="2%">
   <td align="center" rowspan="6" width="2%">
&nbsp;
&nbsp;
   </td>
   </td>
   <td align="center" rowspan="5" bgcolor="lightgrey">
   <td align="center" rowspan="6" bgcolor="lightgrey">
<b>Figure 1b</b><br />
<b>Figure 1b</b><br />
[[File:COLLADAb28c256OldModel.png|300px|EFE Model b28c256]]
[[File:COLLADAb28c256OldModel.png|300px|EFE Model b28c256]]
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''Direct''
''Direct''
   </td>
   </td>
   <td align="center" width="2%" rowspan="3">
   <td align="center" width="2%" rowspan="4">
&nbsp;
&nbsp;
   </td>  
   </td>  
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   <td align="center">
   <td align="center">
<math>~\lambda_\mathrm{EFE} = - 0.456676</math>
<math>~\lambda_\mathrm{EFE} = - 0.456676</math>
  </td>
</tr>
<tr>
  <td align="center">
<math>~f = - 0.174510</math>
  </td>
  <td align="center">
<math>~f = - 85.0007</math>
   </td>
   </td>
</tr>
</tr>
</table>
</table>


The subscript "EFE" on &Omega; and &lambda; means that the relevant frequency is given in units that have been adopted in [<b>[[User:Tohline/Appendix/References#EFE|<font color="red">EFE</font>]]</b>], that is, in units of <math>~[\pi G\rho]^{1 / 2}</math>.  In Figure 1a, the solid purple circular marker (where the pair of purple lines cross) identifies the location of this model in the "c/a versus b/a" diagram that appears as Figure 2 on p. 902 of [http://adsabs.harvard.edu/abs/1965ApJ...142..890C S. Chandrasekhar (1965)]; essentially the same diagram appears in &sect;49 (p. 147) of [<b>[[User:Tohline/Appendix/References#EFE|<font color="red">EFE</font>]]</b>].
The subscript "EFE" on &Omega; and &lambda; means that the relevant frequency is given in units that have been adopted in [<b>[[User:Tohline/Appendix/References#EFE|<font color="red">EFE</font>]]</b>], that is, in units of <math>~[\pi G\rho]^{1 / 2}</math>.  In Figure 1a, the yellow circular marker, that has been placed where the pair of purple dashed lines cross, identifies the location of this model in the "c/a versus b/a" ''[[User:Tohline/ThreeDimensionalConfigurations/RiemannStype#Fig2|EFE Diagram]]'' that appears as Figure 2 on p. 902 of [http://adsabs.harvard.edu/abs/1965ApJ...142..890C S. Chandrasekhar (1965)]; essentially the same diagram appears in &sect;49 (p. 147) of [<b>[[User:Tohline/Appendix/References#EFE|<font color="red">EFE</font>]]</b>].


==Coding Steps==
==Coding Steps==
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   </ul>
   </ul>
   <li><font color="darkgreen"><b>Pencil90.dae</b></font>
   <li><font color="darkgreen"><b>Pencil90.dae</b></font>
<br />Identical to <b>FastRot79.dae</b> except wall-mounted labeling has been changed to reflect new values of b/a and c/a.
<br />Identical to <b>FastRot79.dae</b> except wall-mounted labeling has been changed to reflect new values of b/a and c/a.  <font color="red">This works in both visualization venues</font>.
   </li>
   </li>
</ul>
  <li><font color="darkgreen"><b>Pencil91.dae</b></font>
 
<br />Inserted correct surface geometry of this rapidly rotating Riemann ellipsoid.    <font color="red">This works in both visualization venues</font>.
===Part B===
  </li>
<ul>
   <li><font color="darkgreen"><b>Pencil92.dae</b></font>
   <li><font color="darkgreen"><b>FastRot76.dae</b></font>
<br />Inserted the correct ''animated'' depiction of the 9 Lagrangian fluid elements.
<br />Inserted correct surface geometry of this rapidly rotating Riemann ellipsoid. <font color="red">This works in both visualization venues</font>.
  </li>
  <li><font color="darkgreen"><b>Pencil93.dae</b></font>
<br />Placed 51 yellow, equatorial-plane markers.   <font color="red">This works in both visualization venues</font>
   </li>
   </li>
   <li><font color="darkgreen"><b>FastRot78.dae</b></font>
   <li><font color="darkgreen"><b>Pencil94.dae</b></font>
<br />All the animation elements have been inserted and debugged, but as if internal fluid motion is regrograde (clockwise). Need to flip the fluid motion so that it is prograde (counter-clockwise) even in the rotating frame of reference.
<br />Finished specifying correct behavior of clock, which gives the final, fully functional model.   <font color="red">This works in both visualization venues</font>
   </li>
   </li>
   <li><font color="darkgreen"><b>FastRot79.dae</b></font>
   <li><font color="darkgreen"><b>PencilInertial95.dae</b></font>
<br />All the animation elements have been inserted and debugged, with internal fluid correctly moving prograde (counter-clockwise) even in the rotating frame of reference. <font color="red">This works in both visualization venues</font>.
<br />Flipped from rotating- to inertial-frame of reference.   <font color="red">This works in both visualization venues</font>
   </li>
   </li>
   <li><font color="darkgreen"><b>FastInertial80.dae</b></font>
   <li><font color="darkgreen"><b>PencilInertial96.dae</b></font>
<br />Test.
<br />Enlarged red "Lagrange01" marker from 0.03 to 0.075; and changed transparency of ellipsoid surface to (totally opaque) 1.0.    <font color="red">This works in both visualization venues</font>
   </li>
   </li>
</ul>
</ul>


===Best b28c256 Models===
===Best b28c256 Models===
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The example models created for display in the Oculus Rift S are the following:
The example models created for display in the Oculus Rift S are the following:
<ol>
<ol>
   <li>Inertial Frame:  <font color="lightgreen">[KEEP]</font> </li>
   <li>Inertial Frame:  <font color="lightgreen">[KEEP]</font> PencilInertial96.dae [04 June 2020]  </li>
   <li>Rotating Frame:  <font color="lightgreen">[KEEP]</font> </li>
   <li>Rotating Frame:  <font color="lightgreen">[KEEP]</font> Pencil94.dae [04 June 2020] </li>
</ol>
</ol>


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* Discussion of [[User:Tohline/ThreeDimensionalConfigurations/RiemannStype|Ou's Riemann-Like Ellipsoids]]
* Discussion of [[User:Tohline/ThreeDimensionalConfigurations/RiemannStype|Ou's Riemann-Like Ellipsoids]]


* [[User:Tohline/ThreeDimensionalConfigurations/MeetsCOLLADAandOculusRiftS|Riemann Meets COLLADA &amp; Oculus Rift S]]
* [[User:Tohline/ThreeDimensionalConfigurations/MeetsCOLLADAandOculusRiftS|Riemann Meets COLLADA &amp; Oculus Rift S]]: Example <b>(b/a, c/a) = (0.41, 0.385)</b>
** [[User:Tohline/Appendix/Ramblings/VirtualReality#Virtual_Reality_and_3D_Printing|Virtual Reality and 3D Printing]]
** [[User:Tohline/Appendix/Ramblings/VirtualReality#Virtual_Reality_and_3D_Printing|Virtual Reality and 3D Printing]]
** [[User:Tohline/Appendix/Ramblings/OculusRift_S|Success Importing Animated Scene into Oculus Rift S]]
** [[User:Tohline/Appendix/Ramblings/OculusRift_S|Success Importing Animated Scene into Oculus Rift S]]
** [[User:Tohline/Appendix/Ramblings/RiemannMeetsOculus|Carefully (Re)Build Riemann Type S Ellipsoids Inside Oculus Rift Environment]]: Example <b>(b/a, c/a) = (0.41, 0.385)</b>
** [[User:Tohline/Appendix/Ramblings/RiemannMeetsOculus|Carefully (Re)Build Riemann Type S Ellipsoids Inside Oculus Rift Environment]]
** Other Example S-type Riemann Ellipsoids:
** Other Example S-type Riemann Ellipsoids:
*** <b>[[User:Tohline/Appendix/Ramblings/RiemannB90C333|(b/a, c/a) = (0.90, 0.333)]]</b>
*** <b>[[User:Tohline/Appendix/Ramblings/RiemannB90C333|(b/a, c/a) = (0.90, 0.333)]]</b>

Latest revision as of 03:58, 14 June 2020

Another S-type Example b28c256

This chapter is an extension of the chapter we have titled, "Riemann Meets COLLADA & Oculus Rift S." In that chapter we used as our first example of a Riemann S-type ellipsoid the model with parameters, (b/a, c/a) = (0.41, 0.385). Here we construct a model with parameters, (b/a, c/a) = (0.28, 0.256). Other closely related chapters are listed below under the heading, "See Also".

Whitworth's (1981) Isothermal Free-Energy Surface
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Key Physical Parameters

The model that we have chosen to use in our second successful construction of a COLLADA-based, 3D and interactive animation has the following properties; this model has been selected from Table 2 of our accompanying discussion of Riemann S-type ellipsoids:

Figure 1a
 
EFE Parameter Space

 

<math>~\frac{b}{a} = 0.28</math>

 

Figure 1b
EFE Model b28c256

<math>~\frac{c}{a} = 0.256</math>

Direct

 

Adjoint

<math>~\Omega_\mathrm{EFE} = 0.456676</math>

<math>~\Omega_\mathrm{EFE} = - 0.020692</math>

<math>~\lambda_\mathrm{EFE} = 0.020692</math>

<math>~\lambda_\mathrm{EFE} = - 0.456676</math>

<math>~f = - 0.174510</math>

<math>~f = - 85.0007</math>

The subscript "EFE" on Ω and λ means that the relevant frequency is given in units that have been adopted in [EFE], that is, in units of <math>~[\pi G\rho]^{1 / 2}</math>. In Figure 1a, the yellow circular marker, that has been placed where the pair of purple dashed lines cross, identifies the location of this model in the "c/a versus b/a" EFE Diagram that appears as Figure 2 on p. 902 of S. Chandrasekhar (1965); essentially the same diagram appears in §49 (p. 147) of [EFE].

Coding Steps

Part A

Here we begin with a working model of b90c333 and use incremental changes in the COLLADA-based code to construct a working model of b28c256.

  • This pair of starting models has been copied from the successful modeling of Riemann S-type ellipsoids that have (b/a, c/a) = (0.90, 0.333)
    • Inertial Frame: [KEEP] FastInertial80.dae [04 June 2020]
    • Rotating Frame: [KEEP] FastRot79.dae [04 June 2020]
  • Pencil90.dae
    Identical to FastRot79.dae except wall-mounted labeling has been changed to reflect new values of b/a and c/a. This works in both visualization venues.
  • Pencil91.dae
    Inserted correct surface geometry of this rapidly rotating Riemann ellipsoid. This works in both visualization venues.
  • Pencil92.dae
    Inserted the correct animated depiction of the 9 Lagrangian fluid elements.
  • Pencil93.dae
    Placed 51 yellow, equatorial-plane markers. This works in both visualization venues
  • Pencil94.dae
    Finished specifying correct behavior of clock, which gives the final, fully functional model. This works in both visualization venues
  • PencilInertial95.dae
    Flipped from rotating- to inertial-frame of reference. This works in both visualization venues
  • PencilInertial96.dae
    Enlarged red "Lagrange01" marker from 0.03 to 0.075; and changed transparency of ellipsoid surface to (totally opaque) 1.0. This works in both visualization venues


Best b28c256 Models

The example models created for display in the Oculus Rift S are the following:

  1. Inertial Frame: [KEEP] PencilInertial96.dae [04 June 2020]
  2. Rotating Frame: [KEEP] Pencil94.dae [04 June 2020]

COLLADA Model Files

Direct Configurations

b28c256DI.dae [Direct Inertial Frame]    …     a COLLADA code containing nnnn lines of <xml>-formatted ASCII text
Original filename used above: xxx.dae

<?xml version="1.0" encoding="UTF-8" standalone="no" ?>


b28c256DRot.dae [Direct Rotating Frame]    …     a COLLADA code containing nnnn lines of <xml>-formatted ASCII text
Original filename used above: xxx.dae

<?xml version="1.0" encoding="UTF-8" standalone="no" ?>

See Also


Whitworth's (1981) Isothermal Free-Energy Surface

© 2014 - 2021 by Joel E. Tohline
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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