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

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   <li><font color="darkgreen"><b>Pencil94.dae</b></font>
   <li><font color="darkgreen"><b>Pencil94.dae</b></font>
<br />Finished specifying correct behavior of clock, which gives the final, fully functional model.    <font color="red">This works in both visualization venues</font>
<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><font color="darkgreen"><b>PencilInertial95.dae</b></font>
<br />Flipped from rotating- to inertial-frame of reference.    <font color="red">This works in both visualization venues</font>
   </li>
   </li>
</ul>
</ul>


===Part B===
<ul>
  <li><font color="darkgreen"><b>FastRot78.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.
  </li>
  <li><font color="darkgreen"><b>FastRot79.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>.
  </li>
  <li><font color="darkgreen"><b>FastInertial80.dae</b></font>
<br />Test.
  </li>
</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> PencilInertial95.dae [04 June 2020]  </li>
   <li>Rotating Frame:  <font color="lightgreen">[KEEP]</font> Pencil94.dae [04 June 2020] </li>
   <li>Rotating Frame:  <font color="lightgreen">[KEEP]</font> Pencil94.dae [04 June 2020] </li>
</ol>
</ol>

Revision as of 03:44, 5 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>

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 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 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


Best b28c256 Models

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

  1. Inertial Frame: [KEEP] PencilInertial95.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