Editing LSUsimulations (section)

====1<sup>st</sup> Video====

Our initially axisymmetric "Model A" configuration is dynamically unstable toward the development of a so-called bar-mode instability; actually, the unstable eigenfunction has a slight two-armed spiral character.  The caption of the icon shown here, on the left, contains a link to a YouTube video that shows the nonlinear development of this instability.

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<tr><td align="center">Model A Barmode Instability</td></tr>
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[[File:VideoCoverModelABarmodeInstability.png|250px|Model A Bar-mode Instability]]
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<b>YouTube</b> video: &nbsp;[https://www.youtube.com/watch?v=BhRUqZe0Ly4 BhRUqZe0Ly4]
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<font color="red">Resolution &hellip;</font> &nbsp; <math>[128, 128, 128]</math> in <math>[\varpi, Z, \varphi]</math>
<ul>
  <li>Radial: &nbsp; Model A was evolved on a cylindrical grid that contained 128 radial zones, but the equatorial radius of the initial axisymmetric model extended out to only zone 53.  Hence, ample room was allowed for radial expansion of the model as it deformed into a two-armed spiral, then bar-like, configuration.</li>
  <li>Vertical: &nbsp; Although the model was initially quite flat &#8212; having a pole-to-equatorial axis ratio, <math>c/a = 0.208</math>, meaning that the vertical extent above its equatorial plane was substantially less than 53 vertical zones &#8212; it was evolved on a grid that contained 128 vertical zones in this "northern" hemisphere. (Our technique for solving the Poisson equation imposed this grid size.)  We assumed reflection symmetry through the equatorial plane, so it was not necessary to include an additional 128 zones in the "southern" hemisphere.</li>
  <li>Azimuthal: &nbsp; In the azimuthal direction, each grid zone had an angular extent of <math>2\pi/256</math>.  However, by forcing the evolution to maintain a two-fold "&pi;-symmetry" only 128 grid zones were required to evolve the system with this resolution.</li>
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This evolution is viewed from an inertial frame of reference in which the initial symmetry (vertical) axis is tipped somewhat toward the viewer.  As a consequence, even though the initial model is axisymmetric, it appears to be slightly ellipsoidal in even the earliest frames of the video.  After "ejecting" a small portion of its mass into a "circumstellar" disk/ring, the model settles down into a ''nearly'' steady-state, rotating bar-like configuration that, for all intents and purposes is a compressible analog of a Riemann ellipsoid.  (This is the theme of the {{ CT2000 }} publication.)