User:Tohline/Appendix/Ramblings/ForDurisen

For Richard H. Durisen

Highlights Mentioned on 1 March 2020

• Tiled Menu:  Most tiles presented on this menu page contain a short title that is linked to a hypertext-enhanced chapter in which a technical discussion of the identified topic is discussed.
• Ramblings:  This appendix contains a long list of additional (mostly technical) topics that have been explored, to date — topics that are related to, but usually are not highlighted as a tile, on the primary menu page.

  
  

• Equilibrium Sequence Turning Points:  As the abstract of this hypertext-enhanced chapter highlights, we have proven analytically that a turning point along the equilibrium sequence of pressure-truncated (spherical) polytropes is precisely associated with the onset of a dynamical instability. This has generally been expected/assumed, but as far as we have been able to determine, it has not previously been proven analytically.
• Type I Riemann Ellipsoids: With the assistance of COLLADA (an XML-formatted 3D visualization language), we have determined that when a Type-I Riemann ellipsoid is viewed from a frame of reference in which the ellipsoid is stationary, each Lagrangian fluid element moves along an elliptical orbit …
  1. that is inclined to the equatorial plane of the ellipsoid (this is not an unexpected feature of Type-I ellipsoids);
  2. whose center is offset from the rotation axis — as well as from any of the principal geometric axes — of the ellipsoid (as far as we have been able to determine, this has not previously been documented in the published literature).

  If you like, I can send you the COLLADA file — title = SimplifyTest01.dae — that has been used to generated Figure 3 of this hypertext-enhanced chapter.

• Saturn's Hexagon Storm:  In this "Ramblings" chapter, we ask whether the underlying physical principles that sometimes lead to the nonlinear development of triangle-, box-, and pentagonal-shaped structures on the accretor in our simulations of binary mass-transfer — see, for example, this YouTube Animation — are related to the underlying physical principles that lead to the development and persistence of Saturn's Hexagon Storm.

© 2014 - 2021 by Joel E. Tohline |   H_Book Home   |   YouTube   | Appendices: | Equations | Variables | References | Ramblings | Images | myphys.lsu | ADS | 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