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For Richard H. Durisen

Whitworth's (1981) Isothermal Free-Energy Surface
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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 where you can find a technical discussion of the identified topic. Have fun reading any one of these discussions, as you please.
  • 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. The "Preview" application on a Mac can be used to view and interact with this time-dependent 3D scene; I am not yet sure how to view and interact with this scene on a PC that runs the Microsoft OS.

  • 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.

Highlights Added on 2 March 2020

  • Imamura & Hadley Collaboration:  You might also enjoy skimming through this chapter, as it focuses on an analysis of work that Jimmy's group has published over the past decade. Figure 3 is the climax of my analysis, as it directly compares a prediction drawn from the analytic work of Blaes (1985) with the results from numerical simulations conducted by the Imamura & Hadley collaboration.
  • Using Toroidal Coordinates to Determine the Gravitational Potential of Axisymmetric Systems:  This page summarizes, and provides links to, several of my favorite chapters. Most significantly, it highlights the overlap that exists between Howard Cohl's dissertation research (remember that Howie was an IU undergraduate astronomy major) and Wong's (1973) fabulous, but little appreciated, analytic derivation of the gravitational potential both inside and outside of a uniform-density, circular torus.

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) publication,

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