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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.


Whitworth's (1981) Isothermal Free-Energy Surface

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