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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 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).

Whitworth's (1981) Isothermal Free-Energy Surface

© 2014 - 2020 by Joel E. Tohline
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