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Much of the astrophysics community's present understanding of the structure, stability, and dynamical evolution of individual stars, short-period binary star systems, and the gaseous disks that are associated with numerous types of stellar systems (including galaxies) are derived from an examination of the behavior of a specific set of coupled, partial differential equations. These equations — most of which also are heavily utilized in studies of continuum flows in terrestrial environments — are thought to govern the underlying physics of all macroscopic fluid systems in astronomy. Although relatively simple in form, they prove to be very rich in nature.

The literature on this subject is enormous, as serious discussions of the structure and dynamical properties of stars and galaxies date back well over a century. The primary purpose of this work is two-fold:

1. To document in an electronically accessible format many of the key physical principles that underlie modern discussions of the structure, stability, and dynamical evolution of astrophysical fluid systems.
2. To take advantage of the added dimensions offered by the hypertext medium — such as color, text/equation linkages, animation, and virtual reality environments — to effectively illustrate many of these physical principles.

We have adopted MediaWiki as the hosting environment of choice most significantly because, after incorporating the proper set of extensions, it facilitates the insertion of complex, LaTeX-formulated mathematical expressions into the text.

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Pages Worth Visiting

• Introductory Web Page
• Temporary …
• Key Directories and Files on xxx.phys.lsu.edu
• Experimenting With the a2Hosting Environment
• Riemann (1861)
• Appendix: Equation Templates
• Appendix: Special Functions
• Appendix: Variables Templates
• Appendix: SGF Images
• Appendix: Mathematics/EulerAngles
• Appendix: References
• Appendix: Ramblings
• Appendix: Permissions     <==     Not usable; editing error
• Appendix: Copyright Permissions
• Appendix: Format Recommendations
• Tiled Menu
• Table of Contents
• Total pressure quartic solution
• Spherically Symmetric Configurations (SSC) Index
• Virial Equilibrium of Adiabatic Spheres
• Virial Equilibrium of Adiabatic Spheres (Summary)
• Virial Equilibrium of Isothermal Spheres
• Virial Equilibrium of Uniform-Density Spheres
• Virial of Embedded Polytropes (Outline)
  • First Effort     $\Leftarrow$     Same as "Virial Equilibrium of Adiabatic Spheres"
  • Second Effort     $\Leftarrow$     Same as "Virial Equilibrium of Adiabatic Spheres (Summary)"
  • Third Effort     $\Leftarrow$     FormFactors
  • First Effort, Second Time Around     $\Leftarrow$     We reproduce discussion associated with "First Effort," but correct expressions for ${\mathfrak{𝔣}}_W$ and ${\mathfrak{𝔣}}_A$ as identified in our "Third Effort" and, accordingly reserve various affected expressions that follow.
  • Second Effort, Second Time Around     $\Leftarrow$     We reproduce the discussion associated with our "Second Effort," but revise key sections to incorporate corrected expressions for the structural form factors.
• SSC Synopsis (Using Style Sheet)
• PP Tori: Structure & Stability
  • Menu Tile:  Papaloizou-Pringle Tori (1984) = Apps/PapaloizouPringleTori; this chapter focuses on equilibrium structure.
  • Menu Tile:  (Massless) Papaloizou-Pringle Tori = Apps/PapaloizouPringle84; in mid-July of 2020, Blaes granted permission to include in this chapter some reprinted material from his 1985 paper.
  • Menu Tile:  Analytic Analysis by Blaes (1985) = Apps/ImamuraHadleyCollaboration; compare Blaes85 against Imamura-Hadley Collaboration]; in mid-July of 2020, Blaes granted permission to include in this chapter some reprinted material from his 1985 paper.
  • Oscillations in the Slim Torus limit = Apps/Blaes85SlimLimit
• Earlier version of the PGE/Euler chapter
• Explains Whitworth's chosen scaling
• Details regarding Stahler's (1983) derived mass-radius relation
• Practice use of image map (Image:SchonbergChandra1942.jpg)
• Mass Upper Limits
• Bipolytrope Generalization:
  • Bipolytrope Generalization (original)
  • Bipolytrope Generalization (Version 2)
• Note that …Template: "SSCstructure" points to original "table of contents"
• Stability of Spherically Symmetric Configurations (Eulerian Perspective) <-- Includes scratch work with rarely used html characters, such as ⑧
• Supports Free-Energy PowerPoint Presentation
• Free-Energy Stability Analysis (early version)
• Attempt at Formulating an Analytic Solution to oscillating n = 1 polytrope; see also the Challenge
• ProjectsUnderway/Core_Collapse_Supernovae  $\Leftarrow$   Referenced in our discussion of Goldreich & Weber (1980)
• Power-Law Density Distribution
• Nonlinear PGEs in Cylindrical Coordinates
• Linearized Equations in Cylindrical Coordinates     <==     Referenced, for example, in out discussion of PP84

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