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• 19:33, 14 July 2024 Joel2 talk contribs uploaded File:WhitworthPlot2.png
• 19:32, 14 July 2024 Joel2 talk contribs created page File:Horedt EmbeddedPolytrope.png
• 19:32, 14 July 2024 Joel2 talk contribs uploaded File:Horedt EmbeddedPolytrope.png
• 19:31, 14 July 2024 Joel2 talk contribs created page File:Horedt PRdiagram0.png
• 19:31, 14 July 2024 Joel2 talk contribs uploaded File:Horedt PRdiagram0.png
• 19:30, 14 July 2024 Joel2 talk contribs created page File:HoredtPlot2.png
• 19:30, 14 July 2024 Joel2 talk contribs uploaded File:HoredtPlot2.png
• 18:31, 14 July 2024 Joel2 talk contribs created page Appendix/Ramblings/T3CharacteristicVector (Created page with "{{LSU_HBook_header}} =Characteristic Vector for T3 Coordinates= Let's apply Jay's Characteristic Vector approach to Joel's T3 Coordinate System. ==Brute Force Manipulations== Starting from '''Equation CV.02''', and plugging in expressions for various User:Tohline/Appendix/Ramblings/T3Integrals#Logarithmic_Derivatives_of_Scale_Factors|lo...")
• 18:18, 14 July 2024 Joel2 talk contribs created page Jaycall/KillingVectorApproach (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Characteristic Vector Approach to Integrals of Motion Problem= Motivated by our recent work in relativistic fluid dynamics, one insightful approach to the integrals of motion problem involves rewriting the equations of motion in terms of an arbitrary vector field, which we're currently calling a ''characteristic vector''. The benefit here is that we can produce a mathematical condition that tells us what combintatio...")
• 20:04, 11 July 2024 Joel2 talk contribs created page SSC/Virial/Polytropes (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Virial Equilibrium of Adiabatic Spheres= Highlights of the rather detailed discussion presented below have been summarized in an accompanying chapter of this H_Book. ==Review== ===Adopted Normalizations=== In an introductory discussion of the virial equilibrium structure of spherically symmetric configuration...")
• 19:45, 11 July 2024 Joel2 talk contribs created page SSC/VirialEquilibrium/UniformDensity (Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =Uniform-Density Sphere= ==Review== In an introductory discussion of the virial equilibrium structure of spherically symmetric configurations — see especially the section titled, ''Energy Extrema'' — we deduced that a system's equilibrium radius, <math>~R_\mathrm{eq}</math>, measured...")
• 19:38, 11 July 2024 Joel2 talk contribs created page SSC/Virial/PolytropesEmbedded/FirstEffortAgain (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Virial Equilibrium of Adiabatic Spheres= Highlights of the rather detailed discussion presented below have been summarized in an accompanying chapter of this H_Book. ==Review== ===Adopted Normalizations=== In an introductory discussion o...")
• 19:25, 11 July 2024 Joel2 talk contribs created page StabilityVariationalPrinciple (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Free-Energy Stability Analysis= ==Most General Case== Consider a free-energy function of the form, <div align="center"> <table border="0" cellpadding="5" align="center"> <tr> <td align="right"> <math>~\mathcal{G}</math> </td> <td align="center"> <math>~=</math> </td> <td align="left"> <math>~- a\chi^{-1} + b \chi^{-3/n} + c \chi^{-3/j} + \mathcal{G}_0 \, ,</math> </td> </tr> </table> </div> where, <math>...")
• 19:22, 11 July 2024 Joel2 talk contribs created page File:RosselandEq2.18.png
• 19:22, 11 July 2024 Joel2 talk contribs uploaded File:RosselandEq2.18.png
• 19:22, 11 July 2024 Joel2 talk contribs created page File:LedouxWalraven1958Eq57.23.png
• 19:22, 11 July 2024 Joel2 talk contribs uploaded File:LedouxWalraven1958Eq57.23.png
• 19:19, 11 July 2024 Joel2 talk contribs created page File:Bonnor1957Eq2.10.png
• 19:19, 11 July 2024 Joel2 talk contribs uploaded File:Bonnor1957Eq2.10.png
• 19:18, 11 July 2024 Joel2 talk contribs created page File:Bonnor1957Eq2.7.png
• 19:18, 11 July 2024 Joel2 talk contribs uploaded File:Bonnor1957Eq2.7.png
• 19:18, 11 July 2024 Joel2 talk contribs created page File:Bonnor1957Eq2.1.png
• 19:18, 11 July 2024 Joel2 talk contribs uploaded File:Bonnor1957Eq2.1.png
• 19:16, 11 July 2024 Joel2 talk contribs created page File:JamesJeans1928Eq314.6.png
• 19:16, 11 July 2024 Joel2 talk contribs uploaded File:JamesJeans1928Eq314.6.png
• 19:16, 11 July 2024 Joel2 talk contribs created page File:Jeans1902Eq12.png
• 19:16, 11 July 2024 Joel2 talk contribs uploaded File:Jeans1902Eq12.png
• 19:15, 11 July 2024 Joel2 talk contribs created page File:Jeans1902Title.png
• 19:15, 11 July 2024 Joel2 talk contribs uploaded File:Jeans1902Title.png
• 19:11, 11 July 2024 Joel2 talk contribs created page SSC/StabilityEulerianPerspective (Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =Stability of Spherically Symmetric Configurations (Eulerian Perspective)= A standard technique that is used throughout astrophysics to test the stability of self-gravitating fluids involves ''perturbing'' physical variables away from their initial (usually equilibrium) values then ''linearizing'' each of the principal governing equations before seeking solutions d...")
• 19:07, 11 July 2024 Joel2 talk contribs created page SSC/Structure/StahlerMassRadius (Created page with "__FORCETOC__ =Stahler's Mass-Radius Relationship for Embedded Polytropes= ==Review== In an accompanying chapter that discusses detailed force-balanced models of embedded (and pressure-truncated) polytropes, we review [http://adsabs.harvard.edu/abs/1983ApJ...268..165S S. W. Stahler's (1983)] pair of parametric SSC/Structure/PolytropesEmbedded#Stahler.27s_Presentation|relations for the equilibrium mass an...")
• 19:07, 11 July 2024 Joel2 talk contribs created page File:Whitworth1981Eq5.jpg
• 19:07, 11 July 2024 Joel2 talk contribs uploaded File:Whitworth1981Eq5.jpg
• 19:04, 11 July 2024 Joel2 talk contribs created page File:WhitworthScalingText.png
• 19:04, 11 July 2024 Joel2 talk contribs uploaded File:WhitworthScalingText.png
• 19:03, 11 July 2024 Joel2 talk contribs created page SSC/Structure/PolytropesASIDE1 (Created page with "__FORCETOC__ =ASIDE: Whitworth's Scaling= This provides details in support of our associated discussion of embedded polytropic spheres. In his study of the "global gravitational stability [of] one-dimensional polytropes," [http://adsabs.harvard.edu/abs/1981MNRAS.195..967W Whitworth] (1981, MNRAS, 195, 967) normalizes (or "references") various derived mathematical expressions for configuration radii, <math>R</math>, and for the pre...")
• 18:32, 11 July 2024 Joel2 talk contribs created page Appendix/SGFimages (Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =Available SGF_Images= ==List of Uploaded Files== See Special:ListFiles ==June 2021== <table border="1" align="center" cellpadding="5"> <tr> <td align="left">Thumbnail</td> <td align="right">Folder</td> <td align="center">Sub-folder</td> <td align="left">Filename</td> <td align="left">Used?</td> </tr> <tr> <td align="left">File...")
• 18:32, 11 July 2024 Joel2 talk contribs created page File:SelfSquareAug2004Dated.png
• 18:32, 11 July 2024 Joel2 talk contribs uploaded File:SelfSquareAug2004Dated.png
• 18:30, 11 July 2024 Joel2 talk contribs created page File:SelfSquareAug2004.png
• 18:30, 11 July 2024 Joel2 talk contribs uploaded File:SelfSquareAug2004.png
• 18:22, 11 July 2024 Joel2 talk contribs created page File:READMEdownloadMathExtension.png
• 18:22, 11 July 2024 Joel2 talk contribs uploaded File:READMEdownloadMathExtension.png
• 18:13, 11 July 2024 Joel2 talk contribs created page File:RmodeImage5big.png
• 18:13, 11 July 2024 Joel2 talk contribs uploaded File:RmodeImage5big.png
• 18:13, 11 July 2024 Joel2 talk contribs created page File:RmodeHBookImage3.png
• 18:13, 11 July 2024 Joel2 talk contribs uploaded File:RmodeHBookImage3.png
• 18:12, 11 July 2024 Joel2 talk contribs created page A2HostingEnvironment (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =a2Hosting MediaWiki Environment= ==Tests and Lessons in 2021== ===June 4=== right|r-mode image (300 x 225 px) I successfully uploaded the "r-mode image" — shown here, on the right — from my Mac to the a2Hosting file system. <ol> <li>I pointed my browser to the URL: Tohline.education/SelfGravitatingFluids; this opened the "Main Page" of my MediaWiki app</li> <li>I logged...")
• 18:05, 11 July 2024 Joel2 talk contribs created page Appendix/Mathematics/Hypergeometric (Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Hypergeometric Differential Equation= ==Gradshteyn & Ryzhik== According to §9.151 (p. 1045) of [http://www.mathtable.com/gr/ Gradshteyn & Ryzhik (1965)], <font color="darkgreen">"… a hypergeometric series is one of the solutions of the differential equation, <table border="0" cellpadding="5" align="center"> <tr> <td align="right"> <math>0</math> </td> <td align="center"> <math>=</math> </...")
• 17:52, 11 July 2024 Joel2 talk contribs created page Appendix/Ramblings/DarkMatterMusings (Created page with "<!-- __FORCETOC__ will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =Musings Regarding Dark Matter and Dark Energy= [<font color="red">Joel E. Tohline recollection on 3/8/2015</font>] It was during my first year (July 1978 - June 1979) as a J. Willard Gibbs Instructor in the Astronomy Department at Yale University that I started wondering whether the nearly ubiquitous display of "flat rotation curves" in disk galaxies might be exp...")