User contributions for Joel2

14 July 2024

• 17:3617:36, 14 July 2024 diff hist −5 Appendix/Ramblings/T3CharacteristicVector No edit summary
• 17:3417:34, 14 July 2024 diff hist −26 Appendix/Ramblings/T3CharacteristicVector →Binney and Tremaine Formalism
• 17:3317:33, 14 July 2024 diff hist −58 Appendix/Ramblings/T3CharacteristicVector No edit summary
• 17:3117:31, 14 July 2024 diff hist +14,892 N 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..."
• 17:2817:28, 14 July 2024 diff hist −13 Jaycall/KillingVectorApproach →Application to T3 Coordinates current
• 17:2817:28, 14 July 2024 diff hist −13 Jaycall/KillingVectorApproach →Strategic Choice of Characteristic Vector
• 17:1817:18, 14 July 2024 diff hist +30,714 N 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..."

11 July 2024

• 19:1519:15, 11 July 2024 diff hist −89 Appendix/Ramblings →Other Pages Worth Visiting
• 19:0419:04, 11 July 2024 diff hist +124,905 N 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..." current
• 18:4518:45, 11 July 2024 diff hist +17,650 N 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..." current
• 18:3918:39, 11 July 2024 diff hist −24 SSC/Virial/PolytropesEmbedded/FirstEffortAgain →n=5 Polytropic current
• 18:3818:38, 11 July 2024 diff hist +84,927 N 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..."
• 18:2518:25, 11 July 2024 diff hist +46,805 N 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>..." current
• 18:2218:22, 11 July 2024 diff hist 0 N File:RosselandEq2.18.png No edit summary current
• 18:2218:22, 11 July 2024 diff hist 0 N File:LedouxWalraven1958Eq57.23.png No edit summary current
• 18:1918:19, 11 July 2024 diff hist 0 N File:Bonnor1957Eq2.10.png No edit summary current
• 18:1818:18, 11 July 2024 diff hist 0 N File:Bonnor1957Eq2.7.png No edit summary current
• 18:1818:18, 11 July 2024 diff hist 0 N File:Bonnor1957Eq2.1.png No edit summary current
• 18:1718:17, 11 July 2024 diff hist +1 SSC/StabilityEulerianPerspective →Summary and Combinations current
• 18:1618:16, 11 July 2024 diff hist 0 N File:JamesJeans1928Eq314.6.png No edit summary current
• 18:1618:16, 11 July 2024 diff hist 0 N File:Jeans1902Eq12.png No edit summary current
• 18:1518:15, 11 July 2024 diff hist 0 N File:Jeans1902Title.png No edit summary current
• 18:1118:11, 11 July 2024 diff hist +48,274 N 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..."
• 18:0718:07, 11 July 2024 diff hist +23,526 N 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..."
• 18:0718:07, 11 July 2024 diff hist 0 N File:Whitworth1981Eq5.jpg No edit summary current
• 18:0418:04, 11 July 2024 diff hist 0 N File:WhitworthScalingText.png No edit summary current
• 18:0318:03, 11 July 2024 diff hist +4,163 N 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..." current
• 17:3217:32, 11 July 2024 diff hist +4,735 N 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..." current
• 17:3217:32, 11 July 2024 diff hist 0 N File:SelfSquareAug2004Dated.png No edit summary current
• 17:3017:30, 11 July 2024 diff hist 0 N File:SelfSquareAug2004.png No edit summary current
• 17:2217:22, 11 July 2024 diff hist 0 N File:READMEdownloadMathExtension.png No edit summary current
• 17:1317:13, 11 July 2024 diff hist 0 N File:RmodeImage5big.png No edit summary current
• 17:1317:13, 11 July 2024 diff hist 0 N File:RmodeHBookImage3.png No edit summary current
• 17:1217:12, 11 July 2024 diff hist +8,855 N 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..." current
• 17:0517:05, 11 July 2024 diff hist +110,662 N 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> </..." current
• 16:5716:57, 11 July 2024 diff hist +193 Appendix/Ramblings/DarkMatterMusings No edit summary
• 16:5216:52, 11 July 2024 diff hist +4,131 N 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..."
• 13:0813:08, 11 July 2024 diff hist −18 Appendix/Ramblings/StrongNuclearForce →With Logarithmic Potential Included current
• 13:0613:06, 11 July 2024 diff hist −8 Appendix/Ramblings/StrongNuclearForce →ASTR4422 Class Notes
• 13:0513:05, 11 July 2024 diff hist −4 Appendix/Ramblings/StrongNuclearForce →Standard Presentation
• 13:0413:04, 11 July 2024 diff hist 0 N File:ImlayFig1 cropped.png No edit summary current
• 13:0213:02, 11 July 2024 diff hist +24,294 N Appendix/Ramblings/StrongNuclearForce Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Radial Dependence of the Strong Nuclear Force= <!-- {{LSU_HBook_header}} --> ==Wikipedia as a Resource== [https://en.wikipedia.org/wiki/Quark–gluon_plasma QGP]:   <ul> <li> "QGP (quark-gluon plasma) is a state of matter in which the elementary particles that make up the hadrons of baryonic matter are freed of their strong attraction for one another under extremely high energy densities." </li> <li> "In normal..."
• 12:5512:55, 11 July 2024 diff hist +78 DarkMatter/CK2015 →Building Equilibrium Models with Flat Rotation Curves current
• 12:4212:42, 11 July 2024 diff hist −13 DarkMatter/CK2015 →Discovery
• 12:4112:41, 11 July 2024 diff hist −13 DarkMatter/CK2015 →A Potential Problem
• 12:4012:40, 11 July 2024 diff hist −26 DarkMatter/CK2015 →Building Equilibrium Models with Flat Rotation Curves
• 12:3912:39, 11 July 2024 diff hist +16,125 N DarkMatter/CK2015 Created page with "__FORCETOC__ <!-- __FORCETOC__ will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =Remarks on Christodoulou & Kazanas (2015)= <font color="red">Remarks by J. E. Tohline</font><p></p> Date: 8 October 2015 <!-- {{LSU_HBook_header}} --> First, let me say that I very much enjoyed reading this paper by Christodoulou & Kazanas (2015; hereafter CK15), which was sent to me in draft form. The first couple of times I read thro..."
• 12:3712:37, 11 July 2024 diff hist +8,999 N DarkMatter/UniformSphere Created page with "<!-- __FORCETOC__ will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =Force Exerted by a Uniform-Density Shell or Sphere= <!-- {{LSU_HBook_header}} --> ==Tohline 1982== ===General Derivation from Notes Dated 29 November 1982=== If the force per unit mass exerted at the position, <math>~\vec{r}</math>, from a single point mass, <math>~m</math>, is given by, <div align="center"> <table border="0" cellpadding="5" align="center"> <..."
• 12:3412:34, 11 July 2024 diff hist 0 DarkMatter/VeraRubin →Princeton IAS
• 12:1912:19, 11 July 2024 diff hist 0 N File:Rood1983postcard combined.png No edit summary current