User contributions for Joel2

15 July 2024

• 17:5717:57, 15 July 2024 diff hist 0 N File:ModelC Table1Again.png No edit summary current
• 17:5417:54, 15 July 2024 diff hist +66 Appendix/Ramblings →Ramblings
• 17:5117:51, 15 July 2024 diff hist +18,779 N Appendix/Ramblings/BiPolytrope51ContinueSearch Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Continue Search for Marginally Unstable (5,1) Bipolytropes= This ''Ramblings Appendix'' chapter — see also, various trials — provides some detailed trial derivations in support of the SSC/Stability/BiPolytropes#Eigenvectors_for_Marginally_Unstable_Models_with_.28.CE.B3c.2C_.CE.B3e.29_.3D_.286.2F5.2C_2.29|accompanying, thorough discussion of this topic..." current
• 17:4817:48, 15 July 2024 diff hist +114,829 N Appendix/Ramblings/BiPolytrope51AnalyticStability Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Marginally Unstable (n_c,n_e) = (5,1) Bipolytropes= This ''Ramblings Appendix'' chapter provides some detailed trial derivations — mostly blind alleyways — in support of the accompanying, thorough discussion of this topic. ==Fundamental Modes== We decided to ex..." current
• 17:4617:46, 15 July 2024 diff hist 0 N File:Bipolytrope51Boundaries03b.png No edit summary current
• 17:4517:45, 15 July 2024 diff hist 0 N File:TangentTrialAnalytic51movie.gif No edit summary current
• 17:4417:44, 15 July 2024 diff hist 0 N File:Frame06good.png No edit summary current
• 17:4317:43, 15 July 2024 diff hist 0 N File:AnalyticAttempt2.png No edit summary current
• 17:4217:42, 15 July 2024 diff hist 0 N File:AnalyticAttempt1.png No edit summary current
• 17:3817:38, 15 July 2024 diff hist +111,989 N Appendix/Ramblings/BiPolytropeStability Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Ramblings: Marginally Unstable Bipolytropes= Our aim is to determine whether or not there is a relationship between (1) equilibrium models at turning points along bipolytrope sequences and (2) bipolytropic models that are marginally (dynamically) unstable toward collapse (or dynamical expansion). ==Overview== <!-- <table border="0" cellpadding="8" align="right"> <tr> <th align="center">File:DataFileButton02.png|r..." current

14 July 2024

• 19:3919:39, 14 July 2024 diff hist 0 N File:N5Sequence04B.png No edit summary current
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• 19:3719:37, 14 July 2024 diff hist 0 N File:N5Sequence01B.png No edit summary current
• 19:3519:35, 14 July 2024 diff hist 0 N File:Stahler1983TitlePage0.png No edit summary current
• 19:3419:34, 14 July 2024 diff hist 0 N File:Whitworth1981TitlePage0.png No edit summary current
• 19:3419:34, 14 July 2024 diff hist 0 N File:WhitworthFig1bCopy.jpg No edit summary current
• 19:3319:33, 14 July 2024 diff hist 0 N File:WhitworthPlot2.png No edit summary current
• 19:3219:32, 14 July 2024 diff hist 0 N File:Horedt EmbeddedPolytrope.png No edit summary current
• 19:3119:31, 14 July 2024 diff hist 0 N File:Horedt PRdiagram0.png No edit summary current
• 19:3019:30, 14 July 2024 diff hist 0 N File:HoredtPlot2.png No edit summary current
• 18:5118:51, 14 July 2024 diff hist +11 Appendix/Ramblings/T3CharacteristicVector →Implications current
• 18:4118:41, 14 July 2024 diff hist −10 Appendix/Ramblings/T3CharacteristicVector →Implications
• 18:3618:36, 14 July 2024 diff hist −13 Appendix/Ramblings/T3CharacteristicVector →Binney and Tremaine Formalism
• 18:3618:36, 14 July 2024 diff hist −5 Appendix/Ramblings/T3CharacteristicVector No edit summary
• 18:3418:34, 14 July 2024 diff hist −26 Appendix/Ramblings/T3CharacteristicVector →Binney and Tremaine Formalism
• 18:3318:33, 14 July 2024 diff hist −58 Appendix/Ramblings/T3CharacteristicVector No edit summary
• 18:3118:31, 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..."
• 18:2818:28, 14 July 2024 diff hist −13 Jaycall/KillingVectorApproach →Application to T3 Coordinates current
• 18:2818:28, 14 July 2024 diff hist −13 Jaycall/KillingVectorApproach →Strategic Choice of Characteristic Vector
• 18:1818:18, 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

• 20:1520:15, 11 July 2024 diff hist −89 Appendix/Ramblings →Other Pages Worth Visiting
• 20:0420:04, 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
• 19:4519:45, 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
• 19:3919:39, 11 July 2024 diff hist −24 SSC/Virial/PolytropesEmbedded/FirstEffortAgain →n=5 Polytropic current
• 19:3819:38, 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..."
• 19:2519:25, 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
• 19:2219:22, 11 July 2024 diff hist 0 N File:RosselandEq2.18.png No edit summary current
• 19:2219:22, 11 July 2024 diff hist 0 N File:LedouxWalraven1958Eq57.23.png No edit summary current
• 19:1919:19, 11 July 2024 diff hist 0 N File:Bonnor1957Eq2.10.png No edit summary current
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• 19:1719:17, 11 July 2024 diff hist +1 SSC/StabilityEulerianPerspective →Summary and Combinations current
• 19:1619:16, 11 July 2024 diff hist 0 N File:JamesJeans1928Eq314.6.png No edit summary current
• 19:1619:16, 11 July 2024 diff hist 0 N File:Jeans1902Eq12.png No edit summary current
• 19:1519:15, 11 July 2024 diff hist 0 N File:Jeans1902Title.png No edit summary current
• 19:1119:11, 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..."
• 19:0719:07, 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..."
• 19:0719:07, 11 July 2024 diff hist 0 N File:Whitworth1981Eq5.jpg No edit summary current
• 19:0419:04, 11 July 2024 diff hist 0 N File:WhitworthScalingText.png No edit summary current