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10:45, 9 January 2024 Joel2 talk contribs uploaded File:N5Truncated2.gif
10:44, 9 January 2024 Joel2 talk contribs created page File:OurImprovedSummary2.png
10:44, 9 January 2024 Joel2 talk contribs uploaded File:OurImprovedSummary2.png
10:43, 9 January 2024 Joel2 talk contribs created page File:N1osc06.gif
10:43, 9 January 2024 Joel2 talk contribs uploaded File:N1osc06.gif
16:54, 8 January 2024 Joel2 talk contribs created page File:VariationOf2Modes.png
16:54, 8 January 2024 Joel2 talk contribs uploaded File:VariationOf2Modes.png
16:48, 8 January 2024 Joel2 talk contribs created page File:FourModesMuRatio100.png
16:48, 8 January 2024 Joel2 talk contribs uploaded File:FourModesMuRatio100.png
16:46, 8 January 2024 Joel2 talk contribs created page File:NEWCompositeDlabeled.png
16:46, 8 January 2024 Joel2 talk contribs uploaded File:NEWCompositeDlabeled.png
16:45, 8 January 2024 Joel2 talk contribs created page File:Mod0MuRatio100.png
16:45, 8 January 2024 Joel2 talk contribs uploaded File:Mod0MuRatio100.png
16:44, 8 January 2024 Joel2 talk contribs created page File:Mode0EigenfunctionsCombinedSmall.png
16:44, 8 January 2024 Joel2 talk contribs uploaded File:Mode0EigenfunctionsCombinedSmall.png
15:15, 8 January 2024 Joel2 talk contribs created page SSC/Stability/BiPolytropes/Pt2 (Created page with "=Review of the Analysis by Murphy & Fiedler (1985b)= As we have detailed separately, the boundary condition at the center of a polytropic configuration is, <div align="center"> <math>\frac{dx}{d\xi} \biggr|_{\xi=0} = 0 \, ;</math> </div> and the boundary condition at the surface of an isolated polytropic configuration is, <table border="0" cellpadding="5" align="center"> <tr> <td align="right"> <math>\frac{d\ln x}{...")
15:09, 8 January 2024 Joel2 talk contribs created page SSC/Stability/BiPolytropes/Pt3 (Created page with "=Radial Oscillations of (n<sub>c</sub>, n<sub>e</sub>) = (5, 1) Models= ==Foundation== In an accompanying discussion, we derived the so-called, <div align="center" id="2ndOrderODE"> <font color="#770000">'''Adiabatic Wave''' (or ''Radial Pulsation'') '''Equation'''</font><br /> {{Math/EQ_RadialPulsation01}} </div> whose solution gives eigenfunctions that describe various radial modes of oscillation in spherically symmetric, self-gravi...")
14:53, 8 January 2024 Joel2 talk contribs created page SSC/Stability/BiPolytropes/Pt4 (Created page with " =Reconciliation= <table border="0" cellpadding="8" align="right"> <tr> <th align="center">Figure 7: Conflicting Instability Regions</th> </tr> <tr> <td align="center" colspan="10">400px|Marginally unstable models</td> </tr> </table> Figure 7, shown here on the right, is identical to the right-hand panel of Figure 4, as displayed above. From a standard global, free-energy analysis — such as the one #Virial_Sta...")
19:26, 3 January 2024 Joel2 talk contribs created page File:Sterne1937CritGamma1.png
19:26, 3 January 2024 Joel2 talk contribs uploaded File:Sterne1937CritGamma1.png
19:21, 3 January 2024 Joel2 talk contribs created page SSC/Stability/GammaVariation (Created page with "=How Does Stability Change with γ<sub>g</sub>?= ==Isolated Uniform-Density Configuration== =How Does Stability Change with P<sub>e</sub>?=")
19:02, 3 January 2024 Joel2 talk contribs created page SSC/Structure/OtherAnalyticRamblings (Created page with "__FORCETOC__  =Ramblings Regarding the Stability of Other Analytically Definable, Spherical Equilibrium Models= The material presented in this chapter was originally developed as a subsection of a chapter that discusses "Other" Analytic Equilibrium Models." {{ SGFworkInProgress }} ===Generic Setup===")
18:53, 3 January 2024 Joel2 talk contribs created page SSC/Structure/OtherAnalyticModels (Created page with "__FORCETOC__  =Other Analytically Definable, Spherical Equilibrium Models= ==Linear Density Distribution== In an article titled, "A Survey with Analytic Models," {{ Stein66full }} defines the "Linear Stellar Model" as a star whose density "varies linearly from the center to the surface," that is (see his equation 3.1), <div align="center"> <math>\rho(r) = \rho_c\biggl( 1 - \frac{r}{R} \biggr) \, ,</math> </div> where, <math>~\rho_c</...")
18:47, 3 January 2024 Joel2 talk contribs created page Appendix/Ramblings/NonlinarOscillation (Created page with "__FORCETOC__  =Radial Oscillations in Pressure-Truncated n = 5 Polytropes= <table border="1" width="90%" align="center" cellpadding="15"> <tr><td align="center"> <table border="0" cellpadding="8"> <tr><td align="center"> <font size="+2"><b>Summary</b></font><br />Joel E. Tohline (May, 2017) </td></tr> <tr><td align="center"> <table border="0" width="80%" align="center" cellpadding="0"> <tr><td align="left"> <font color="darkgreen">"… a static c...")
18:41, 3 January 2024 Joel2 talk contribs created page SSC/Stability/NeutralMode (Created page with "__FORCETOC__  =LAWE= ==Most General Form== In an accompanying discussion, we derived the so-called, <div align="center" id="2ndOrderODE"> <font color="#770000">'''Adiabatic Wave''' (or ''Radial Pulsation'') '''Equation'''</font><br /> {{Math/EQ_RadialPulsation01}} </div> <!-- <div align="center" id="2ndOrderODE"> <font color="#770000">'''Adiabatic Wave Equation'''</font><br /> <math> \frac{d^2x}{...")
18:34, 3 January 2024 Joel2 talk contribs created page File:Hologram2004.JPG
18:34, 3 January 2024 Joel2 talk contribs uploaded File:Hologram2004.JPG
18:29, 3 January 2024 Joel2 talk contribs created page Appendix/Ramblings (Created page with "__FORCETOC__  =Ramblings= Sometimes I explore some ideas to a sufficient depth that it seems worthwhile for me to archive the technical derivations even if the idea itself does not immediately produce a publishable result. This page, which has a simple outline layout, provides links to these various pages of technical notes. <ol> <li>Files on LSU P&A servers (myPhys)</li> <li>Orthogonal Curvil...")
17:32, 3 January 2024 Joel2 talk contribs created page File:WolframAlphaCubicSolver.png
17:32, 3 January 2024 Joel2 talk contribs uploaded File:WolframAlphaCubicSolver.png
17:20, 3 January 2024 Joel2 talk contribs created page File:PlotTheta5F.png
17:20, 3 January 2024 Joel2 talk contribs uploaded File:PlotTheta5F.png
17:09, 3 January 2024 Joel2 talk contribs created page Template:Srivastava62hereafter (Created page with "Srivastava62")
17:08, 3 January 2024 Joel2 talk contribs created page Template:Srivastava62full (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/1962ApJ...136..680S/abstract S. Srivastava (1962, ApJ, Vol. 136, pp. 680 - 681)]")
17:06, 3 January 2024 Joel2 talk contribs created page Template:Srivastava62figure (Created page with "[https://ui.adsabs.harvard.edu/abs/1962ApJ...136..680S/abstract S. Srivastava (1962)]<br />''A New Solution of the Lane-Emden Equation of Index n = 5''<br /> The Astrophysical Journal, Vol. 136, pp. 680 - 681")
17:03, 3 January 2024 Joel2 talk contribs created page Template:Srivastava62 (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/1962ApJ...136..680S/abstract Srivastava (1962)]")
14:53, 3 January 2024 Joel2 talk contribs created page Template:MF85ahereafter (Created page with "MF85a")
14:53, 3 January 2024 Joel2 talk contribs created page Template:MF85afull (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/1985PASA....6..219M/abstract J. O. Murphy & R. Fiedler (1985a, Proc. Astron. Soc. Australia, Vol. 6, no. 2, pp. 219 - 222)]")
14:51, 3 January 2024 Joel2 talk contribs created page Template:MF85afigure (Created page with "[https://ui.adsabs.harvard.edu/abs/1985PASA....6..219M/abstract J. O. Murphy & R. Fiedler (1985)]<br />''Physical Structure of a Sequence of Two Zone Polytropic Stellar Models''<br />Proceedings of the Astronomical Society of Australia, Vol. 6, no. 2, pp. 219 - 222")
14:48, 3 January 2024 Joel2 talk contribs created page Template:MF85a (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/1985PASA....6..219M/abstract Murphy & Fiedler (1985a)]")
18:02, 2 January 2024 Joel2 talk contribs created page Template:Murphy83ahereafter (Created page with "Murphy83a")
18:01, 2 January 2024 Joel2 talk contribs created page Template:Murphy83afull (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/1983PASA....5..175M/abstract J. O. Murphy (1983a, Proc. Astron. Soc. Australia, Vol. 5, no. 2, pp. 175 - 179)]")
17:58, 2 January 2024 Joel2 talk contribs created page Template:Murphy83afigure (Created page with "[https://ui.adsabs.harvard.edu/abs/1983PASA....5..175M/abstract J. O. Murphy (1983)]<br />''Composite Analytical Solutions of the Lane-Emden Equation with Polytropic Indices n = 1 and n = 5''<br />Proceedings of the Astronomical Society of Australia, Vol. 5, no. 2, pp. 175 - 179")
17:54, 2 January 2024 Joel2 talk contribs created page Template:Murphy83a (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/1983PASA....5..175M/abstract Murphy (1983a)]")
17:45, 2 January 2024 Joel2 talk contribs created page Template:MF85bhereafter (Created page with "MF85b")
17:45, 2 January 2024 Joel2 talk contribs created page Template:MF85bfull (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/1985PASA....6..222M/abstract J. O. Murphy & R. Fiedler (1985b, Proc. Astron. Soc. Australia, Vol. 6, no. 2, pp. 222 - 226)]")
17:44, 2 January 2024 Joel2 talk contribs created page Template:MF85bfigure (Created page with "[https://ui.adsabs.harvard.edu/abs/1985PASA....6..222M/abstract J. O. Murphy & R. Fiedler (1985)]<br />''Radial Pulsations and Vibrational Stability of a Sequence of Two Zone Polytropic Stellar Models''<br />Proceedings of the Astronomical Society of Australia, Vol. 6, no. 2, pp. 222 - 226")
17:43, 2 January 2024 Joel2 talk contribs created page Template:MF85b (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/1985PASA....6..222M/abstract Murphy & Fiedler (1985b)]")
22:54, 31 December 2023 Joel2 talk contribs created page File:PresXi30.jpg
22:54, 31 December 2023 Joel2 talk contribs uploaded File:PresXi30.jpg

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