User contributions for Joel2

10 January 2024

• 22:1922:19, 10 January 2024 diff hist 0 N File:Figure s.ps.png No edit summary current
• 22:1822:18, 10 January 2024 diff hist +74,321 N SSC/Stability/MurphyFiedler85 Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Review of the BiPolytrope Stability Analysis by Murphy & Fiedler (1985b)= ==Overview== In the stability analysis presented by [http://adsabs.harvard.edu/abs/1985PASAu...6..222M Murphy & Fiedler (1985b)], the relevant polytropic indexes are, <math>~(n_c, n_e) = (1,5)</math>. Structural properties of the underlying equilibrium models have been reviewed in SSC/Structure/BiPolytropes/Analytic15#BiPolytrope_with..." current
• 22:1222:12, 10 January 2024 diff hist +86,533 N Appendix/Ramblings/PatrickMotl Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Discussing Patrick Motl's 2019 - 2020 Simulations= ==May 1 (from Patrick)== <table border="1" cellpadding="10" width="60%" align="center"><tr><td align="left"> Hi Joel, I hope things are well for you and yours. I did finally have a couple research students this semester that were able to slog their way into unix, programming, etc. far enough to do some useful things. They ran two spherical bipolytropes with my ol..."
• 22:0922:09, 10 January 2024 diff hist +36,042 N SSC/Stability/UniformDensity Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =The Stability of Uniform-Density Spheres= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffeeee;" | <font size="-1"><b>Sterne's<br />Analytic Sol'n<br />of Eigenvalue<br />Problem</b><br />(1937)<..." current
• 17:4017:40, 10 January 2024 diff hist +26 SSC/Stability/GammaVariation →Comments on Uniform-Density Configurations
• 17:3917:39, 10 January 2024 diff hist +1,899 SSC/Stability/GammaVariation →Comments on Uniform-Density Configurations
• 16:5516:55, 10 January 2024 diff hist +432 SSC/Stability/GammaVariation →Entropy Distribution

9 January 2024

• 19:1619:16, 9 January 2024 diff hist +1,462 SSC/Stability/GammaVariation No edit summary
• 18:2918:29, 9 January 2024 diff hist +102 SSC/Stability/GammaVariation →The Sterne37 Solution
• 18:2218:22, 9 January 2024 diff hist 0 N File:Sterne37OmegaVsGammaLabeled.png No edit summary current
• 13:0713:07, 9 January 2024 diff hist −7 Appendix/References →TVH74
• 13:0613:06, 9 January 2024 diff hist +35 N Template:TVH74hereafter Created page with "TVH74" current
• 13:0513:05, 9 January 2024 diff hist +181 N Template:TVH74full Created page with "📚 [https://ui.adsabs.harvard.edu/abs/1974MNRAS.168..427T/abstract L. G. Taff, & H. M. van Horn (1974, MNRAS, Vol. 168, pp. 427 - 432)]" current
• 13:0413:04, 9 January 2024 diff hist +249 N Template:TVH74figure Created page with "[https://ui.adsabs.harvard.edu/abs/1974MNRAS.168..427T/abstract L. G. Taff, & H. M. van Horn (1974)]<br />''Radial Pulsations of Finite Isothermal Gas Spheres''<br />Monthly Notices of the Royal Astronomical Society,<br />Vol. 168, pp. 427 - 432" current
• 13:0213:02, 9 January 2024 diff hist +137 N Template:TVH74 Created page with "📚 [https://ui.adsabs.harvard.edu/abs/1974MNRAS.168..427T/abstract Taff, & van Horn (1974)]" current
• 12:5212:52, 9 January 2024 diff hist +129,131 N SSC/Stability/Isothermal Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Radial Oscillations of Pressure-Truncated Isothermal Spheres= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:white;" | <font size="-1"><b>via<br />Direct<br />Numerical<br />Integration</b></font> |} ==Overview== Both {{ Ebert55full }} and {{ Bonnor56f..." current
• 12:4612:46, 9 January 2024 diff hist +108,000 N SSC/Stability/n5PolytropeLAWE Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Radial Oscillations of n = 5 Polytropic Spheres= ==Background== ===General Form of the LAWE for Spherical Polytropes=== 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 eigenfunction..." current
• 12:4312:43, 9 January 2024 diff hist +50,018 N SSC/Stability/n3PolytropeLAWE Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Radial Oscillations of n = 3 Polytropic Spheres= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:white;" | <font size="-1"><b>Isolated<br />n = 3<br />Polytrope</b></font> |} ==Background==  <br />  <br />  <br />  <br /> ===Our..." current
• 12:3912:39, 9 January 2024 diff hist +4 Template:LAWEsolutions No edit summary current
• 12:2812:28, 9 January 2024 diff hist −2 SSC/Structure/BiPolytropes/Analytic51Renormalize/Pt2 →BiPolytrope with (nc, ne) = (5, 1) Renormalized
• 12:2412:24, 9 January 2024 diff hist +51,912 N SSC/Structure/BiPolytropes/Analytic51Renormalize Created page with "__FORCETOC__ =BiPolytrope with (n_c, n_e) = (5, 1) Renormalized= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"><br />Part I:   (5, 1) Analytic Renormalize<br /> </td> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"><br />SSC/Structure/BiPolytropes/Analytic51Renormalize/Pt2|Part II:  E..." current
• 12:2312:23, 9 January 2024 diff hist +71,790 N SSC/Structure/BiPolytropes/Analytic51Renormalize/Pt2 Created page with "__FORCETOC__ =BiPolytrope with (n_c, n_e) = (5, 1) Renormalized= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"><br />Part I:   (5, 1) Analytic Renormalize<br /> </td> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"><br />SSC/Structure/BiPolytropes/Analytic51Renormalize/Pt2|Part II:  E..."
• 12:1312:13, 9 January 2024 diff hist +27,514 SSC/Structure/BiPolytropes/Analytic51Renormalize/Pt3 No edit summary current
• 12:0812:08, 9 January 2024 diff hist +688 N SSC/Structure/BiPolytropes/Analytic51Renormalize/Pt3 Created page with "__FORCETOC__ =BiPolytrope with (n_c, n_e) = (5, 1) Renormalized= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"><br />Part I:   (5, 1) Analytic Renormalize<br /> </td> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"><br />SSC/Structure/BiPolytropes/Analytic51Renormalize/Pt2|Part II:  E..."
• 11:5111:51, 9 January 2024 diff hist +92,622 N Appendix/Ramblings/OriginOfPlanetaryNebulae Created page with "<!-- __FORCETOC__ will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =On the Origin of Planetary Nebulae= This chapter — initially created by J. E. Tohline on 19 November 2016 — is intended primarily to provide a summary of the research that has been undertaken following <font color="red">a discussion that took place on 3 July 2013</font> with Kundan Kadam (an LSU graduate student, at the time) regarding the stability of..." current
• 11:4711:47, 9 January 2024 diff hist +1,349 N SSC/Stability/BiPolytropes/Index Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Organizational Index= This index helps organize and summarize the insight that we have gained from our broad investigation into the relative stability of spherically symmetric bipolytropic configurations. The most relevant summary chapter is named, SSC/Stability/BiPolytropes. ==Motivation== Schönberg-Chandrasekhar mass limit: <ul> <li> SSC/Structure/LimitingMasses#Schönberg-C..." current
• 11:4611:46, 9 January 2024 diff hist +2,963 N Template:LAWEsolutions Created page with "<table border="1" align="center" cellpadding="5"> <tr> <td align="center" colspan="3"><b>Isolated n = 1 Polytrope</b></td> </tr> <tr> <td align="center" rowspan="2"><math>\gamma_g = (n+1)/n = 2</math><br /><p><br /><p><br />250px|n = 1 Eigenvectors</td> <td align="center" rowspan="2"><math>\gamma_g = \tfrac{5}{3}</math><br />250px|n = 1 Eigenvectors</td> <td align="left">Key Reference(s): <ul><li>{{ Chatterj..."
• 11:4511:45, 9 January 2024 diff hist 0 N File:N5Truncated2.gif No edit summary current
• 11:4411:44, 9 January 2024 diff hist 0 N File:OurImprovedSummary2.png No edit summary current
• 11:4311:43, 9 January 2024 diff hist 0 N File:N1osc06.gif No edit summary current

8 January 2024

• 18:5118:51, 8 January 2024 diff hist +3,298 SSC/Stability/GammaVariation No edit summary
• 18:4218:42, 8 January 2024 diff hist +1,439 SSC/Stability/BiPolytropes/Pt3 →MuRatio 0.310
• 18:2918:29, 8 January 2024 diff hist +345 SSC/Stability/BiPolytropes/Pt3 →MuRatio 0.310
• 18:2418:24, 8 January 2024 diff hist +702 SSC/Stability/BiPolytropes/Pt3 →MuRatio 0.310
• 18:1018:10, 8 January 2024 diff hist +169 SSC/Stability/BiPolytropes/Pt3 →MuRatio 0.310
• 18:0618:06, 8 January 2024 diff hist +397 SSC/Stability/BiPolytropes/Pt3 →MuRatio 0.310
• 17:5917:59, 8 January 2024 diff hist +104 SSC/Stability/BiPolytropes/Pt3 →Other Modes
• 17:5417:54, 8 January 2024 diff hist 0 N File:VariationOf2Modes.png No edit summary current
• 17:4817:48, 8 January 2024 diff hist 0 N File:FourModesMuRatio100.png No edit summary current
• 17:4617:46, 8 January 2024 diff hist 0 N File:NEWCompositeDlabeled.png No edit summary current
• 17:4517:45, 8 January 2024 diff hist 0 N File:Mod0MuRatio100.png No edit summary current
• 17:4417:44, 8 January 2024 diff hist 0 N File:Mode0EigenfunctionsCombinedSmall.png No edit summary current
• 16:2116:21, 8 January 2024 diff hist +662 SSC/Stability/BiPolytropes/Pt4 No edit summary
• 16:2016:20, 8 January 2024 diff hist +663 SSC/Stability/BiPolytropes/Pt3 →Radial Oscillations of (nc, ne) = (5, 1) Models
• 16:2016:20, 8 January 2024 diff hist +662 SSC/Stability/BiPolytropes/Pt2 No edit summary
• 16:1716:17, 8 January 2024 diff hist +4 SSC/Stability/BiPolytropes →Organizational Index
• 16:1716:17, 8 January 2024 diff hist −10,869 SSC/Stability/BiPolytropes →Review of the Analysis by Murphy & Fiedler (1985b)
• 16:1516:15, 8 January 2024 diff hist +10,884 N 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}{..."
• 16:0916:09, 8 January 2024 diff hist +58,200 N SSC/Stability/BiPolytropes/Pt3 Created page with "=Radial Oscillations of (n_c, n_e) = (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..."
• 16:0716:07, 8 January 2024 diff hist −58,185 SSC/Stability/BiPolytropes →Radial Oscillations of (nc, ne) = (5, 1) Models