User contributions for Joel2

18 July 2024

• 12:1912:19, 18 July 2024 diff hist 0 N File:N35SequenceA.png No edit summary current
• 12:1712:17, 18 July 2024 diff hist 0 N File:N305SequenceA.png No edit summary current
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• 12:1512:15, 18 July 2024 diff hist 0 N File:N25SequenceA.png No edit summary current
• 12:1212:12, 18 July 2024 diff hist +25 SSC/Structure/Polytropes/Numerical →Tabulated Global Properties current

17 July 2024

• 17:3717:37, 17 July 2024 diff hist +3 SSC/Structure/Lane1870 →SEGMENT III
• 17:2917:29, 17 July 2024 diff hist +229 SSC/Structure/Lane1870 No edit summary
• 13:4513:45, 17 July 2024 diff hist −28 SSC/FreeEnergy/PowerPoint →Case M Equilibrium Conditions current
• 13:4013:40, 17 July 2024 diff hist +79 Appendix/Ramblings →Ramblings
• 13:3413:34, 17 July 2024 diff hist −1 SSC/FreeEnergy/PowerPoint →Basic Properties
• 13:3313:33, 17 July 2024 diff hist −14 SSC/FreeEnergy/PowerPoint →Coincidence Between Points of Secular and Dynamical Instability
• 13:3313:33, 17 July 2024 diff hist −56 SSC/FreeEnergy/PowerPoint →Basic Properties
• 13:3013:30, 17 July 2024 diff hist −26 SSC/FreeEnergy/PowerPoint →Case P Equilibrium Conditions
• 13:2613:26, 17 July 2024 diff hist −67 SSC/FreeEnergy/PowerPoint →Case M Equilibrium Conditions
• 13:2413:24, 17 July 2024 diff hist −123 SSC/FreeEnergy/PowerPoint No edit summary
• 13:1013:10, 17 July 2024 diff hist +61,190 N SSC/FreeEnergy/PowerPoint Created page with "__FORCETOC__ =Supporting Derivations for Free-Energy PowerPoint Presentation= The derivations presented here are an extension of our accompanying free-energy synopsis. These additional details proved to be helpful while developing an overarching PowerPoint presentation. {{LSU_HBook_header}} ==General Free-Energy Expression== We're considering a free-energy function of the following form: <div a..."
• 12:4212:42, 17 July 2024 diff hist 0 N File:N500SequenceB.png No edit summary current
• 12:4112:41, 17 July 2024 diff hist 0 N File:WolframN5polytropeMass.jpg No edit summary current
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• 12:3712:37, 17 July 2024 diff hist 0 N File:WolframN1polytropeMass.jpg No edit summary current
• 11:5211:52, 17 July 2024 diff hist 0 N File:Lane1870Diagram0.png No edit summary current
• 11:3811:38, 17 July 2024 diff hist −132 SSC/Virial/PolytropesSummary →When ~\eta_\mathrm{ad} is zero current
• 11:3311:33, 17 July 2024 diff hist −32 SSC/Virial/PolytropesSummary →Physical Meaning of Parameter ηad ~\eta_\mathrm{ad}

16 July 2024

• 16:4116:41, 16 July 2024 diff hist −39 SSC/Structure/PolytropesEmbedded/Other →Related Discussions current
• 16:3716:37, 16 July 2024 diff hist −18 SSC/Virial/PolytropesSummary →Physical Meaning of Parameter ~\eta_\mathrm{ad}
• 16:2816:28, 16 July 2024 diff hist 0 N File:KimuraEq01.png No edit summary current
• 16:2716:27, 16 July 2024 diff hist 0 N File:KimuraEq00.png No edit summary current
• 16:2716:27, 16 July 2024 diff hist 0 N File:HoredtEq01.png No edit summary current
• 16:2616:26, 16 July 2024 diff hist 0 N File:HoredtEq00.png No edit summary current
• 16:1316:13, 16 July 2024 diff hist +4,153 N Appendix/Ramblings/Interrelating51and00Bipolytropes/Organization Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Interrelating (5, 1) and (0, 0) Bipolytropes= ==Structure of (n_c, n_e) = (0, 0) Bipolytropes== Here we draw heavily from an accompanying discussion to construct a bipolytrope in which both the core and the envelope have uniform densities, that is, the structure of both the core and the envelope will be modeled us..." current

15 July 2024

• 19:0819:08, 15 July 2024 diff hist +67,533 N Appendix/Ramblings/51BiPolytropeStability/RethinkEnvelope Created page with "__FORCETOC__ =Rethink Handling of n = 1 Envelope= ==Solution Steps== Drawing from an accompanying discussion … * Step 1: Choose <math>n_c</math> and <math>n_e</math>. * Step 2: Adopt boundary conditions at the center of the core (<math>\theta = 1</math> and <math>d\theta/d\xi = 0</math> at <math>\xi=0</math>), then solve the Lane-Emden equation to obtain the solution, <math>\theta(\xi)</math>, and its first derivati..." current
• 19:0719:07, 15 July 2024 diff hist 0 N File:QnuPlotB2annotated.png No edit summary current
• 19:0719:07, 15 July 2024 diff hist 0 N File:ModelB2fourthAnnotated.png No edit summary current
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• 19:0619:06, 15 July 2024 diff hist 0 N File:ModelB2firstAnnotated.png No edit summary current
• 19:0419:04, 15 July 2024 diff hist 0 N File:PhiVSmu.png No edit summary current
• 19:0319:03, 15 July 2024 diff hist 0 N File:PhsVSdelta.png No edit summary current
• 19:0119:01, 15 July 2024 diff hist +1,144 N Appendix/Ramblings/51BiPolytropeStability/CleanMethodicalExaminatioin Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Radial Oscillations of Polytropic Spheres= ===Adiabatic (Polytropic) Wave Equation=== Copied from here … 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> =BiPolytrope..." current
• 18:5818:58, 15 July 2024 diff hist 0 N File:EigenfunctionCorrected.png No edit summary current
• 18:5718:57, 15 July 2024 diff hist 0 N File:MinMassProfile0.25.png No edit summary current
• 18:5618:56, 15 July 2024 diff hist −3 SSC/Stability/BiPolytropes/HeadScratching →Rethink Evolution and Stability current
• 18:5518:55, 15 July 2024 diff hist 0 N File:NuVq0.25B.png No edit summary current
• 18:5418:54, 15 July 2024 diff hist 0 N File:MassVradius0.25B.png No edit summary current
• 18:5218:52, 15 July 2024 diff hist 0 N File:EigenvectorStability.png No edit summary current
• 18:4818:48, 15 July 2024 diff hist +106 Appendix/Ramblings No edit summary
• 18:4718:47, 15 July 2024 diff hist +73,349 N SSC/Stability/BiPolytropes/HeadScratching Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Broader Examination of Bipolytrope Stability= <!-- 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).--> {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: b..."
• 18:3918:39, 15 July 2024 diff hist +26,578 N Appendix/Ramblings/51BiPolytropeStability/NoAnalytic Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Analog of Bonnor-Ebert Limiting Pressure= As has been demonstrated in an accompanying discussion, the mass of a pressure-truncated, n = 5 polytrope is, <table border="0" align="center" cellpadding="5"> <tr> <td align="right"> <math>\frac{M}{M_\mathrm{SWS}} </math> </td> <td align="center"><math>=</math></td> <td align="left"> <math> \biggl[ \biggl( \f..." current
• 18:3818:38, 15 July 2024 diff hist +10,610 N Appendix/Ramblings/51AnalyticStabilitySynopsis Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =More Focused Search for Analytic EigenVector of (5,1) Bipolytropes= The ideas that are captured in this chapter have arisen after a review of a previous hunt for the desired analytic eigenvector and as an extension of our SSC/Structure/BiPolytropes/Analytic51Renormalize|accompanying "renormalization" of the A..." current