User contributions for Joel2

16 July 2024

• 17:2817:28, 16 July 2024 diff hist 0 N File:KimuraEq01.png No edit summary current
• 17:2717:27, 16 July 2024 diff hist 0 N File:KimuraEq00.png No edit summary current
• 17:2717:27, 16 July 2024 diff hist 0 N File:HoredtEq01.png No edit summary current
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• 17:1317:13, 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

• 20:0820:08, 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
• 20:0720:07, 15 July 2024 diff hist 0 N File:QnuPlotB2annotated.png No edit summary current
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• 20:0420:04, 15 July 2024 diff hist 0 N File:PhiVSmu.png No edit summary current
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• 20:0120:01, 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
• 19:5819:58, 15 July 2024 diff hist 0 N File:EigenfunctionCorrected.png No edit summary current
• 19:5719:57, 15 July 2024 diff hist 0 N File:MinMassProfile0.25.png No edit summary current
• 19:5619:56, 15 July 2024 diff hist −3 SSC/Stability/BiPolytropes/HeadScratching →Rethink Evolution and Stability current
• 19:5519:55, 15 July 2024 diff hist 0 N File:NuVq0.25B.png No edit summary current
• 19:5419:54, 15 July 2024 diff hist 0 N File:MassVradius0.25B.png No edit summary current
• 19:5219:52, 15 July 2024 diff hist 0 N File:EigenvectorStability.png No edit summary current
• 19:4819:48, 15 July 2024 diff hist +106 Appendix/Ramblings No edit summary
• 19:4719:47, 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..."
• 19:3919:39, 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
• 19:3819:38, 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
• 19:3419:34, 15 July 2024 diff hist +97,020 N SSC/Structure/BiPolytropes/AnalyzeStepFunction Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =More Careful Examination of Step Function Behavior= The ideas that are captured in this chapter have arisen as an extension of our accompanying "renormalization" of the Analytic51 bipolytrope. ==Discontinuous Density Distribution== ===Expectations=== From among the set of SSC/Perturbations#Governing_Equatio..." current
• 19:3219:32, 15 July 2024 diff hist 0 N File:DisplacementFunctionAModel2.png No edit summary current
• 19:3219:32, 15 July 2024 diff hist 0 N File:G0variationBipolytrope.png No edit summary current
• 19:3119:31, 15 July 2024 diff hist 0 N File:DensityPert51Core02.png No edit summary current
• 19:3019:30, 15 July 2024 diff hist 0 N File:FiniteDifferenceLAWE01.png No edit summary current
• 19:2619:26, 15 July 2024 diff hist +97,233 N Appendix/Ramblings/51BiPolytropeStability/BetterInterface Created page with "__FORCETOC__ =Better Interface for 51BiPolytrope Stability Study= ==Content Pointing to Previous Work== ===Tilded Menu Pointers=== <ol type="I"> <li>Murphy & Fiedler (1985b): SSC/Stability/MurphyFiedler85 <ol type="A"><li>Interface Conditions as promoted by Ledoux & Walraven (1958)</li> <li>SSC/Stability/MurphyFiedler85#Numerical_Integration|Numerical Int..." current
• 19:1719:17, 15 July 2024 diff hist +110,273 N Appendix/Ramblings/51BiPolytropeStability/BetterInterfacePt2 Created page with "__FORCETOC__ =Better Interface for 51BiPolytrope Stability Study= This is Part 2 of an extended chapter discussion. For Part 1, go here. ==Discretize for Numerical Integration (continued)== ===General Discretization=== ====Fourth Approximation==== Let's assume that we know the four quantities, <math>x_{J-1}, x_J,(x_J)^' \equiv (dx/d\tilde{r})_J</math>, and <math>(x_{J-1})^' \equiv (dx/d\tilde{r})_{J-1}</ma..." current
• 19:1019:10, 15 July 2024 diff hist +22,319 N SSC/Stability/BiPolytropes/SuccinctDiscussion Created page with "__FORCETOC__ =BiPolytrope with n_c = 5 and n_e = 1= Here we construct and analyze the relative stability of a bipolytrope in which the core has an <math>n_c=5</math> polytropic index and the envelope has an <math>n_e=1</math> polytropic index. ==Structure== <ol> <li>Individual model profiles, taken from: <ul><li>SSC/Structure/BiPolytropes/Analytic51#Examples|SSC/Structure/BiPolytropes/Analyti..." current
• 18:5818:58, 15 July 2024 diff hist 0 N File:FundModeLocations05Labels.png No edit summary current
• 18:5618:56, 15 July 2024 diff hist +67 SSC/Stability/BiPolytropes/51Models →Model Sequence:  μe/μc = 0.31 current
• 18:3218:32, 15 July 2024 diff hist 0 N File:Omega2for1stOvertone2.png No edit summary current
• 18:3118:31, 15 July 2024 diff hist 0 N File:Evolve031B.png No edit summary current
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• 18:2818:28, 15 July 2024 diff hist 0 N File:ConvectiveBoundary2Labeled.png No edit summary current
• 18:2718:27, 15 July 2024 diff hist 0 N File:FundModeLocations02Labels.png No edit summary current
• 18:2618:26, 15 July 2024 diff hist 0 N File:TurningPoints51Bpairing.png No edit summary current
• 18:2418:24, 15 July 2024 diff hist +48,935 N SSC/Stability/BiPolytropes/51Models Created page with "__FORCETOC__ =BiPolytrope with n_c = 5 and n_e = 1= Here we construct and analyze the relative stability of a bipolytrope in which the core has an <math>n_c=5</math> polytropic index and the envelope has an <math>n_e=1</math> polytropic index. ==Structure== <ol> <li>Individual model profiles, taken from: <ul><li>SSC/Structure/BiPolytropes/Analytic51#Examples|SSC/Structure/BiPolytropes/Analyti..."
• 18:2418:24, 15 July 2024 diff hist 0 N File:TurningPoints51BipolytropesLabels.png No edit summary current
• 18:2218:22, 15 July 2024 diff hist +113 Appendix/Ramblings →Ramblings
• 18:0818:08, 15 July 2024 diff hist +42,762 N SSC/Structure/BiPolytropes/51RenormaizePart3 Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =BiPolytrope with n_c = 5 and n_e = 1= After studying {{ Yabushita75full }} in depth, here we renormalize our original construction of bipolytropic models with <math>(n_c, n_e) = (5, 1)</math> such that both entropy values, <math>(K_c, K_e)</math>, are held fixed along each model sequence. ==Original Derivation== ===Throughout the Core=== Drawing from our..." current
• 18:0618:06, 15 July 2024 diff hist 0 N File:Yabushita75MuRatio100MassesLabeled.png No edit summary current
• 18:0118:01, 15 July 2024 diff hist +82,843 N SSC/Structure/BiPolytropes/51RenormaizePart2 Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Radial Oscillations in (n_c,n_e) = (5,1) Bipolytropes= Logically, this chapter extends the discussion — specifically the subsection titled, ''Try Again'' — found in the "Ramblings" chapter in which we introduced a total-mass-based renormalization of models along sequences of <math>(n_c, n_e) = (5, 1)</math> bipolytropes. ==B..." current
• 17:5917:59, 15 July 2024 diff hist 0 N File:ModelC Fig3.png No edit summary current
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• 17:5817:58, 15 July 2024 diff hist 0 N File:ModelC Fig2.png No edit summary current
• 17:5717:57, 15 July 2024 diff hist 0 N File:ModelC Fig1.png No edit summary current