User contributions for Joel2

15 July 2024

• 19:0619:06, 15 July 2024 diff hist 0 N File:ModelB2thirdAnnotated.png No edit summary current
• 19:0619:06, 15 July 2024 diff hist 0 N File:ModelB2secondAnnotated.png No edit summary current
• 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
• 18:3418:34, 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
• 18:3218:32, 15 July 2024 diff hist 0 N File:DisplacementFunctionAModel2.png No edit summary current
• 18:3218:32, 15 July 2024 diff hist 0 N File:G0variationBipolytrope.png No edit summary current
• 18:3118:31, 15 July 2024 diff hist 0 N File:DensityPert51Core02.png No edit summary current
• 18:3018:30, 15 July 2024 diff hist 0 N File:FiniteDifferenceLAWE01.png No edit summary current
• 18:2618:26, 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
• 18:1718:17, 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
• 18:1018:10, 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
• 17:5817:58, 15 July 2024 diff hist 0 N File:FundModeLocations05Labels.png No edit summary current
• 17:5617:56, 15 July 2024 diff hist +67 SSC/Stability/BiPolytropes/51Models →Model Sequence:  μe/μc = 0.31 current
• 17:3217:32, 15 July 2024 diff hist 0 N File:Omega2for1stOvertone2.png No edit summary current
• 17:3117:31, 15 July 2024 diff hist 0 N File:Evolve031B.png No edit summary current
• 17:3117:31, 15 July 2024 diff hist 0 N File:FundModeLocations01Labels.png No edit summary current
• 17:2817:28, 15 July 2024 diff hist 0 N File:ConvectiveBoundary2Labeled.png No edit summary current
• 17:2717:27, 15 July 2024 diff hist 0 N File:FundModeLocations02Labels.png No edit summary current
• 17:2617:26, 15 July 2024 diff hist 0 N File:TurningPoints51Bpairing.png No edit summary current
• 17:2417:24, 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..."
• 17:2417:24, 15 July 2024 diff hist 0 N File:TurningPoints51BipolytropesLabels.png No edit summary current
• 17:2217:22, 15 July 2024 diff hist +113 Appendix/Ramblings →Ramblings
• 17:0817:08, 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
• 17:0617:06, 15 July 2024 diff hist 0 N File:Yabushita75MuRatio100MassesLabeled.png No edit summary current
• 17:0117:01, 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
• 16:5916:59, 15 July 2024 diff hist 0 N File:ModelC Fig3.png No edit summary current
• 16:5916:59, 15 July 2024 diff hist 0 N File:ModelC Table2.png No edit summary current
• 16:5816:58, 15 July 2024 diff hist 0 N File:ModelC Fig2.png No edit summary current
• 16:5716:57, 15 July 2024 diff hist 0 N File:ModelC Fig1.png No edit summary current
• 16:5716:57, 15 July 2024 diff hist 0 N File:ModelC Table1Again.png No edit summary current
• 16:5416:54, 15 July 2024 diff hist +66 Appendix/Ramblings →Ramblings
• 16:5116:51, 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
• 16:4816:48, 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..."
• 16:4616:46, 15 July 2024 diff hist 0 N File:Bipolytrope51Boundaries03b.png No edit summary current
• 16:4516:45, 15 July 2024 diff hist 0 N File:TangentTrialAnalytic51movie.gif No edit summary current
• 16:4416:44, 15 July 2024 diff hist 0 N File:Frame06good.png No edit summary current
• 16:4316:43, 15 July 2024 diff hist 0 N File:AnalyticAttempt2.png No edit summary current