User contributions for Joel2

18:3418:34, 15 July 2024 diff hist +97,020 N SSC/Structure/BiPolytropes/AnalyzeStepFunction Created page with "__FORCETOC__   =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
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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 nc = 5 and ne = 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
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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 nc = 5 and ne = 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__  =BiPolytrope with nc = 5 and ne = 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__  =Radial Oscillations in (nc,ne) = (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__  =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__  =Marginally Unstable (nc,ne) = (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
16:4216:42, 15 July 2024 diff hist 0 N File:AnalyticAttempt1.png No edit summary current
16:3816:38, 15 July 2024 diff hist +111,989 N Appendix/Ramblings/BiPolytropeStability Created page with "__FORCETOC__  =Ramblings: Marginally Unstable Bipolytropes= 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). ==Overview== <!-- <table border="0" cellpadding="8" align="right"> <tr> <th align="center">File:DataFileButton02.png|r..." current

18:3918:39, 14 July 2024 diff hist 0 N File:N5Sequence04B.png No edit summary current
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18:3718:37, 14 July 2024 diff hist 0 N File:N5Sequence01B.png No edit summary current
18:3518:35, 14 July 2024 diff hist 0 N File:Stahler1983TitlePage0.png No edit summary current
18:3418:34, 14 July 2024 diff hist 0 N File:Whitworth1981TitlePage0.png No edit summary current
18:3418:34, 14 July 2024 diff hist 0 N File:WhitworthFig1bCopy.jpg No edit summary current
18:3318:33, 14 July 2024 diff hist 0 N File:WhitworthPlot2.png No edit summary current
18:3218:32, 14 July 2024 diff hist 0 N File:Horedt EmbeddedPolytrope.png No edit summary current
18:3118:31, 14 July 2024 diff hist 0 N File:Horedt PRdiagram0.png No edit summary current
18:3018:30, 14 July 2024 diff hist 0 N File:HoredtPlot2.png No edit summary current
17:5117:51, 14 July 2024 diff hist +11 Appendix/Ramblings/T3CharacteristicVector →Implications current
17:4117:41, 14 July 2024 diff hist −10 Appendix/Ramblings/T3CharacteristicVector →Implications
17:3617:36, 14 July 2024 diff hist −13 Appendix/Ramblings/T3CharacteristicVector →Binney and Tremaine Formalism

User contributions for Joel2

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14 July 2024

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