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18:43, 21 June 2024 Joel2 talk contribs created page Template:LSU CT99CommonTheme1Awhite (Created page with "In §102 of a book titled, [https://www.amazon.com/Theory-Potential-W-D-Macmillan/dp/0486604861/ref=sr_1_2?s=books&ie=UTF8&qid=1503444466&sr=1-2&keywords=the+theory+of+the+potential ''The Theory of the Potential'', MacMillan (1958; originally, 1930)] derives an analytic expression for the gravitational potential of a uniform, infinitesimally thin, circular "hoop" of radius, <math>~a</math>. Throughout our related discussions, we generally will refer to this addition...")
18:41, 21 June 2024 Joel2 talk contribs created page Template:LSU CT99CommonTheme1 (Created page with "The gravitational potential (both inside and outside) of any axisymmetric mass distribution may be determined from the following integral expression that we will refer to as the, <div align="center"> '''Gravitational Potential of an Axisymmetric Mass Distribution (Version 1)''' {{ Math/EQ_CT99Axisymmetric }} </div> and, <math>~K(\mu)</math> is the complete elliptic integral of the first kind. This Key Equation† may be strai...")
18:38, 21 June 2024 Joel2 talk contribs created page AxisymmetricConfigurations/SolvingPE (Created page with "__FORCETOC__  =Common Theme: Determining the Gravitational Potential for Axisymmetric Mass Distributions= You have arrived at this page from our ''Tiled Menu'' by clicking on the chapter title that is also identified, below, by the light-blue-colored icon. You may proceed directly to that chapter by clicking (again) on that highlighted chapter icon. However, we have brought y...")
18:37, 21 June 2024 Joel2 talk contribs created page AxisymmetricConfigurations/HSCF (Created page with "__FORCETOC__  =Introduction= {| class="AxisymmetricConfigurations" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 150px; width: 150px; background-color:white;" |Hachisu Self- Consistent-Field [HSCF] Technique |} Text colored dark green has been extracted ''verbatim'' from...")
18:34, 21 June 2024 Joel2 talk contribs created page AxisymmetricConfigurations/Equilibria (Created page with "__FORCETOC__  =Axisymmetric Configurations (Steady-State Structures)= {| class="AxisymmetricConfigurations" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 150px; width: 150px; background-color:lightgreen;" |Constructing Steady-State Axisymmetric Configurations |} Equilibr...")
18:33, 21 June 2024 Joel2 talk contribs created page AxisymmetricConfigurations/PGE (Created page with "__FORCETOC__  =Axisymmetric Configurations (Governing Equations)= {| class="AxisymmetricConfigurationsPGE" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:lightgreen;" |PGEs for Axisymmetric Systems |} If the self-gravitating configura...")
18:32, 21 June 2024 Joel2 talk contribs created page AxisymmetricConfigurations/Storyline (Created page with "__FORCETOC__  =(Initially) Axisymmetric Configurations= {| class="AxisymmetricConfigurations" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 150px; width: 150px; background-color:black;" |Storyline |} <table border="0" cellpadding="3" align="center" width="60%"> <t...")
18:31, 21 June 2024 Joel2 talk contribs created page Apps/GoldreichWeber80 (Created page with "__FORCETOC__  =Homologously Collapsing Stellar Cores= {| class="n3Dynamics" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffff99;;" |Collapse of an Isolated n = 3Polytrope |} ==Review of Goldreich and Weber (1980)== This is principally a review of the...")
18:30, 21 June 2024 Joel2 talk contribs created page SSC/Dynamics/IsothermalSimilaritySolution (Created page with "__FORCETOC__  =Similarity Solution= {| class="IsothermalCollapse" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 150px; width: 150px; background-color:#ffff99;;" |Similarity Solution |} Much of the material in this chapter has been drawn from §4.1 of a [http://adsabs.harvard.edu/abs/1982FCPh.......")
18:28, 21 June 2024 Joel2 talk contribs created page SSC/Dynamics/IsothermalCollapse (Created page with "__FORCETOC__  =Collapse of Isothermal Spheres= {| class="IsothermalCollapse" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 150px; width: 150px; background-color:#ffff99;;" |Collapse of Isothermal Spheres |} <br /...")
18:23, 21 June 2024 Joel2 talk contribs created page SSC/Dynamics/FreeFall (Created page with "__FORCETOC__  =Free-Fall= {| class="PolytropeStability" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffff99;;" |Free-Fall Collapse |} In our broad study of the "dynamics of self-gravitating fluids," we are interested in examining how, in a wide variety of phys...")
18:19, 21 June 2024 Joel2 talk contribs created page SSC/StabilityConjecture/Bipolytrope51 (Created page with "__FORCETOC__ =Examine B-KB74 Conjecture in the Context of <math>(n_c, n_e) = (5 , 1)</math> Bipolytropes= {| 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;" |B-KB74 Conjecture RE: Bipolytrope (nc, ne) = (5, 1) |} In §6 of their paper, [...")
18:15, 21 June 2024 Joel2 talk contribs created page SSC/Stability/Yabushita75 (Created page with "__FORCETOC__  =Stability of a BiPolytrope with an Isothermal Core= This analysis pulls largely from {{ Yabushita75full }}; the focus is on bipolytropes having <math>(n_c, n_e) = (\infty, \tfrac{3}{2})</math>. In an accompanying discussion, we summarize the steps that Yabushita took — from 1968 and 1974, to 1975 — that led up to his discovery of an analytic description of the...")
22:24, 21 January 2024 Joel2 talk contribs created page SSC/Stability/Polytropes/Pt3 (Created page with "__FORCETOC__  =Radial Oscillations of Polytropic Spheres= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"> Part I: Wave Equation </td> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"> Part II: Boundary Conditions </td> <td align="...")
22:23, 21 January 2024 Joel2 talk contribs created page SSC/Stability/Polytropes/Pt2 (Created page with "__FORCETOC__  =Radial Oscillations of Polytropic Spheres= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"> Part I: Wave Equation </td> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"> Part II: Boundary Conditions </td> <td align="...")
22:18, 21 January 2024 Joel2 talk contribs created page SSC/Stability/Polytropes (Created page with "=Radial Oscillations of Polytropic Spheres= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"> Part I: Wave Equation </td> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"> Part II: Boundary Conditions </td> <td align="center" rowspan="1" bgcolor="lightblue"> SSC/...")
22:05, 21 January 2024 Joel2 talk contribs created page File:BruteForceWhiteBoardsmall.png
22:05, 21 January 2024 Joel2 talk contribs uploaded File:BruteForceWhiteBoardsmall.png
21:57, 21 January 2024 Joel2 talk contribs created page File:TrialN1Eigenfunction.png
21:57, 21 January 2024 Joel2 talk contribs uploaded File:TrialN1Eigenfunction.png
20:53, 20 January 2024 Joel2 talk contribs created page SSC/Stability/n1PolytropeLAWE/Pt3 (Created page with "__FORCETOC__ =Radial Oscillations of n = 1 Polytropic Spheres (Pt 3)= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"> Part I: Search for Analytic Solutions </td> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"> Part II: New Ideas </td> <td align="center" ro...")
20:52, 20 January 2024 Joel2 talk contribs created page SSC/Stability/n1PolytropeLAWE/Pt2 (Created page with "__FORCETOC__ =Radial Oscillations of n = 1 Polytropic Spheres (Pt 2)= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"> Part I: Search for Analytic Solutions </td> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"> Part II: New Ideas </td> <td align="center" ro...")
20:52, 20 January 2024 Joel2 talk contribs created page SSC/Stability/n1PolytropeLAWE (Created page with "__FORCETOC__ =Radial Oscillations of n = 1 Polytropic Spheres (Pt 1)= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"> Part I: Search for Analytic Solutions </td> <td align="center" rowspan="1" bgcolor="lightblue" width="33%"> Part II: New Ideas </td> <td align="center" ro...")
16:51, 18 January 2024 Joel2 talk contribs created page File:Chatterji51Summary2.png
16:51, 18 January 2024 Joel2 talk contribs uploaded File:Chatterji51Summary2.png
14:36, 18 January 2024 Joel2 talk contribs created page SSC/VariationalPrinciple/Pt2 (Created page with "__FORCETOC__  =Ledoux's Variational Principle= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" bgcolor="lightblue" width="50%"> Part I: Ledoux & Pekeris (1941) </td> <td align="center" bgcolor="lightblue"> Part II: Exploratory Ideas </td> </tr> </table> =Related, Exploratory Ideas= <!-- OM...")
14:34, 18 January 2024 Joel2 talk contribs created page SSC/VariationalPrinciple (Created page with "__FORCETOC__  =Ledoux's Variational Principle= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" bgcolor="lightblue" width="50%"> Part I: Ledoux & Pekeris (1941) </td> <td align="center" bgcolor="lightblue"> Part II: Exploratory Ideas </td> </tr> </table> {| class="PGEclass" style="float:lef...")
14:18, 18 January 2024 Joel2 talk contribs created page SSC/SoundWaves (Created page with "__FORCETOC__   =Sound Waves= {| 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;" | Relationship to Sound Waves |} A standard technique that is used throughout astrophysic...")
13:48, 18 January 2024 Joel2 talk contribs created page SSC/Structure/BiPolytropes/FreeEnergy51/Pt3 (Created page with "=Free Energy of BiPolytrope with (nc, ne) = (5, 1)= <table border="1" align="center" width="100%" colspan="8"> <td align="center" bgcolor="lightblue" width="33%"> Part I: Mass Profile </td> <td align="center" bgcolor="lightblue"3 width="33%"> Part II: Gravitational Potential Energy </td> <td align="center" bgcolo...")
13:45, 18 January 2024 Joel2 talk contribs created page SSC/Structure/BiPolytropes/FreeEnergy51/Pt2 (Created page with "__FORCETOC__ =Free Energy of BiPolytrope with (nc, ne) = (5, 1)= <table border="1" align="center" width="100%" colspan="8"> <td align="center" bgcolor="lightblue" width="33%"> Part I: Mass Profile </td> <td align="center" bgcolor="lightblue"3 width="33%"> Part II: Gravitational Potential Energy </td> <td align="c...")
13:40, 18 January 2024 Joel2 talk contribs created page SSC/Structure/BiiPolytropes/FreeEnergy51 (Created page with "__FORCETOC__ =Free Energy of BiPolytrope with (nc, ne) = (5, 1)= <table border="1" align="center" width="100%" colspan="8"> <td align="center" bgcolor="lightblue" width="33%"> Part I: Mass Profile </td> <td align="center" bgcolor="lightblue"3 width="33%"> Part II: Gravitational Potential Energy </td> <td align="ce...")
18:27, 17 January 2024 Joel2 talk contribs created page SSC/Virial/PolytropesEmbedded/SecondEffortAgain (Created page with "__FORCETOC__   =Virial Equilibrium of Adiabatic Spheres (Summary)= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" bgcolor="lightblue" width="33%"> Part I: Groundwork </td> <td align="center" bgcolor="lightblue" width="33%"> SSC/Virial/PolytropesEmbedded/SecondEf...")
15:19, 17 January 2024 Joel2 talk contribs created page Template:PK2007hereafter (Created page with "PK2007")
15:19, 17 January 2024 Joel2 talk contribs created page Template:PK2007full (Created page with "📚 [https://www.sciencedirect.com/science/article/pii/S0021999106002555 A. Y. Poludnenko & A. M. Khokhlov (2007, J. Comp. Phys., Vol. 220, Issue 2, pp. 678 - 711)]")
15:18, 17 January 2024 Joel2 talk contribs created page Template:PK2007figure (Created page with "[https://www.sciencedirect.com/science/article/pii/S0021999106002555 A. Y. Poludnenko & A. M. Khokhlov (2007)] ''Computation of Fluid Flows in Non-inertial Contracting, Expanding, and Rotating Reference Frames'' Journal of Computational Physics, Vol. 220, Issue 2, pp. 678 - 711")
15:17, 17 January 2024 Joel2 talk contribs created page Template:PK2007 (Created page with "📚 [https://www.sciencedirect.com/science/article/pii/S0021999106002555 Poludnenko & Khokhlov (2007)]")
15:15, 17 January 2024 Joel2 talk contribs created page Template:OTM2007hereafter (Created page with "OTM2007")
15:15, 17 January 2024 Joel2 talk contribs created page Template:OTM2007full (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/2007ApJ...665.1074O/abstract S. Ou, J. E. Tohline, & P. M. Motl (2007, ApJ, Vol. 665, pp. 1074 - 1083)]")
15:13, 17 January 2024 Joel2 talk contribs created page Template:OTM2007figure (Created page with "[https://ui.adsabs.harvard.edu/abs/2007ApJ...665.1074O/abstract S. Ou, J. E. Tohline, & P. M. Motl (2007)] ''Further Evidence for an Elliptical Instability in Rotating Fluid Bars and Ellipsoidal Stars'' The Astrophysical Journal, Vol. 665, pp. 1074 - 1083)]")
15:13, 17 January 2024 Joel2 talk contribs created page Template:OTM2007 (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/2007ApJ...665.1074O/abstract Ou, Tohline, & Motl (2007)]")
15:10, 17 January 2024 Joel2 talk contribs created page Template:Ou2006hereafter (Created page with "Ou2006")
15:10, 17 January 2024 Joel2 talk contribs created page Template:Ou2006full (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/2006ApJ...639..549O/abstract S. Ou (2006, ApJ, Vol. 639, pp. 549 - 558)]")
15:09, 17 January 2024 Joel2 talk contribs created page Template:Ou2006figure (Created page with "[https://ui.adsabs.harvard.edu/abs/2006ApJ...639..549O/abstract S. Ou (2006)] ''An Approximate Solver for Riemann and Riemann-Like Ellipsoidal Configurations'' The Astrophysical Journal, Vol. 639, pp. 549 - 558")
15:08, 17 January 2024 Joel2 talk contribs created page Template:Ou2006 (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/2006ApJ...639..549O/abstract Ou (2006)]")
15:06, 17 January 2024 Joel2 talk contribs created page Template:OT2006hereafter (Created page with "OT2006")
15:06, 17 January 2024 Joel2 talk contribs created page Template:OT2006full (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/2006ApJ...651.1068O/abstract S. Ou & J. E. Tohline (2006, ApJ, Vol. 651, pp. 1068 - 1078)]")
15:05, 17 January 2024 Joel2 talk contribs created page Template:OT2006figure (Created page with "[https://ui.adsabs.harvard.edu/abs/2006ApJ...651.1068O/abstract S. Ou & J. E. Tohline (2006)] ''Unexpected Dynamical Instabilities in Differentially Rotating Neutron Stars'' The Astrophysical Journal, Vol. 651, pp. 1068 - 1078")
15:04, 17 January 2024 Joel2 talk contribs created page Template:OT2006 (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/2006ApJ...651.1068O/abstract Ou & Tohline (2006)]")
15:02, 17 January 2024 Joel2 talk contribs created page Template:Hunter2005hereafter (Created page with "Hunter2005")
15:00, 17 January 2024 Joel2 talk contribs created page Template:Hunter2005full (Created page with "📚 [https://ui.adsabs.harvard.edu/abs/2005NYASA1045..120H/abstract C. Hunter (2005, Ann. N. Y. Acad. Sci., Vol. 1045, pp. 120 - 138)]")

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