User contributions for Joel2

20:0020:00, 18 December 2023 diff hist +727 SSC/Structure/PolytropesEmbedded/n1 No edit summary
19:5919:59, 18 December 2023 diff hist +727 SSC/Structure/PolytropesEmbedded/n5 No edit summary
19:5819:58, 18 December 2023 diff hist +728 SSC/Structure/PolytropesEmbedded/Other No edit summary
19:5819:58, 18 December 2023 diff hist +698 SSC/Structure/PolytropesEmbedded No edit summary
19:4319:43, 18 December 2023 diff hist −72,045 SSC/Structure/PolytropesEmbedded No edit summary
19:4319:43, 18 December 2023 diff hist +17,609 N SSC/Structure/PolytropesEmbedded/n1 Created page with " ==Polytropic Configurations with n = 1== Drawing from the earlier discussion of isolated polytropes, we will reference various radial locations within the spherical configuration by the dimensionless radius, <div align="center"> <math> \xi \equiv \frac{r}{a_\mathrm{n=1}} , </math> </div> where, <div align="center"> <math> a_\mathrm{n=1} \equiv \biggl[\frac{1}{4\pi G}~ \biggl( \frac{H_c}{\rho_c} \biggr)_{n=1}\biggr]^{1/2} = \biggl[\frac{K}{2..."
19:4119:41, 18 December 2023 diff hist +31,595 N SSC/Structure/PolytropesEmbedded/n5 Created page with " ==Polytropic Configurations with n = 5== Drawing from the earlier discussion of isolated polytropes, we will reference various radial locations within a spherical {{Math/MP_PolytropicIndex}} = 5 polytrope by the dimensionless radius, <div align="center"> <math> \xi \equiv \frac{r}{a_\mathrm{n=5}} , </math> </div> where, <div align="center"> <math> a_{n=5} = \biggr[ \frac{(n+1)K}{4\pi G} \rho_c^{(1/n - 1)} \biggr]^{1/2}_{n=5} = \biggr[ \frac..."
19:3919:39, 18 December 2023 diff hist +22,838 N SSC/Structure/PolytropesEmbedded/Other Created page with " ==Additional, Numerically Constructed Polytropic Configurations== As has been detailed in an accompanying chapter, using numerical techniques we have solved the Lane-Emden equation, and thereby discerned the internal structural profiles, for polytropes having a wide variety of polytropic indexes. The righthand panel of Figure 3 presents a diagram in which the mass-radius "sequences" corresponding to eight different polytr..."
19:3519:35, 18 December 2023 diff hist +325 Contents →Equilibrium Structures
18:5618:56, 18 December 2023 diff hist +95,048 N Appendix/Ramblings/TurningPoints Created page with "__FORCETOC__ =Turning Points= {| 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;" | Turning-Points (Broader Context) |} The material presented below has been gathered together and expanded in preparation for developing a primary chapter that discusses SSC/FreeEnergy/Equil..."
18:5418:54, 18 December 2023 diff hist +450 Contents →Spherically Symmetric Configurations
18:4318:43, 18 December 2023 diff hist +314 Contents →Equilibrium Structures
18:2618:26, 18 December 2023 diff hist +103,550 N SSC/Structure/PolytropesEmbedded Created page with "__FORCETOC__  =Embedded Polytropic Spheres= {| 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;" | Embedded Polytropes |}  In a separate discussion we have..."
15:0415:04, 18 December 2023 diff hist +80,762 N SSC/Stability/InstabilityOnsetOverview Created page with "__FORCETOC__  =Marginally Unstable Pressure-Truncated Gas Clouds= <table border="1" width="90%" align="center" cellpadding="15"> <tr><td align="center"> <table border="0" cellpadding="8"> <tr><td align="center"> Abstract Joel E. Tohline (April, 2017) </td></tr> <tr><td align="left"> right|200px|center|Pressure-Truncated Isothermal Equilibrium SequenceWhen an isotherm..."
14:5514:55, 18 December 2023 diff hist +43,007 N SSC/Structure/BonnorEbert Created page with "__FORCETOC__ =Pressure-Bounded Isothermal Sphere= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffeeee;" | Bonnor-Ebert (Isothermal) Spheres (1955-56) |} As has been derived and discussed elsewhere, a..."
14:4914:49, 18 December 2023 diff hist +76 Contents →Equilibrium Structures
14:4514:45, 18 December 2023 diff hist −43 H BookTiledMenu →Equilibrium Structures
14:3714:37, 18 December 2023 diff hist +18,705 N SSC/Structure/WhiteDwarfs Created page with "__FORCETOC__  =White Dwarfs= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffff99;" | Zero-Temperature White Dwarf |} (More introductory material is needed here.) <br..." current
14:2514:25, 18 December 2023 diff hist 0 SSC/Structure/Polytropes/Numerical →Polytropic Spheres
14:2514:25, 18 December 2023 diff hist 0 SSC/Structure/Polytropes →Polytropic Spheres
14:2414:24, 18 December 2023 diff hist 0 SSC/Structure/Polytropes/Analytic →Polytropic Spheres
14:2114:21, 18 December 2023 diff hist −181 Contents →Equilibrium Structures
14:1214:12, 18 December 2023 diff hist +138 SSC/Structure/Polytropes/Numerical No edit summary
14:1114:11, 18 December 2023 diff hist +138 SSC/Structure/Polytropes/Analytic No edit summary
14:1014:10, 18 December 2023 diff hist +641 SSC/Structure/Polytropes →Polytropic Spheres
14:0514:05, 18 December 2023 diff hist +502 SSC/Structure/Polytropes/Analytic No edit summary
14:0414:04, 18 December 2023 diff hist +502 SSC/Structure/Polytropes/Numerical No edit summary
13:4413:44, 18 December 2023 diff hist +51 H BookTiledMenu →Equilibrium Structures
13:4013:40, 18 December 2023 diff hist −60,618 SSC/Structure/Polytropes →Known Analytic Solutions
13:3813:38, 18 December 2023 diff hist +60,693 N SSC/Structure/Polytropes/Analytic Created page with "==Known Analytic Solutions== {| 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;" | Known Analytic Solutions |} While the Lane-Emden equation has been studied for over 100 years, to date, analytic solutions to the equation (subject to the above specified boun..."
13:3613:36, 18 December 2023 diff hist +47 SSC/Structure/Polytropes →Numerical Solutions
13:3513:35, 18 December 2023 diff hist −28,534 SSC/Structure/Polytropes →Numerical Solutions
13:3313:33, 18 December 2023 diff hist +28,557 N SSC/Structure/Polytropes/Numerical Created page with "==Numerical Solutions== Here we explain how an Excel workbook can be used to numerically solve the Lane-Emden equation, evaluating the Lane-Emden function across a one-dimensional, discrete grid. ===Techniques=== ====HSCF Technique==== {| 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;" | H_BookTiledMenu#Equilibrium_St..."
13:2413:24, 18 December 2023 diff hist −47 H BookTiledMenu →Equilibrium Structures

19:4319:43, 17 December 2023 diff hist 0 N File:Our2019Diagram2.png No edit summary current
19:4019:40, 17 December 2023 diff hist −364 SSC/Structure/Lane1870 →SEGMENT III
19:3919:39, 17 December 2023 diff hist −364 SSC/Structure/Lane1870 →SEGMENT II
19:3619:36, 17 December 2023 diff hist −411 SSC/Structure/Lane1870 →Lane's 1870 Work
19:2219:22, 17 December 2023 diff hist +50 Contents →Equilibrium Structures
19:2019:20, 17 December 2023 diff hist +48,505 N SSC/Structure/Lane1870 Created page with "__FORCETOC__  =Lane's 1870 Work= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffeeee;" | Lane (1870) |} In what follows, text presented in a dark green font (and/or, as indicated, each equation) has been copied ''verbatim''..."
14:5214:52, 17 December 2023 diff hist +60 Contents →Equilibrium Structures
14:4414:44, 17 December 2023 diff hist +185 Contents →Equilibrium Structures
14:3914:39, 17 December 2023 diff hist +105 Contents →Spherically Symmetric Configurations
14:3614:36, 17 December 2023 diff hist +11,847 N SSC/Structure/UniformDensity Created page with "  =Isolated Uniform-Density Sphere= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffff99;" | Uniform-Density Sphere |} Here we derive the interior structural..." current
14:3214:32, 17 December 2023 diff hist +168 Contents →Equilibrium Structures
14:2014:20, 17 December 2023 diff hist +149 Contents →Spherically Symmetric Configurations
14:1514:15, 17 December 2023 diff hist +21,896 N SSC/SynopsisStyleSheet Created page with "__FORCETOC__   =Spherically Symmetric Configurations Synopsis (Using Style Sheet)= ==Structure== ===Tabular Overview=== {| class="Synopsis1A" style="margin: auto; color:black; width:85%;" border="1" cellpadding="12" |+ style="height:30px;" | '''Spherically Symmetric Configurations that undergo Adiabatic Compression/Expansion''' — adiabatic index, <m..." current

20:3820:38, 16 December 2023 diff hist +132 Contents →Primary (Tiled Menu) Chapters
20:3720:37, 16 December 2023 diff hist −141 Contents →See Also
20:3220:32, 16 December 2023 diff hist +14,443 N SSCpt2/IntroductorySummary Created page with "__FORCETOC__  =Applications= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:lightgreen;" | Hydrostatic Balance Equations |} ==Spherically Symmetric Configurations== ===Structure:=== Here we show how the set of PGE#Principal_G..."

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