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20:49, 22 December 2023 Joel2 talk contribs created page SSC/Virial/PolytropesEmbedded/SecondEffortAgain/Pt3 (Created page with " ==Discussion== A spherically symmetric, self-gravitating gas cloud whose effective adiabatic exponent is <math>\gamma < 4/3</math> — equivalently, <math>n > 3</math> — cannot exist in a dynamically stable equilibrium state, in isolation. Such clouds can be stabilized, however, if they are embedded in a hot, tenuous external medium and effectively confined by an external pressure, <math>~P_e</math>. The pressure-truncated, <math>n = 5 (\gamma = 6/5)</math>...")
20:43, 22 December 2023 Joel2 talk contribs created page SSC/Virial/PolytropesEmbedded/SecondEffortAgain/Pt1 (Created page with "__FORCETOC__   =Virial Equilibrium of Adiabatic Spheres (Summary)= The summary presented here has been drawn from our accompanying detailed analysis of the structure of pressure-truncated polytropes. ==Detailed Force-Balanced Solution== As has been SSC/Structure/PolytropesEmbedded#Embedded_Polytropic_Spheres|discussed in de...")
18:31, 22 December 2023 Joel2 talk contribs created page SSC/FreeEnergy/PolytropesEmbedded/Pt3C (Created page with "=Free Energy of Embedded Polytropes= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" rowspan="2" bgcolor="lightblue" width="25%"> Part I: Synopsis </td> <td align="center" rowspan="2" bgcolor="lightblue" width="25%"> Part II: Truncated Polytropes </td> <td align="center" rowspan="1" colspan="3"bgcolor="l...")
18:28, 22 December 2023 Joel2 talk contribs created page SSC/FreeEnergy/PolytropesEmbedded/Pt3B (Created page with "=Free Energy of Embedded Polytropes= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" rowspan="2" bgcolor="lightblue" width="25%"> Part I: Synopsis </td> <td align="center" rowspan="2" bgcolor="lightblue" width="25%"> Part II: Truncated Polytropes </td> <td align="center" rowspan="1" colspan="3"bgcolor="l...")
18:26, 22 December 2023 Joel2 talk contribs created page SSC/FreeEnergy/PolytropesEmbedded/Pt3A (Created page with "=Free Energy of Embedded Polytropes= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" rowspan="2" bgcolor="lightblue" width="25%"> Part I: Synopsis </td> <td align="center" rowspan="2" bgcolor="lightblue" width="25%"> Part II: Truncated Polytropes </td> <td align="center" rowspan="1" colspan="3"bgcolor="l...")
18:23, 22 December 2023 Joel2 talk contribs created page SSC/FreeEnergy/PolytropesEmbedded/Pt2 (Created page with "=Free Energy of Embedded Polytropes= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" rowspan="2" bgcolor="lightblue" width="25%"> Part I: Synopsis </td> <td align="center" rowspan="2" bgcolor="lightblue" width="25%"> Part II: Truncated Polytropes </td> <td align="center" rowspan="1" colspan="3"bgcolor="l...")
18:20, 22 December 2023 Joel2 talk contribs created page SSC/FreeEnergy/PolytropesEmbedded/Pt1 (Created page with "=Free Energy of Embedded Polytropes= <table border="1" align="center" width="100%" colspan="8"> <tr> <td align="center" rowspan="2" bgcolor="lightblue" width="25%"> Part I: Synopsis </td> <td align="center" rowspan="2" bgcolor="lightblue" width="25%"> Part II: Truncated Polytropes </td> <td align="center" rowspan="1" colspan="3"bgcolor="l...")
17:17, 22 December 2023 Joel2 talk contribs created page SSC/FreeEnergy/PolytropesEmbedded (Created page with "=Chapter Divisions= In October 2023, this very long chapter was subdivided in order to more effectively accommodate edits. Here is a list of the resulting set of shorter chapters: <ol> <li>Free-Energy Synopsis</li> <li>Free-Energy of Truncated Polytropes</li> <li>Free-Energy of BiPolytropes <ul> <li>SSC/FreeEnergy/PolytropesEmbedded/Pt3A|Focus on Five...")
17:06, 22 December 2023 Joel2 talk contribs created page SSC/Structure/Polytropes/VirialSummary (Created page with "__FORCETOC__ =Virial Equilibrium of Pressure-Truncated Polytropes= {| 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;" | Virial Equilibrium of Pressure-Truncated Polytropes |} Here we will draw heavily from: [1] An accompanying SSC/FreeEnergy/PolytropesEmbedded#...")
19:38, 18 December 2023 Joel2 talk contribs created page Appendix/Ramblings/Radiation/RadHydro (Created page with "__FORCETOC__  =Radiation-Hydrodynamics= ==Governing Equations== ===Hayes et al. (2006) — But Ignoring the Effects of Magnetic Fields=== First, referencing §2 of [http://adsabs.harvard.edu/abs/2006ApJS..165..188H J. C. Hayes et al. (2006, ApJS, 165, 188 - 228)] — alternatively see §2.1 of [http://adsabs.harvard.edu/abs/2012ApJS..199...35M D. C. Marcello & J. E. Tohline (2012, ApJS, 199, id. 35, 29 pp)] &#821...")
19:14, 18 December 2023 Joel2 talk contribs created page File:YabushitaMontageB.png
19:14, 18 December 2023 Joel2 talk contribs uploaded File:YabushitaMontageB.png
19:11, 18 December 2023 Joel2 talk contribs created page File:Yabushita1975Combined.png
19:11, 18 December 2023 Joel2 talk contribs uploaded File:Yabushita1975Combined.png
19:09, 18 December 2023 Joel2 talk contribs created page File:IsothermalTrunc12.png
19:09, 18 December 2023 Joel2 talk contribs uploaded File:IsothermalTrunc12.png
19:09, 18 December 2023 Joel2 talk contribs created page File:IsothermalTrunc11.png
19:09, 18 December 2023 Joel2 talk contribs uploaded File:IsothermalTrunc11.png
19:08, 18 December 2023 Joel2 talk contribs created page File:IsothermalTrunc4.png
19:08, 18 December 2023 Joel2 talk contribs uploaded File:IsothermalTrunc4.png
19:06, 18 December 2023 Joel2 talk contribs created page File:DataFileButton02.png
19:06, 18 December 2023 Joel2 talk contribs uploaded File:DataFileButton02.png
18:43, 18 December 2023 Joel2 talk contribs created page 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...")
18:41, 18 December 2023 Joel2 talk contribs created page 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...")
18:39, 18 December 2023 Joel2 talk contribs created page 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...")
17:56, 18 December 2023 Joel2 talk contribs created page 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...")
17:26, 18 December 2023 Joel2 talk contribs created page 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...")
14:04, 18 December 2023 Joel2 talk contribs created page 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...")
13:55, 18 December 2023 Joel2 talk contribs created page 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...")
13:37, 18 December 2023 Joel2 talk contribs created page 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...")
12:38, 18 December 2023 Joel2 talk contribs created page 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...")
12:33, 18 December 2023 Joel2 talk contribs created page 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...")
18:43, 17 December 2023 Joel2 talk contribs created page File:Our2019Diagram2.png
18:43, 17 December 2023 Joel2 talk contribs uploaded File:Our2019Diagram2.png
18:20, 17 December 2023 Joel2 talk contribs created page 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''...")
13:36, 17 December 2023 Joel2 talk contribs created page 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...")
13:15, 17 December 2023 Joel2 talk contribs created page 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...")
19:32, 16 December 2023 Joel2 talk contribs created page 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...")
19:06, 16 December 2023 Joel2 talk contribs created page SSCpt1/Virial/FormFactors (Created page with "__FORCETOC__  =Structural Form Factors= {| 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;" | Structural Form Factors |} As has been defined in SSCpt1/Virial#Structural_Form_Factors|a companion, introduct...")
18:54, 16 December 2023 Joel2 talk contribs created page SSCpt1/Virial/PolytropesEmbeddedOutline (Created page with "__FORCETOC__   =Virial Equilibrium of Embedded Polytropic Spheres= <div align="center" id="IntroFigures"> <table border="1" cellpadding="8" align="center"> <tr> <th align="center" colspan="2"> Figure 1: Free-Energy Surfaces for Pressure-Truncated Structures </th> <tr> <td align="center" colspan="1" bgcolor="#CCFFFF"> File:FreeNRGmassRadiusN5.png|300px|n = 5 Free-Ene...")
18:41, 16 December 2023 Joel2 talk contribs created page SSC/Index (Created page with "__FORCETOC__  =Spherically Symmetric Configurations (SSC) Index= ==Detailed Force Balance== <ol type="A"> <li> SGF Menu Tile: One-Dimensional PGEs SGF link: '''SSCpt1/PGE''' <math>\leftarrow</math> backup: "Chapters" B001 File Headline: PGE for Spherically Symmetric Configurations (old) VisTrails link: &nbs...")
18:25, 16 December 2023 Joel2 talk contribs created page SSC/Structure/IsothermalSphere (Created page with "__FORCETOC__  =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:#ffff99;" | Isothermal Sphere |} Here we supplement the simplified set of principal governing equations with an isothermal equation...")
18:21, 16 December 2023 Joel2 talk contribs created page SSCpt2/SolutionStrategies (Created page with "__FORCETOC__   =Spherically Symmetric Configurations (Part II)=  Equilibrium, spherically symmetric '''structures''' are obtained by searching for time-independent solutions to the identified set of simplified governing equations. The steady-state flow field that...")
15:14, 16 December 2023 Joel2 talk contribs created page SSCpt1/PGE (Created page with "__FORCETOC__  =PGE for Spherically Symmetric Configurations= {| 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;" | One-Dimensional PGEs |} If the self-gravitating configuration that we wish to construct is spheri...")
14:50, 16 December 2023 Joel2 talk contribs created page File:Andalib.vel43Small.jpeg
14:50, 16 December 2023 Joel2 talk contribs uploaded File:Andalib.vel43Small.jpeg
14:50, 16 December 2023 Joel2 talk contribs created page File:Andalib.vel36Small.jpeg
14:50, 16 December 2023 Joel2 talk contribs uploaded File:Andalib.vel36Small.jpeg
14:49, 16 December 2023 Joel2 talk contribs created page File:Andalib.vel30Small.jpeg
14:49, 16 December 2023 Joel2 talk contribs uploaded File:Andalib.vel30Small.jpeg

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