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18:40, 11 December 2023 Joel2 talk contribs created page Apps/RiemannEllipsoidsCompressible (Created page with "__FORCETOC__   =Compressible Analogs of Riemann S-Type Ellipsoids= Here we attempt to develop a self-consistent-field type, iterative technique that will permit the construction of steady-state structures that are compressible analogs of Riemann S-Type (incompressible) ellipsoids. We will build upon the recent work of [http://adsabs.harvard.edu/abs/2006ApJ...639..549O Ou (2006)]. ==Standard Stea...")
18:35, 11 December 2023 Joel2 talk contribs created page PGE/RotatingFrame (Created page with "__FORCETOC__  NOTE to Eric Hirschmann & David Neilsen... I have moved the earlier contents of this page to a new Wiki location called Compressible Riemann Ellipsoids. =Rotating Reference Frame= At times, it can be useful to view the motion of a fluid from a frame of reference that is rotating with a uniform (''i.e.,'' time-independent) angular velocity <math>~\Omega_f</math>...")
18:28, 11 December 2023 Joel2 talk contribs created page AxisymmetricConfigurations/SolutionStrategies (Created page with "__FORCETOC__  =Axisymmetric Configurations (Solution Strategies)= <!-- Equilibrium, axisymmetric '''structures''' are obtained by searching for time-independent, steady-state solutions to the identified set of simplified governing equations. We begin by writing each governing equation in Eulerian form and setting all partial time-derivatives to zero: <div a...")
18:17, 11 December 2023 Joel2 talk contribs created page Template:Math/EQ Euler04 (Created page with "<math>\frac{\partial\vec{v}}{\partial t} + \vec\zeta \times \vec{v}= - \frac{1}{\rho} \nabla P - \nabla \biggl[\Phi + \frac{1}{2}v^2 \biggr] </math>")
18:15, 11 December 2023 Joel2 talk contribs created page Template:Math/EQ Euler03 (Created page with "<math>\frac{\partial(\rho\vec{v})}{\partial t} + \nabla\cdot [(\rho\vec{v})\vec{v}]= - \nabla P - \rho \nabla \Phi</math>")
18:13, 11 December 2023 Joel2 talk contribs created page Template:Math/EQ Euler02 (Created page with "<math>\frac{\partial\vec{v}}{\partial t} + (\vec{v}\cdot \nabla) \vec{v}= - \frac{1}{\rho} \nabla P - \nabla \Phi</math>")
18:10, 11 December 2023 Joel2 talk contribs created page Template:Math/EQ Continuity02 (Created page with "<math>\frac{\partial\rho}{\partial t} + \nabla \cdot (\rho \vec{v}) = 0</math>")
18:04, 11 December 2023 Joel2 talk contribs created page Cylindrical3D (Created page with "  =Equations Cast in Cylindrical Coordinates= <table align="center" border="0" cellpadding="5"> <tr> <td colspan="3" align="center"> Spatial Operators in Cylindrical Coordinates </td> </tr> <tr> <td align="right"> <math> \nabla f </math> </td> <td align="center"> = </td> <td align="left"> <math> {\hat{e}}_\varpi \biggl[ \frac{\p...")
18:01, 11 December 2023 Joel2 talk contribs created page Template:SGFfooter (Created page with "{| class="wikitable" width=100% style="margin-right: auto; margin-left: 0px; border-style: solid; border-width: 3px; border-color:black;" |- ! style="height: 50px; background-color:black;"|780px|link=H_BookTiledMenu|Tiled Menu |} <table border="0" cellpadding="2" align="center" width="100%"> <tr><td colspan="3" align="center"> Appendices: | [https://www.vistrails.org/index.php/User:Tohline/Appendix/Equation_templates Vis...")
18:00, 11 December 2023 Joel2 talk contribs created page Template:Math/VAR VelocityVector01 (Created page with "<math>\vec{v}</math>")
17:59, 11 December 2023 Joel2 talk contribs created page Template:Math/VAR Time01 (Created page with "<math>t</math>")
17:58, 11 December 2023 Joel2 talk contribs created page Template:Math/VAR Temperature01 (Created page with "<math>T</math>")
17:57, 11 December 2023 Joel2 talk contribs created page Template:Math/VAR SpecificInternalEnergy01 (Created page with "<math>\epsilon</math>")
17:56, 11 December 2023 Joel2 talk contribs created page Template:Math/VAR SpecificEntropy01 (Created page with "<math>s</math>")
17:55, 11 December 2023 Joel2 talk contribs created page Template:Math/VAR Pressure01 (Created page with "<math>P</math>")
17:54, 11 December 2023 Joel2 talk contribs created page Template:Math/VAR PositionVector01 (Created page with "<math>\vec{x}</math>")
17:54, 11 December 2023 Joel2 talk contribs created page Template:Math/VAR NewtonianPotential01 (Created page with "<math>\Phi</math>")
17:52, 11 December 2023 Joel2 talk contribs created page Template:Math/VAR Density01 (Created page with "<math>\rho</math>")
17:51, 11 December 2023 Joel2 talk contribs created page Template:Math/EQ Poisson01 (Created page with "<table border="0" cellpadding="2"> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Principal_Governing_Equations </td> <td align="center"> <math>\nabla^2 \Phi = 4\pi G \rho</math> </td> </tr> </table>")
17:50, 11 December 2023 Joel2 talk contribs created page File:LSUkey.png
17:50, 11 December 2023 Joel2 talk contribs uploaded File:LSUkey.png
17:43, 11 December 2023 Joel2 talk contribs created page Template:Math/EQ FirstLaw02 (Created page with "<math>\frac{d\epsilon}{dt} + P \frac{d}{dt} \biggl(\frac{1}{\rho}\biggr) = 0</math>")
17:42, 11 December 2023 Joel2 talk contribs created page Template:Math/EQ FirstLaw01 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Principal_Governing_Equations </td> <td align="center"> <math>T \frac{ds}{dt} = \frac{d\epsilon}{dt} + P \frac{d}{dt} \biggl(\frac{1}{\rho}\biggr)</math> </td> </tr> </table>")
17:39, 11 December 2023 Joel2 talk contribs created page Template:Math/EQ Euler01 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Principal_Governing_Equations </td> <td align="center"> <math>\frac{d\vec{v}}{dt} = - \frac{1}{\rho} \nabla P - \nabla \Phi</math> </td> </tr> </table>")
17:37, 11 December 2023 Joel2 talk contribs created page Template:Math/EQ Continuity01 (Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Principal_Governing_Equations </td> <td align="center"> <math>\frac{d\rho}{dt} + \rho \nabla \cdot \vec{v} = 0</math> </td> </tr> </table>")
17:36, 11 December 2023 Joel2 talk contribs created page Template:Math/C GravitationalConstant (Created page with "<math>G</math>")
16:24, 11 December 2023 Joel2 talk contribs created page File:OriginButton.jpg
16:24, 11 December 2023 Joel2 talk contribs uploaded File:OriginButton.jpg
16:24, 11 December 2023 Joel2 talk contribs created page File:OtherFormsButton.jpg
16:24, 11 December 2023 Joel2 talk contribs uploaded File:OtherFormsButton.jpg
16:19, 11 December 2023 Joel2 talk contribs created page VE (Created page with "__FORCETOC__   =Global Energy Considerations= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#9390DB;" | Global Energy Considerations |} ==Preface== The astrophysics community relies heavi...")
16:17, 11 December 2023 Joel2 talk contribs created page File:SSC SynopsisImage2.png
16:17, 11 December 2023 Joel2 talk contribs uploaded File:SSC SynopsisImage2.png
16:16, 11 December 2023 Joel2 talk contribs created page File:SSC SynopsisImage1.png
16:16, 11 December 2023 Joel2 talk contribs uploaded File:SSC SynopsisImage1.png
16:12, 11 December 2023 Joel2 talk contribs created page File:FreeNRGpressureRadiusIsothermal.png
16:12, 11 December 2023 Joel2 talk contribs uploaded File:FreeNRGpressureRadiusIsothermal.png
16:07, 11 December 2023 Joel2 talk contribs created page File:HBook title Fluids2.png
16:07, 11 December 2023 Joel2 talk contribs uploaded File:HBook title Fluids2.png
16:03, 11 December 2023 Joel2 talk contribs created page SR/IdealGas (Created page with "__FORCETOC__   =Ideal Gas Equation of State= {| 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;" | Ideal Gas |} Much of the following overview of ideal gas relations is drawn from Chapter I...")
16:01, 11 December 2023 Joel2 talk contribs created page Apps/SMS (Created page with "__FORCETOC__   =Rotating, Supermassive Stars= {| 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;" | Bond, Arnett, & Carr (1984) |} Here we draw upon the work of {{ BAC84full }} — her...")
16:00, 11 December 2023 Joel2 talk contribs created page SR/PressureCombinations (Created page with "__FORCETOC__   =Total Pressure= {| 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;" | Total Pressure |} In our overview of equations of state, we identified analytic e...")
15:59, 11 December 2023 Joel2 talk contribs created page SR (Created page with "__FORCETOC__   =Supplemental Relations= {| 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;" | Equation of State (EOS) |} <table border="0" cellpadding="3" align="center" width="...")
14:56, 11 December 2023 Joel2 talk contribs created page PGE/PoissonOrigin (Created page with "__FORCETOC__   =Origin of the Poisson Equation= {| 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;" | Poisson |} We will follow closely the presentation found in §2.1 of [Appendix/...")
14:55, 11 December 2023 Joel2 talk contribs created page PGE/FirstLawOfThermodynamics (Created page with "__FORCETOC__   =First Law of Thermodynamics= {| 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;" | 1st Law of Thermodynamics |} ==Standard Presentation== Following the detail...")
14:54, 11 December 2023 Joel2 talk contribs created page PGE/Euler (Created page with "__FORCETOC__  =Euler Equation= {| 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;" | Euler |} ==Lagrangian Representation== ===in terms of velocity:=== Among the principal governing equations we have inc...")
14:53, 11 December 2023 Joel2 talk contribs created page PGE/ConservingMass (Created page with "__FORCETOC__  =Continuity Equation= {| 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;" | Continuity |} ==Various Forms== ===Lagrangian Representation=== Among the principal governing equations we have in...")
14:52, 11 December 2023 Joel2 talk contribs created page PGE (Created page with "__FORCETOC__  =Principal Governing Equations= {| 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;" | Principle Governing Equations (PGEs) |} According to the eloquent discussion of the broad subject of ''Fluid Mechanics'' pres...")
14:45, 11 December 2023 Joel2 talk contribs created page H BookTiledMenu (Created page with "__NOTOC__  =Tiled Menu= {| class="TopBanner" width=100% style="margin-right: auto; margin-left: 0px; border-style: solid; border-width: 3px; border-color:black;" |- ! style="height: 50px; background-color:black;"|780px|link=User:Tohline/SSC/Virial/PolytropesEmbeddedOutline#Virial_Equilibrium_of_Embedded_Polytropic_Spheres|Whitworth's (1981) Isothermal Free-Energy Surface |} ATTEN...")
18:52, 10 December 2023 User account Joel2 talk contribs was created

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