User contributions for Joel2

18:4018:40, 11 December 2023 diff hist +24,389 N 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..." current
18:3818:38, 11 December 2023 diff hist −3 PGE/RotatingFrame →When v_z = 0
18:3718:37, 11 December 2023 diff hist −8 PGE/RotatingFrame →Align {\vec\Omega}_f with z-axis
18:3518:35, 11 December 2023 diff hist +10,459 N 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>..."
18:2818:28, 11 December 2023 diff hist +60,269 N 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..."
18:2418:24, 11 December 2023 diff hist +78 Main Page No edit summary
18:1718:17, 11 December 2023 diff hist +148 N 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>" current
18:1518:15, 11 December 2023 diff hist +121 N 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>" current
18:1318:13, 11 December 2023 diff hist +120 N 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>" current
18:1018:10, 11 December 2023 diff hist +78 N Template:Math/EQ Continuity02 Created page with "<math>\frac{\partial\rho}{\partial t} + \nabla \cdot (\rho \vec{v}) = 0</math>" current
18:0418:04, 11 December 2023 diff hist +21,047 N 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..." current
18:0118:01, 11 December 2023 diff hist +1,005 N 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..." current
18:0018:00, 11 December 2023 diff hist +75 N Template:Math/VAR VelocityVector01 Created page with "<math>\vec{v}</math>" current
17:5917:59, 11 December 2023 diff hist +40 N Template:Math/VAR Time01 Created page with "<math>t</math>" current
17:5817:58, 11 December 2023 diff hist +47 N Template:Math/VAR Temperature01 Created page with "<math>T</math>" current
17:5717:57, 11 December 2023 diff hist +67 N Template:Math/VAR SpecificInternalEnergy01 Created page with "<math>\epsilon</math>" current
17:5617:56, 11 December 2023 diff hist +52 N Template:Math/VAR SpecificEntropy01 Created page with "<math>s</math>" current
17:5517:55, 11 December 2023 diff hist +44 N Template:Math/VAR Pressure01 Created page with "<math>P</math>" current
17:5417:54, 11 December 2023 diff hist +75 N Template:Math/VAR PositionVector01 Created page with "<math>\vec{x}</math>" current
17:5417:54, 11 December 2023 diff hist +72 N Template:Math/VAR NewtonianPotential01 Created page with "<math>\Phi</math>" current
17:5217:52, 11 December 2023 diff hist +51 N Template:Math/VAR Density01 Created page with "<math>\rho</math>" current
17:5117:51, 11 December 2023 diff hist +235 N 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>" current
17:5017:50, 11 December 2023 diff hist 0 N File:LSUkey.png No edit summary current
17:4317:43, 11 December 2023 diff hist +83 N Template:Math/EQ FirstLaw02 Created page with "<math>\frac{d\epsilon}{dt} + P \frac{d}{dt} \biggl(\frac{1}{\rho}\biggr) = 0</math>" current
17:4217:42, 11 December 2023 diff hist +288 N 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>" current
17:3917:39, 11 December 2023 diff hist +265 N 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>" current
17:3717:37, 11 December 2023 diff hist +252 N 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>" current
17:3617:36, 11 December 2023 diff hist +83 N Template:Math/C GravitationalConstant Created page with "<math>G</math>" current
16:2416:24, 11 December 2023 diff hist 0 N File:OriginButton.jpg No edit summary current
16:2416:24, 11 December 2023 diff hist 0 N File:OtherFormsButton.jpg No edit summary current
16:2016:20, 11 December 2023 diff hist −1 H BookTiledMenu →Context
16:1916:19, 11 December 2023 diff hist +44,818 N 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..."
16:1716:17, 11 December 2023 diff hist 0 N File:SSC SynopsisImage2.png No edit summary current
16:1616:16, 11 December 2023 diff hist 0 N File:SSC SynopsisImage1.png No edit summary current
16:1216:12, 11 December 2023 diff hist 0 N File:FreeNRGpressureRadiusIsothermal.png No edit summary current
16:0716:07, 11 December 2023 diff hist 0 N File:HBook title Fluids2.png No edit summary current
16:0316:03, 11 December 2023 diff hist +12,573 N 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..." current
16:0116:01, 11 December 2023 diff hist +33,244 N 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..." current
16:0016:00, 11 December 2023 diff hist +11,062 N 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..." current
15:5915:59, 11 December 2023 diff hist +28,179 N 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="..." current
14:5614:56, 11 December 2023 diff hist +12,239 N 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/..." current
14:5514:55, 11 December 2023 diff hist +31,160 N 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..."
14:5414:54, 11 December 2023 diff hist +5,207 N 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..."
14:5314:53, 11 December 2023 diff hist +3,504 N 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..." current
14:5214:52, 11 December 2023 diff hist +4,691 N 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..." current
14:4514:45, 11 December 2023 diff hist +52,796 N 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..."
14:4414:44, 11 December 2023 diff hist +142 Main Page →Old Tile Menu
14:3914:39, 11 December 2023 diff hist +38 Main Page →Old Tile Menu

19:0619:06, 10 December 2023 diff hist +92 Main Page →Old Tile Menu
19:0419:04, 10 December 2023 diff hist +86 Main Page No edit summary

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