User contributions for Joel2

12 December 2023

• 19:4719:47, 12 December 2023 diff hist +60,651 N SSC/Structure/BiPolytropes/Analytic1.53 Created page with "__FORCETOC__ =BiPolytrope with (n_c, n_e) = (3/2, 3)= {| 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;" | <font size="-1"><b>Milne</b><br /> (1930)</font> |} Here we lay out the procedure for constructing a bipolytrope in which the core has an..."
• 19:4119:41, 12 December 2023 diff hist +15,592 N 2DStructure/AxisymmetricInstabilities Created page with "__FORCETOC__ <!-- __NOTOC__ will force TOC off --> =Axisymmetric Instabilities to Avoid= {| 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;" |<b>Axisymmetric<br />Instabilities<br />to Avoid</b> |} When constructing rotating equilibrium configurations..." current
• 19:3119:31, 12 December 2023 diff hist +4,636 N PGE/ConservingMomentum Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =Euler Equation (Conserving Momentum)= ==Various Forms== ===Lagrangian Representation=== Among the principal governing equations we have included the <div align="center"> <span id="ConservingMomentum:Lagrangian"><font color="#770000">'''Lagrangian Representation'''</font></span><br /> of the Euler Equation, {{ Math/EQ_Euler01 }} </div> Multiplying thi..." current
• 13:5813:58, 12 December 2023 diff hist 0 N File:JacobiMaclaurin2.gif No edit summary current
• 13:5513:55, 12 December 2023 diff hist 0 N File:Dissertation.fig3cropped.png No edit summary current
• 13:5313:53, 12 December 2023 diff hist 0 N File:Minitorus.animated.gif No edit summary current
• 13:4913:49, 12 December 2023 diff hist 0 N File:N1.5j2 Combinedsmall.png No edit summary current
• 13:4513:45, 12 December 2023 diff hist 0 N File:TorusMovie1.gif No edit summary current
• 13:4213:42, 12 December 2023 diff hist 0 N File:Apollonian myway4.png No edit summary current
• 13:3913:39, 12 December 2023 diff hist 0 N File:MovieWongN4.gif No edit summary current

11 December 2023

• 20:1420:14, 11 December 2023 diff hist 0 N File:OutputC.gif No edit summary current
• 20:0720:07, 11 December 2023 diff hist 0 N File:Schwarzschild1941movie.gif No edit summary current
• 20:0520:05, 11 December 2023 diff hist 0 N File:TaffVanHorn1974Harmonic.gif No edit summary current
• 20:0520:05, 11 December 2023 diff hist 0 N File:TaffVanHorn1974Fundamental.gif No edit summary current
• 20:0320:03, 11 December 2023 diff hist 0 N File:Sterne1937SolutionPlot1.png No edit summary current
• 20:0120:01, 11 December 2023 diff hist 0 N File:ImageOfDerivations08GoodRosseland.png No edit summary current
• 20:0120:01, 11 December 2023 diff hist 0 N File:ImageOfDerivations07GoodLedouxWalraven.png No edit summary current
• 20:0120:01, 11 December 2023 diff hist 0 N File:ImageOfDerivations06GoodJeansBonnor.png No edit summary current
• 19:5619:56, 11 December 2023 diff hist 0 N File:TurningPoints51Bipolytropes.png No edit summary current
• 19:5219:52, 11 December 2023 diff hist 0 N File:MassVsRadiusCombined02.png No edit summary current
• 18:5418:54, 11 December 2023 diff hist 0 N File:Maclaurin01.gif No edit summary current
• 18:5018:50, 11 December 2023 diff hist +272 N Template:Math/EQ SShydrostaticBalance01 Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Traditional_Equations_of_.28Spherical.29_Stellar_Structure </td> <td align="center"> <math>\frac{dP}{dr} = - \frac{GM_r \rho}{r^2}</math> </td> </tr> </table>" current
• 18:4918:49, 11 December 2023 diff hist +316 N Template:Math/EQ SSLaneEmden02 Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Traditional_Equations_of_.28Spherical.29_Stellar_Structure </td> <td align="center"> <math>\frac{1}{\xi^2} \frac{d}{d\xi}\biggl( \xi^2 \frac{d\psi}{d\xi} \biggr) = e^{-\psi}</math> </td> </tr> </table>" current
• 18:4818:48, 11 December 2023 diff hist +323 N Template:Math/EQ SSLaneEmden01 Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Traditional_Equations_of_.28Spherical.29_Stellar_Structure </td> <td align="center"> <math>\frac{1}{\xi^2} \frac{d}{d\xi}\biggl( \xi^2 \frac{d\Theta_H}{d\xi} \biggr) = - \Theta_H^n</math> </td> </tr> </table>" current
• 18:4718:47, 11 December 2023 diff hist +709 N Template:Math/EQ RadialPulsation03 Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Stability:_Radial_Pulsation </td> <td align="center"> <math>0 = \frac{d^2x}{d\xi^2} + \biggl[4 - \xi \biggl( \frac{d\psi}{d\xi} \biggr) \biggr] \frac{1}{\xi} \cdot \frac{dx}{d\xi} + \biggl[ \biggl( \frac{\sigma_c^2}{6\gamma_\mathrm{g}}\biggr)\xi^2 - \alpha \xi \biggl( \frac{d\psi}{d\xi} \biggr) \biggr] \frac{x}{\xi^2} </math> </td> </tr> <tr> <td alig..." current
• 18:4618:46, 11 December 2023 diff hist +734 N Template:Math/EQ RadialPulsation02 Created page with "<table border=0 cellpadding=2> <tr> <td align="right"> 25px|link=Appendix/EquationTemplates#Stability:_Radial_Pulsation </td> <td align="center"> <math>0 = \frac{d^2x}{d\xi^2} + \biggl[ 4 - (n+1) Q \biggr] \frac{1}{\xi} \cdot \frac{dx}{d\xi} + (n+1) \biggl[ \biggl( \frac{\sigma_c^2}{6\gamma_g } \biggr) \frac{\xi^2}{\theta} - \alpha Q\biggr] \frac{x}{\xi^2} </math> </td> </tr> <tr> <td align="center" colspan="2"> where:    <math>Q(\x..." current
• 18:4018:40, 11 December 2023 diff hist +24,389 N Apps/RiemannEllipsoidsCompressible Created page with "__FORCETOC__ <!-- will force the creation of a Table of Contents --> <!-- __NOTOC__ --> =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__ <!-- __NOTOC__ --> <font color="red"><b> NOTE to Eric Hirschmann & David Neilsen... </b></font> 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__ <!-- __NOTOC__ will force TOC off --> =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 "<!-- __FORCETOC__ will force the creation of a Table of Contents --> <!-- __NOTOC__ will force TOC off --> =Equations Cast in Cylindrical Coordinates= <table align="center" border="0" cellpadding="5"> <tr> <td colspan="3" align="center"> <font color="#770000"><b>Spatial Operators in Cylindrical Coordinates</b></font> </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"> <font size="-1"> 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 "<span title="Euclidean 3-space velocity vector"><math>\vec{v}</math></span>" current
• 17:5917:59, 11 December 2023 diff hist +40 N Template:Math/VAR Time01 Created page with "<span title="Time"><math>t</math></span>" current
• 17:5817:58, 11 December 2023 diff hist +47 N Template:Math/VAR Temperature01 Created page with "<span title="Temperature"><math>T</math></span>" current
• 17:5717:57, 11 December 2023 diff hist +67 N Template:Math/VAR SpecificInternalEnergy01 Created page with "<span title="Specific internal energy"><math>\epsilon</math></span>" current
• 17:5617:56, 11 December 2023 diff hist +52 N Template:Math/VAR SpecificEntropy01 Created page with "<span title="Specific entropy"><math>s</math></span>" current
• 17:5517:55, 11 December 2023 diff hist +44 N Template:Math/VAR Pressure01 Created page with "<span title="Pressure"><math>P</math></span>" current
• 17:5417:54, 11 December 2023 diff hist +75 N Template:Math/VAR PositionVector01 Created page with "<span title="Euclidean 3-space position vector"><math>\vec{x}</math></span>" current
• 17:5417:54, 11 December 2023 diff hist +72 N Template:Math/VAR NewtonianPotential01 Created page with "<span title="Newtonian gravitational potential"><math>\Phi</math></span>" current
• 17:5217:52, 11 December 2023 diff hist +51 N Template:Math/VAR Density01 Created page with "<span title="Mass density"><math>\rho</math></span>" 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