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13:47, 5 July 2024 Joel2 talk contribs created page File:CKST95dAnnotated.png
13:47, 5 July 2024 Joel2 talk contribs uploaded File:CKST95dAnnotated.png
13:46, 5 July 2024 Joel2 talk contribs created page File:FirstIdeasAnnotated.png
13:46, 5 July 2024 Joel2 talk contribs uploaded File:FirstIdeasAnnotated.png
13:43, 5 July 2024 Joel2 talk contribs created page Appendix/Ramblings/TrigFunctions (Created page with "__FORCETOC__  =Analytic Expressions for Selected Trigonometric Functions= In what follows we generally will provide expressions that result from evaluating <math>\sin\theta</math>, with the understanding that <math>\cos\theta</math> and <math>\tan\theta</math> then also can be evaluated straightforwardly via the familiar relations, <table border="0" align="center" cellpadding="5"> <tr> <td align="right"><math>\cos\theta</math></td...")
13:39, 5 July 2024 Joel2 talk contribs created page File:OurHE84Fig1annotated.png
13:39, 5 July 2024 Joel2 talk contribs uploaded File:OurHE84Fig1annotated.png
18:41, 4 July 2024 Joel2 talk contribs created page PGE/RotatingFrameOld (Created page with "__FORCETOC__  <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>...")
18:23, 4 July 2024 Joel2 talk contribs created page Appendix/Ramblings/HybridSchemeImplications (Created page with "__FORCETOC__  =Implications of Hybrid Scheme= ==Background== ===Key H_Book Chapters=== [Ref01] Inertial-Frame Euler Equation [Ref02] Traditional Description of Rotating Reference Frame [Ref03] Hybrid Advection Scheme [Ref04] ThreeDimensionalConfigurations/RiemannStype#Based_on_Detailed_Force_Balance|Rieman...")
18:10, 4 July 2024 Joel2 talk contribs created page Appendix/Ramblings/HybridSchemeOld (Created page with "__FORCETOC__  =Hybrid Advection Scheme= ==Preface== ''March 1, 2014'' by Joel E. Tohline <full preface> … This seemed too good to be true. The discovered code modification would allow us to conserve angular momentum very accurately and, at the same time, allow us to use a rotating grid and thereby minimize numerical diffusion … <read more> In his dissertation research, Jay Call...")
18:07, 4 July 2024 Joel2 talk contribs created page PGE/AStarScheme (Created page with "__FORCETOC__  =Hybrid Advection Scheme (Background)= ''March 1, 2014'' by Joel E. Tohline As is mentioned in the preface to our primary discussion of the Hybrid Advection Scheme, my early notes on this topic were included in my earliest version of this web-based H_Book. The relevant page can be accessed [http://www.phys.lsu.edu/astro/H_Book.current/Context/PGE/angmom.conserve.html via this...")
18:05, 4 July 2024 Joel2 talk contribs created page PGE/HybridSchemePreface (Created page with "__FORCETOC__  =Hybrid Advection Scheme (Preface)= Go to: Hybrid Advection Scheme ''March 1, 2014'' by Joel E. Tohline Throughout my research career, I have sought new or modified techniques and algorithms that would allow my group to perform more accurate numerical simulations of astrophysical fluid flows. At the beginning — following the advice of my dissertation co-advisors, Pete...")
17:58, 4 July 2024 Joel2 talk contribs created page Appendix/PolytropicBinaries (Created page with "__FORCETOC__  =Polytropic Models of Close Binary Star Systems= Over the past half-a-dozen years, Patrick Motl, Mario D'Souza, and Wes Even have used the Hachisu SCF technique to construct 3D equilibrium models of synchronously rotating, tidally distorted binary polytropes. To date, four of these models have been used extensively as initial states for our dynamical simulations of binary mass-transfer. Various properties of these f...")
17:38, 4 July 2024 Joel2 talk contribs created page Appendix/Ramblings/Photosphere (Created page with "__FORCETOC__  ==Locating the Photosphere of Stably Accreting Double White Dwarf Binaries== ===Context=== At our regularly scheduled astrophysics group meeting on Monday, 2 May 2011, Juhan Frank and I started debating the answer to the following question: What should the photospheric radius be of the common envelope that surrounds a stably accreting, double white dwarf (DWD) binary? That is, does an accreting DWD binary that is des...")
17:37, 4 July 2024 Joel2 talk contribs created page Appendix/Ramblings/Radiation/InitialTemperatures (Created page with "__FORCETOC__  =Initial Temperature Distributions= In an accompanying Wiki page we've discussed in detail (or see the summary page) how to transform back and forth between cgs units and the dimensionless code units that have been adopted by Dominic Marcello in his radiation-hydro simulations of binary mass-transfer. Here w...")
17:35, 4 July 2024 Joel2 talk contribs created page Appendix/Ramblings/Radiation/SummaryScalings (Created page with "__FORCETOC__  =Summary of Scalings= On an accompanying Wiki page we have explained how to interpret the set of dimensionless units that Dominic Marcello is using in his rad-hydrocode. The following tables summarize some of the mathematical relationships that have been derived in that accompanying discussion. <!-- ***************************************** * * * FIRST TABLE * * ***********...")
17:28, 4 July 2024 Joel2 talk contribs created page Appendix/Ramblings/Radiation/CodeUnits (Created page with "__FORCETOC__  =Marcello's Radiation-Hydro Simulations= ==Determining Code Units== ===Logic Used by Dominic Marcello=== At our group meeting on 21 July 2010, Dominic explained how he had established the values of various coupling constants in his first, long, <math>q_0 = 0.7</math> simulations. In place of the physical constants, {{Math/C_GravitationalConstant}}, {{Math/C_SpeedOfLight}}, {{Math/C_GasConstant}}, and {{Math/C_Radiat...")
15:23, 4 July 2024 Joel2 talk contribs created page Apps/RotatingPolytropes/BarmodeLinearTimeDependent (Created page with "__FORCETOC__  =Onset of Bar-mode Instability in Differentially Rotating, Axisymmetric Polytropes= {| class="CazesDissertation" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:white;" |<b>Initially<br />Axisymmetric<br />& Differentially<br />Rotating<br />Polytropes</b>...")
15:19, 4 July 2024 Joel2 talk contribs created page Aps/MaclaurinSpheroidFreeFall (Created page with "__FORCETOC__  =Free-Fall Collapse of an Homogeneous Spheroid= {| class="FreeFallSpheroid" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffff99;" |<b>Free-Fall<br />Collapse<br />of an<br />Homogeneous<br />Spheroid</b> |} <table border="0" cellpadding="3" align="center" wi...")
15:08, 4 July 2024 Joel2 talk contribs created page Jaycall/T3Coordinates/SpecialCase (Created page with "__FORCETOC__  ==Coordinate Transformations== If the special case <math>q^2=2</math> is considered, it is possible to invert the coordinate transformations in closed form. The coordinate transformations and their inversions become <table align="center" border="0" cellpadding="2"> <tr> <td align="right"> <math> \lambda_1 </math> </td> <td align="center"> <math>\equiv</math> </td> <td align="left"> <math>\left( R^2+2z^2 \r...")
15:05, 4 July 2024 Joel2 talk contribs created page Appendix/Ramblings/T3Integrals/QuadraticCase (Created page with "__FORCETOC__  =T3 Coordinates (continued)= On one accompanying wiki page we have introduced T3 Coordinates and on another we have described how Jay Call's Characteristic Vector applies to T3 Coordinates. Here we investigate the properties of our T3 Coordinate system in the sp...")
14:28, 4 July 2024 Joel2 talk contribs created page File:EUREKA 21Jan2021 sm.png
14:28, 4 July 2024 Joel2 talk contribs uploaded File:EUREKA 21Jan2021 sm.png
14:09, 4 July 2024 Joel2 talk contribs created page Appendix/Ramblings/ForOuShangli (Created page with "  =For Shangli Ou= In order to download any one of (a selected subset of) the COLLADA-based model files referenced below, go to … <table border="3" align="center" cellpadding="10"><tr><td align="center" bgcolor="red"> <table border="0" cellpadding="8" align="center"> <tr> <td align="center"> Appendix/Ramblings/COLLADA/RiemannSType|<font color="white" size...")
14:03, 4 July 2024 Joel2 talk contribs created page Appendix/Ramblings/COLLADA/RiemannSType (Created page with "__FORCETOC__   =COLLADA-based Models of Riemann S-Type Ellipsoids= <div align="center"><font color="darkgreen">(Initially posted January 2021)</font> </div> ==Instructions== Table 1 provides links to a variety of COLLADA-based animated 3D models that have been developed for use wi...")
13:51, 4 July 2024 Joel2 talk contribs created page ThreeDimensionalConfigurations/DescriptionOfRiemannTypeI (Created page with "__FORCETOC__   =Description of Riemann Type I Ellipsoids= {| class="RiemannType1" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#ffeeee;" |<b>Type I<br />Riemann<br />Ellipsoids</b> |} A more succinct version of this...")
13:02, 4 July 2024 Joel2 talk contribs created page File:CropTopB.png
13:02, 4 July 2024 Joel2 talk contribs uploaded File:CropTopB.png
13:02, 4 July 2024 Joel2 talk contribs created page File:WolframAlphaTorusVolume.png
13:02, 4 July 2024 Joel2 talk contribs uploaded File:WolframAlphaTorusVolume.png
19:21, 3 July 2024 Joel2 talk contribs created page File:YZplaneXm085.png
19:21, 3 July 2024 Joel2 talk contribs uploaded File:YZplaneXm085.png
19:20, 3 July 2024 Joel2 talk contribs created page File:YZplane3.png
19:20, 3 July 2024 Joel2 talk contribs uploaded File:YZplane3.png
19:12, 3 July 2024 Joel2 talk contribs created page ThreeDimensionalConfigurations/ChallengesPt6 (Created page with "__FORCETOC__  =Challenges Constructing Ellipsoidal-Like Configurations (Pt. 6)= This chapter has been created in February 2022, after letting this discussion lie dormant for close to one year. We begin the chapter by grabbing large segments of our earlier derivations found primarily in the "Ramblings" chapter titled, ThreeDimensionalConfigurations/ChallengesPt4|''Construction...")
19:10, 3 July 2024 Joel2 talk contribs created page ThreeDimensionalConfigurations/ChallengesPt5 (Created page with "__FORCETOC__  =Challenges Constructing Ellipsoidal-Like Configurations (Pt. 5)= This chapter extends the accompanying chapters titled, ''Construction Challenges (Pt. 1)'', ''(Pt. 2)'', ''(Pt. 3)'', and ThreeDimensionalConfigurations/Ch...")
19:09, 3 July 2024 Joel2 talk contribs created page ThreeDimensionalConfigurations/ChallengesPt4 (Created page with "__FORCETOC__  =Challenges Constructing Ellipsoidal-Like Configurations (Pt. 4)= This chapter extends the accompanying chapters titled, ''Construction Challenges (Pt. 1)'', ''(Pt. 2)'', and ''(Pt. 3)''. The focus here is on firming up ou...")
19:07, 3 July 2024 Joel2 talk contribs created page ThreeDimensionalConfigurations/ChallengesPt3 (Created page with "__FORCETOC__  =Challenges Constructing Ellipsoidal-Like Configurations (Pt. 3)= This chapter extends the accompanying chapters titled, ''Construction Challenges (Pt. 1)'' and ''(Pt. 2)''. The focus here is on firming up our understanding of the relationships between various "tilted" C...")
19:06, 3 July 2024 Joel2 talk contribs created page ThreeDimensionalConfigurations/ChallengesPt2 (Created page with "__FORCETOC__  =Challenges Constructing Ellipsoidal-Like Configurations (Pt. 2)= This chapter extends an accompanying chapter titled, ''Construction Challenges (Pt. 1)''. The focus here is on an SCF technique that will incorporate specification of a Lagrangian flow-flied. ==Motivation== ===Where Are We Headed?=== In a ThreeDimensi...")
18:47, 3 July 2024 Joel2 talk contribs created page ThreeDimensionalConfigurations/Challenges (Created page with "__FORCETOC__  =Challenges Constructing Ellipsoidal-Like Configurations= First, let's review the three different approaches that we have described for constructing Riemann S-type ellipsoids. Then let's see how these relate to the technique that has been used to construct infinitesimally thin, nonaxisymmetric disks. ==Riemann S-type Ellipsoids== Usually, the density, <math>~\r...")
18:26, 3 July 2024 Joel2 talk contribs created page File:PrimedCoordinates3.png
18:26, 3 July 2024 Joel2 talk contribs uploaded File:PrimedCoordinates3.png
18:24, 3 July 2024 Joel2 talk contribs created page File:EFEfig17firstSmall.png
18:24, 3 July 2024 Joel2 talk contribs uploaded File:EFEfig17firstSmall.png
18:22, 3 July 2024 Joel2 talk contribs created page File:F McA.png
18:22, 3 July 2024 Joel2 talk contribs uploaded File:F McA.png
18:12, 3 July 2024 Joel2 talk contribs created page ThreeDimensionalConfigurations/CAREs (Created page with "__FORCETOC__  =New Thoughts Regarding the Formation of Binary Stars= {| class="CAREs" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:white;" |<b>Thoughts<br />&<br />Challenges</b> |} It is February, 2020 and I hav...")
15:09, 3 July 2024 Joel2 talk contribs created page File:ProjectedOrbitsFlipped2.png
15:09, 3 July 2024 Joel2 talk contribs uploaded File:ProjectedOrbitsFlipped2.png
15:08, 3 July 2024 Joel2 talk contribs created page File:B125c470B.cropped.png

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