Editing Appendix/Ramblings (section)

=Ramblings=

Sometimes I explore some ideas to a sufficient depth that it seems worthwhile for me to archive the technical derivations even if the idea itself does not immediately produce a publishable result.  This page, which has a simple outline layout, provides links to these various pages of technical notes.

<ol>
  <li>[[Appendix/Ramblings/myPhys|Files on LSU P&amp;A servers (myPhys)]]</li>
  <li>Orthogonal Curvilinear Coordinate Systems
<ol type="a">
  <li>[[Appendix/Ramblings/DirectionCosines|Direction Cosines]]</li>
  <li>[[Appendix/Ramblings/EllipticCylinderCoordinates|(Confocal) Elliptic Cylinder Coordinates]] plus Concentric Analog ([[Appendix/Ramblings/EllipticCylinderCoordinates#T5_Coordinates|T5 Coordinates]])</li>
  <li>Concentric Ellipsoidal Coordinates:
  <ol>
  <li>[[Appendix/Ramblings/ConcentricEllipsoidalCoordinates|T6 Coordinates (pt. 1)]]</li>
  <li>[[Appendix/Ramblings/T6CoordinatesPt2|T6 Coordinates (pt. 2)]] </li>
  <li>[[Appendix/Ramblings/T6CoordinatesPt3|T6 Coordinates (pt. 3)]] </li>
  <li>[[Appendix/Ramblings/ConcentricEllipsoidalT8Coordinates|Concentric Ellipsoidal (T8) Coordinates]] </li>
  <li>[[Appendix/Ramblings/T9Coordinates|T9 Coordinates]]</li>
  <li>[[Appendix/Ramblings/ConcentricEllipsoidalT12Coordinates|Concentric Ellipsoidal (T12) Coordinates]]</li>
  </ol>
  </li>
  <li>[[Appendix/Ramblings/ConcentricEllipsoidalDaringAttack|Daring Attack]]</li>
</ol>
  </li>
  <li>[[Appendix/Ramblings/T1Coordinates|Relationship between HNM82 models and T1 coordinates]]</li>
  <li>[[Appendix/Ramblings/SphericalWaveEquation|Playing with the Spherical Wave Equation]]</li>
  <li>Analyzing Azimuthal Distortions
     <ol style="list-style-type:lower-latin">
        <li>[[Appendix/Ramblings/ToHadleyAndImamura|Summary for Hadley &amp; Imamura]]</li>
        <li>[[Appendix/Ramblings/AzimuthalDistortions#Analyzing_Azimuthal_Distortions|Detailed Notes]] &nbsp; [[Appendix/Ramblings/AzimuthalDistortions#Constant_Phase_Loci|<font size="+1">&#x1F3A6;</font>]] </li>
        <li>[[Appendix/Ramblings/HadleyAndImamuraSupplementaryDatabase|Supplementary database generated by the Hadley &amp; Imamura collaboration]]</li>
        <li>[http://pages.uoregon.edu/khadley/ Large supplementary dataset accumulated by the Hadley &amp; Imamura collaboration] &hellip; access to this server may be denied</li>
        <li>[[Apps/WoodwardTohlineHachisu94#Online_Movies|YouTube videos]] that supplement simulations of [http://adsabs.harvard.edu/abs/1994ApJ...420..247W J. W. Woodward, J. E. Tohline, &amp; I. Hachisu (1994)]</li>
        <li>[[Appendix/Ramblings/PPToriPt1A|Stability Analyses of PP Tori]] (Part 1A)</li>
        <li>[[Appendix/Ramblings/PPToriPt2A|Stability Analyses of PP Tori]] (Part 2A)</li>
     </ol>
  <li>Integrals of Motion</li>
    <ol style="list-style-type:lower-latin">
      <li>[http://www.phys.lsu.edu/astro/H_Book.current/Appendices/Integrals/integrals.of.motion.pdf Old discussion]</li>
      <li>[[Appendix/Ramblings/T3Integrals|T3 Coordinates]]</li>
          <ol style="list-style-type:lower-roman">
            <li>Special (quadratic) case: [[Appendix/Ramblings/T3Integrals/QuadraticCase|Joel's Derivation]] vs. 
             [[Jaycall/T3Coordinates/SpecialCase|Jay's Derivation]]</li>
          </ol>
      <li>[[Jaycall/KillingVectorApproach|Killing Vector Approach]]; Jay Call's related [[Jaycall/KillingVectorApproach#Related_Talk_Session|''Talk'' session]]</li>
      <li>[[Appendix/Ramblings/T3CharacteristicVector|Characteristic Vector for T3 Coordinates]]</li>
      <li>[[Appendix/Ramblings/T4Integrals|T4 Coordinates]] (Abandoned by Joel 7/6/2010 because non-orthogonal)</li>
    </ol>
  <li>Marcello's Radiation-Hydro Simulations</li>
    <ol style="list-style-type:lower-latin">
      <li>[[Appendix/Ramblings/Radiation/RadHydro|Radiation-Hydrodynamics]]</li>
      <li>[[Appendix/Ramblings/Radiation/CodeUnits|Determining Code Units]]</li>
      <li>[[Appendix/Ramblings/Radiation/SummaryScalings#Summary_of_Scalings|Summary of Scalings]]</li>
      <li>[[Appendix/Ramblings/Radiation/InitialTemperatures|Initial Temperature Distributions]]</li>
    </ol>
  <li>[[Appendix/Ramblings/Photosphere|Photosphere of Stably Accreting DWD]]</li>
  <li>[[Appendix/PolytropicBinaries|Binary Polytropes]]</li>
  <li>A* Scheme
    <ol type="a">
      <li>[[PGE/HybridSchemePreface|Hybrid Scheme Preface]]</li>
      <li>[[PGE/AStarScheme|A<sup>*</sup> Scheme]]</li>
      <li>[[Appendix/Ramblings/HybridSchemeOld|Initial Effort to Explain Jay Call's ''Hybrid'' Scheme in the Context of Zach Byerly's Dissertation]]</li>
      <li>[[Appendix/Ramblings/HybridSchemeImplications|Implications of Hybrid Scheme]]
    </ol>
  </li>
  <li>Other Structural and/or Stability Considerations for Spherically Symmetric Configurations
    <ol type="a">
      <li>
[[Appendix/Ramblings/NonlinarOscillation|Exploring the Properties of Radial Oscillations in Pressure-Truncated n = 5 Polytropes]]
      </li>
      <li>
[[SSC/Stability/NeutralMode|Radial Pulsation Neutral Mode]]
      </li>
      <li>
[[SSC/Structure/OtherAnalyticModels#Parabolic_Density_Distribution|Other Analytic Models]], e.g., Parabolic Density Distribution
      </li>
      <li>
[[SSC/Structure/OtherAnalyticRamblings|Other Analytic Ramblings]]
      </li>
      <li>
[[SSC/FreeEnergy/PowerPoint|SSC/FreeEnergy/PowerPoint]]
      </li>
      <li>
[https://ui.adsabs.harvard.edu/abs/1970PASA....1..325V/abstract R. Van der Borght (1970), Proc. Astronomical Soc. Australia, Vol. 1, Issue 7, pp. 325 - 326)]: &nbsp; ''Adiabatic Oscillations of Stars''
      </li>
      <li>
[[SSC/Stability/GammaVariation|How Does Stability Change With &gamma;<sub>g</sub> and P<sub>e</sub>?]] &nbsp; &nbsp; &lArr; &nbsp; Contains Lane-Emden equation in terms of Entropy
      </li>
    </ol>
  </li>
  <li>[[Appendix/Ramblings/TurningPoints#Turning_Points|Instabilities Associated with Equilibrium Sequence Turning Points]]</li>
  <li>[[Appendix/Ramblings/LedouxVariationalPrinciple|Derivations Related to Ledoux's Variational Principle]]
  <li>More on Zero-Zero Bipolytropes</li>
    <ol style="list-style-type:lower-latin">
      <li>[[SSC/Stability/BiPolytrope00Old#Radial_Oscillations_of_a_Zero-Zero_Bipolytrope|Pt 1: Radial Oscillations of a Zero-Zero-Bipolytrope (Early Flawed Summary)]]</li>
      <li>[[SSC/Stability/BiPolytrope00Details#Radial_Oscillations_of_a_Zero-Zero_Bipolytrope|Pt 2:  Details]]</li>
      <li>[[Appendix/Ramblings/AdditionalAnalyticallySpecifiedEigenvectors00Bipolytropes#Searching_for_Additional_Eigenvectors_of_Zero-Zero_Bipolytropes|Pt 3: Searching for Additional Eigenvectors]]</li>
      <li>[[SSC/Stability/BiPolytrope00#Radial_Oscillations_of_a_Zero-Zero_Bipolytrope|Pt 4:  Good Summary]]</li>
      <li>[[Appendix/Ramblings/NumericallyDeterminedEigenvectors|Numerically Determined Eigenvectors]]; &nbsp;&nbsp;&nbsp;Also originally saved with preface [[User:Tohline/Appendix/Ramblings/NumericallyDeterminedEigenvectors|"User:Tohline"]]</li>
      <li>[[SSC/Stability/BiPolytrope00CompareApproaches|Compare Approaches]]</li>
    </ol>
  <li>Analyzing Five-One Bipolytropes</li>
    <ol style="list-style-type:lower-latin">
      <li>[[SSC/Stability/BiPolytropes/51Models|BiPolytropes with (n<sub>c</sub>, n<sub>e</sub>) = (5, 1)]]</li>
      <li>[[SSC/Stability/BiPolytropes/HeadScratching|Broader Examination of BiPolytrope Stability]]</li>
      <li>[[Appendix/Ramblings/BiPolytropeStability|Assessing the Stability of Spherical, BiPolytropic Configurations]]</li>
      <li>[[Appendix/Ramblings/BiPolytrope51AnalyticStability|Searching for Analytic EigenVector for (5,1) Bipolytropes]]</li>
      <li>See (below) Discussing Patrick Motl's 2019 BiPolytrope Simulations</li>
      <li>[[Appendix/Ramblings/BiPolytrope51ContinueSearch|Continue Search]]</li>
      <li>[[SSC/Structure/BiPolytropes/Analytic51Renormalize|Renormalize Structure]] &nbsp; &nbsp; &lArr; &nbsp; &nbsp; Broken into 3 chapter segments</li>
      <li>[[SSC/Structure/BiPolytropes/51RenormaizePart2|Renormalize Structure (Part 2)]]</li>
      <li>[[SSC/Structure/BiPolytropes/51RenormaizePart3|Renormalize Structure (Part 3)]]</li>
      <li>[[SSC/Structure/BiPolytropes/AnalyzeStepFunction|More Carefully Exam Step Function Behavior]]</li>
      <li>[[Appendix/Ramblings/51AnalyticStabilitySynopsis|More Focused Search]] for Analytic EigenVector if (5,1) Bipolytropes</li>
      <li>[[Appendix/Ramblings/51BiPolytropeStability/NoAnalytic|Do Not Confine Search to Analytic Eigenvector]]</li>
      <li>[[Appendix/Ramblings/51BiPolytropeStability/CleanMethodicalExaminatioin|Clean, Methodical Examination]]</li>
      <li>[[Appendix/Ramblings/51BiPolytropeStability/RethinkEnvelope|Rethink Handling of n = 1 Envelope]]</li>
      <li>Improved Treatment of Core-Envelope Interface:
          <ol>
          <li>[[Appendix/Ramblings/51BiPolytropeStability/BetterInterface|Part 1]]</li>
          <li>[[Appendix/Ramblings/51BiPolytropeStability/BetterInterfacePt2|Part 2]]</li>
          </ol>
      </li>

    </ol>
  <li>Interrelating 51 and 00 Bipolytropes</li>
    <ol style="list-style-type:lower-latin">
      <li>[[Appendix/Ramblings/Interrelating51and00Bipolytropes/Organization|Organization]]</li>
    </ol>
  <li>[[Appendix/Ramblings/OriginOfPlanetaryNebulae|On the Origin of Planetary Nebulae]] (Investigation Resulting from a July, 2013 Discussion with Kundan Kadam)</li>
  <li>[[Appendix/Ramblings/InsideOut|Looking outward, from Inside a Black Hole]]</li>
  <li>[[Appendix/Ramblings/Dyson1893Part1|Dyson (1893a) Part I: &nbsp;Some Details]]</li>
  <li>[[Appendix/Ramblings/Saturn#Saturn|Saturn]]</li>
  <li>[[Appendix/Ramblings/MyDoctoralStudents|Doctoral students Tohline has advised]] over the years</li>
  <li>[[Appendix/Ramblings/PatrickMotl|Discussing Patrick Motl's 2019 BiPolytrope Simulations]]</li>
  <li>[[Appendix/Ramblings/ForDurisen|For Richard H. Durisen]]</li>
  <li>[[Appendix/Ramblings/ForOuShangli|For Shangli Ou]]</li>
  <li>For Howard Cohl:
<ol type="a">
      <li>[[Appendix/Ramblings/ForCohlHoward|Ongoing Collaborative Discussions]]</li>
      <li>[[Appendix/Ramblings/MacSphCriticalPoints|Critical Points along the Maclaurin Spheroid Sequence]]</li>
</ol>
  </li>
  <li>[[Appendix/Ramblings/ForPaulFisher|For Paul Fisher]]</li>
  <li>[[Appendix/Ramblings/ForPJinApril2021|For PJ in April 2021]]</li>
<li>Challenges Constructing Ellipsoidal-Like Configurations
    <ol type="a">
    <li>[[3Dconfigurations/DescriptionOfRiemannTypeI|Riemann Type I Description]]&nbsp; &nbsp; <math>\Leftarrow</math> &nbsp; &nbsp; Most succinct description</li>
    <li>[[ThreeDimensionalConfigurations/DescriptionOfRiemannTypeI|Riemann Type I Description]]&nbsp; &nbsp; (early presentation)</li>
    <li>[[ThreeDimensionalConfigurations/Challenges#Challenges_Constructing_Ellipsoidal-Like_Configurations|Construction Challenges (Pt. 1)]]</li>
    <li>[[ThreeDimensionalConfigurations/ChallengesPt2|Construction Challenges (Pt. 2)]]</li>
    <li>[[ThreeDimensionalConfigurations/ChallengesPt3|Construction Challenges (Pt. 3)]]</li>
    <li>[[ThreeDimensionalConfigurations/ChallengesPt4|Construction Challenges (Pt. 4)]]</li>
    <li>[[ThreeDimensionalConfigurations/ChallengesPt5|Construction Challenges (Pt. 5)]]</li>
    <li>[[ThreeDimensionalConfigurations/ChallengesPt6|Construction Challenges (Pt. 6)]]</li>
    <li>[[ThreeDimensionalConfigurations/RiemannTypeI|Example Type I: b1.23c0.470]]</li>
    <li>Related discussions of models viewed from a rotating reference frame:
        <ol type="i">
        <li>[[PGE/RotatingFrame#Rotating_Reference_Frame|PGE/RotatingFrame]]</li>
        <li><font color="red"><b>NOTE to Eric Hirschmann &amp; David Neilsen...  </b></font>I have moved the earlier contents of this page to a new Wiki location called [[Apps/RiemannEllipsoidsCompressible|Compressible Riemann Ellipsoids]].</li>
        </ol>
    </li>
    <li>[[Apps/RiemannEllipsoidsCompressible|Compressible Analogs of Riemann Ellipsoids]] (CAREs)</li>
    </ol>
</li>
<li>[[ThreeDimensionalConfigurations/MeetsCOLLADAandOculusRiftS#Riemann_Meets_COLLADA_.26_Oculus_Rift_S|Riemann Meets COLLADA and Oculus Rift S]]: Example '''(b/a, c/a) = (0.41, 0.385)'''
  <ol type="a">
  <li>[[Appendix/Ramblings/VirtualReality#Virtual_Reality_and_3D_Printing|Virtual Reality and 3D Printing]]</li>
  <li>[[Appendix/Ramblings/OculusRiftS|Success Importing Animated Scene into Oculus Rift S]]</li>
  <li>[[Appendix/Ramblings/RiemannMeetsOculus|Carefully (Re)Build Riemann Type S Ellipsoids Inside Oculus Rift Environment]]</li>
  <li>Other Example S-type Riemann Ellipsoids:
      <ol type="i">
      <li>[[Appendix/Ramblings/RiemannB90C333|(b/a, c/a) = (0.90, 0.333)]]</li>
      <li>[[Appendix/Ramblings/RiemannB74C692|(b/a, c/a) = (0.74, 0.692)]]</li>
      <li>[[Appendix/Ramblings/RiemannB28C256|(b/a, c/a) = (0.28, 0.256)]]</li>
      </ol>
  </li>
  <li>[[Appendix/Ramblings/COLLADA/RiemannSType|Pointers to a collection of COLLADA-based Models of Riemann S-Type Ellipsoids]]</li>
  </ol>
</li>
<li>Bordeaux University
  <ol type="a">
<li>[[Appendix/Ramblings/Bordeaux|External Gravitational Potential of Toroids]]</li>
<li>[[Appendix/Ramblings/BordeauxSequences|Spheroid-Ring Sequences]]</li>
<li>[[Appendix/Ramblings/BordeauxPostDefense|Discussions Following Dissertation Defense]]</li>
  </ol>
</li>
<li>[[Appendix/Ramblings/CopyrightIssues|Copyright Issues]]</li>
<li>Old VisTrails Title Page
  <ol type="a">
  <li>[[Appendix/Ramblings/OldVistrailsTitlePage|Entire (Old) Vistrails Title Page]]. &nbsp; &nbsp; <font color="red"><== &nbsp; NO!  Replaced by [[OldVistrailsCoverPage|''Old (Vistrails) Cover Page'']]</font></li>
  <li>[[Appendix/Ramblings/DarkMatterMusings|Musings Regarding Dark Matter and Dark Energy]]</li>
  <li>[[Appendix/Ramblings/StrongNuclearForce|Radial Dependence of the Strong Nuclear Force]]</li>
  </ol>
</li>
<li>
  Journal Refereeing
  <ol>
<li><b>ApJ (2023):</b> &nbsp;[[Appendix/Ramblings/BdHN|Binary-driven Hypernovae (BdHN)]]</li>
  </ol>
</li>
<li>
  Parabolic Density Distribution
  <ol>
<li>[[ParabolicDensity/GravPot|Gravitational Potential]]</li>
<li>[[ParabolicDensity/Spheres/Structure|Spherical Structures]]</li>
<li>[[ParabolicDensity/Axisymmetric/Structure|Axisymmetric Equilibrium Structures]]</li>
<li>[[ParabolicDensity/Triaxial/Structure|Triaxial Equilibrium Structures (Exploration)]]</li>
  </ol>
</li>
<li>
  [[Appendix/QED|Feymann's Path-Integral Formulation (QED)]]
</li>
<li>
  [[Appendix/MediaWiki_Schubotz|Debugging math alignment in MediaWiki]]
</li>
</ol>