Editing Appendix/Ramblings

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=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>

=Mathematics=
<ol>
  <li>Roots of Cubic Equation</li>
      <ol style="list-style-type:lower-latin">
          <li>In the context of [[Appendix/Ramblings/T1Coordinates#Second_Special_Case_.28cubic.29|T2 Coordinates]], when <math>q^2 = (a_1/a_3)^2=3</math>.</li>
          <li>[[Appendix/Ramblings/PPToriPt1A#Cubic_Equation_Solution|PP Tori]] &#8212; Also includes [[Appendix/Ramblings/PPToriPt1A#CubeRootImaginary|cube root of a complex number]]</li>
          <li>[[SSC/Structure/Polytropes#CubicRoot|Srivastava's F-Type solution]] for <math>n=5</math> polytropes.</li>
          <li>[[SSC/Structure/BiPolytropes/Analytic15#Analytic_Solution_of_Key_Interface_Relation|Murphy &amp; Fiedler's Bipolytrope]] with <math>(n_c, n_e) = (1,5)</math></li>
          <li>[[Appendix/Ramblings/AdditionalAnalyticallySpecifiedEigenvectors00Bipolytropes#Solve_Cubic_Equation|Analytic Eigenfunctions for Bipolytropes]] with <math>(n_c, n_e) = (0, 0)</math> &#8212; also involves cube root of a complex number</li>
       </ol>
  <li> Roots of Quartic Equation</li>
      <ol style="list-style-type:lower-latin">
         <li>[[SSC/Stability/BiPolytrope00Details#Roots_of_Quartic_Equation|Analytic Eigenfunction for Bipolytropes]] with <math>(n_c, n_e) = (0, 0)</math></li>
         <li>[[SR/Ptot_QuarticSolution#Quartic_Equation_Solution|Determine temperature from total pressure]]
      </ol>
  <li>Singular Sturm-Liouville (eigenvalue) Problem</li>
      <ol style="list-style-type:lower-latin">
          <li>[[Apps/Blaes85SlimLimit#Singular_Sturm-Liouville_Problem|Oscillations of PP Tori]] in the slim torus limit</li>
          <li>[[Apps/ImamuraHadleyCollaboration#Singular_Sturm-Liouville_Problem|Characteristics of unstable eigenvectors in self-gravitating tori]]</li>
     </ol>
  <li>[[Appendix/Ramblings/PowerSeriesExpressions|Approximate Power-Series Expressions]]</li>
  <li>[[Appendix/Ramblings/FourierSeries|Fourier Series]]</li>
  <li>[[Appendix/Ramblings/TrigFunctions|Analytic Expressions for Selected Trigonometric Functions]]</li>
  <li>[[AxisymmetricConfigurations/PoissonEq#Special_Functions_.26_Other_Broadly_Used_Representations|Special Functions &amp; Other Broadly Used Representations]]</li>
      <ol>
        <li>[[AxisymmetricConfigurations/PoissonEq#Spherical_Harmonics_and_Associated_Legendre_Functions|Spherical Harmonics and Associated Legendre Functions]]</li>
        <li>[[AxisymmetricConfigurations/PoissonEq#Multipole_Expansions|Multipole Expansions]]</li>
        <li>[[AxisymmetricConfigurations/PoissonEq#Familiar_Expression_for_the_Cylindrical_Green.27s_Function_Expansion|Familiar Expression for the Cylindrical Green's Function Expansion]]</li>
        <li>[[AxisymmetricConfigurations/PoissonEq#Toroidal_Functions|Toroidal Functions]]</li>
      </ol>
  <li>Green's Function in terms of Toroidal Functions</li>
      <ol style="list-style-type:lower-latin">
          <li>[[Appendix/Ramblings/CCGF|Compact Cylindrical Green Function]]</li>
          <li>[[Appendix/Ramblings/ToroidalCoordinates#Relating_CCGF_Expansion_to_Toroidal_Coordinates|Toroidal configurations &amp; related coordinate systems]] &#8212; Includes <b><font color="red">EUREKA!</font></b> moment; also uses [[Appendix/Ramblings/ToroidalCoordinates#Examples|wikitable overflow]] (scrolling) box</li>
          <li>[[2DStructure/ToroidalCoordinateIntegrationLimits#Evaluation_of_Elliptic_Integrals|Toroidal Coordinate Integration Limits]] <math>\Leftarrow ~~</math>  Includes Table of Example K(k) and E(k) Function Values; see a separate set of K(k) and E(k) evaluations in the context of [[Apps/DysonPotential#Our_Attempt_to_Replicate|Our Attempt to Replicate]] Dyson's results.</li>
          <li>[[2DStructure/ToroidalCoordinates#Using_Toroidal_Coordinates_to_Determine_the_Gravitational_Potential|Using Toroidal Coordinates to Determine the Gravitational Potential]] (Initial Presentation)</li>
          <li>[[2DStructure/ToroidalGreenFunction#Appendix_B:_Elliptic_Integrals|Using Toroidal Coordinates to Determine the Gravitational Potential]] (Improved Presentation) &nbsp; <math>\Leftarrow</math>&nbsp; &nbsp; includes [[2DStructure/ToroidalGreenFunction#Series_Expansions|series expansions]] for K(k) and E(k)</li>
          <li>[[Appendix/Mathematics/ToroidalFunctions|Relationships between Toroidal Functions]] <math>\Leftarrow ~~</math> 5 plots of [<b>[[Appendix/References#MF53|<font color="red">MF53</font>]]</b>] data included here</li>
          <li>[[Appendix/Mathematics/ToroidalConfusion|Confusion Regarding Whipple Formulae]]</li>
          <li>[[Appendix/Mathematics/ToroidalSynopsis01|Pulling It All Together]] <math>\Leftarrow ~~</math> 2 additional plots of [<b>[[Appendix/References#MF53|<font color="red">MF53</font>]]</b>] data included here</li>
      </ol>
<li>[[Appendix/Mathematics/ScaleFactors|Scale Factors for Orthogonal Curvilinear Coordinate Systems]]</li>
<li>[[Appendix/Mathematics/EulerAngles|Euler Angles]]</li>
<li>[[Appendix/Mathematics/StepFunction|Step Function and its Derivative]]</li>
<li>[[Appendix/Mathematics/Hypergeometric|Hypergeometric Equation and Its Solutions]]</li>
</ol>

=Other Pages Worth Visiting=

<ul>
  <li>[[OldVistrailsCoverPage|Old (VisTrails) Cover Page]]
  <li>[https://tohline.education Introductory Web Page]</li>
  <li>[[Temporary|Temporary &hellip;]]
  <li>[[Appendix/lsuPhys|Key Directories and Files on xxx.phys.lsu.edu]]
  <li>[[A2HostingEnvironment|Experimenting With the a2Hosting Environment]]</li>
  <li>[[3Dconfigurations/RiemannEllipsoids|Riemann (1861)]]</li>
  <li>[[Appendix/EquationTemplates|Appendix:  Equation Templates]]</li>
  <li>[[Appendix/SpecialFunctions|Appendix:  Special Functions]]</li>
  <li>[[Appendix/VariablesTemplates|Appendix:  Variables Templates]]</li>
  <li>[[Appendix/SGFimages|Appendix:  SGF Images]]</li>
  <li>[[Appendix/Mathematics/EulerAngles|Appendix:  Mathematics/EulerAngles]]</li>
  <li>[[Appendix/References|Appendix:  References]]</li>
  <li>[[Appendix/Ramblings|Appendix:  Ramblings]]</li>
  <li>[[Appendix/Permissions|Appendix:  Permissions]] &nbsp; &nbsp; &lArr; &nbsp; &nbsp; Not usable; editing error</li>
  <li>[[Appendix/CopyrightPermissions|Appendix:  Copyright Permissions]]</li>
  <li>[[Appendix/FormatRecommendations|Appendix:  Format Recommendations]]</li>
  <li>[[H_BookTiledMenu|Tiled Menu]]</li>
  <li>[[Contents|Table of Contents]]</li>
  <li>[[SR/Ptot_QuarticSolution#Determining_Temperature_from_Density_and_Pressure|Total pressure quartic solution]]</li>
  <li>[[SSC/Index|Spherically Symmetric Configurations (SSC) Index]]</li>
  <li>[[SSC/Virial/Polytropes|Virial Equilibrium of Adiabatic Spheres]]</li>
  <li>[[SSC/Virial/PolytropesSummary|Virial Equilibrium of Adiabatic Spheres (Summary)]]</li>
  <li>[[SSC/Virial/Isothermal|Virial Equilibrium of Isothermal Spheres]]</li>
  <li>[[SSC/VirialEquilibrium/UniformDensity|Virial Equilibrium of Uniform-Density Spheres]]</li>
  <li>[[SSC/Virial/PolytropesEmbeddedOutline|Virial of Embedded Polytropes (Outline)]]
<ul>
  <li>[[SSC/Virial/Polytropes|First Effort]] &nbsp; &nbsp; &lArr; &nbsp; &nbsp; 
      Same as "Virial Equilibrium of Adiabatic Spheres"</li>
  <li>[[SSC/Virial/PolytropesSummary|Second Effort]] &nbsp; &nbsp; &lArr; &nbsp; &nbsp; 
      Same as "Virial Equilibrium of Adiabatic Spheres (Summary)"</li>
  <li>[[SSCpt1/Virial/FormFactors|Third Effort]] &nbsp; &nbsp; &lArr; &nbsp; &nbsp; 
      FormFactors</li>
  <li>[[SSC/Virial/PolytropesEmbedded/FirstEffortAgain|First Effort, Second Time Around]] &nbsp; &nbsp; &lArr; &nbsp; &nbsp; We reproduce discussion associated with "First Effort," but correct expressions for <math>\mathfrak{f}_W</math> and <math>\mathfrak{f}_A</math> as identified in our "Third Effort" and, accordingly reserve various affected expressions that follow. </li>
  <li>[[SSC/Virial/PolytropesEmbedded/SecondEffortAgain|Second Effort, Second Time Around]] &nbsp; &nbsp; &lArr; &nbsp; &nbsp; We reproduce the discussion associated with our "Second Effort," but revise key sections to incorporate corrected expressions for the structural form factors.</li>
</ul>
  </li>
  <li>[[SSC/SynopsisStyleSheet|SSC Synopsis (Using Style Sheet)]]</li>
  <li>PP Tori: Structure &amp; Stability
    <ul>
    <li>Menu Tile: &nbsp;[https://www.vistrails.org/index.php/User:Tohline/Apps/PapaloizouPringleTori Papaloizou-Pringle Tori (1984)] = '''Apps/PapaloizouPringleTori'''; this chapter focuses on equilibrium structure.<li>
    <li>Menu Tile: &nbsp;[https://www.vistrails.org/index.php/User:Tohline/Apps/PapaloizouPringle84 (Massless) Papaloizou-Pringle Tori] = '''Apps/PapaloizouPringle84'''; in mid-July of 2020, <font color="red">Blaes granted permission</font> to include in this chapter some reprinted material from his 1985 paper.</li>
    <li>Menu Tile: &nbsp;[https://www.vistrails.org/index.php/User:Tohline/Apps/ImamuraHadleyCollaboration Analytic Analysis by Blaes (1985)] = '''Apps/ImamuraHadleyCollaboration'''; compare Blaes85 against Imamura-Hadley Collaboration]; in mid-July of 2020, <font color="red">Blaes granted permission</font> to include in this chapter some reprinted material from his 1985 paper.</li>
    <li>[https://www.vistrails.org/index.php/User:Tohline/Apps/Blaes85SlimLimit#Oscillations_of_PP_Tori_in_the_Slim_Torus_Limit Oscillations in the Slim Torus limit] = '''Apps/Blaes85SlimLimit'''</li>
    <li>[[Apps/Blaes85SlimLimit|Apps/Blaes85SlimLimit]]</li>  
    </ul>
  </li>
  <li>[[PGE/ConservingMomentum|Earlier version of the PGE/Euler chapter]]</li>
  <li>[[SSC/Structure/PolytropesASIDE1|Explains Whitworth's chosen scaling]]</li>
  <li>[[SSC/Structure/StahlerMassRadius|Details regarding Stahler's (1983) derived mass-radius relation]]</li>
  <li>[[SSC/Structure/BiPolytropes|Practice use of ''image map'']] (Image:SchonbergChandra1942.jpg)</li>
  <li>[[SSC/Structure/LimitingMasses|Mass Upper Limits]]</li>
  <li>Bipolytrope Generalization:
    <ul>
     <li>[[SSC/BipolytropeGeneralization|Bipolytrope Generalization]] (original)</li>
     <li>[[SSC/BipolytropeGeneralizationVersion2|Bipolytrope Generalization (Version 2)]]</li>
    </ul>
  </li>
  <li>Note that &hellip;Template: "SSCstructure" points to original "table of contents"</li>
  <li>[[SSC/StabilityEulerianPerspective|Stability of Spherically Symmetric Configurations (Eulerian Perspective)]] <-- Includes ''scratch work'' with rarely used html characters, such as <font color="green" size="+1">&#x2467;</font></li>
  <li>[[SSC/FreeEnergy/Powerpoint|Supports Free-Energy PowerPoint Presentation]]</li>
  <li>[[StabilityVariationalPrinciple|Free-Energy Stability Analysis]] (early version)</li>
  <li>[[SSC/Stability/n1PolytropeLAWE|Attempt at Formulating an Analytic Solution to oscillating n = 1 polytrope]]; see also the [[MathProjects/EigenvalueProblemN1|Challenge]]</li>
  <li>[[ProjectsUnderway/CoreCollapseSupernovae|ProjectsUnderway/Core_Collapse_Supernovae]] &nbsp;&lArr; &nbsp; Referenced in [[Apps/GoldreichWeber80|our discussion of Goldreich &amp; Weber (1980)]]</li>
  <li>[[SSC/Structure/PowerLawDensity|Power-Law Density Distribution]]</li>
  <li>[[Cylindrical3D|Nonlinear PGEs in Cylindrical Coordinates]] </li>
  <li>[[Cylindrical3D/Linearization|Linearized Equations in Cylindrical Coordinates]] &nbsp; &nbsp; &lArr; &nbsp; &nbsp; Referenced, for example, in our [[Apps/PapaloizouPringle84#Linearized_Principal_Governing_Equations_in_Cylindrical_Coordinates|discussion of PP84]]</li>
  <li>[[SSC/Structure/BiPolytropes/MurphyUVplane|Murphy UV Plane]] regarding (n<sub>c</sub>, n<sub>e</sub>) = (1, 5) bipolytropes</li>
</ul>

=Getting Started=
* <b>MediaWiki has been installed.</b> &nbsp; &nbsp; Consult the [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents User's Guide] for information on using the wiki software.
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Configuration_settings Configuration settings list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* [https://lists.wikimedia.org/mailman/listinfo/mediawiki-announce MediaWiki release mailing list]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Localisation#Translation_resources Localise MediaWiki for your language]
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:Combating_spam Learn how to combat spam on your wiki]

=Computer-Generated Holography=
<table border="1" align="right" cellpadding="8">
<tr>
<td align="center">
Computer Generated Holgram (Fall 2004)<br />in collaboration with <b>[https://digitalcommons.lsu.edu/gradschool_dissertations/2127/ Richard Muffoletto]</b><br />and others from [https://www.utsouthwestern.edu utsouthwestern.edu] as cited
</td>
</tr>
<tr><td align="center">[[File:Hologram2004.JPG|400px|Muffoletto's CGH]]</tr>
</table>
<ol type="I" start="0">
  <li>Lead in &hellip;</li>
  <ol type="A">
    <li>[http://www.phys.lsu.edu/faculty/tohline/phys4412/howto/ Original Table of Contents]</li>
    <li>[[Appendix/CGH/Preface|Preface]] </li>
  </ol>
  <li>Apertures that are Parallel to the Image Screen:</li>
  <ol type="A">
    <li>One-dimensional Aperture
      <ol type="1">
      <li>
[[Appendix/CGH/ParallelApertures|Initial Ideas]] 
      </li>
      <li>
[[Appendix/CGH/ParallelAperturesConsolidate|Consolidate Expressions]] 
      </li>
      <li>
[[Appendix/CGH/KAH2001|T. Kreis, P. Aswendt, &amp; R. H&ouml;fling (2001)]], Optical Engineering, vol. 40, no. 6, 926 - 933: &nbsp; ''Hologram reconstruction using a digital micromirror device''
      </li>
      </ol>
    </li>
    <li>[[Appendix/CGH/ParallelApertures2D|Two-dimensional, Rectangular Aperture]] </li>
    <li>[[Appendix/CGH/ParallelAperturesHolograms|Relevance to Holograms]]</li>
    <li>[[Appendix/CGH/ParallelAperturesWisdom|Caution and Words of Wisdom]]</li>
  </ol>
  <li>Apertures that are Tilted with Respect to the Image Screen:</li>
  <li>Building Holograms from VRML Files:</li>
  <li>[[Appendix/CGH/ZebraImaging|ZebraImaging and Southwestern Medical Center]]</li>
  <li>Embracing COLLADA (2020)</li>
  <ol type="A">
    <li>[[Appendix/CGH/COLLADAprincipal|Principal Illustration]]</li>
    <li>[[Appendix/CGH/COLLADAdemonstration|Demonstration Steps]]</li>
  </ol>
  <li>Quantum Mechanics</li>
    <ul>
  <li>[[Appendix/CGH/WhatIsReal|What is Real?]]</li>
  <li>[[Appendix/CGH/QuantumTransitions|Speculation Regarding Quantum Transitions]]</li>
    </ul>
  <li>On 4/15/2021, Google brought the following article to my attention:  &nbsp;[https://doi.org/10.1364/OE.26.010773 S. Igarashi, T. Nakamura, K. Matsushima, &amp; M. Yamaguchi (2018)], Optics Express, Vol. 26, Issue 8, pp.10773-10786, ''Efficient tiled calculation of over-10-gigapixel holograms using ray-wavefront conversion.''  It heavily references [22] the 2007 (Opt. Express, '''15'''(9), 5631-5640, ''Shifted Fresnel diffraction for computational holography'') work that I published in collaboration with R. Muffoletto and John Tyler.
</ol>

=Computer Algorithms=

<ol type="1">
<li>Directory &hellip;/fortran/FreeEnergy/EFE: [[Appendix/ComputerAlgorithms/EFE|README]]</li>
<li>Directory [[Appendix/ComputerAlgorithms/Riemann|&hellip;/numRecipes/EllipticIntegrals/Riemann]]</li>
</ol>


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