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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. | 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. | ||
#[[User:Tohline/Appendix/Ramblings/ | <ol> | ||
#[[User:Tohline/Appendix/Ramblings/ | <li>[[User:Tohline/Appendix/Ramblings/T1Coordinates|Relationship between HNM82 models and T1 coordinates]]</li> | ||
<li>[[User:Tohline/Appendix/Ramblings/DirectionCosines|Orthogonal Curvilinear Coordinates]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/SphericalWaveEquation|Playing with the Spherical Wave Equation]]</li> | |||
: | <li>Analyzing Azimuthal Distortions | ||
<ol style="list-style-type:lower-latin"> | |||
: | <li>[[User:Tohline/Appendix/Ramblings/To_Hadley_and_Imamura|Summary for Hadley & Imamura]]</li> | ||
<li>[[User:Tohline/Appendix/Ramblings/Azimuthal_Distortions#Analyzing_Azimuthal_Distortions|Detailed Notes]] [[User:Tohline/Appendix/Ramblings/Azimuthal_Distortions#Constant_Phase_Loci|<font size="+1">🎦</font>]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/Hadley_and_Imamura_Supplementary_Database|Supplementary database generated by the Hadley & Imamura collaboration]]</li> | |||
<li>[http://pages.uoregon.edu/khadley/ Large supplementary dataset accumulated by the Hadley & Imamura collaboration]</li> | |||
<li>[[User:Tohline/Apps/WoodwardTohlineHachisu94#Online_Movies|YouTube videos]] that supplement simulations of [http://adsabs.harvard.edu/abs/1994ApJ...420..247W J. W. Woodward, J. E. Tohline, & I. Hachisu (1994)]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/PPTori|Stability Analyses of PP Tori]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/PPToriPt2|Stability Analyses of PP Tori]] (Part 2)</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>[[User:Tohline/Appendix/Ramblings/T3Integrals|T3 Coordinates]]</li> | |||
<ol style="list-style-type:lower-roman"> | |||
<li>Special (quadratic) case: [[User:Tohline/Appendix/Ramblings/T3Integrals/QuadraticCase|Joel's Derivation]] vs. | |||
[[User:Jaycall/T3_Coordinates/Special_Case|Jay's Derivation]]</li> | |||
</ol> | |||
<li>[[User:Jaycall/KillingVectorApproach|Killing Vector Approach]]; Jay Call's related [[User_talk:Jaycall|Talk page]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/T3CharacteristicVector|Characteristic Vector for T3 Coordinates]]</li> | |||
<li>[[User:Tohline/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>[[User:Tohline/Appendix/Ramblings/Radiation/CodeUnits|Determining Code Units]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/Radiation/SummaryScalings#Summary_of_Scalings|Summary of Scalings]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/Radiation/InitialTemperatures|Initial Temperature Distributions]]</li> | |||
</ol> | |||
<li>[[User:Tohline/Appendix/Ramblings/Photosphere|Photosphere of Stably Accreting DWD]]</li> | |||
<li>[[User:Tohline/Appendix/PolytropicBinaries|Binary Polytropes]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/Hybrid_Scheme_old|Initial Effort to Explain Jay Call's ''Hybrid'' Scheme in the Context of Zach Byerly's Dissertation]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/Nonlinar_Oscillation|Exploring the Properties of Radial Oscillations in Pressure-Truncated n = 5 Polytropes]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/Turning_Points#Turning_Points|Instabilities Associated with Equilibrium Sequence Turning Points]]</li> | |||
<li>[[User:Tohline/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>[[User:Tohline/SSC/Stability/BiPolytrope0_0Old#Radial_Oscillations_of_a_Zero-Zero_Bipolytrope|Pt 1: Radial Oscillations of a Zero-Zero-Bipolytrope (Early Flawed Summary)]]</li> | |||
<li>[[User:Tohline/SSC/Stability/BiPolytrope0_0Details#Radial_Oscillations_of_a_Zero-Zero_Bipolytrope|Pt 2: Details]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/Additional_Analytically_Specified_Eigenvectors_for_Zero-Zero_Bipolytropes#Searching_for_Additional_Eigenvectors_of_Zero-Zero_Bipolytropes|Pt 3: Searching for Additional Eigenvectors]]</li> | |||
<li>[[User:Tohline/SSC/Stability/BiPolytrope0_0#Radial_Oscillations_of_a_Zero-Zero_Bipolytrope|Pt 4: Good Summary]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/NumericallyDeterminedEigenvectors|Numerically Determined Eigenvectors]]</li> | |||
</ol> | |||
<li>Analyzing Five-One Bipolytropes</li> | |||
<ol style="list-style-type:lower-latin"> | |||
<li>[[User:Tohline/Appendix/Ramblings/BiPolytropeStability|Assessing the Stability of Spherical, BiPolytropic Configurations]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/BiPolytrope51AnalyticStability|Searching for Analytic EigenVector for (5,1) Bipolytropes]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/PatrickMotl|Discussing Patrick Motl's 2019 Simulations]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/BiPolytrope51ContinueSearch|Continue Search]]</li> | |||
</ol> | |||
<li>[[User:Tohline/Appendix/Ramblings/OriginOfPlanetaryNebulae|On the Origin of Planetary Nebulae]] (Investigation Resulting from a July, 2013 Discussion with Kundan Kadam)</lli> | |||
<li>[[User:Tohline/Appendix/Ramblings/InsideOut|Looking outward, from Inside a Black Hole]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/StrongNuclearForce|Radial Dependence of the Strong Nuclear Force]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/Dyson1893Part1|Dyson (1893a) Part I: Some Details]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/RadiationHydro|Radiation-Hydrodynamics]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/Saturn#Saturn|Saturn]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/MyDoctoralStudents|Doctoral students Tohline has advised]] over the years</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/ForDurisen|For Richard H. Durisen]]</li> | |||
<li>[[User:Tohline/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>[[User:Tohline/Appendix/Ramblings/VirtualReality#Virtual_Reality_and_3D_Printing|Virtual Reality and 3D Printing]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/OculusRift_S|Success Importing Animated Scene into Oculus Rift S]]</li> | |||
<li>[[User:Tohline/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>[[User:Tohline/Appendix/Ramblings/RiemannB90C333|(b/a, c/a) = (0.90, 0.333)]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/RiemannB74C692|(b/a, c/a) = (0.74, 0.692)]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/RiemannB28C256|(b/a, c/a) = (0.28, 0.256)]]</li> | |||
</ol> | |||
</li> | |||
</ol> | |||
</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/Bordeaux|Bordeaux University]]</li> | |||
</ol> | |||
==Mathematics== | |||
<ol> | |||
<li>Roots of Cubic Equation</li> | |||
<ol style="list-style-type:lower-latin"> | |||
<li>[[User:Tohline/Appendix/Ramblings/PPTori#Cubic_Equation_Solution|PP Tori]] — Also includes [[User:Tohline/Appendix/Ramblings/PPTori#CubeRootImaginary|cube root of a complex number]]</li> | |||
<li>[[User:Tohline/SSC/Structure/Polytropes#CubicRoot|Srivastava's F-Type solution]] for <math>~n=5</math> polytropes.</li> | |||
<li>[[User:Tohline/SSC/Structure/BiPolytropes/Analytic1_5#Analytic_Solution_of_Key_Interface_Relation|Murphy & Fiedler's Bipolytrope]] with <math>~(n_c, n_e) = (1,5)</math></li> | |||
<li>[[User:Tohline/Appendix/Ramblings/Additional_Analytically_Specified_Eigenvectors_for_Zero-Zero_Bipolytropes#Solve_Cubic_Equation|Analytic Eigenfunctions for Bipolytropes]] with <math>~(n_c, n_e) = (0, 0)</math> — also involves cube root of a complex number</li> | |||
</ol> | |||
<li> Roots of Quartic Equation</li> | |||
<ol style="list-style-type:lower-latin"> | |||
<li>[[User:Tohline/SSC/Stability/BiPolytrope0_0Details#Roots_of_Quartic_Equation|Analytic Eigenfunction for Bipolytropes]] with <math>~(n_c, n_e) = (0, 0)</math></li> | |||
<li>[[User:Tohline/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>[[User:Tohline/Apps/Blaes85SlimLimit#Singular_Sturm-Liouville_Problem|Oscillations of PP Tori]] in the slim torus limit</li> | |||
<li>[[User:Tohline/Apps/ImamuraHadleyCollaboration#Singular_Sturm-Liouville_Problem|Characteristics of unstable eigenvectors in self-gravitating tori]]</li> | |||
</ol> | |||
<li>[[User:Tohline/Appendix/Ramblings/PowerSeriesExpressions|Approximate Power-Series Expressions]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/FourierSeries|Fourier Series]]</li> | |||
<li>[[User:Tohline/AxisymmetricConfigurations/PoissonEq#Special_Functions_.26_Other_Broadly_Used_Representations|Special Functions & Other Broadly Used Representations]]</li> | |||
<ol> | |||
<li>[[User:Tohline/AxisymmetricConfigurations/PoissonEq#Spherical_Harmonics_and_Associated_Legendre_Functions|Spherical Harmonics and Associated Legendre Functions]]</li> | |||
<li>[[User:Tohline/AxisymmetricConfigurations/PoissonEq#Multipole_Expansions|Multipole Expansions]]</li> | |||
<li>[[User:Tohline/AxisymmetricConfigurations/PoissonEq#Familiar_Expression_for_the_Cylindrical_Green.27s_Function_Expansion|Familiar Expression for the Cylindrical Green's Function Expansion]]</li> | |||
<li>[[User:Tohline/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>[[User:Tohline/Appendix/Ramblings/CCGF|Compact Cylindrical Green Function]]</li> | |||
<li>[[User:Tohline/Appendix/Ramblings/ToroidalCoordinates#Relating_CCGF_Expansion_to_Toroidal_Coordinates|Toroidal configurations & related coordinate systems]] — Includes <b><font color="red">EUREKA!</font></b> moment; also uses [[User:Tohline/Appendix/Ramblings/ToroidalCoordinates#Examples|wikitable overflow]] (scrolling) box</li> | |||
<li>[[User:Tohline/2DStructure/ToroidalCoordinateIntegrationLimits|Toroidal Coordinate Integration Limits]] <math>~\Leftarrow ~~</math> Includes Table of Example K(k) and E(k) Function Values</li> | |||
<li>[[User:Tohline/2DStructure/ToroidalCoordinates#Using_Toroidal_Coordinates_to_Determine_the_Gravitational_Potential|Using Toroidal Coordinates to Determine the Gravitational Potential]] (Initial Presentation)</li> | |||
<li>[[User:Tohline/2DStructure/ToroidalGreenFunction#Appendix_B:_Elliptic_Integrals|Using Toroidal Coordinates to Determine the Gravitational Potential]] (Improved Presentation) <math>~\Leftarrow</math> includes [[User:Tohline/2DStructure/ToroidalGreenFunction#Series_Expansions|series expansions]] for K(k) and E(k)</li> | |||
<li>[[User:Tohline/Appendix/Mathematics/ToroidalFunctions|Relationships between Toroidal Functions]] <math>~\Leftarrow ~~</math> 5 plots of [<b>[[User:Tohline/Appendix/References#MF53|<font color="red">MF53</font>]]</b>] data included here</li> | |||
<li>[[User:Tohline/Appendix/Mathematics/ToroidalConfusion|Confusion Regarding Whipple Formulae]]</li> | |||
<li>[[User:Tohline/Appendix/Mathematics/ToroidalSynopsis01|Pulling It All Together]] <math>~\Leftarrow ~~</math> 2 additional plots of [<b>[[User:Tohline/Appendix/References#MF53|<font color="red">MF53</font>]]</b>] data included here</li> | |||
</ol> | |||
</ol> | |||
==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 …</li> | |||
<ol type="A"> | |||
<li>[http://www.phys.lsu.edu/faculty/tohline/phys4412/howto/ Original Table of Contents]</li> | |||
<li>[[User:Tohline/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> | |||
[[User:Tohline/Appendix/CGH/ParallelApertures|Initial Ideas]] | |||
</li> | |||
<li> | |||
[[User:Tohline/Appendix/CGH/ParallelAperturesConsolidate|Consolidate Expressions]] | |||
</li> | |||
<li> | |||
[[User:Tohline/Appendix/CGH/KAH2001|T. Kreis, P. Aswendt, & R. Höfling (2001)]], Optical Engineering, vol. 40, no. 6, 926 - 933: ''Hologram reconstruction using a digital micromirror device'' | |||
</li> | |||
</ol> | |||
</li> | |||
<li>[[User:Tohline/Appendix/CGH/ParallelApertures2D|Two-dimensional, Rectangular Aperture]] </li> | |||
<li>[[User:Tohline/Appendix/CGH/ParallelAperturesHolograms|Relevance to Holograms]]</li> | |||
<li>[[User:Tohline/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>[[User:Tohline/Appendix/CGH/ZebraImaging|ZebraImaging and Southwestern Medical Center]]</li> | |||
<li>Embracing COLLADA (2020)</li> | |||
<ol type="A"> | |||
<li>[[User:Tohline/Appendix/CGH/COLLADAprincipal|Principal Illustration]]</li> | |||
<li>[[User:Tohline/Appendix/CGH/COLLADAdemonstration|Demonstration Steps]]</li> | |||
</ol> | |||
<li>Quantum Mechanics</li> | |||
<ul> | |||
<li>[[User:Tohline/Appendix/CGH/WhatIsReal|What is Real?]]</li> | |||
<li>[[User:Tohline/Appendix/CGH/QuantumTransitions|Speculation Regarding Quantum Transitions]]</li> | |||
</ul> | |||
</ol> | |||
==Computer Algorithms== | |||
<ol type="1"> | |||
<li>Directory …/fortran/FreeEnergy/EFE: [[User:Tohline/Appendix/ComputerAlgorithms/EFE|README]]</li> | |||
<li>Directory [[User:Tohline/Appendix/ComputerAlgorithms/Riemann|…/numRecipes/EllipticIntegrals/Riemann]]</li> | |||
</ol> | |||
<br /> | <br /> | ||
{{LSU_HBook_footer}} | {{LSU_HBook_footer}} |
Revision as of 01:38, 7 July 2020
| Tiled Menu | Tables of Content | Banner Video | Tohline Home Page | |
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.
- Relationship between HNM82 models and T1 coordinates
- Orthogonal Curvilinear Coordinates
- Playing with the Spherical Wave Equation
- Analyzing Azimuthal Distortions
- Summary for Hadley & Imamura
- Detailed Notes 🎦
- Supplementary database generated by the Hadley & Imamura collaboration
- Large supplementary dataset accumulated by the Hadley & Imamura collaboration
- YouTube videos that supplement simulations of J. W. Woodward, J. E. Tohline, & I. Hachisu (1994)
- Stability Analyses of PP Tori
- Stability Analyses of PP Tori (Part 2)
- Integrals of Motion
- Old discussion
- T3 Coordinates
- Special (quadratic) case: Joel's Derivation vs. Jay's Derivation
- Killing Vector Approach; Jay Call's related Talk page
- Characteristic Vector for T3 Coordinates
- T4 Coordinates (Abandoned by Joel 7/6/2010 because non-orthogonal)
- Marcello's Radiation-Hydro Simulations
- Photosphere of Stably Accreting DWD
- Binary Polytropes
- Initial Effort to Explain Jay Call's Hybrid Scheme in the Context of Zach Byerly's Dissertation
- Exploring the Properties of Radial Oscillations in Pressure-Truncated n = 5 Polytropes
- Instabilities Associated with Equilibrium Sequence Turning Points
- Derivations Related to Ledoux's Variational Principle
- More on Zero-Zero Bipolytropes
- Pt 1: Radial Oscillations of a Zero-Zero-Bipolytrope (Early Flawed Summary)
- Pt 2: Details
- Pt 3: Searching for Additional Eigenvectors
- Pt 4: Good Summary
- Numerically Determined Eigenvectors
- Analyzing Five-One Bipolytropes
- Assessing the Stability of Spherical, BiPolytropic Configurations
- Searching for Analytic EigenVector for (5,1) Bipolytropes
- Discussing Patrick Motl's 2019 Simulations
- Continue Search
- On the Origin of Planetary Nebulae (Investigation Resulting from a July, 2013 Discussion with Kundan Kadam)</lli>
- Looking outward, from Inside a Black Hole
- Radial Dependence of the Strong Nuclear Force
- Dyson (1893a) Part I: Some Details
- Radiation-Hydrodynamics
- Saturn
- Doctoral students Tohline has advised over the years
- For Richard H. Durisen
- Riemann Meets COLLADA and Oculus Rift S: Example (b/a, c/a) = (0.41, 0.385)
- Bordeaux University
Mathematics
- Roots of Cubic Equation
- PP Tori — Also includes cube root of a complex number
- Srivastava's F-Type solution for <math>~n=5</math> polytropes.
- Murphy & Fiedler's Bipolytrope with <math>~(n_c, n_e) = (1,5)</math>
- Analytic Eigenfunctions for Bipolytropes with <math>~(n_c, n_e) = (0, 0)</math> — also involves cube root of a complex number
- Roots of Quartic Equation
- Analytic Eigenfunction for Bipolytropes with <math>~(n_c, n_e) = (0, 0)</math>
- Determine temperature from total pressure
- Singular Sturm-Liouville (eigenvalue) Problem
- Oscillations of PP Tori in the slim torus limit
- Characteristics of unstable eigenvectors in self-gravitating tori
- Approximate Power-Series Expressions
- Fourier Series
- Special Functions & Other Broadly Used Representations
- Spherical Harmonics and Associated Legendre Functions
- Multipole Expansions
- Familiar Expression for the Cylindrical Green's Function Expansion
- Toroidal Functions
- Green's Function in terms of Toroidal Functions
- Compact Cylindrical Green Function
- Toroidal configurations & related coordinate systems — Includes EUREKA! moment; also uses wikitable overflow (scrolling) box
- Toroidal Coordinate Integration Limits <math>~\Leftarrow ~~</math> Includes Table of Example K(k) and E(k) Function Values
- Using Toroidal Coordinates to Determine the Gravitational Potential (Initial Presentation)
- Using Toroidal Coordinates to Determine the Gravitational Potential (Improved Presentation) <math>~\Leftarrow</math> includes series expansions for K(k) and E(k)
- Relationships between Toroidal Functions <math>~\Leftarrow ~~</math> 5 plots of [MF53] data included here
- Confusion Regarding Whipple Formulae
- Pulling It All Together <math>~\Leftarrow ~~</math> 2 additional plots of [MF53] data included here
Computer-Generated Holography
Computer Generated Holgram (Fall 2004) |
- Lead in …
- Apertures that are Parallel to the Image Screen:
- One-dimensional Aperture
- Initial Ideas
- Consolidate Expressions
- T. Kreis, P. Aswendt, & R. Höfling (2001), Optical Engineering, vol. 40, no. 6, 926 - 933: Hologram reconstruction using a digital micromirror device
- Two-dimensional, Rectangular Aperture
- Relevance to Holograms
- Caution and Words of Wisdom
- Apertures that are Tilted with Respect to the Image Screen:
- Building Holograms from VRML Files:
- ZebraImaging and Southwestern Medical Center
- Embracing COLLADA (2020)
- Quantum Mechanics
Computer Algorithms
- Directory …/fortran/FreeEnergy/EFE: README
- Directory …/numRecipes/EllipticIntegrals/Riemann
© 2014 - 2021 by Joel E. Tohline |