Difference between revisions of "User:Tohline/Appendix/Ramblings"
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<li>[[User:Tohline/Appendix/Ramblings/T1Coordinates|Relationship between HNM82 models and T1 coordinates]]</li> | <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/DirectionCosines|Orthogonal Curvilinear Coordinates]]</li> | ||
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<li>More on Zero-Zero Bipolytropes</li> | <li>More on Zero-Zero Bipolytropes</li> | ||
<ol style="list-style-type:lower-latin"> | <ol style="list-style-type:lower-latin"> | ||
<li>[[User:Tohline/Appendix/Ramblings/Additional_Analytically_Specified_Eigenvectors_for_Zero-Zero_Bipolytropes#Searching_for_Additional_Eigenvectors_of_Zero-Zero_Bipolytropes|Searching for Additional Eigenvectors]]</li> | <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> | <li>[[User:Tohline/Appendix/Ramblings/NumericallyDeterminedEigenvectors|Numerically Determined Eigenvectors]]</li> | ||
</ol> | </ol> | ||
<li>[[User:Tohline/Appendix/Ramblings/OriginOfPlanetaryNebulae|On the Origin of Planetary Nebulae]] (Investigation Resulting from a July, 2013 Discussion with Kundan Kadam) | <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/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> | |||
</ol> | </ol> | ||
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<li>[[User:Tohline/Appendix/Ramblings/PowerSeriesExpressions|Approximate Power-Series Expressions]]</li> | <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/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> | </ol> | ||
==Computer-Generated Holography== | |||
<ol> | |||
<li>[[User:Tohline/Appendix/CGH/Preface|Preface]] </li> | |||
<li>[[User:Tohline/Appendix/CGH/ParallelApertures|Apertures that are Parallel to the Image Screen]] </li> | |||
<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> | |||
<br /> | <br /> | ||
{{LSU_HBook_footer}} | {{LSU_HBook_footer}} |
Revision as of 16:32, 16 August 2019
| 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
- 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
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)
- 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
- Preface
- Apertures that are Parallel to the Image Screen
- Quantum Mechanics
© 2014 - 2021 by Joel E. Tohline |