# User:Tohline/Appendix/Ramblings

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<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</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</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/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/ToroidalCoordinates#Using_Toroidal_Coordinates_to_Determine_the_Gravitational_Potential|Using Toroidal Coordinates to Determine the Gravitational Potential]] (Initial Presentation) <math>~\Leftarrow ~~</math> uses wikitable overflow (scrolling) box</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/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/ToroidalConfusion|Confusion Regarding Whipple Formulae]]</li> |

## Revision as of 11:00, 30 August 2018

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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.

- 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
- On the Origin of Planetary Nebulae (Investigation Resulting from a July, 2013 Discussion with Kundan Kadam)
- Looking outward, from Inside a Black Hole
- Radial Dependence of the Strong Nuclear Force

## Mathematics

- Roots of Cubic Equation
- PP Tori — Also includes cube root of a complex number
- Srivastava's F-Type solution for polytropes.
- Murphy & Fiedler's Bipolytrope with
- Analytic Eigenfunctions for Bipolytropes with — also involves cube root of a complex number
- Roots of Quartic Equation
- 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
- Green's Function in terms of Toroidal Functions
- Compact Cylindrical Green Function
- Toroidal configurations & related coordinate systems — Includes
**EUREKA!**moment - Toroidal Coordinate Integration Limits Includes Table of Example K(k) and E(k) Function Values
- Using Toroidal Coordinates to Determine the Gravitational Potential (Initial Presentation) uses wikitable overflow (scrolling) box
- Relationships between Toroidal Functions 5 plots of [
**MF53**] data included here - Confusion Regarding Whipple Formulae
- Pulling It All Together 2 additional plots of [
**MF53**] data included here

## Computer-Generated Holography

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