# User:Tohline/Appendix/Ramblings

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<li>[[User:Tohline/SSC/Structure/Polytropes#CubicRoot|Srivastava's F-Type solution]] for <math>~n=5</math> polytropes.</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/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></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> | </ol> | ||

<li> Roots of Quartic Equation</li> | <li> Roots of Quartic Equation</li> |

## Revision as of 22:17, 21 December 2016

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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.

- Toroidal configurations & related coordinate systems
- 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
- Searching for Additional Eigenvectors for Zero-Zero Bipolytropes
- Investigation Resulting from a July, 2013 Discussion with Kundan Kadam

## 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

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