User:Tohline/Appendix/Ramblings
Jump to navigation
Jump to search
|
|---|
| | 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
- 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
- Dyson (1893a) Part I: Some Details
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
- 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
|
|
|---|
|
© 2014 - 2021 by Joel E. Tohline |