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.
- Orthogonal Curvilinear Coordinate Systems
- Direction Cosines
- (Confocal) Elliptic Cylinder Coordinates plus Concentric Analog (T5 Coordinates)
- Concentric Ellipsoidal (T6) Coordinates
- Concentric Ellipsoidal (T8) Coordinates
- Concentric Ellipsoidal (T12) Coordinates
- Daring Attack
- Relationship between HNM82 models and T1 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
- Determining Code Units
- Summary of Scalings
- Initial Temperature Distributions
- Photosphere of Stably Accreting DWD
- Binary Polytropes
- A* Scheme
- Initial Effort to Explain Jay Call's Hybrid Scheme in the Context of Zach Byerly's Dissertation
- Implications of Hybrid Scheme
- 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)
- 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
- For Shangli Ou
- For Paul Fisher
- For PJ in April 2021
- Riemann Meets COLLADA and Oculus Rift S: Example (b/a, c/a) = (0.41, 0.385)
- Virtual Reality and 3D Printing
- Success Importing Animated Scene into Oculus Rift S
- Carefully (Re)Build Riemann Type S Ellipsoids Inside Oculus Rift Environment
- Other Example S-type Riemann Ellipsoids:
- (b/a, c/a) = (0.90, 0.333)
- (b/a, c/a) = (0.74, 0.692)
- (b/a, c/a) = (0.28, 0.256)
- Challenges Constructing Ellipsoidal-Like Configurations
- Riemann Type 1 Ellipsoids
- Construction Challenges (Pt. 1)
- Construction Challenges (Pt. 2)
- Construction Challenges (Pt. 3)
- Construction Challenges (Pt. 4)
- Construction Challenges (Pt. 5)
- Related discussions of models viewed from a rotating reference frame:
- PGE
- NOTE to Eric Hirschmann & David Neilsen... I have moved the earlier contents of this page to a new Wiki location called Compressible Riemann Ellipsoids.
- Bordeaux University
- External Gravitational Potential of Toroids
- Spheroid-Ring Sequences
- Discussions Following Dissertation Defense
- Copyright Issues
Mathematics
- Roots of Cubic Equation
- In the context of T2 Coordinates, when <math>~q^2 = (a_1/a_3)^2=3</math>.
- 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; see a separate set of K(k) and E(k) evaluations in the context of Our Attempt to Replicate Dyson's results.
- 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
- Scale Factors for Orthogonal Curvilinear Coordinate Systems
Computer-Generated Holography
- Lead in …
- Original Table of Contents
- Preface
- 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)
- Principal Illustration
- Demonstration Steps
- Quantum Mechanics
- On 4/15/2021, Google brought the following article to my attention: S. Igarashi, T. Nakamura, K. Matsushima, & M. Yamaguchi (2018), Optics Express, Vol. 26, Issue 8, pp.10773-10786, Efficient tiled calculation of over-10-gigapixel holograms using ray-wavefront conversion. It heavily references [22] the 2007 (Opt. Express, 15(9), 5631-5640, Shifted Fresnel diffraction for computational holography) work that I published in collaboration with R. Muffoletto and John Tyler.
Computer Algorithms
- Directory …/fortran/FreeEnergy/EFE: README
- Directory …/numRecipes/EllipticIntegrals/Riemann
