User:Tohline/Appendix/Ramblings
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<li>[[User:Tohline/Appendix/Ramblings/EllipticCylinderCoordinates|(Confocal) Elliptic Cylinder Coordinates]] plus Concentric Analog ([[User:Tohline/Appendix/Ramblings/EllipticCylinderCoordinates#T5_Coordinates|T5 Coordinates]])</li> | <li>[[User:Tohline/Appendix/Ramblings/EllipticCylinderCoordinates|(Confocal) Elliptic Cylinder Coordinates]] plus Concentric Analog ([[User:Tohline/Appendix/Ramblings/EllipticCylinderCoordinates#T5_Coordinates|T5 Coordinates]])</li> | ||
<li>[[User:Tohline/Appendix/Ramblings/ConcentricEllipsodalCoordinates|Concentric Ellipsoidal (T6) Coordinates]]</li> | <li>[[User:Tohline/Appendix/Ramblings/ConcentricEllipsodalCoordinates|Concentric Ellipsoidal (T6) Coordinates]]</li> | ||
+ | <li>[[User:Tohline/Appendix/Ramblings/ConcentricEllipsodalT8Coordinates|Concentric Ellipsoidal (T8) Coordinates]]</li> | ||
+ | <li>[[User:Tohline/Appendix/Ramblings/ConcentricEllipsodalT12Coordinates|Concentric Ellipsoidal (T12) Coordinates]]</li> | ||
+ | <li>[[User:Tohline/Appendix/Ramblings/ConcentricEllipsodalDaringAttack|Daring Attack]]</li> | ||
</ol> | </ol> | ||
</li> | </li> | ||
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<li>[[User:Tohline/Appendix/Ramblings/BiPolytrope51ContinueSearch|Continue Search]]</li> | <li>[[User:Tohline/Appendix/Ramblings/BiPolytrope51ContinueSearch|Continue Search]]</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>[[User:Tohline/Appendix/Ramblings/OriginOfPlanetaryNebulae|On the Origin of Planetary Nebulae]] (Investigation Resulting from a July, 2013 Discussion with Kundan Kadam)</li> |
<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/StrongNuclearForce|Radial Dependence of the Strong Nuclear Force]]</li> | ||
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<li>[[User:Tohline/Appendix/Ramblings/MyDoctoralStudents|Doctoral students Tohline has advised]] over the years</li> | <li>[[User:Tohline/Appendix/Ramblings/MyDoctoralStudents|Doctoral students Tohline has advised]] over the years</li> | ||
<li>[[User:Tohline/Appendix/Ramblings/ForDurisen|For Richard H. Durisen]]</li> | <li>[[User:Tohline/Appendix/Ramblings/ForDurisen|For Richard H. Durisen]]</li> | ||
+ | <li>[[User:Tohline/Appendix/Ramblings/ForOuShangli|For Shangli Ou]]</li> | ||
+ | <li>[[User:Tohline/Appendix/Ramblings/ForPaulFisher|For Paul Fisher]]</li> | ||
+ | <li>[[User:Tohline/Appendix/Ramblings/ForPJ_April2021|For PJ in April 2021]]</li> | ||
<li>[[User:Tohline/ThreeDimensionalConfigurations/MeetsCOLLADAandOculusRiftS#Riemann_Meets_COLLADA_.26_Oculus_Rift_S|Riemann Meets COLLADA and Oculus Rift S]]: Example '''(b/a, c/a) = (0.41, 0.385)''' | <li>[[User:Tohline/ThreeDimensionalConfigurations/MeetsCOLLADAandOculusRiftS#Riemann_Meets_COLLADA_.26_Oculus_Rift_S|Riemann Meets COLLADA and Oculus Rift S]]: Example '''(b/a, c/a) = (0.41, 0.385)''' | ||
<ol type="a"> | <ol type="a"> | ||
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</li> | </li> | ||
</ol> | </ol> | ||
+ | </li> | ||
+ | <li>Challenges Constructing Ellipsoidal-Like Configurations | ||
+ | <ol type="a"> | ||
+ | |||
+ | <li>[[User:Tohline/ThreeDimensionalConfigurations/RiemannTypeI#Riemann_Type_1_Ellipsoids|Riemann Type 1 Ellipsoids]]</li> | ||
+ | <li>[[User:Tohline/ThreeDimensionalConfigurations/Challenges#Challenges_Constructing_Ellipsoidal-Like_Configurations|Construction Challenges (Pt. 1)]]</li> | ||
+ | <li>[[User:Tohline/ThreeDimensionalConfigurations/ChallengesPt2|Construction Challenges (Pt. 2)]]</li> | ||
+ | <li>[[User:Tohline/ThreeDimensionalConfigurations/ChallengesPt3|Construction Challenges (Pt. 3)]]</li> | ||
+ | <li>[[User:Tohline/ThreeDimensionalConfigurations/ChallengesPt4|Construction Challenges (Pt. 4)]]</li> | ||
+ | <li>[[User:Tohline/ThreeDimensionalConfigurations/ChallengesPt5|Construction Challenges (Pt. 5)]]</li> | ||
+ | <li>Related discussions of models viewed from a rotating reference frame: | ||
+ | <ol type="i"> | ||
+ | <li>[[User:Tohline/PGE/RotatingFrame#Rotating_Reference_Frame|PGE]]</li> | ||
+ | <li><font color="red"><b>NOTE to Eric Hirschmann & David Neilsen... </b></font>I have moved the earlier contents of this page to a new Wiki location called [[User:Tohline/Apps/RiemannEllipsoids_Compressible|Compressible Riemann Ellipsoids]].</li> | ||
+ | </ol> | ||
+ | </li> | ||
+ | |||
+ | </ol> | ||
</li> | </li> | ||
<li>Bordeaux University | <li>Bordeaux University | ||
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<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> | <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> | ||
+ | <li>[[User:Tohline/Appendix/Mathematics/ScaleFactors|Scale Factors for Orthogonal Curvilinear Coordinate Systems]]</li> | ||
</ol> | </ol> | ||
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<li>[[User:Tohline/Appendix/CGH/QuantumTransitions|Speculation Regarding Quantum Transitions]]</li> | <li>[[User:Tohline/Appendix/CGH/QuantumTransitions|Speculation Regarding Quantum Transitions]]</li> | ||
</ul> | </ul> | ||
+ | <li>On 4/15/2021, Google brought the following article to my attention: [https://doi.org/10.1364/OE.26.010773 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. | ||
</ol> | </ol> | ||
Current revision as of 11:10, 28 May 2021
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Contents |
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
- 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
- Photosphere of Stably Accreting DWD
- Binary Polytropes
- A* 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)
- 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
- Copyright Issues
Mathematics
- Roots of Cubic Equation
- In the context of T2 Coordinates, when .
- 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
- 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 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) includes series expansions for K(k) and E(k)
- 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
- Scale Factors for Orthogonal Curvilinear Coordinate Systems
Computer-Generated Holography
Computer Generated Holgram (Fall 2004) |
- Lead in …
- 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)
- 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
© 2014 - 2021 by Joel E. Tohline |