User:Tohline/Appendix/Ramblings/Bordeaux - Revision history

Tohline at 00:05, 17 December 2020

2020-12-17T00:05:16Z

← Older revision		Revision as of 00:05, 17 December 2020
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	</table>		</table>

			=See Also=
			<ul>
			<li>Université de Bordeaux (Part 2):  [[User:Tohline/Appendix/Ramblings/BordeauxSequences\|Spheroid-Ring Sequences]]</li>
			<li>Université de Bordeaux (Part 3):  [[User:Tohline/Appendix/Ramblings/BordeauxPostDefense\|Discussions Following Dissertation Defense]]</li>
			</ul>


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Tohline at 03:56, 24 July 2020

2020-07-24T03:56:03Z

← Older revision		Revision as of 03:56, 24 July 2020
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	=Université de Bordeaux=		=Université de Bordeaux (Part 1)=

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			==Spheroid-Ring Systems==
			Through a research collaboration at the [https://www.u-bordeaux.com Université de Bordeaux], [https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.4504B/abstract B. Basillais & J. -M. Huré (2019), MNRAS, 487, 4504-4509] have published a paper titled, ''Rigidly Rotating, Incompressible Spheroid-Ring Systems: New Bifurcations, Critical Rotations, and Degenerate States.''

			We discuss this topic in a [[User:Tohline/Appendix/Ramblings/BordeauxSequences#Spheroid-Ring_Systems\|separate, accompanying chapter]].

	==Exterior Gravitational Potential of Toroids==		==Exterior Gravitational Potential of Toroids==
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	</tr>		</tr>
	</table>		</table>

	~~==Spheroid-Ring Systems==~~
	Through a research collaboration at the [https://www.u-bordeaux.com Université de Bordeaux], [https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.4504B/abstract B. Basillais & J. -M. Huré (2019), MNRAS, 487, 4504-4509] have published a paper titled, ''Rigidly Rotating, Incompressible Spheroid-Ring Systems: New Bifurcations, Critical Rotations, and Degenerate States.''

	~~Here are some relevant publications:~~
	~~<ul>~~
	~~<li>[https://ui.adsabs.harvard.edu/abs/1986ApJS...61..479H/abstract Hachisu (1986a, ApJS, 61, 479)]:   ''A Versatile Method for Obtaining Structures of Rapidly Rotating Stars''</li>~~
	~~<li>[https://ui.adsabs.harvard.edu/abs/2014MNRAS.438L..61F/abstract Fujisawa & Eriguchi (2014, MNRAS, 438, L61)]:   ''Prolate stars due to meridional flows''</li>~~
	~~<li>[https://ui.adsabs.harvard.edu/abs/2018MNRAS.475...63H/abstract Huré, Hersant & Nasello (2018, MNRAS, 475, 63)]:   ''The equilibrium of overpressurized polytropes''</li>~~
	<li>[https://ui.adsabs.harvard.edu/abs/1984Ap%26SS..99...71H/abstractHachisu & Eriguchi (1984, Ap&SS, 99, 71)]:   ''Fission Sequence and Equilibrium Models of [Rigidly] Rotating Polytropes''</li>
	~~<li>[https://ui.adsabs.harvard.edu/abs/1986ApJ...311..214H/abstract Hachisu, Eriguchi & Nomoto (1986b, ApJ, 311, 214)]:   ''Fate of merging double white dwarfs. II - Numerical method''</li>~~
	~~<li>[https://ui.adsabs.harvard.edu/abs/1992ApJ...401..618N/abstract Nishida, Eriguchi & Lanza (1992, ApJ, 401, 618)]:   ''General Relativistic Structure of Star-Toroid Systems''</li>~~
	<li>[https://ui.adsabs.harvard.edu/abs/1992ApJ...394..248W/abstract Woodward, Sankaran & Tohline (1992 ApJ, 394, 248)]:   ''Tidal Disruption of a Star by a Massive Disk (The Axisymmetric Roche Problem)''</li>
	~~</ul>~~
	~~Especially,~~
	~~<ul>~~
	<li>[https://ui.adsabs.harvard.edu/abs/1983PThPh..69.1131E/abstract Eriguchi & Hachisu (1983, Prog. Theor. Phys., 69, 1131)]:   ''Two Kinds of Axially Symmetric Equilibrium Sequences of Self-Gravitating and Rotating Incompressible Fluids — Two-Ring Sequence and Core-Ring Sequence''</li>
	<li>[https://ui.adsabs.harvard.edu/abs/2003MNRAS.339..515A/abstract Ansorg, Kleinwächter & Meinel (2003, MNRAS, 339, 515)]:   ''Uniformly rotating axisymmetric fluid configurations bifurcating from highly flattened Maclaurin spheroids''</li>
	~~<li>[https://ui.adsabs.harvard.edu/abs/1986ApJ...308..161H/abstract Hachisu, Eriguchi & Nomoto (1986a, ApJ, 308, 161)]:   ''Fate of Merging Double White Dwarfs''</li>~~
	~~</ul>~~


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Tohline: /* Spheroid-Ring Systems */

2020-07-24T03:39:25Z

Spheroid-Ring Systems

← Older revision		Revision as of 03:39, 24 July 2020
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	<li>[https://ui.adsabs.harvard.edu/abs/1984Ap%26SS..99...71H/abstractHachisu & Eriguchi (1984, Ap&SS, 99, 71)]:   ''Fission Sequence and Equilibrium Models of [Rigidly] Rotating Polytropes''</li>		<li>[https://ui.adsabs.harvard.edu/abs/1984Ap%26SS..99...71H/abstractHachisu & Eriguchi (1984, Ap&SS, 99, 71)]:   ''Fission Sequence and Equilibrium Models of [Rigidly] Rotating Polytropes''</li>
	<li>[https://ui.adsabs.harvard.edu/abs/1986ApJ...311..214H/abstract Hachisu, Eriguchi & Nomoto (1986b, ApJ, 311, 214)]:   ''Fate of merging double white dwarfs. II - Numerical method''</li>		<li>[https://ui.adsabs.harvard.edu/abs/1986ApJ...311..214H/abstract Hachisu, Eriguchi & Nomoto (1986b, ApJ, 311, 214)]:   ''Fate of merging double white dwarfs. II - Numerical method''</li>
	<li>Nishida, Eriguchi & Lanza (1992, ApJ, 401, 618)</li>		<li>[https://ui.adsabs.harvard.edu/abs/1992ApJ...401..618N/abstract Nishida, Eriguchi & Lanza (1992, ApJ, 401, 618)]:   ''General Relativistic Structure of Star-Toroid Systems''</li>
	<li>Woodward, Sankaran & Tohline (1992 ApJ, 394, 248)</li>		<li>[https://ui.adsabs.harvard.edu/abs/1992ApJ...394..248W/abstract Woodward, Sankaran & Tohline (1992 ApJ, 394, 248)]:   ''Tidal Disruption of a Star by a Massive Disk (The Axisymmetric Roche Problem)''</li>
	</ul>		</ul>
	Especially,		Especially,

Tohline: /* Spheroid-Ring Systems */

2020-07-23T23:21:03Z

Spheroid-Ring Systems

← Older revision		Revision as of 23:21, 23 July 2020
Line 7,230:		Line 7,230:
	Here are some relevant publications:		Here are some relevant publications:
	<ul>		<ul>
	<li>Hachisu (1986a, ApJS, 61, 479)</li>		<li>[https://ui.adsabs.harvard.edu/abs/1986ApJS...61..479H/abstract Hachisu (1986a, ApJS, 61, 479)]:   ''A Versatile Method for Obtaining Structures of Rapidly Rotating Stars''</li>
	<li>Fujisawa & Eriguchi (2014, MNRAS, 438, L61)</li>		<li>[https://ui.adsabs.harvard.edu/abs/2014MNRAS.438L..61F/abstract Fujisawa & Eriguchi (2014, MNRAS, 438, L61)]:   ''Prolate stars due to meridional flows''</li>
	<li>Huré, Hersant & Nasello (2018, MNRAS, 475, 63)</li>		<li>[https://ui.adsabs.harvard.edu/abs/2018MNRAS.475...63H/abstract Huré, Hersant & Nasello (2018, MNRAS, 475, 63)]:   ''The equilibrium of overpressurized polytropes''</li>
	<li>~~Hachisu~~ & Eriguchi (1984, Ap&SS, 99, 71)</li>		<li>[https://ui.adsabs.harvard.edu/abs/1984Ap%26SS..99...71H/abstractHachisu & Eriguchi (1984, Ap&SS, 99, 71)]:   ''Fission Sequence and Equilibrium Models of [Rigidly] Rotating Polytropes''</li>
	<li>[https://ui.adsabs.harvard.edu/abs/1986ApJ...311..214H/abstract Hachisu, Eriguchi & Nomoto (1986b, ApJ, 311, 214)]:   ''Fate of merging double white dwarfs. II - Numerical method''</li>		<li>[https://ui.adsabs.harvard.edu/abs/1986ApJ...311..214H/abstract Hachisu, Eriguchi & Nomoto (1986b, ApJ, 311, 214)]:   ''Fate of merging double white dwarfs. II - Numerical method''</li>
	<li>Nishida, Eriguchi & Lanza (1992, ApJ, 401, 618)</li>		<li>Nishida, Eriguchi & Lanza (1992, ApJ, 401, 618)</li>

Tohline: /* Spheroid-Ring Systems */

2020-07-23T23:04:41Z

Spheroid-Ring Systems

← Older revision		Revision as of 23:04, 23 July 2020
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	<li>Huré, Hersant & Nasello (2018, MNRAS, 475, 63)</li>		<li>Huré, Hersant & Nasello (2018, MNRAS, 475, 63)</li>
	<li>Hachisu & Eriguchi (1984, Ap&SS, 99, 71)</li>		<li>Hachisu & Eriguchi (1984, Ap&SS, 99, 71)</li>
	<li>Hachisu, Eriguchi & Nomoto (1986b, ApJ, 311, 214)</li>		<li>[https://ui.adsabs.harvard.edu/abs/1986ApJ...311..214H/abstract Hachisu, Eriguchi & Nomoto (1986b, ApJ, 311, 214)]:   ''Fate of merging double white dwarfs. II - Numerical method''</li>
	<li>Nishida, Eriguchi & Lanza (1992, ApJ, 401, 618)</li>		<li>Nishida, Eriguchi & Lanza (1992, ApJ, 401, 618)</li>
	<li>Woodward, Sankaran & Tohline (1992 ApJ, 394, 248)</li>		<li>Woodward, Sankaran & Tohline (1992 ApJ, 394, 248)</li>
Line 7,240:		Line 7,240:
	Especially,		Especially,
	<ul>		<ul>
	<li>Eriguchi & Hachisu (1983, Prog. Theor. Phys., 69, 1131)</li>		<li>[https://ui.adsabs.harvard.edu/abs/1983PThPh..69.1131E/abstract Eriguchi & Hachisu (1983, Prog. Theor. Phys., 69, 1131)]:   ''Two Kinds of Axially Symmetric Equilibrium Sequences of Self-Gravitating and Rotating Incompressible Fluids — Two-Ring Sequence and Core-Ring Sequence''</li>
	<li>Ansorg, Kleinwächter & Meinel (2003, MNRAS, 339, 515)</li>		<li>[https://ui.adsabs.harvard.edu/abs/2003MNRAS.339..515A/abstract Ansorg, Kleinwächter & Meinel (2003, MNRAS, 339, 515)]:   ''Uniformly rotating axisymmetric fluid configurations bifurcating from highly flattened Maclaurin spheroids''</li>
	<li>Hachisu, Eriguchi & Nomoto (1986a, ApJ, 308, 161)</li>		<li>[https://ui.adsabs.harvard.edu/abs/1986ApJ...308..161H/abstract Hachisu, Eriguchi & Nomoto (1986a, ApJ, 308, 161)]:   ''Fate of Merging Double White Dwarfs''</li>
	</ul>		</ul>


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Tohline: /* Spheroid-Ring Systems */

2020-07-23T22:48:58Z

Spheroid-Ring Systems

← Older revision		Revision as of 22:48, 23 July 2020
Line 7,230:		Line 7,230:
	Here are some relevant publications:		Here are some relevant publications:
	<ul>		<ul>
	<li>Hachisu (1986a)</li>		<li>Hachisu (1986a, ApJS, 61, 479)</li>
	<li>Fujisawa & Eriguchi (2014)</li>		<li>Fujisawa & Eriguchi (2014, MNRAS, 438, L61)</li>
	<li>Huré, Hersant & Nasello (2018)</li>		<li>Huré, Hersant & Nasello (2018, MNRAS, 475, 63)</li>
	<li>Hachisu & Eriguchi (1984)</li>		<li>Hachisu & Eriguchi (1984, Ap&SS, 99, 71)</li>
	<li>Hachisu, Eriguchi & Nomoto (1986b)</li>		<li>Hachisu, Eriguchi & Nomoto (1986b, ApJ, 311, 214)</li>
	<li>Nishida, Eriguchi & Lanza (1992)</li>		<li>Nishida, Eriguchi & Lanza (1992, ApJ, 401, 618)</li>
	<li>Woodward, Sankaran & Tohline (1992)</li>		<li>Woodward, Sankaran & Tohline (1992 ApJ, 394, 248)</li>
	</ul>		</ul>
	Especially,		Especially,
	<ul>		<ul>
	<li>Eriguchi & Hachisu (1983)</li>		<li>Eriguchi & Hachisu (1983, Prog. Theor. Phys., 69, 1131)</li>
	<li>Ansorg, Kleinwächter & Meinel (2003)</li>		<li>Ansorg, Kleinwächter & Meinel (2003, MNRAS, 339, 515)</li>
	<li>Hachisu, Eriguchi & Nomoto (1986a)</li>		<li>Hachisu, Eriguchi & Nomoto (1986a, ApJ, 308, 161)</li>
	</ul>		</ul>


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Tohline: /* Spheroid-Ring Systems */

2020-07-23T22:40:42Z

Spheroid-Ring Systems

← Older revision		Revision as of 22:40, 23 July 2020
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	Through a research collaboration at the [https://www.u-bordeaux.com Université de Bordeaux], [https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.4504B/abstract B. Basillais & J. -M. Huré (2019), MNRAS, 487, 4504-4509] have published a paper titled, ''Rigidly Rotating, Incompressible Spheroid-Ring Systems: New Bifurcations, Critical Rotations, and Degenerate States.''		Through a research collaboration at the [https://www.u-bordeaux.com Université de Bordeaux], [https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.4504B/abstract B. Basillais & J. -M. Huré (2019), MNRAS, 487, 4504-4509] have published a paper titled, ''Rigidly Rotating, Incompressible Spheroid-Ring Systems: New Bifurcations, Critical Rotations, and Degenerate States.''

	~~'''TO BE DISCUSSED'''~~ &~~hellip~~;		Here are some relevant publications:
			<ul>
			<li>Hachisu (1986a)</li>
			<li>Fujisawa & Eriguchi (2014)</li>
			<li>Huré, Hersant & Nasello (2018)</li>
			<li>Hachisu & Eriguchi (1984)</li>
			<li>Hachisu, Eriguchi & Nomoto (1986b)</li>
			<li>Nishida, Eriguchi & Lanza (1992)</li>
			<li>Woodward, Sankaran & Tohline (1992)</li>
			</ul>
			Especially,
			<ul>
			<li>Eriguchi & Hachisu (1983)</li>
			<li>Ansorg, Kleinwächter & Meinel (2003)</li>
			<li>Hachisu, Eriguchi & Nomoto (1986a)</li>
			</ul>


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Tohline: /* Include Second Wong Term */

2020-07-14T21:56:56Z

Include Second Wong Term

← Older revision		Revision as of 21:56, 14 July 2020
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	</td>		</td>
	</tr>		</tr>
			</table>

			====Leading (Upsilon) Coefficient====

			<table border="0" cellpadding="5" align="center">

	<tr>		<tr>
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	</td></tr>		</td></tr>
			</table>

			====Geometric Factor====

			By definition,

			<table border="0" cellpadding="5" align="center">

			<tr>
			<td align="right">
			<math>~\Delta_0^2</math>
			</td>
			<td align="center">
			<math>~=</math>
			</td>
			<td align="left">
			<math>~
			(\varpi_W + R_c)^2 + z_W^2 \, ,
			</math>
			</td>
			</tr>

			<tr>
			<td align="right">
			<math>~r_1^2</math>
			</td>
			<td align="center">
			<math>~=</math>
			</td>
			<td align="left">
			<math>~\biggl[ \varpi_W + R_c (1 - e^2 )^{1 / 2}\biggr]^2 + z_W^2 \, ,</math>
			</td>
			</tr>

			<tr>
			<td align="right">
			<math>~r_2^2</math>
			</td>
			<td align="center">
			<math>~=</math>
			</td>
			<td align="left">
			<math>~\biggl[ \varpi_W - R_c (1 - e^2 )^{1 / 2}\biggr]^2 + z_W^2 \, ,</math>
			</td>
			</tr>

			<tr>
			<td align="right">
			<math>~\cos^2\theta</math>
			</td>
			<td align="center">
			<math>~=</math>
			</td>
			<td align="left">
			<math>~\biggl[ \frac{r_1^2 + r_2^2 - 4R_c^2(1-e^2)}{2r_1 r_2} \biggr]^2 \, .</math>
			</td>
			</tr>
			</table>
			Hence,
			<table border="0" cellpadding="5" align="center">

			<tr>
			<td align="right">
			<math>~r_2^2 - \Delta_0^2 \cdot \cos^2\theta</math>
			</td>
			<td align="center">
			<math>~=</math>
			</td>
			<td align="left">
			<math>~</math>
			</td>
			</tr>
	</table>		</table>

Tohline: /* Include Second Wong Term */

2020-07-14T21:33:03Z

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← Older revision		Revision as of 21:33, 14 July 2020
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	\biggl\{ \boldsymbol{E}(k_H) + \frac{\pi}{2}\cdot \delta_E \biggr\}		\biggl\{ \boldsymbol{E}(k_H) + \frac{\pi}{2}\cdot \delta_E \biggr\}
	\biggl\{ \frac{\Delta_0 \cdot \cos\theta}{r_2} \biggr\}		\biggl\{ \frac{\Delta_0 \cdot \cos\theta}{r_2} \biggr\}
	\biggl[ \biggl( \frac{2^{2} }{~~3\pi~~^2} \biggr) \~~Upsilon_~~{W1}(~~\eta_0~~) \biggr]		\biggl[- \biggl(\frac{11}{2\cdot 3} \biggr) e + \biggl(\frac{5}{2^5}\biggr) e^2 + \mathcal{O}(e^{5}) \biggr]\cdot (1 - e^2)^{1 / 2} \, .
	</math>		</math>
	</td>		</td>

Tohline: /* Include Second Wong Term */

2020-07-14T21:27:19Z

Include Second Wong Term

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