AxisymmetricConfigurations/SolutionStrategies - Revision history

Jet53man: /* j-Constant Rotation */

2023-04-21T17:45:57Z

j-Constant Rotation

← Older revision		Revision as of 13:45, 21 April 2023
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	</table>		</table>

	[K}  Alternatively,		[K]   Alternatively,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

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	</table>		</table>

	[L}  Or,		[L]   Or,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

Jet53man: /* Uniform vφ */

2023-04-21T17:45:15Z

Uniform vφ

← Older revision		Revision as of 13:45, 21 April 2023
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	</table>		</table>

	[H}  Alternatively,		[H]   Alternatively,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

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	</table>		</table>

	[I}  Or,		[I]   Or,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

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	</table>		</table>
	This demonstrates that, in the case of a constant <math>~v_\varphi</math> profile, all three expressions are identical.		This demonstrates that, in the case of a constant <math>~v_\varphi</math> profile, all three expressions are identical.


	===j-Constant Rotation===		===j-Constant Rotation===

Jet53man: /* Power Law */

2023-04-21T17:44:27Z

Power Law

← Older revision		Revision as of 13:44, 21 April 2023
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	</table>		</table>

	[E}  Alternatively,		[E]   Alternatively,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

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	</table>		</table>

	[F}  Or,		[F]   Or,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

Jet53man: /* Uniform Rotation */

2023-04-21T17:43:40Z

Uniform Rotation

← Older revision		Revision as of 13:43, 21 April 2023
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	</table>		</table>

	[B}  Alternatively,		[B]   Alternatively,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

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	</table>		</table>

	[C}  Or,		[C]   Or,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

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	</table>		</table>
	This demonstrates that, in the case of uniform angular velocity, all three expressions are identical.		This demonstrates that, in the case of uniform angular velocity, all three expressions are identical.


	===Power Law===		===Power Law===

Jet53man: /* Centrally Condensed Initially (n' > 0) */

2023-04-20T19:17:16Z

Centrally Condensed Initially (n' > 0)

← Older revision		Revision as of 15:17, 20 April 2023
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	{{ OB68 }}, p. 1090, Eq. (6)<br />		{{ OB68 }}, p. 1090, Eq. (6)<br />
	{{ BO73 }}, §II, Eq. (4)<br />		{{ BO73 }}, §II, Eq. (4)<br />
			[<b>[[Appendix/References#T78\|<font color="red">T78</font>]]</b>], §10.4 (p. 254), Eq. (44)<br />
	{{ PDD96 }}, §2.1, Figure 1		{{ PDD96 }}, §2.1, Figure 1
	</td>		</td>

Jet53man: /* Specifying Radial Rotation Profile in the Equilibrium Configuration */

2023-03-24T17:59:48Z

Specifying Radial Rotation Profile in the Equilibrium Configuration

← Older revision		Revision as of 13:59, 24 March 2023
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	<sup>c</sup>{{ WTH94full }}<br />		<sup>c</sup>{{ WTH94full }}<br />
	<sup>m</sup>{{ PDD96full }}<br />		<sup>m</sup>{{ PDD96full }}<br />
	<sup>b</sup>~~Ou, S. & Tohline, J.E. [http://iopscience.iop.org/0004-637X/651/2/1068/pdf/0004-637X_651_2_1068.pdf 2006, ApJ, 651, 1068-1078]~~		<sup>b</sup>{{ OT2006full }} (especially §2.1)<br />
	(especially §2.1)<br />
	<sup>h</sup>The [[Appendix/Ramblings/HadleyAndImamuraSupplementaryDatabase#See_Also\|Hadley & Imamura collaboration]] (circa 2015)  [Note that, as detailed [[Appendix/Ramblings/HadleyAndImamuraSupplementaryDatabase#Simple_Rotation_Profiles\|elsewhere]], their definition of the power-law index, <math>q</math>, is different from ours.]		<sup>h</sup>The [[Appendix/Ramblings/HadleyAndImamuraSupplementaryDatabase#See_Also\|Hadley & Imamura collaboration]] (circa 2015)  [Note that, as detailed [[Appendix/Ramblings/HadleyAndImamuraSupplementaryDatabase#Simple_Rotation_Profiles\|elsewhere]], their definition of the power-law index, <math>q</math>, is different from ours.]

Jet53man: /* Simple Rotation Profile and Centrifugal Potential */

2023-03-22T21:13:52Z

Simple Rotation Profile and Centrifugal Potential

← Older revision		Revision as of 17:13, 22 March 2023
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	</td></tr>		</td></tr>
	<tr><td align="right">		<tr><td align="right">
	— Drawn from ~~[https://ui~~.~~adsabs.harvard.edu/abs/1967ARA%26A...5..465L/abstract N. R. Lebovitz (1967)], ARAA, 5, 465~~		— Drawn from p. 466 of {{ Lebovitz67_XXXIV }}
	</td></tr></table>		</td></tr></table>
	===Specifying Radial Rotation Profile in the Equilibrium Configuration===		===Specifying Radial Rotation Profile in the Equilibrium Configuration===
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	<sup>b</sup>Ou, S. & Tohline, J.E. [http://iopscience.iop.org/0004-637X/651/2/1068/pdf/0004-637X_651_2_1068.pdf 2006, ApJ, 651, 1068-1078]		<sup>b</sup>Ou, S. & Tohline, J.E. [http://iopscience.iop.org/0004-637X/651/2/1068/pdf/0004-637X_651_2_1068.pdf 2006, ApJ, 651, 1068-1078]
	(especially §2.1)<br />		(especially §2.1)<br />
	<sup>h</sup>The [[Appendix/Ramblings/HadleyAndImamuraSupplementaryDatabase#See_Also\|Hadley & Imamura collaboration]] (circa 2015)  [Note that, as detailed [[Appendix/Ramblings/HadleyAndImamuraSupplementaryDatabase#Simple_Rotation_Profiles\|elsewhere]], their definition of the power-law index, <math>~q</math>, is different from ours.]		<sup>h</sup>The [[Appendix/Ramblings/HadleyAndImamuraSupplementaryDatabase#See_Also\|Hadley & Imamura collaboration]] (circa 2015)  [Note that, as detailed [[Appendix/Ramblings/HadleyAndImamuraSupplementaryDatabase#Simple_Rotation_Profiles\|elsewhere]], their definition of the power-law index, <math>q</math>, is different from ours.]

	</td>		</td>

Jet53man: /* Specifying Radial Rotation Profile in the Equilibrium Configuration */

2023-03-22T17:59:49Z

Specifying Radial Rotation Profile in the Equilibrium Configuration

← Older revision		Revision as of 13:59, 22 March 2023
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	<sup>g</sup>{{ PP84full }}<br />		<sup>g</sup>{{ PP84full }}<br />
	<sup>a</sup>{{ Hachisu86afull }} (especially §II.c)<br />		<sup>a</sup>{{ Hachisu86afull }} (especially §II.c)<br />
	<sup>d</sup>~~Tohline, J.E. & Hachisu, I. [http://adsabs.harvard.edu/abs/1990ApJ...361..394T 1990, ApJ, 361, 394-407]~~<br />		<sup>d</sup>{{ TH90full }}<br />
	<sup>c</sup>~~Woodward, J.W., Tohline, J.E. & Hachisu, I. [http://adsabs.harvard.edu/abs/1994ApJ...420..247W 1994, ApJ, 420, 247-267]~~<br />		<sup>c</sup>{{ WTH94full }}<br />
	<sup>m</sup>{{ PDD96full }}<br />		<sup>m</sup>{{ PDD96full }}<br />
	<sup>b</sup>Ou, S. & Tohline, J.E. [http://iopscience.iop.org/0004-637X/651/2/1068/pdf/0004-637X_651_2_1068.pdf 2006, ApJ, 651, 1068-1078]		<sup>b</sup>Ou, S. & Tohline, J.E. [http://iopscience.iop.org/0004-637X/651/2/1068/pdf/0004-637X_651_2_1068.pdf 2006, ApJ, 651, 1068-1078]

Jet53man: /* Specifying Radial Rotation Profile in the Equilibrium Configuration */

2023-03-22T17:28:51Z

Specifying Radial Rotation Profile in the Equilibrium Configuration

← Older revision		Revision as of 13:28, 22 March 2023
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	<sup>i</sup>{{ Clement79full }}<br />		<sup>i</sup>{{ Clement79full }}<br />
	<sup>e</sup>{{ HNM82full }}<br />		<sup>e</sup>{{ HNM82full }}<br />
	<sup>g</sup>~~Papaloizou, J.C.B. & Pringle, J.E. [http://adsabs.harvard.edu/abs/1984MNRAS.208..721P 1984, MNRAS, 208, 721-750]~~<br />		<sup>g</sup>{{ PP84full }}<br />
	<sup>a</sup>{{ Hachisu86afull }} (especially §II.c)<br />		<sup>a</sup>{{ Hachisu86afull }} (especially §II.c)<br />
	<sup>d</sup>Tohline, J.E. & Hachisu, I. [http://adsabs.harvard.edu/abs/1990ApJ...361..394T 1990, ApJ, 361, 394-407]<br />		<sup>d</sup>Tohline, J.E. & Hachisu, I. [http://adsabs.harvard.edu/abs/1990ApJ...361..394T 1990, ApJ, 361, 394-407]<br />

Jet53man: /* Centrally Condensed Initially (n' > 0) */

2023-03-21T21:45:39Z

Centrally Condensed Initially (n' > 0)

← Older revision		Revision as of 17:45, 21 March 2023
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	<td align="center" colspan="6">		<td align="center" colspan="6">
	<b>Coefficients for <math>~h(m)</math> Expression</b><br />		<b>Coefficients for <math>~h(m)</math> Expression</b><br />
	used by ~~[https://ui.adsabs.harvard.edu/abs/1968ApJ...151.1089O/abstract Ostriker & Bodenheimer (1968)]~~, p. 1090, Eq. (6)		used by {{ OB68 }}, p. 1090, Eq. (6)
	</td>		</td>
	</tr>		</tr>