User:Tohline/Apps/ImamuraHadleyCollaboration - Revision history

Tohline: /* Setup */

2020-07-31T20:56:56Z

Setup

← Older revision		Revision as of 20:56, 31 July 2020
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	====Setup====		====Setup====

	<table border="1" cellpadding="5" align="right">		<table border="1" cellpadding="5" align="right" width="30%">
	<tr><td align="center" bgcolor="orange">		<tr><td align="center" bgcolor="orange">
	Fig. 1 extracted without modification from p. 554 of [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B Blaes (1985)]<p></p>		Fig. 1 extracted without modification from p. 554 of [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B Blaes (1985)]<p></p>
	"''Oscillations of Slender Tori''"<p></p>		"''Oscillations of Slender Tori''"<p></p>
	Monthly Notices of the Royal Astronomical Society, <~~p><~~/p>		Monthly Notices of the Royal Astronomical Society, <br />vol. 216, Issue 3, October 1985, pp. 553-563<br />© Royal Astronomical Society<br />
	vol. 216, pp. 553-563 © Royal Astronomical Society		https://doi.org/10.1093/mnras/216.3.553
	</td></tr>		</td></tr>
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	<td align="~~center~~">		<td align="left">
	~~Permission to post this~~ digital image ~~granted~~ (via email~~<br />~~		This digital image has been posted by permission of author, O.M. Blaes (via email dated 19 July 2020), and by permission of Oxford University Press on behalf of the Royal Astronomical Society (via email dated 31 July 2020).
	dated 7/19/2020) by ~~author, O~~. ~~Blaes~~.		<div align="center">Original publication website: https://academic.oup.com/mnras/article/216/3/553/1005987</div>
	</td>		</td>
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Tohline: /* Setup */

2020-07-31T20:53:07Z

Setup

← Older revision		Revision as of 20:53, 31 July 2020
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	<table border="1" cellpadding="5" width="80%">		<table border="1" cellpadding="5" width="80%">
	<tr><td align="center" bgcolor="orange">		<tr><td align="center" bgcolor="orange">
	Equation (3.2) extracted without modification from p. 558 of [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B Blaes (1985)]<p></p>		Equation (3.2) extracted without modification from p. 558 of [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B O. M. Blaes (1985)]<p></p>
	"''Oscillations of Slender Tori''"<p></p>		"''Oscillations of Slender Tori''"<p></p>
	Monthly Notices of the Royal Astronomical Society, vol. 216, pp. 553-563 © Royal Astronomical Society		Monthly Notices of the Royal Astronomical Society, vol. 216, Issue 3, October 1985, pp. 553-563<br />© Royal Astronomical Society<br />
			https://doi.org/10.1093/mnras/216.3.553
	</td></tr>		</td></tr>
	<tr>		<tr>
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	<td align="left">		<td align="left">
	~~Permission to post this~~ digital image ~~granted~~ (via email dated 7/19/2020) by ~~author, O~~. ~~Blaes~~.		This digital image has been posted by permission of author, O.M. Blaes (via email dated 19 July 2020), and by permission of Oxford University Press on behalf of the Royal Astronomical Society (via email dated 31 July 2020).
			<div align="center">Original publication website: https://academic.oup.com/mnras/article/216/3/553/1005987</div>
	</td>		</td>
	</tr>		</tr>

Tohline: /* Establishing the Simpler Eigenvalue Problem */

2020-07-31T20:50:51Z

Establishing the Simpler Eigenvalue Problem

← Older revision		Revision as of 20:50, 31 July 2020
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	<table border="1" cellpadding="5" width="80%">		<table border="1" cellpadding="5" width="80%">
	<tr><td align="center" bgcolor="orange">		<tr><td align="center" bgcolor="orange">
	Equation (1.6) — identical to Eq. (3.5) — extracted without modification from p. 555 of [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B Blaes (1985)]<p></p>		Equation (1.6) — identical to Eq. (3.5) — extracted without modification from p. 555 of [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B O. M. Blaes (1985)]<p></p>
	"''Oscillations of Slender Tori''"<p></p>		"''Oscillations of Slender Tori''"<p></p>
	Monthly Notices of the Royal Astronomical Society, vol. 216, pp. 553-563 © Royal Astronomical Society		Monthly Notices of the Royal Astronomical Society, vol. 216, Issue 3, October 1985, pp. 553-563<br />© Royal Astronomical Society<br />
			https://doi.org/10.1093/mnras/216.3.553
	</td></tr>		</td></tr>
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	<td align="center">		<td align="center">
	[[File:Blaes85Eq1.6.png\|600px\|center\|Blaes (1985, MNRAS, 216, 553)]]		[[File:Blaes85Eq1.6.png\|600px\|center\|Blaes (1985, MNRAS, 216, 553)]]
			<!-- [[Image:AAAwaiting01.png\|400px\|center\|Whitworth (1981) Eq. 5]] -->
	</td>		</td>
	</tr>		</tr>
	<tr>		<tr>
	<td align="left">		<td align="left">
	~~Permission to post this~~ digital image ~~granted~~ (via email dated 7/19/2020) by ~~author, O~~. ~~Blaes~~.		This digital image has been posted by permission of author, O.M. Blaes (via email dated 19 July 2020), and by permission of Oxford University Press on behalf of the Royal Astronomical Society (via email dated 31 July 2020).
			<div align="center">Original publication website: https://academic.oup.com/mnras/article/216/3/553/1005987</div>
	</td>		</td>
	</tr>		</tr>

Tohline: /* Establishing the Simpler Eigenvalue Problem */

2020-07-20T21:23:17Z

Establishing the Simpler Eigenvalue Problem

← Older revision		Revision as of 21:23, 20 July 2020
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	<div align="center" id="EigenvalueBlaes85">		<div align="center" id="EigenvalueBlaes85">
	<table border="1" cellpadding="5" width="80%">		<table border="1" cellpadding="5" width="80%">
	<tr><td align="center">		<tr><td align="center" bgcolor="orange">
	Equation (1.6) — identical to Eq. (3.5) — extracted without modification from p. 555 of [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B Blaes (1985)]<p></p>		Equation (1.6) — identical to Eq. (3.5) — extracted without modification from p. 555 of [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B Blaes (1985)]<p></p>
	"''Oscillations of Slender Tori''"<p></p>		"''Oscillations of Slender Tori''"<p></p>

Tohline: /* Setup */

2020-07-20T21:22:48Z

Setup

← Older revision		Revision as of 21:22, 20 July 2020
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	<table border="1" cellpadding="5" align="right">		<table border="1" cellpadding="5" align="right">
	<tr><td align="center">		<tr><td align="center" bgcolor="orange">
	Fig. 1 extracted without modification from p. 554 of [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B Blaes (1985)]<p></p>		Fig. 1 extracted without modification from p. 554 of [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B Blaes (1985)]<p></p>
	"''Oscillations of Slender Tori''"<p></p>		"''Oscillations of Slender Tori''"<p></p>
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	<div align="center" id="EigenvalueBlaes85">		<div align="center" id="EigenvalueBlaes85">
	<table border="1" cellpadding="5" width="80%">		<table border="1" cellpadding="5" width="80%">
	<tr><td align="center">		<tr><td align="center" bgcolor="orange">
	Equation (3.2) extracted without modification from p. 558 of [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B Blaes (1985)]<p></p>		Equation (3.2) extracted without modification from p. 558 of [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B Blaes (1985)]<p></p>
	"''Oscillations of Slender Tori''"<p></p>		"''Oscillations of Slender Tori''"<p></p>

Tohline: /* Papaloizou & Pringle (1985) */

2020-07-20T21:21:24Z

Papaloizou & Pringle (1985)

← Older revision		Revision as of 21:21, 20 July 2020
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	<div align="center" id="EigenvaluePP85">		<div align="center" id="EigenvaluePP85">
	<table border="1" cellpadding="5" width="80%">		<table border="1" cellpadding="5" width="80%">
	<tr><td align="center">		<tr><td align="center" bgcolor="orange">
	Equation (2.19) extracted without modification from p. 803 of [http://adsabs.harvard.edu/abs/1985MNRAS.213..799P Papaloizou & Pringle (1985)]<p></p>		Equation (2.19) extracted without modification from p. 803 of [http://adsabs.harvard.edu/abs/1985MNRAS.213..799P Papaloizou & Pringle (1985)]<p></p>
	"''The dynamical stability of differentially rotating discs. II''"<p></p>		"''The dynamical stability of differentially rotating discs. II''"<p></p>

Tohline: /* Establishing the Simpler Eigenvalue Problem */

2020-07-19T17:52:35Z

Establishing the Simpler Eigenvalue Problem

← Older revision		Revision as of 17:52, 19 July 2020
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	<td align="center">		<td align="center">
	[[File:Blaes85Eq1.6.png\|600px\|center\|Blaes (1985, MNRAS, 216, 553)]]		[[File:Blaes85Eq1.6.png\|600px\|center\|Blaes (1985, MNRAS, 216, 553)]]
			</td>
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			<tr>
			<td align="left">
			Permission to post this digital image granted (via email dated 7/19/2020) by author, O. Blaes.
	</td>		</td>
	</tr>		</tr>

Tohline: /* Setup */

2020-07-19T17:52:05Z

Setup

← Older revision		Revision as of 17:52, 19 July 2020
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	<td align="center">		<td align="center">
	[[File:Blaes85Fig1.png\|center\|300px\|Figure 1 from Blaes (1985)]]		[[File:Blaes85Fig1.png\|center\|300px\|Figure 1 from Blaes (1985)]]
			</td>
			</tr>
			<tr>
			<td align="center">
			Permission to post this digital image granted (via email<br />
			dated 7/19/2020) by author, O. Blaes.
	</td>		</td>
	</tr>		</tr>
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	[[File:Blaes85Eq3.2.png\|600px\|center\|Blaes (1985, MNRAS, 216, 553)]]		[[File:Blaes85Eq3.2.png\|600px\|center\|Blaes (1985, MNRAS, 216, 553)]]
	<!-- [[Image:AAAwaiting01.png\|400px\|center\|Whitworth (1981) Eq. 5]] -->		<!-- [[Image:AAAwaiting01.png\|400px\|center\|Whitworth (1981) Eq. 5]] -->
			</td>
			</tr>
			<tr>
			<td align="left">
			Permission to post this digital image granted (via email dated 7/19/2020) by author, O. Blaes.
	</td>		</td>
	</tr>		</tr>

Tohline: /* Visual Comparison */ Insert link to new chapter providing portal into HI database/repository

2016-06-11T15:17:34Z

Visual Comparison: Insert link to new chapter providing portal into HI database/repository

← Older revision		Revision as of 15:17, 11 June 2016
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	=====Visual Comparison=====		=====Visual Comparison=====
	With the above information in hand, we can now directly compare the eigenfunction of the unstable, ''m'' = 2 mode discovered and defined analytically by [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B Blaes (1985)] with the eigenfunction of unstable, ''m'' = 2 modes found by the [[#See_Also\|Imamura & Hadley collaboration]] while using numerical hydrodynamic techniques to simulate the evolution of similarly slim tori. Panel A of Figure 3 displays a pair of plots, extracted from [http://adsabs.harvard.edu/abs/2014Ap%26SS.353..191H Hadley et al. (2014; Paper II)], that present information regarding the ''m'' = 2 mode, nonaxisymmetric structure that developed in the equatorial plane of their model P4. The model P4 disk/torus is geometrically slim <math>~(\beta \approx 0.18)</math> and its mass, although not zero, is only 1% of the mass of the central star <math>~(M_/M_\mathrm{disk} = 10^2)</math>. Panel B of Figure 3 displays a similar pair of plots from a separate, unpublished Hadley et al. model evolution; in this model, the disk/torus mass is only 0.1% that of the central star <math>~(M_/M_\mathrm{disk} = 10^3)</math>. In both panels, the blue curves show the geometric structure of non-axisymmetric, equatorial-plane density fluctuations, <math>~\|\rho^'/\rho_0\|_2</math>, and the red curves show the structure of the "enthalpy + gravity" perturbation, <math>~\mathcal{W}</math>: The left-hand plot displays log<sub>10</sub> of (the modulus of) the amplitude versus radius; while the right-hand plot displays the unstable mode's constant phase locus. In each of these plots, the radial coordinate is, <math>~\chi \equiv \varpi/\varpi_0</math>.		With the above information in hand, we can now directly compare the eigenfunction of the unstable, ''m'' = 2 mode discovered and defined analytically by [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B Blaes (1985)] with the eigenfunction of unstable, ''m'' = 2 modes found by the [[#See_Also\|Imamura & Hadley collaboration]] while using numerical hydrodynamic techniques to simulate the evolution of similarly slim tori. Panel A of Figure 3 displays a pair of plots, extracted from [http://adsabs.harvard.edu/abs/2014Ap%26SS.353..191H Hadley et al. (2014; Paper II)], that present information regarding the ''m'' = 2 mode, nonaxisymmetric structure that developed in the equatorial plane of their model P4. The model P4 disk/torus is geometrically slim <math>~(\beta \approx 0.18)</math> and its mass, although not zero, is only 1% of the mass of the central star <math>~(M_/M_\mathrm{disk} = 10^2)</math>. Panel B of Figure 3 displays a similar pair of plots from a separate, [[User:Tohline/Appendix/Ramblings/Hadley_and_Imamura_Supplementary_Database#Supplementary_Dataset_Generated_by_Hadley_.26_Imamura_Collaboration\|unpublished Hadley et al. model evolution]]; in this model, the disk/torus mass is only 0.1% that of the central star <math>~(M_/M_\mathrm{disk} = 10^3)</math>. In both panels, the blue curves show the geometric structure of non-axisymmetric, equatorial-plane density fluctuations, <math>~\|\rho^'/\rho_0\|_2</math>, and the red curves show the structure of the "enthalpy + gravity" perturbation, <math>~\mathcal{W}</math>: The left-hand plot displays log<sub>10</sub> of (the modulus of) the amplitude versus radius; while the right-hand plot displays the unstable mode's constant phase locus. In each of these plots, the radial coordinate is, <math>~\chi \equiv \varpi/\varpi_0</math>.


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	[[File:Montage01Apart1.png\|500px\|center\|Imamura & Hadley collaboration]]		[[File:Montage01Apart1.png\|500px\|center\|Imamura & Hadley collaboration]]
	</td></tr>		</td></tr>
	<tr><th><font size="+1">Panel B:    Unpublished model from Imamura & Hadley collaboration;</font><p></p>		<tr><th><font size="+1">Panel B:    [[User:Tohline/Appendix/Ramblings/Hadley_and_Imamura_Supplementary_Database#Supplementary_Dataset_Generated_by_Hadley_.26_Imamura_Collaboration\|Unpublished model]] from Imamura & Hadley collaboration;</font><p></p>
	<math>~M_*/M_\mathrm{disk} = 1000</math></th></tr>		<math>~M_*/M_\mathrm{disk} = 1000</math></th></tr>
	<tr><td align="right">		<tr><td align="right">

Tohline: /* Visual Comparison */ Add tag to Figure 3

2016-06-05T01:43:08Z

Visual Comparison: Add tag to Figure 3

← Older revision		Revision as of 01:43, 5 June 2016
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			<div align="center" id="Figure3">
	<table border="1" align="center" cellpadding="5">		<table border="1" align="center" cellpadding="5">
	<tr><th><font size="+1">Figure 3: Comparison</font></th></tr>		<tr><th><font size="+1">Figure 3: Comparison</font></th></tr>
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	</td></tr>		</td></tr>
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	=====Details Regarding Radial Coordinate Specification=====		=====Details Regarding Radial Coordinate Specification=====