Jet53man at 23:25, 20 September 2021

2021-09-20T23:25:49Z

← Older revision		Revision as of 19:25, 20 September 2021
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	=Stability Analyses of PP Tori (Part 2)=		=Stability Analyses of PP Tori (Part 2)=

	<font color="red"><b>[Comment by J. E. Tohline on 24 May 2016]</b></font>   This chapter contains a set of technical notes and accompanying discussion that I put together several months ago as I was trying to gain a foundational understanding of the results of a large study of instabilities in self-gravitating tori published by the Imamura & Hadley collaboration. I have come to appreciate that some of the logic and interpretation of published results that are presented, below, has serious flaws. Therefore, anyone reading this should be quite cautious in deciding what subsections provide useful insight. I have written a separate chapter titled, "[[~~User:Tohline/~~Apps/ImamuraHadleyCollaboration#Characteristics_of_Unstable_Eigenvectors_in_Self-Gravitating_Tori\|Characteristics of Unstable Eigenvectors in Self-Gravitating Tori]]," that contains a much more trustworthy analysis of this very interesting problem.		<font color="red"><b>[Comment by J. E. Tohline on 24 May 2016]</b></font>   This chapter contains a set of technical notes and accompanying discussion that I put together several months ago as I was trying to gain a foundational understanding of the results of a large study of instabilities in self-gravitating tori published by the Imamura & Hadley collaboration. I have come to appreciate that some of the logic and interpretation of published results that are presented, below, has serious flaws. Therefore, anyone reading this should be quite cautious in deciding what subsections provide useful insight. I have written a separate chapter titled, "[[Apps/ImamuraHadleyCollaboration#Characteristics_of_Unstable_Eigenvectors_in_Self-Gravitating_Tori\|Characteristics of Unstable Eigenvectors in Self-Gravitating Tori]]," that contains a much more trustworthy analysis of this very interesting problem.

	{{ SGFworkInProgress }}		{{ SGFworkInProgress }}

	This is a direct extension of our [[~~User:Tohline/~~Appendix/Ramblings/~~PPTori~~#Check_Validity_of_Blaes85_Eigenvector\|Part 1 discussion]]. Here we continue our effort to check the validity of the Blaes85 eigenvector. The relevant reference is:		This is a direct extension of our [[Appendix/Ramblings/PPToriPt1A#Check_Validity_of_Blaes85_Eigenvector\|Part 1 discussion]]. Here we continue our effort to check the validity of the Blaes85 eigenvector. The relevant reference is:

	* [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B Blaes (1985), MNRAS, 216, 553] (''aka'' Blaes85) — ''Oscillations of slender tori.''		* [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B Blaes (1985), MNRAS, 216, 553] (''aka'' Blaes85) — ''Oscillations of slender tori.''
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	Evaluating various terms using the parameter set,		Evaluating various terms using the parameter set,
	<math>~(n, \theta, x/\beta) = (1, \tfrac{\pi}{3}, \tfrac{1}{4})</math>		<math>~(n, \theta, x/\beta) = (1, \tfrac{\pi}{3}, \tfrac{1}{4})</math>
	as [[~~User:Tohline/~~Appendix/Ramblings/~~PPTori~~#Examples\|begun in our "Part 1" analysis]], we have:		as [[Appendix/Ramblings/PPToriPt1A#Examples\|begun in our "Part 1" analysis]], we have:
	<div align="center">		<div align="center">
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

Jet53man: /* Sum of TERM$ and TERM5 */

2021-07-23T15:50:27Z

Sum of TERM$ and TERM5

← Older revision		Revision as of 11:50, 23 July 2021
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	</div>		</div>

	=====Sum of ~~TERM$~~ and TERM5=====		=====Sum of TERM4 and TERM5=====

	When added together, we obtain,		When added together, we obtain,

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2021-07-23T15:49:15Z

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Appendix/Ramblings/PPToriPt2A - Revision history

Jet53man at 23:25, 20 September 2021

Jet53man: /* Sum of TERM$ and TERM5 */

Jet53man: Created page with " =Stability Analyses of PP Tori (Part 2)= [Comm..."