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	<id>https://tohline.education/SelfGravitatingFluids/index.php?action=history&amp;feed=atom&amp;title=Appendix%2FRamblings%2FToHadleyAndImamura</id>
	<title>Appendix/Ramblings/ToHadleyAndImamura - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://tohline.education/SelfGravitatingFluids/index.php?action=history&amp;feed=atom&amp;title=Appendix%2FRamblings%2FToHadleyAndImamura"/>
	<link rel="alternate" type="text/html" href="https://tohline.education/SelfGravitatingFluids/index.php?title=Appendix/Ramblings/ToHadleyAndImamura&amp;action=history"/>
	<updated>2026-04-21T14:07:50Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://tohline.education/SelfGravitatingFluids/index.php?title=Appendix/Ramblings/ToHadleyAndImamura&amp;diff=3512&amp;oldid=prev</id>
		<title>Jet53man: /* Movie */</title>
		<link rel="alternate" type="text/html" href="https://tohline.education/SelfGravitatingFluids/index.php?title=Appendix/Ramblings/ToHadleyAndImamura&amp;diff=3512&amp;oldid=prev"/>
		<updated>2021-10-04T17:56:07Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;Movie&lt;/span&gt;&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 13:56, 4 October 2021&lt;/td&gt;
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&lt;/table&gt;</summary>
		<author><name>Jet53man</name></author>
	</entry>
	<entry>
		<id>https://tohline.education/SelfGravitatingFluids/index.php?title=Appendix/Ramblings/ToHadleyAndImamura&amp;diff=899&amp;oldid=prev</id>
		<title>Jet53man at 23:13, 22 July 2021</title>
		<link rel="alternate" type="text/html" href="https://tohline.education/SelfGravitatingFluids/index.php?title=Appendix/Ramblings/ToHadleyAndImamura&amp;diff=899&amp;oldid=prev"/>
		<updated>2021-07-22T23:13:43Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 19:13, 22 July 2021&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l6&quot;&gt;Line 6:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 6:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;font color=&amp;quot;red&amp;quot;&amp;gt;&amp;lt;b&amp;gt;[Comment by J. E. Tohline on 24 May 2016]&amp;lt;/b&amp;gt;&amp;lt;/font&amp;gt; &amp;amp;nbsp; 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 &amp;amp;amp; 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, &amp;quot;[[User:Tohline/Apps/ImamuraHadleyCollaboration#Characteristics_of_Unstable_Eigenvectors_in_Self-Gravitating_Tori|Characteristics of Unstable Eigenvectors in Self-Gravitating Tori]],&amp;quot; that contains a much more trustworthy analysis of this very interesting problem.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;font color=&amp;quot;red&amp;quot;&amp;gt;&amp;lt;b&amp;gt;[Comment by J. E. Tohline on 24 May 2016]&amp;lt;/b&amp;gt;&amp;lt;/font&amp;gt; &amp;amp;nbsp; 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 &amp;amp;amp; 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, &amp;quot;[[User:Tohline/Apps/ImamuraHadleyCollaboration#Characteristics_of_Unstable_Eigenvectors_in_Self-Gravitating_Tori|Characteristics of Unstable Eigenvectors in Self-Gravitating Tori]],&amp;quot; that contains a much more trustworthy analysis of this very interesting problem.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{ &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;WorkInProgress &lt;/del&gt;}}&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{ &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;SGFworkInProgress &lt;/ins&gt;}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This MediaWiki-based document is especially provided for Jimmy Imamura and Kathryn Hadley.  It summarizes the contents of a much longer [[User:Tohline/Appendix/Ramblings/Azimuthal_Distortions#Analyzing_Azimuthal_Distortions|set of technical notes that discusses the analysis of nonaxisymmetric distortions in rotating, self-gravitating fluids]].  The punchline is provided by the [[User:Tohline/Appendix/Ramblings/To_Hadley_and_Imamura#Put_It_Together|animation sequence shown in Figure 2, below]].&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This MediaWiki-based document is especially provided for Jimmy Imamura and Kathryn Hadley.  It summarizes the contents of a much longer [[User:Tohline/Appendix/Ramblings/Azimuthal_Distortions#Analyzing_Azimuthal_Distortions|set of technical notes that discusses the analysis of nonaxisymmetric distortions in rotating, self-gravitating fluids]].  The punchline is provided by the [[User:Tohline/Appendix/Ramblings/To_Hadley_and_Imamura#Put_It_Together|animation sequence shown in Figure 2, below]].&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l423&quot;&gt;Line 423:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 423:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;/ol&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;/ol&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;LSU_WorkInProgress&lt;/del&gt;}}&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{ &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;SGFworkInProgress &lt;/ins&gt;}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Analytic Analysis of Zero-Mass Papaloizou-Pringle Tori==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Analytic Analysis of Zero-Mass Papaloizou-Pringle Tori==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Jet53man</name></author>
	</entry>
	<entry>
		<id>https://tohline.education/SelfGravitatingFluids/index.php?title=Appendix/Ramblings/ToHadleyAndImamura&amp;diff=898&amp;oldid=prev</id>
		<title>Jet53man: Created page with &quot;__FORCETOC__ &lt;!-- __NOTOC__ will force TOC off --&gt;  =Summary for Hadley &amp;amp; Imamura=  &lt;font color=&quot;red&quot;&gt;&lt;b&gt;[Comment by J. E. Tohline on 24 May 2016]&lt;/b&gt;&lt;/font&gt; &amp;nbsp; This c...&quot;</title>
		<link rel="alternate" type="text/html" href="https://tohline.education/SelfGravitatingFluids/index.php?title=Appendix/Ramblings/ToHadleyAndImamura&amp;diff=898&amp;oldid=prev"/>
		<updated>2021-07-22T23:07:13Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;__FORCETOC__ &amp;lt;!-- __NOTOC__ will force TOC off --&amp;gt;  =Summary for Hadley &amp;amp; Imamura=  &amp;lt;font color=&amp;quot;red&amp;quot;&amp;gt;&amp;lt;b&amp;gt;[Comment by J. E. Tohline on 24 May 2016]&amp;lt;/b&amp;gt;&amp;lt;/font&amp;gt;   This c...&amp;quot;&lt;/p&gt;
&lt;a href=&quot;https://tohline.education/SelfGravitatingFluids/index.php?title=Appendix/Ramblings/ToHadleyAndImamura&amp;amp;diff=898&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>Jet53man</name></author>
	</entry>
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