https://www.vistrails.org//index.php?title=User:Tohline/Appendix/Ramblings/PatrickMotl&feed=atom&action=historyUser:Tohline/Appendix/Ramblings/PatrickMotl - Revision history2024-03-28T16:15:17ZRevision history for this page on the wikiMediaWiki 1.36.2https://www.vistrails.org//index.php?title=User:Tohline/Appendix/Ramblings/PatrickMotl&diff=21382&oldid=prevTohline: /* January 7, 2021 (from Joel) */2021-01-08T22:12:03Z<p><span dir="auto"><span class="autocomment">January 7, 2021 (from Joel)</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:12, 8 January 2021</td>
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<tr><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could simply re-create the same linear-linear "time-dependent eigenfunction" movie, and add to every movie frame Joel's (time independent) '''blue segment''' eigenfunction; I guess, in this case, Joel's function should be normalized to unity at the center. Make sure that the normalization of the radius (horizontal axis) is the same in Patrick's time-dependent plots as it is in Joel's time-independent dataset.</li></div></td><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could simply re-create the same linear-linear "time-dependent eigenfunction" movie, and add to every movie frame Joel's (time independent) '''blue segment''' eigenfunction; I guess, in this case, Joel's function should be normalized to unity at the center. Make sure that the normalization of the radius (horizontal axis) is the same in Patrick's time-dependent plots as it is in Joel's time-independent dataset.</li></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could generate a new eigenfunction movie in which the vertical axis is log-amplitude; Joel's time-independent eigenfunction should be added to every movie frame but, of course, in this case it should also be plotted as log-amplitude versus radius.</li></div></td><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could generate a new eigenfunction movie in which the vertical axis is log-amplitude; Joel's time-independent eigenfunction should be added to every movie frame but, of course, in this case it should also be plotted as log-amplitude versus radius.</li></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div> <li>Better yet, turn Joel's eigenfunction into a time-dependent eigenfunction! Using the evolutionary time that corresponds to each frame of the movie, multiply every x(xi) value by <math>~d_c \cdot e^{\sqrt{\omega^2}t}</math> with, I suppose, d_c = 1.5e-3. <del style="font-weight: bold; text-decoration: none;">Plot </del>this time-evolving curve on top of Patrick's numerically generated x(x_0,t) values and let's see how well they match over time!</li></div></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div> <li>Better yet, turn Joel's eigenfunction into a time-dependent eigenfunction! Using the evolutionary time that corresponds to each frame of the movie, multiply every x(xi) value by <math>~d_c \cdot e^{\sqrt{\omega^2}t}</math> with, I suppose, d_c = 1.5e-3. <ins style="font-weight: bold; text-decoration: none;">Using a semi-log diagram, plot </ins>this time-evolving curve on top of Patrick's numerically generated x(x_0,t) values and let's see how well they match over time!</li></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div></ol></div></td><td class="diff-marker"></td><td style="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;"><div></ol></div></td></tr>
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</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/Appendix/Ramblings/PatrickMotl&diff=21381&oldid=prevTohline: /* January 7, 2021 (from Joel) */2021-01-08T22:10:36Z<p><span dir="auto"><span class="autocomment">January 7, 2021 (from Joel)</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:10, 8 January 2021</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1764">Line 1,764:</td>
<td colspan="2" class="diff-lineno">Line 1,764:</td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could simply re-create the same linear-linear "time-dependent eigenfunction" movie, and add to every movie frame Joel's (time independent) '''blue segment''' eigenfunction; I guess, in this case, Joel's function should be normalized to unity at the center. Make sure that the normalization of the radius (horizontal axis) is the same in Patrick's time-dependent plots as it is in Joel's time-independent dataset.</li></div></td><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could simply re-create the same linear-linear "time-dependent eigenfunction" movie, and add to every movie frame Joel's (time independent) '''blue segment''' eigenfunction; I guess, in this case, Joel's function should be normalized to unity at the center. Make sure that the normalization of the radius (horizontal axis) is the same in Patrick's time-dependent plots as it is in Joel's time-independent dataset.</li></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could generate a new eigenfunction movie in which the vertical axis is log-amplitude; Joel's time-independent eigenfunction should be added to every movie frame but, of course, in this case it should also be plotted as log-amplitude versus radius.</li></div></td><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could generate a new eigenfunction movie in which the vertical axis is log-amplitude; Joel's time-independent eigenfunction should be added to every movie frame but, of course, in this case it should also be plotted as log-amplitude versus radius.</li></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div> <li>Better yet, turn Joel's eigenfunction into a time-dependent eigenfunction! Using the evolutionary time that corresponds to each frame of the movie, multiply every x(xi) value by <math>~d_c \cdot e^{\sqrt{\omega^2}t}</math> with, I suppose, <del style="font-weight: bold; text-decoration: none;"><math>~</del>d_c = 1.<del style="font-weight: bold; text-decoration: none;">5\times 10^{</del>-<del style="font-weight: bold; text-decoration: none;">2}</math></del>. Plot this time-evolving curve on top of Patrick's numerically generated x(x_0,t) values and let's see how well they match over time!</li></div></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div> <li>Better yet, turn Joel's eigenfunction into a time-dependent eigenfunction! Using the evolutionary time that corresponds to each frame of the movie, multiply every x(xi) value by <math>~d_c \cdot e^{\sqrt{\omega^2}t}</math> with, I suppose, d_c = 1.<ins style="font-weight: bold; text-decoration: none;">5e</ins>-<ins style="font-weight: bold; text-decoration: none;">3</ins>. Plot this time-evolving curve on top of Patrick's numerically generated x(x_0,t) values and let's see how well they match over time!</li></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div></ol></div></td><td class="diff-marker"></td><td style="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;"><div></ol></div></td></tr>
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<tr><td class="diff-marker"></td><td style="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;"><div>{{LSU_HBook_footer}}</div></td><td class="diff-marker"></td><td style="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;"><div>{{LSU_HBook_footer}}</div></td></tr>
</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/Appendix/Ramblings/PatrickMotl&diff=21380&oldid=prevTohline: /* January 7, 2021 (from Joel) */2021-01-08T22:09:53Z<p><span dir="auto"><span class="autocomment">January 7, 2021 (from Joel)</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:09, 8 January 2021</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1756">Line 1,756:</td>
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<tr><td class="diff-marker"></td><td style="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;"><div>==January 7, 2021 (from Joel)==</div></td><td class="diff-marker"></td><td style="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;"><div>==January 7, 2021 (from Joel)==</div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><br/></td><td class="diff-marker"></td><td style="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;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div>In an [[#Initial_Comments|earlier paragraph, above]], I pointed to Patrick's "time-dependent eigenfunction" animation and commented on how it should relate to the '''blue segment''' of the eigenfunction plots that I derived from linear perturbation theory (see [[#Fig6|Figure 6, above]]). The data that I have used to generate the '''blue segments''' for the models with <math>~\tilde\xi = 3.25</math> and <math>~\tilde\xi = 3.50</math> is provided in the pair of scrollable tables that I have added to the figure shown immediately above. For either model, the referenced '''blue segment''' can be generated by plotting x(renorm) vs. xi &#8212; i.e., using the first and third columns of either scrollable table &#8212; or by plotting x vs. xi &#8212; using the first and second columns of data. The only difference is that, in the x(xi) plot, x is normalized to unity at the surface of the model; in the x(renorm) vs. xi plot, x is normalized to unity at the center of the model.</div></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;"><table border="0" align="right" cellpadding="15"><tr><td align="center">[[File:Motl n5 eigenfunction3.25.png|200px|Patrick's Eigenfunction for \tilde\xi = 3.25]]</td></tr></table></ins></div></td></tr>
<tr><td colspan="2"></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div> </div></td></tr>
<tr><td colspan="2"></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div>In an [[#Initial_Comments|earlier paragraph, above]], I pointed to Patrick's "time-dependent eigenfunction" animation <ins style="font-weight: bold; text-decoration: none;">(one frame, again, reprinted here on the right) </ins>and commented on how it should relate to the '''blue segment''' of the eigenfunction plots that I derived from linear perturbation theory (see [[#Fig6|Figure 6, above]]). The data that I have used to generate the '''blue segments''' for the models with <math>~\tilde\xi = 3.25</math> and <math>~\tilde\xi = 3.50</math> is provided in the pair of scrollable tables that I have added to the figure shown immediately above. For either model, the referenced '''blue segment''' can be generated by plotting x(renorm) vs. xi &#8212; i.e., using the first and third columns of either scrollable table &#8212; or by plotting x vs. xi &#8212; using the first and second columns of data. The only difference is that, in the x(xi) plot, x is normalized to unity at the surface of the model; in the x(renorm) vs. xi plot, x is normalized to unity at the center of the model.</div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><br/></td><td class="diff-marker"></td><td style="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;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div>Recommendation: </div></td><td class="diff-marker"></td><td style="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;"><div>Recommendation: </div></td></tr>
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<td colspan="2" class="diff-lineno">Line 1,764:</td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could simply re-create the same linear-linear "time-dependent eigenfunction" movie, and add to every movie frame Joel's (time independent) '''blue segment''' eigenfunction; I guess, in this case, Joel's function should be normalized to unity at the center. Make sure that the normalization of the radius (horizontal axis) is the same in Patrick's time-dependent plots as it is in Joel's time-independent dataset.</li></div></td><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could simply re-create the same linear-linear "time-dependent eigenfunction" movie, and add to every movie frame Joel's (time independent) '''blue segment''' eigenfunction; I guess, in this case, Joel's function should be normalized to unity at the center. Make sure that the normalization of the radius (horizontal axis) is the same in Patrick's time-dependent plots as it is in Joel's time-independent dataset.</li></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could generate a new eigenfunction movie in which the vertical axis is log-amplitude; Joel's time-independent eigenfunction should be added to every movie frame but, of course, in this case it should also be plotted as log-amplitude versus radius.</li></div></td><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could generate a new eigenfunction movie in which the vertical axis is log-amplitude; Joel's time-independent eigenfunction should be added to every movie frame but, of course, in this case it should also be plotted as log-amplitude versus radius.</li></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div> <li>Better yet, turn Joel's eigenfunction into a time-dependent eigenfunction! Using the evolutionary time that corresponds to each frame of the movie, multiply every x(xi) value by <math>~d_c \cdot e^{\sqrt{\omega^2}t}</math>. Plot this time-evolving curve on top of Patrick's numerically generated x(x_0,t) values and let's see how well they match over time!</li></div></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div> <li>Better yet, turn Joel's eigenfunction into a time-dependent eigenfunction! Using the evolutionary time that corresponds to each frame of the movie, multiply every x(xi) value by <math>~d_c \cdot e^{\sqrt{\omega^2}t<ins style="font-weight: bold; text-decoration: none;">}</math> with, I suppose, <math>~d_c = 1.5\times 10^{-2</ins>}</math>. Plot this time-evolving curve on top of Patrick's numerically generated x(x_0,t) values and let's see how well they match over time!</li></div></td></tr>
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</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/Appendix/Ramblings/PatrickMotl&diff=21379&oldid=prevTohline: /* Initial Comments */2021-01-08T22:02:16Z<p><span dir="auto"><span class="autocomment">Initial Comments</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:02, 8 January 2021</td>
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<tr><td class="diff-marker"></td><td style="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;"><br/></td><td class="diff-marker"></td><td style="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;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div>===Initial Comments===</div></td><td class="diff-marker"></td><td style="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;"><div>===Initial Comments===</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div>First, I need to make sure that I understand the new plots that you have provided. For discussion purposes, I'll focus on your [http://www.patrickmotl.net/simulations/single_stars/n5_3.25_constp_m12/plots/plots.html plots for n = 5 polytrope &xi; = 3.25 and constant pressure truncation mark 12]. It appears to me that a key plot/animation is the "x ''versus'' m" plot shown in the upper-right corner of this web page; on your web page this plot/animation is labeled, "<math>~(R - R_0)/R_0</math> vs Mass." I presume that this shows the time-evolution of the radial eigenfunction; am I correct? Immediately below, I have reproduced <del style="font-weight: bold; text-decoration: none;">two frames </del>from this movie.</div></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div>First, I need to make sure that I understand the new plots that you have provided. For discussion purposes, I'll focus on your [http://www.patrickmotl.net/simulations/single_stars/n5_3.25_constp_m12/plots/plots.html plots for n = 5 polytrope &xi; = 3.25 and constant pressure truncation mark 12]. It appears to me that a key plot/animation is the "x ''versus'' m" plot shown in the upper-right corner of this web page; on your web page this plot/animation is labeled, "<math>~(R - R_0)/R_0</math> vs Mass." I presume that this shows the time-evolution of the radial eigenfunction; am I correct? Immediately below, I have reproduced <ins style="font-weight: bold; text-decoration: none;">one frame </ins>from this movie.</div></td></tr>
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<tr><td class="diff-marker"></td><td style="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;"><div><table border="1" align="center" cellpadding="8" width="70%"></div></td><td class="diff-marker"></td><td style="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;"><div><table border="1" align="center" cellpadding="8" width="70%"></div></td></tr>
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<tr><td class="diff-marker"></td><td style="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;"><div>{{ LSU_WorkInProgress }}</div></td><td class="diff-marker"></td><td style="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;"><div>{{ LSU_WorkInProgress }}</div></td></tr>
<tr><td colspan="2"></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div>===Additional Information on Frequencies===</div></td><td class="diff-marker"></td><td style="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;"><div>===Additional Information on Frequencies===</div></td></tr>
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</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/Appendix/Ramblings/PatrickMotl&diff=21378&oldid=prevTohline: /* January 4, 2021 (from Patrick) */2021-01-08T01:59:37Z<p><span dir="auto"><span class="autocomment">January 4, 2021 (from Patrick)</span></span></p>
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<tr><td class="diff-marker"></td><td style="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;"><div><tr></div></td><td class="diff-marker"></td><td style="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;"><div><tr></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div><td align="center" colspan="2">Data Used to Plot Radial Displacement Function, <math>~x(\xi)</math>, from Linear-Stability Analysis (see [[#Fig6|Figure 6, above]])</td></div></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div><td align="center" colspan="2">Data Used to Plot Radial Displacement Function, <math>~x(\xi)</math>, from Linear-Stability Analysis (see <ins style="font-weight: bold; text-decoration: none;">'''blue segments''' of </ins>[[#Fig6|Figure 6, above]])</td></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div></tr></div></td><td class="diff-marker"></td><td style="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;"><div></tr></div></td></tr>
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</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/Appendix/Ramblings/PatrickMotl&diff=21377&oldid=prevTohline: /* January 7, 2021 (from Joel) */2021-01-08T01:56:12Z<p><span dir="auto"><span class="autocomment">January 7, 2021 (from Joel)</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 01:56, 8 January 2021</td>
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<tr><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could simply re-create the same linear-linear "time-dependent eigenfunction" movie, and add to every movie frame Joel's (time independent) '''blue segment''' eigenfunction; I guess, in this case, Joel's function should be normalized to unity at the center. Make sure that the normalization of the radius (horizontal axis) is the same in Patrick's time-dependent plots as it is in Joel's time-independent dataset.</li></div></td><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could simply re-create the same linear-linear "time-dependent eigenfunction" movie, and add to every movie frame Joel's (time independent) '''blue segment''' eigenfunction; I guess, in this case, Joel's function should be normalized to unity at the center. Make sure that the normalization of the radius (horizontal axis) is the same in Patrick's time-dependent plots as it is in Joel's time-independent dataset.</li></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could generate a new eigenfunction movie in which the vertical axis is log-amplitude; Joel's time-independent eigenfunction should be added to every movie frame but, of course, in this case it should also be plotted as log-amplitude versus radius.</li></div></td><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could generate a new eigenfunction movie in which the vertical axis is log-amplitude; Joel's time-independent eigenfunction should be added to every movie frame but, of course, in this case it should also be plotted as log-amplitude versus radius.</li></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div> <li>Better yet, turn Joel's eigenfunction into a time-dependent eigenfunction! Using the evolutionary time that corresponds to each frame of the movie, multiply every x(xi) value by <math>~d_c \cdot e^{\sqrt{\omega^2}t}</math>. Plot this time-evolving curve on top of Patrick's numerically generated x(x_0,t) values and let's see how well they match!</li></div></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div> <li>Better yet, turn Joel's eigenfunction into a time-dependent eigenfunction! Using the evolutionary time that corresponds to each frame of the movie, multiply every x(xi) value by <math>~d_c \cdot e^{\sqrt{\omega^2}t}</math>. Plot this time-evolving curve on top of Patrick's numerically generated x(x_0,t) values and let's see how well they match <ins style="font-weight: bold; text-decoration: none;">over time</ins>!</li></div></td></tr>
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</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/Appendix/Ramblings/PatrickMotl&diff=21376&oldid=prevTohline: /* January 7, 2021 (from Joel) */2021-01-08T01:55:27Z<p><span dir="auto"><span class="autocomment">January 7, 2021 (from Joel)</span></span></p>
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<tr><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could simply re-create the same linear-linear "time-dependent eigenfunction" movie, and add to every movie frame Joel's (time independent) '''blue segment''' eigenfunction; I guess, in this case, Joel's function should be normalized to unity at the center. Make sure that the normalization of the radius (horizontal axis) is the same in Patrick's time-dependent plots as it is in Joel's time-independent dataset.</li></div></td><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could simply re-create the same linear-linear "time-dependent eigenfunction" movie, and add to every movie frame Joel's (time independent) '''blue segment''' eigenfunction; I guess, in this case, Joel's function should be normalized to unity at the center. Make sure that the normalization of the radius (horizontal axis) is the same in Patrick's time-dependent plots as it is in Joel's time-independent dataset.</li></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could generate a new eigenfunction movie in which the vertical axis is log-amplitude; Joel's time-independent eigenfunction should be added to every movie frame but, of course, in this case it should also be plotted as log-amplitude versus radius.</li></div></td><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could generate a new eigenfunction movie in which the vertical axis is log-amplitude; Joel's time-independent eigenfunction should be added to every movie frame but, of course, in this case it should also be plotted as log-amplitude versus radius.</li></div></td></tr>
<tr><td colspan="2"></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;"> <li>Better yet, turn Joel's eigenfunction into a time-dependent eigenfunction! Using the evolutionary time that corresponds to each frame of the movie, multiply every x(xi) value by <math>~d_c \cdot e^{\sqrt{\omega^2}t}</math>. Plot this time-evolving curve on top of Patrick's numerically generated x(x_0,t) values and let's see how well they match!</li></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div></ol></div></td><td class="diff-marker"></td><td style="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;"><div></ol></div></td></tr>
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<tr><td class="diff-marker"></td><td style="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;"><br/></td><td class="diff-marker"></td><td style="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;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div>{{LSU_HBook_footer}}</div></td><td class="diff-marker"></td><td style="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;"><div>{{LSU_HBook_footer}}</div></td></tr>
</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/Appendix/Ramblings/PatrickMotl&diff=21375&oldid=prevTohline: /* January 7, 2021 (from Joel) */2021-01-07T21:26:38Z<p><span dir="auto"><span class="autocomment">January 7, 2021 (from Joel)</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 21:26, 7 January 2021</td>
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<tr><td class="diff-marker"></td><td style="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;"><div>==January 7, 2021 (from Joel)==</div></td><td class="diff-marker"></td><td style="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;"><div>==January 7, 2021 (from Joel)==</div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><br/></td><td class="diff-marker"></td><td style="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;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div>In an [[#Initial_Comments|earlier paragraph, above]], I pointed to Patrick's "time-dependent eigenfunction" animation and commented on how it should relate to the '''blue segment''' of the eigenfunction plots that I derived from linear perturbation theory. The data that I have used to generate the '''blue segments''' for the models with <math>~\tilde\xi = 3.25</math> and <math>~\tilde\xi = 3.50</math> is provided in the pair of scrollable tables that I have added to the figure shown immediately above. For either model, the referenced '''blue segment''' can be generated by plotting x(renorm) vs. xi &#8212; i.e., using the first and third columns of either scrollable table &#8212; or by plotting x vs. xi &#8212; using the first and second columns. The only difference is that, in the x(xi) plot, x is normalized to unity at the surface of the model; in the x(renorm) vs. xi plot, x is normalized to unity at the center of the model.</div></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div>In an [[#Initial_Comments|earlier paragraph, above]], I pointed to Patrick's "time-dependent eigenfunction" animation and commented on how it should relate to the '''blue segment''' of the eigenfunction plots that I derived from linear perturbation theory <ins style="font-weight: bold; text-decoration: none;">(see [[#Fig6|Figure 6, above]])</ins>. The data that I have used to generate the '''blue segments''' for the models with <math>~\tilde\xi = 3.25</math> and <math>~\tilde\xi = 3.50</math> is provided in the pair of scrollable tables that I have added to the figure shown immediately above. For either model, the referenced '''blue segment''' can be generated by plotting x(renorm) vs. xi &#8212; i.e., using the first and third columns of either scrollable table &#8212; or by plotting x vs. xi &#8212; using the first and second columns <ins style="font-weight: bold; text-decoration: none;">of data</ins>. The only difference is that, in the x(xi) plot, x is normalized to unity at the surface of the model; in the x(renorm) vs. xi plot, x is normalized to unity at the center of the model.</div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><br/></td><td class="diff-marker"></td><td style="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;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div>Recommendation: </div></td><td class="diff-marker"></td><td style="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;"><div>Recommendation: </div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div><ol></div></td><td class="diff-marker"></td><td style="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;"><div><ol></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div> <li>Patrick could simply re-create the same linear-linear "time-dependent eigenfunction" movie, and add to every movie frame Joel's (time independent) '''blue segment''' eigenfunction; I guess, in this case, Joel's function should be normalized to unity at the center.</li></div></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div> <li>Patrick could simply re-create the same linear-linear "time-dependent eigenfunction" movie, and add to every movie frame Joel's (time independent) '''blue segment''' eigenfunction; I guess, in this case, Joel's function should be normalized to unity at the center<ins style="font-weight: bold; text-decoration: none;">. Make sure that the normalization of the radius (horizontal axis) is the same in Patrick's time-dependent plots as it is in Joel's time-independent dataset</ins>.</li></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could generate a new eigenfunction movie in which the vertical axis is log-amplitude; Joel's time-independent eigenfunction should be added to every movie frame but, of course, in this case it should also be plotted as log-amplitude versus radius.</li></div></td><td class="diff-marker"></td><td style="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;"><div> <li>Patrick could generate a new eigenfunction movie in which the vertical axis is log-amplitude; Joel's time-independent eigenfunction should be added to every movie frame but, of course, in this case it should also be plotted as log-amplitude versus radius.</li></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div></ol></div></td><td class="diff-marker"></td><td style="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;"><div></ol></div></td></tr>
</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/Appendix/Ramblings/PatrickMotl&diff=21374&oldid=prevTohline: /* Good Comparisons With Previously Published Studies */2021-01-07T21:20:36Z<p><span dir="auto"><span class="autocomment">Good Comparisons With Previously Published Studies</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 21:20, 7 January 2021</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l702">Line 702:</td>
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<tr><td class="diff-marker"></td><td style="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;"><div><span id="Fig6">Building upon this set of successful</span> comparisons with stability analyses published by other groups, we have carried out numerical integrations of the relevant LAWE to identify the eigenvectors associated with the fundamental-mode of radial oscillation in pressure-truncated, <math>~n = 5</math> polytropic configurations. Details of this analysis are provided in yet [[User:Tohline/SSC/Stability/n5PolytropeLAWE#Radial_Oscillations_of_n_.3D_5_Polytropic_Spheres|another chapter of this H_Book]]. The following animation sequence illustrates the results of this analysis. As far as we have been able to determine, an analysis of this type has not previously been conducted for pressure-truncated, <math>~n = 5</math> polytropes.</div></td><td class="diff-marker"></td><td style="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;"><div><span id="Fig6">Building upon this set of successful</span> comparisons with stability analyses published by other groups, we have carried out numerical integrations of the relevant LAWE to identify the eigenvectors associated with the fundamental-mode of radial oscillation in pressure-truncated, <math>~n = 5</math> polytropic configurations. Details of this analysis are provided in yet [[User:Tohline/SSC/Stability/n5PolytropeLAWE#Radial_Oscillations_of_n_.3D_5_Polytropic_Spheres|another chapter of this H_Book]]. The following animation sequence illustrates the results of this analysis. As far as we have been able to determine, an analysis of this type has not previously been conducted for pressure-truncated, <math>~n = 5</math> polytropes.</div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><br/></td><td class="diff-marker"></td><td style="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;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div><div align="center<del style="font-weight: bold; text-decoration: none;">" id="Fig6</del>"></div></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div><div align="center"></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div>'''Figure 6'''<br /></div></td><td class="diff-marker"></td><td style="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;"><div>'''Figure 6'''<br /></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div>[[File:N5Truncated2.gif|500px|Fundamental-mode eigenvectors for pressure-truncated n = 5 polytropes]]</div></td><td class="diff-marker"></td><td style="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;"><div>[[File:N5Truncated2.gif|500px|Fundamental-mode eigenvectors for pressure-truncated n = 5 polytropes]]</div></td></tr>
</table>Tohlinehttps://www.vistrails.org//index.php?title=User:Tohline/Appendix/Ramblings/PatrickMotl&diff=21373&oldid=prevTohline: /* January 4, 2021 (from Patrick) */2021-01-07T21:20:09Z<p><span dir="auto"><span class="autocomment">January 4, 2021 (from Patrick)</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 21:20, 7 January 2021</td>
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<tr><td class="diff-marker"></td><td style="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;"><div><tr></div></td><td class="diff-marker"></td><td style="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;"><div><tr></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div><td align="center" colspan="2">Data Used to Plot Radial Displacement Function, <math>~x(\xi)</math>, from Linear-Stability Analysis</td></div></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div><td align="center" colspan="2">Data Used to Plot Radial Displacement Function, <math>~x(\xi)</math>, from Linear-Stability Analysis <ins style="font-weight: bold; text-decoration: none;">(see [[#Fig6|Figure 6, above]])</ins></td></div></td></tr>
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</table>Tohline