Editing Appendix/Ramblings/PatrickMotl (section)

==January 4, 2021 (from Patrick)==

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I didn’t play with the offset value too much. 1e-3 seems too small, 2e-3 is too small so I used 1.5e-3 for both in these plots

What is plotted on the y axis is the base 10 logarithm of the absolute value of the  central density minus 1 (which is the initial density) and then I add
1e-15 to the absolute value to prevent NaN.</td></tr></table>


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  <td align="center"><math>~\tilde\xi = 3.25</math></td>
  <td align="center"><math>~\tilde\xi = 3.5</math></td>
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<td align="center" colspan="2"> Log-Amplitude vs. Time for Central-Density Perturbation</td>
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  <td align="center">[[File:MotlFirstLogPlot.png|500px|Patrick's initial log10 plot]]</td>
  <td align="center">[[File:MotlSecondLogPlot.png|500px|Patrick's initial log10 plot]]</td>
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<td align="center" colspan="2">Data Used to Plot Radial Displacement Function, <math>~x(\xi)</math>, from Linear-Stability Analysis (see '''blue segments''' of [[#Fig6|Figure 6, above]])</td>
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<pre>
Eigenvector for pressure-truncated, n = 5 polytrope.
\tilde\xi = 3.25
sigma_c^2 = -0.039629467
xi      x               x(renorm)
0       1               2.58142807
0.05    0.999843241     2.581023407
0.1     0.999372999     2.579809512
0.15    0.998589419     2.577786756
0.2     0.997492732     2.574955737
0.25    0.99608326      2.571317288
0.3     0.994361421     2.566872483
0.35    0.992327719     2.561622628
0.4     0.98998275      2.55556926
0.45    0.987327199     2.548714147
0.5     0.984361838     2.541059279
0.55    0.981087523     2.53260687
0.6     0.977505195     2.523359349
0.65    0.973615879     2.513319359
0.7     0.969420676     2.502489745
0.75    0.964920768     2.490873556
0.8     0.960117409     2.47847403
0.85    0.955011926     2.465294593
0.9     0.949605715     2.451338848
0.95    0.943900237     2.436610567
1       0.937897015     2.421113681
1.05    0.93159763      2.404852272
1.1     0.925003719     2.387830564
1.15    0.918116967     2.370052909
1.2     0.910939105     2.351523777
1.25    0.903471909     2.332247746
1.3     0.895717187     2.31222949
1.35    0.887676783     2.291473764
1.4     0.879352566     2.269985396
1.45    0.870746428     2.24776927
1.5     0.861860278     2.224830313
1.55    0.852696037     2.201173485
1.6     0.843255633     2.176803761
1.65    0.833540994     2.15172612
1.7     0.823554046     2.12594553
1.75    0.813296701     2.099466934
1.8     0.802770861     2.072295234
1.85    0.791978403     2.044435281
1.9     0.78092118      2.015891854
1.95    0.769601011     1.986669652
2       0.758019678     1.956773273
2.05    0.74617892      1.926207208
2.1     0.734080426     1.894975817
2.15    0.721725831     1.86308332
2.2     0.70911671      1.830533781
2.25    0.696254572     1.797331095
2.3     0.683140852     1.763478971
2.35    0.669776911     1.72898092
2.4     0.656164027     1.693840238
2.45    0.642303388     1.658059994
2.5     0.628196089     1.621643016
2.55    0.613843126     1.584591876
2.6     0.599245391     1.546908873
2.65    0.584403666     1.508596026
2.7     0.569318615     1.469655054
2.75    0.553990785     1.430087363
2.8     0.538420594     1.389894035
2.85    0.52260833      1.349075813
2.9     0.506554143     1.307633084
2.95    0.490258042     1.265565871
3       0.473719888     1.222873816
3.05    0.456939389     1.179556165
3.1     0.439916096     1.135611758
3.15    0.422649396     1.091039014
3.2     0.405138508     1.045835916
3.25    0.387382477     1
</pre>
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<pre>
Eigenvector for pressure-truncated, n = 5 polytrope.
\tilde\xi = 3.50
sigma_c^2 = -0.065282167
xi      x               x(renorm)
0       1               2.685205733
0.05    0.999849654     2.684802023
0.1     0.999398675     2.683591053
0.15    0.998647304     2.681573465
0.2     0.997595921     2.678750286
0.25    0.996245064     2.675122957
0.3     0.994595421     2.670693326
0.35    0.992647831     2.665463647
0.4     0.990403283     2.659436573
0.45    0.987862911     2.652615153
0.5     0.985027997     2.645002826
0.55    0.981899965     2.636603415
0.6     0.978480378     2.62742112
0.65    0.974770937     2.61746051
0.7     0.970773479     2.606726511
0.75    0.966489967     2.595224401
0.8     0.961922494     2.582959797
0.85    0.957073273     2.569938641
0.9     0.951944635     2.556167191
0.95    0.946539021     2.541652007
1       0.940858982     2.526399933
1.05    0.934907168     2.510418088
1.1     0.928686325     2.493713846
1.15    0.922199289     2.476294817
1.2     0.915448976     2.458168838
1.25    0.90843838      2.439343945
1.3     0.901170564     2.419828364
1.35    0.893648652     2.399630484
1.4     0.885875824     2.378758841
1.45    0.877855305     2.357222099
1.5     0.869590363     2.335029028
1.55    0.861084294     2.312188482
1.6     0.85234042      2.288709382
1.65    0.843362079     2.26460069
1.7     0.834152618     2.239871393
1.75    0.824715383     2.214530475
1.8     0.815053713     2.188586903
1.85    0.80517093      2.162049597
1.9     0.795070333     2.134927418
1.95    0.78475519      2.107229136
2       0.774228728     2.078963419
2.05    0.763494125     2.050138802
2.1     0.752554505     2.020763673
2.15    0.741412929     1.990846247
2.2     0.730072383     1.96039455
2.25    0.718535778     1.929416391
2.3     0.706805935     1.89791935
2.35    0.694885583     1.86591075
2.4     0.682777345     1.833397642
2.45    0.67048374      1.800386782
2.5     0.658007165     1.766884612
2.55    0.645349896     1.732897241
2.6     0.632514077     1.698430425
2.65    0.619501711     1.663489547
2.7     0.60631466      1.628079602
2.75    0.59295463      1.592205172
2.8     0.579423168     1.555870413
2.85    0.565721655     1.51907903
2.9     0.551851298     1.481834269
2.95    0.537813125     1.444138887
3       0.523607977     1.405995142
3.05    0.509236501     1.367404772
3.1     0.494699144     1.328368978
3.15    0.479996147     1.288888406
3.2     0.465127536     1.248963127
3.25    0.450093119     1.208592625
3.3     0.434892476     1.167775771
3.35    0.419524954     1.126510812
3.4     0.40398966      1.084795351
3.45    0.388285454     1.042626327
3.5     0.372410943     1
</pre>
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