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==Example Eigenvectors Along 0.31 Sequence== ===First Analysis=== ===Sigma-Squared Scaled to Mean Density, and Better Error Analysis=== ====From the K-BK74 Analysis==== Keep in mind that, from the [[SSC/Structure/BiPolytropes/Analytic51Renormalize#Model_Pairings|accompanying K-BK74 analysis]], we obtained the following eigenvector for the <math>\nu_\mathrm{max}</math> model along the <math>\mu_e/\mu_c = 0.31</math> equilibrium model sequence: <table border="1" align="center" cellpadding="5"><tr><td align="center"> [[File:K-BK74eigenfunctionVsRadius.png|left||450px|File:K-BK74eigenfunctionVsRadius.png]] </td></tr></table> ====ξ<sub>i</sub> = 2.804179398==== <!-- BOXES for xi02804 --> <table border="1" align="center" cellpadding="5"> <tr> <td align="center" colspan="3"> <b>Excel file:Models031 & pages …</b> </td> <td align="center" colspan="2"><b>xi02804gMode0</b><br /><math>\sigma_c^2 \cdot (\rho_c/\bar\rho) = 0.00000000</math></td> <td align="center" colspan="2"><b>xi02804gMode1</b><br /><math>\sigma_c^2 \cdot (\rho_c/\bar\rho) = 11.60356417</math></td> <td align="center" colspan="2"><b>xi02804gMode2</b><br /><math>\sigma_c^2 \cdot (\rho_c/\bar\rho) = 39.16484857</math></td> </tr> <tr> <td align="center" rowspan="8"> [[File:Xi02804gsequence.png|300px|xi02804gsequence]] </td> <td align="center"><math>\xi_i</math></td> <td align="right">2.804179398</td> <td align="center" rowspan="8" bgcolor="white">Linear<br /> [[File:Xi02804gMode0.png|300px|xi02804gMode0]] </td> <td align="center" rowspan="8" bgcolor="white">Log10<br /> [[File:Xi02804gMode0Log.png|300px|xi02804gMode0Log]] </td> <td align="center" rowspan="8">Linear<br /> [[File:Xi02804gMode1.png|300px|xi02804gMode1]] </td> <td align="center" rowspan="8">Log10<br /> [[File:Xi02804gMode1Log.png|300px|xi02804gMode1Log]] </td> <td align="center" rowspan="8">Linear<br /> [[File:Xi02804gMode2.png|300px|xi02804gMode2]] </td> <td align="center" rowspan="8">Log10<br /> [[File:Xi02804gMode2Log.png|300px|xi02804gMode2Log]] </td> </tr> <tr> <td align="center"><math>q</math></td> <td align="right">0.156742251</td> </tr> <tr> <td align="center"><math>\nu</math></td> <td align="right">0.199510368</td> </tr> <tr> <td align="center"><math>\rho_c/\bar\rho</math></td> <td align="right">3.57005807 × 10<sup>2</sup></td> </tr> <tr> <td align="center" colspan="1">Mode</td> <td align="center" colspan="1"><math>\sigma_c^2 \cdot (\rho_c/\bar\rho)</math></td> </tr> <tr> <td align="center" bgcolor="yellow">0</td> <td align="right" bgcolor="yellow">0.0</td> </tr> <tr> <td align="center">1</td> <td align="right">11.60356417</td> </tr> <tr> <td align="center">2</td> <td align="right">39.16484857</td> </tr> </table> ====ξ<sub>i</sub> = 4==== <table border="1" align="center" cellpadding="5"> <tr> <td align="center" colspan="3"> <b>Excel file:Models031 & pages …</b> </td> <td align="center" colspan="2"><b>xi04gMode0</b><br /><math>\sigma_c^2 \cdot (\rho_c/\bar\rho) = -192.1449647</math><br /><font color="red">CAUTION: Surface B.C. not satisfied!</font></td> <td align="center" colspan="2"><b>xi04gMode1</b><br /><math>\sigma_c^2 \cdot (\rho_c/\bar\rho) = 10.58972472</math></td> <td align="center" colspan="2"><b>xi04gMode2</b><br /><math>\sigma_c^2 \cdot (\rho_c/\bar\rho) = 38.57111996</math></td> </tr> <tr> <td align="center" rowspan="8"> [[File:Xi04gsequence.png|300px|xi04gsequence]] </td> <td align="center"><math>\xi_i</math></td> <td align="right">4</td> <td align="center" rowspan="8" bgcolor="white">Linear<br /> [[File:Xi04gMode0.png|300px|xi04gMode0]] </td> <td align="center" rowspan="8" bgcolor="white">Log10<br /> [[File:Xi04gMode0Log.png|300px|xi04gMode0Log]] </td> <td align="center" rowspan="8">Linear<br /> [[File:Xi04gMode1.png|300px|xi04gMode1]] </td> <td align="center" rowspan="8">Log10<br /> [[File:Xi04gMode1Log.png|300px|xi04gMode1Log]] </td> <td align="center" rowspan="8">Linear<br /> [[File:Xi04gMode2.png|300px|xi04gMode2]] </td> <td align="center" rowspan="8">Log10<br /> [[File:Xi04gMode2Log.png|300px|xi04gMode2Log]] </td> </tr> <tr> <td align="center"><math>q</math></td> <td align="right">0.136805779</td> </tr> <tr> <td align="center"><math>\nu</math></td> <td align="right">0.266175482</td> </tr> <tr> <td align="center"><math>\rho_c/\bar\rho</math></td> <td align="right">1.656926473 × 10<sup>3</sup></td> </tr> <tr> <td align="center" colspan="1">Mode</td> <td align="center" colspan="1"><math>\sigma_c^2 \cdot (\rho_c/\bar\rho)</math></td> </tr> <tr> <td align="center" bgcolor="white">0</td> <td align="center" bgcolor="white">-192.1449647</td> </tr> <tr> <td align="center">1</td> <td align="right">+10.58972472</td> </tr> <tr> <td align="center">2</td> <td align="right">+38.57111996</td> </tr> </table> ====ξ<sub>i</sub> = 9==== <table border="1" align="center" cellpadding="5"> <tr> <td align="center" colspan="3"> <b>Excel file:Models031 & pages …</b> </td> <td align="center" colspan="2"><b>xi09gMode0</b><br /><math>\sigma_c^2 \cdot (\rho_c/\bar\rho) = -15553.34096</math><br /><font color="red">CAUTION: Surface B.C. not satisfied!</font></td> <td align="center" colspan="2"><b>xi09gMode1</b><br /><math>\sigma_c^2 \cdot (\rho_c/\bar\rho) = 11.16595582</math></td> <td align="center" colspan="2"><b>xi09gMode2</b><br /><math>\sigma_c^2 \cdot (\rho_c/\bar\rho) = 39.57399551</math></td> </tr> <tr> <td align="center" rowspan="8"> [[File:Xi09gsequence.png|300px|xi09gsequence]] </td> <td align="center"><math>\xi_i</math></td> <td align="right">9</td> <td align="center" rowspan="8" bgcolor="white">Linear<br /> [[File:Xi09gMode0.png|300px|xi09gMode0]] </td> <td align="center" rowspan="8" bgcolor="white">Log10<br /> [[File:Xi09gMode0Log.png|300px|xi09gMode0Log]] </td> <td align="center" rowspan="8">Linear<br /> [[File:Xi09gMode1.png|300px|xi09gMode1]] </td> <td align="center" rowspan="8">Log10<br /> [[File:Xi09gMode1Log.png|300px|xi09gMode1Log]] </td> <td align="center" rowspan="8">Linear<br /> [[File:Xi09gMode2.png|300px|xi09gMode2]] </td> <td align="center" rowspan="8">Log10<br /> [[File:Xi09gMode2Log.png|300px|xi09gMode2Log]] </td> </tr> <tr> <td align="center"><math>q</math></td> <td align="right">0.075617469</td> </tr> <tr> <td align="center"><math>\nu</math></td> <td align="right">0.337216704</td> </tr> <tr> <td align="center"><math>\rho_c/\bar\rho</math></td> <td align="right">1.155525994 × 10<sup>5</sup></td> </tr> <tr> <td align="center" colspan="1">Mode</td> <td align="center" colspan="1"><math>\sigma_c^2 \cdot (\rho_c/\bar\rho)</math></td> </tr> <tr> <td align="center" bgcolor="white">0</td> <td align="center" bgcolor="white">-15553.34096</td> </tr> <tr> <td align="center">1</td> <td align="right">+11.16595582</td> </tr> <tr> <td align="center">2</td> <td align="right">+39.57399551</td> </tr> </table> ====ξ<sub>i</sub> = 14==== <table border="1" align="center" cellpadding="5"> <tr> <td align="center" colspan="3"> <b>Excel file:Models031 & pages …</b> </td> <td align="center" colspan="2"><b>xi09gMode0</b></td> <td align="center" colspan="2"><b>xi09gMode1</b><br /><math>\sigma_c^2 \cdot (\rho_c/\bar\rho) = 11.01793184</math></td> <td align="center" colspan="2"><b>xi09gMode2</b><br /><math>\sigma_c^2 \cdot (\rho_c/\bar\rho) = 39.30533842</math></td> </tr> <tr> <td align="center" rowspan="8"> [[File:Xi14gsequence.png|300px|xi14gsequence]] </td> <td align="center"><math>\xi_i</math></td> <td align="right">14</td> <td align="center" rowspan="8" bgcolor="white">N/A<br /> [[File:Xi14gMode0.png|300px|xi09gMode0]] </td> <td align="center" rowspan="8" bgcolor="white">N/A<br /> [[File:Xi14gMode0Log.png|300px|xi09gMode0Log]] </td> <td align="center" rowspan="8">Linear<br /> [[File:Xi14gMode1.png|300px|xi14gMode1]] </td> <td align="center" rowspan="8">Log10<br /> [[File:Xi14gMode1Log.png|300px|xi14gMode1Log]] </td> <td align="center" rowspan="8">Linear<br /> [[File:Xi14gMode2.png|300px|xi14gMode2]] </td> <td align="center" rowspan="8">Log10<br /> [[File:Xi14gMode2Log.png|300px|xi14gMode2Log]] </td> </tr> <tr> <td align="center"><math>q</math></td> <td align="right">0.04880185</td> </tr> <tr> <td align="center"><math>\nu</math></td> <td align="right">0.316868628</td> </tr> <tr> <td align="center"><math>\rho_c/\bar\rho</math></td> <td align="right">1.4728825 × 10<sup>6</sup></td> </tr> <tr> <td align="center" colspan="1">Mode</td> <td align="center" colspan="1"><math>\sigma_c^2 \cdot (\rho_c/\bar\rho)</math></td> </tr> <tr> <td align="center" bgcolor="white">0</td> <td align="center" bgcolor="white">---</td> </tr> <tr> <td align="center">1</td> <td align="right">+11.01793184</td> </tr> <tr> <td align="center">2</td> <td align="right">+39.30533842</td> </tr> </table>
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