SSC/Stability/BiPolytropes/SuccinctDiscussion - Revision history

Jet53man: /* Structure */

2023-10-15T21:24:42Z

Structure

← Older revision		Revision as of 17:24, 15 October 2023
Line 59:		Line 59:
	<math>\nu \equiv \frac{M_\mathrm{core}}{M_\mathrm{tot}}</math>		<math>\nu \equiv \frac{M_\mathrm{core}}{M_\mathrm{tot}}</math>
	</td>		</td>
	<td align="center" rowspan="7">[[File:~~TurningPoints51Bipolytropes~~.png\|450px\|Extrema along Various Equilibrium Sequences]]</td>		<td align="center" rowspan="7">[[File:TurningPoints51BipolytropesLabels.png\|450px\|Extrema along Various Equilibrium Sequences]]</td>
	</tr>		</tr>

2022-09-25T22:38:23Z

First Analysis

2022-09-25T22:34:56Z

Sigma-Squared Scaled to Mean Density, and Better Error Analysis

← Older revision		Revision as of 18:34, 25 September 2022
Line 793:		Line 793:

	===Sigma-Squared Scaled to Mean Density, and Better Error 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>

2022-09-25T22:20:21Z

ξi = 14

← Older revision		Revision as of 18:20, 25 September 2022
Line 1,018:		Line 1,018:
	<td align="center"><math>\xi_i</math></td>		<td align="center"><math>\xi_i</math></td>
	<td align="right">14</td>		<td align="right">14</td>
	<td align="center" rowspan="8" bgcolor="white">~~Linear~~<br />		<td align="center" rowspan="8" bgcolor="white">N/A<br />
	[[File:Xi14gMode0.png\|300px\|xi09gMode0]]		[[File:Xi14gMode0.png\|300px\|xi09gMode0]]
	</td>		</td>
	<td align="center" rowspan="8" bgcolor="white">~~Log10~~<br />		<td align="center" rowspan="8" bgcolor="white">N/A<br />
	[[File:Xi14gMode0Log.png\|300px\|xi09gMode0Log]]		[[File:Xi14gMode0Log.png\|300px\|xi09gMode0Log]]
	</td>		</td>

2022-09-25T22:16:39Z

ξi = 14

← Older revision		Revision as of 18:16, 25 September 2022
Line 1,010:		Line 1,010:
	<td align="center" colspan="2"><b>xi09gMode0</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>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) = </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>
	<tr>		<tr>
Line 1,063:		Line 1,063:
	<tr>		<tr>
	<td align="center">2</td>		<td align="center">2</td>
	<td align="right">~~---~~</td>		<td align="right">+39.30533842</td>
	</tr>		</tr>
	</table>		</table>

2022-09-25T22:05:12Z

ξi = 9

@@ Line 996: / Line 996: @@
    <td align="center">2</td>
    <td align="right">+39.57399551</td>
 </tr>
 </table>

2022-09-24T22:39:34Z

Sigma Scaled to Mean Density, and Better Error Analysis

← Older revision		Revision as of 18:39, 24 September 2022
Line 792:		Line 792:
	</table>		</table>

	===Sigma Scaled to Mean Density, and Better Error Analysis===		===Sigma-Squared Scaled to Mean Density, and Better Error Analysis===


			====ξ<sub>i</sub> = 2.804179398====


Line 861:		Line 864:


	<~~!-- BOXES for xi04 --~~>		====ξ<sub>i</sub> = 4====


	<table border="1" align="center" cellpadding="5">		<table border="1" align="center" cellpadding="5">
	<tr>		<tr>
Line 927:		Line 932:


	<~~!-- BOXES for xi09 --~~>		====ξ<sub>i</sub> = 9====


	<table border="1" align="center" cellpadding="5">		<table border="1" align="center" cellpadding="5">
	<tr>		<tr>

2022-09-24T22:35:08Z

Sigma Scaled to Mean Density, and Better Error Analysis

← Older revision		Revision as of 18:35, 24 September 2022
Line 933:		Line 933:
	<b>Excel file:Models031 & pages …</b>		<b>Excel file:Models031 & pages …</b>
	</td>		</td>
	<td align="center" colspan="2"><b>xi09gMode0</b><br /><math>\sigma_c^2 \cdot (\rho_c/\bar\rho) = </math><br /><font color="red">CAUTION:  Surface B.C. not satisfied!</font></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>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>		<td align="center" colspan="2"><b>xi09gMode2</b><br /><math>\sigma_c^2 \cdot (\rho_c/\bar\rho) = 39.57399551</math></td>
Line 980:		Line 980:
	<tr>		<tr>
	<td align="center" bgcolor="white">0</td>		<td align="center" bgcolor="white">0</td>
	<td align="center" bgcolor="white">---</td>		<td align="center" bgcolor="white">-15553.34096</td>
	</tr>		</tr>
	<tr>		<tr>

2022-09-24T22:11:43Z

Sigma Scaled to Mean Density, and Better Error Analysis

← Older revision		Revision as of 18:11, 24 September 2022
Line 935:		Line 935:
	<td align="center" colspan="2"><b>xi09gMode0</b><br /><math>\sigma_c^2 \cdot (\rho_c/\bar\rho) = </math><br /><font color="red">CAUTION:  Surface B.C. not satisfied!</font></td>		<td align="center" colspan="2"><b>xi09gMode0</b><br /><math>\sigma_c^2 \cdot (\rho_c/\bar\rho) = </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>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) = </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>
	<tr>		<tr>
Line 988:		Line 988:
	<tr>		<tr>
	<td align="center">2</td>		<td align="center">2</td>
	<td align="right">~~---~~</td>		<td align="right">+39.57399551</td>
	</tr>		</tr>
	</table>		</table>

2022-09-24T21:58:40Z

Sigma Scaled to Mean Density, and Better Error Analysis

@@ Line 923: / Line 923: @@
    <td align="center">2</td>
    <td align="right">+38.57111996</td>
 </tr>
 </table>