Appendix/Ramblings/51BiPolytropeStability/BetterInterfacePt2 - Revision history

Jet53man: /* Better Interface for 51BiPolytrope Stability Study */

2023-09-26T14:03:58Z

Better Interface for 51BiPolytrope Stability Study

← Older revision		Revision as of 10:03, 26 September 2023
Line 4,151:		Line 4,151:
	</table>		</table>

			==Compare Core With Analytic Displacement Functions==

	=See Also=		=See Also=

Jet53man: /* Convert to Implicit Approach */

2023-09-19T17:59:27Z

Convert to Implicit Approach

← Older revision		Revision as of 13:59, 19 September 2023
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	<tr><td bgcolor="lightblue" align="left">		<tr><td bgcolor="lightblue" align="left">
	<b>Best values:</b><br />Nodes 0:  n/a		<b>Best values:</b><br />Nodes 0:  n/a
	<br />Nodes 1:  <math>\sigma_c^2 = 8.~~95879~~\times 10^{-5}</math>		<br />Nodes 1:  <math>\sigma_c^2 = 8.958784\times 10^{-5}</math>
	<br />Nodes 2:  <math>\sigma_c^2 = 3.021\times 10^{-4}</math>		<br />Nodes 2:  <math>\sigma_c^2 = 3.021\times 10^{-4}</math>
	<br />Nodes 3:  <math>\sigma_c^2 = 6.09\times 10^{-4}</math>		<br />Nodes 3:  <math>\sigma_c^2 = 6.09\times 10^{-4}</math>

Jet53man: /* Convert to Implicit Approach */

2023-09-19T17:42:25Z

Convert to Implicit Approach

← Older revision		Revision as of 13:42, 19 September 2023
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	<b>Best values:</b><br />Nodes 0:  n/a		<b>Best values:</b><br />Nodes 0:  n/a
	<br />Nodes 1:  <math>\sigma_c^2 = 8.95879\times 10^{-5}</math>		<br />Nodes 1:  <math>\sigma_c^2 = 8.95879\times 10^{-5}</math>
	<br />Nodes 2:  <math>\sigma_c^2 = 3.02\times 10^{-4}</math>		<br />Nodes 2:  <math>\sigma_c^2 = 3.021\times 10^{-4}</math>
	<br />Nodes 3:  <math>\sigma_c^2 = 6.1\times 10^{-4}</math>		<br />Nodes 3:  <math>\sigma_c^2 = 6.09\times 10^{-4}</math>
	</td></tr>		</td></tr>
	</table>		</table>

Jet53man: /* Convert to Implicit Approach */

2023-09-18T23:01:00Z

Convert to Implicit Approach

← Older revision		Revision as of 19:01, 18 September 2023
Line 3,950:		Line 3,950:
	\biggl\{ 1 - \biggl[-0.3436910 \biggr] \biggr\}^{-1}		\biggl\{ 1 - \biggl[-0.3436910 \biggr] \biggr\}^{-1}
	=		=
	-5.~~0086589~~ \, ;		-4.999354 \, ;
	</math>		</math>
	</td>		</td>

Jet53man: /* Convert to Implicit Approach */

2023-09-18T22:57:42Z

Convert to Implicit Approach

← Older revision		Revision as of 18:57, 18 September 2023
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	</table>		</table>
	<tr><td bgcolor="lightblue" align="left">		<tr><td bgcolor="lightblue" align="left">
	<b>Best ~~value~~:</b><br />Nodes 0:  n/a		<b>Best values:</b><br />Nodes 0:  n/a
	<br />Nodes 1:  <math>\sigma_c^2 = 8.95879\times 10^{-5}</math>		<br />Nodes 1:  <math>\sigma_c^2 = 8.95879\times 10^{-5}</math>
	<br />Nodes 2:  <math>\sigma_c^2 = 3.02\times 10^{-4}</math>		<br />Nodes 2:  <math>\sigma_c^2 = 3.02\times 10^{-4}</math>
			<br />Nodes 3:  <math>\sigma_c^2 = 6.1\times 10^{-4}</math>
	</td></tr>		</td></tr>
	</table>		</table>

Jet53man: /* Convert to Implicit Approach */

2023-09-18T22:48:08Z

Convert to Implicit Approach

← Older revision		Revision as of 18:48, 18 September 2023
Line 3,919:		Line 3,919:
	</tr>		</tr>
	</table>		</table>
	~~<b>Best value:</b> <math>\sigma_c^2 = 9.40368\times 10^{-5}</math>.~~
	</td></tr>		</td></tr>
	<tr><td bgcolor="white" align="center">		<tr><td bgcolor="white" align="center">
Line 3,967:		Line 3,966:
	</td>		</td>
	</tr>		</tr>
			</table>
			<tr><td bgcolor="lightblue" align="left">
			<b>Best value:</b><br />Nodes 0:  n/a
			<br />Nodes 1:  <math>\sigma_c^2 = 8.95879\times 10^{-5}</math>
			<br />Nodes 2:  <math>\sigma_c^2 = 3.02\times 10^{-4}</math>
			</td></tr>
	</table>		</table>
	</td></tr></table>		</td></tr></table>

Jet53man: /* Convert to Implicit Approach */

2023-09-18T21:33:45Z

Convert to Implicit Approach

← Older revision		Revision as of 17:33, 18 September 2023
Line 3,907:		Line 3,907:
	<td align="center" bgcolor="white"><math>x_{J-1}</math></td>		<td align="center" bgcolor="white"><math>x_{J-1}</math></td>
	<td align="center" bgcolor="white"><math>p_{J-1}</math></td>		<td align="center" bgcolor="white"><math>p_{J-1}</math></td>
	<td align="center" bgcolor="white"><font size="-1">~~determind~~</font><br /><math>x_J</math></td>		<td align="center" bgcolor="white"><font size="-1">determined</font><br /><math>x_J</math></td>
	<td align="center" bgcolor="white"><font size="-1">~~determind~~</font><br /><math>p_J</math></td>		<td align="center" bgcolor="white"><font size="-1">determined</font><br /><math>p_J</math></td>
	</tr>		</tr>

	<tr>		<tr>
	<td align="center" bgcolor="white">0.001936393</td>		<td align="center" bgcolor="white">0.001936393</td>
	<td align="center" bgcolor="white">-4.~~695376~~</td>		<td align="center" bgcolor="white">-4.755073</td>
	<td align="center" bgcolor="white">23.~~209561~~</td>		<td align="center" bgcolor="white">32.25497</td>
	<td align="center" bgcolor="white">-4.~~952871~~</td>		<td align="center" bgcolor="white">-4.999355</td>
	<td align="center" bgcolor="white">35.~~082432~~</td>		<td align="center" bgcolor="white">34.874915</td>
	</tr>		</tr>
	</table>		</table>
Line 3,951:		Line 3,951:
	\biggl\{ 1 - \biggl[-0.3436910 \biggr] \biggr\}^{-1}		\biggl\{ 1 - \biggl[-0.3436910 \biggr] \biggr\}^{-1}
	=		=
			-5.0086589 \, ;
	</math>		</math>
	</td>		</td>
Line 3,962:		Line 3,962:
	<math>		<math>
	\biggl[ p_{J-1} + (\mathfrak{C}\Delta\tilde{r}) x_J \biggr]( 1 - \mathfrak{D}\Delta\tilde{r} )^{-1}		\biggl[ p_{J-1} + (\mathfrak{C}\Delta\tilde{r}) x_J \biggr]( 1 - \mathfrak{D}\Delta\tilde{r} )^{-1}
			=
			34.87491 \, .
	</math>		</math>
	</td>		</td>

Jet53man: /* Convert to Implicit Approach */

2023-09-17T23:07:11Z

Convert to Implicit Approach

@@ Line 3,938: / Line 3,938: @@
 + \frac{(\mathfrak{B} \Delta\tilde{r}) (\mathfrak{C}\Delta\tilde{r})}{ ( 1 - \mathfrak{D}\Delta\tilde{r} ) }
 \biggr] \biggr\}^{-1}
 </math>
    </td>

Jet53man: /* Convert to Implicit Approach */

2023-09-17T22:44:06Z

Convert to Implicit Approach

← Older revision		Revision as of 18:44, 17 September 2023
Line 3,895:		Line 3,895:
	<td align="center" bgcolor="white">3359266.406</td>		<td align="center" bgcolor="white">3359266.406</td>

	<td align="center" bgcolor="white">0.00</td>		<td align="center" bgcolor="white">-155.14459</td>
	<td align="center" bgcolor="white">0.00</td>		<td align="center" bgcolor="white">-25.85743</td>
	<td align="center" bgcolor="white">0.00</td>		<td align="center" bgcolor="white">4.0162932</td>
	<td align="center" bgcolor="white">0.00</td>		<td align="center" bgcolor="white">91.443479</td>
	</tr>		</tr>
	</table>		</table>
Line 3,905:		Line 3,905:
	<tr>		<tr>
	<td align="center" bgcolor="white"><math>\Delta\tilde{r}</math></td>		<td align="center" bgcolor="white"><math>\Delta\tilde{r}</math></td>
	~~<td align="center" bgcolor="white"><math>x_J</math></td>~~
	<td align="center" bgcolor="white"><math>x_{J-1}</math></td>		<td align="center" bgcolor="white"><math>x_{J-1}</math></td>
	<td align="center" bgcolor="white"><math>~~(x_J)^'~~</math></td>		<td align="center" bgcolor="white"><math>p_{J-1}</math></td>
	<td align="center" bgcolor="white"><math>~~(x_{J~~-1~~})^'~~</math></td>		<td align="center" bgcolor="white"><font size="-1">determind</font><br /><math>x_J</math></td>
			<td align="center" bgcolor="white"><font size="-1">determind</font><br /><math>p_J</math></td>
	</tr>		</tr>

Line 3,914:		Line 3,914:
	<td align="center" bgcolor="white">0.001936393</td>		<td align="center" bgcolor="white">0.001936393</td>
	<td align="center" bgcolor="white">-4.695376</td>		<td align="center" bgcolor="white">-4.695376</td>
	<td align="center" bgcolor="white">-4.~~547832~~</td>		<td align="center" bgcolor="white">23.209561</td>
	<td align="center" bgcolor="white">-~~116~~.~~0119~~</td>		<td align="center" bgcolor="white">-4.952871</td>
	<td align="center" bgcolor="white">~~-76~~.~~19513~~</td>		<td align="center" bgcolor="white">35.082432</td>
	</tr>		</tr>
	</table>		</table>
Line 3,926:		Line 3,926:

	<tr>		<tr>
	<td align="right"><math>~~x_{J+1}~~</math></td>		<td align="right"><math>
			x_J
			</math></td>
	<td align="center"><math>=</math></td>		<td align="center"><math>=</math></td>
	<td align="left">		<td align="left">
	<math>		<math>
	\biggl~~[5x_~~{J-1} - ~~4x_J~~ \biggr]		\biggl\{ x_{J-1}
	+		+ \biggl[\frac{(\mathfrak{B} \Delta\tilde{r})}{( 1 - \mathfrak{D}\Delta\tilde{r} )}\biggr] p_{J-1} \biggr\}
	\biggl[ 4(~~x_J~~)^' + 2 (x_{J-1})^'\biggr]\Delta\tilde{r}		\biggl\{ 1 - \biggl[
	=		(\mathfrak{A} \Delta\tilde{r})
	-~~5.15132~~		+ \frac{(\mathfrak{B} \Delta\tilde{r}) (\mathfrak{C}\Delta\tilde{r})}{ ( 1 - \mathfrak{D}\Delta\tilde{r} ) }
	\~~, .~~		\biggr] \biggr\}^{-1}
			</math>
			</td>
			</tr>

			<tr>
			<td align="right"><math>p_{J}( 1 - \mathfrak{D}\Delta\tilde{r} ) </math></td>
			<td align="center"><math>=</math></td>
			<td align="left">
			<math>
			\biggl[ p_{J-1} + (\mathfrak{C}\Delta\tilde{r}) x_J \biggr]( 1 - \mathfrak{D}\Delta\tilde{r} )^{-1}
	</math>		</math>
	</td>		</td>
	</tr>		</tr>
	</table>		</table>
	~~</td></tr>~~
	</td></tr></table>		</td></tr></table>

Jet53man: /* Convert to Implicit Approach */

2023-09-17T22:23:17Z

Convert to Implicit Approach

← Older revision		Revision as of 18:23, 17 September 2023
Line 3,919:		Line 3,919:
	</tr>		</tr>
	</table>		</table>
			<b>Best value:</b> <math>\sigma_c^2 = 9.40368\times 10^{-5}</math>.
	</td></tr>		</td></tr>
	<tr><td bgcolor="white" align="center">		<tr><td bgcolor="white" align="center">