BA Elias Saarmann - Revision history

Elias.S: Update: aktuelle Probleme

2026-08-16T22:50:24Z

Update: aktuelle Probleme

← Older revision		Revision as of 00:50, 17 August 2026
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	** keine Schwankungen		** keine Schwankungen
	* in beiden Fällen		* in beiden Fällen
	** Akkretionsrate nähert sich Asymptote an bei \(f_\text{acc} \approx 1\) während nach Theorie \(f_\text{acc} \approx 4\cdot10^{-4}\)		** Akkretionsrate nähert sich Asymptote an bei \(f_\text{acc} \approx 1\) (entspricht \(\tilde{L}_\infty \approx 2\cdot10^5\)) während nach Theorie \(f_\text{acc} \approx 4\cdot10^{-4}\) (entspricht \(\tilde{L}_\infty \approx 8\cdot10^1\)) erwartet wird
	** in vx_1 ist Schock erkennbar der noch nicht ganz durchgelaufen ist		** in vx_1 ist Schock erkennbar der noch nicht ganz durchgelaufen ist
	** Dichteverteilung fehlt das Minimum aus Fig 6 im Paper		** Dichteverteilung fehlt das Minimum aus Fig 6 im Paper
	** T und E_rad ähneln Verlauf in Figure 6		** T und E_rad ähneln Verlauf in Figure 6
	**		-> Fragen:
			* Ist es Korrekt Innenrand X_Beg als \(r_\text(s)\) für Akkretionsluminosität zu behandeln?
			* Kann ich die Luminosität direkt in den Daten sehen oder muss ich diese über Akkretionsrate berechnen?
			** Könnte es sein dass Probleme beim Strahlungstransport vorliegen?
			** Warum brauchen die Simulationen so lange?
			** Spielt der Schock der noch unterwegs ist eine größere Rolle oder ändert sich an \(f_\text{acc}\) später auch nichts mehr?

	=== Versuch \(\tau_\text{B} = 10^{-1}\) und \(\beta = 10^{-3}\) zu untersuchen ===		=== Versuch \(\tau_\text{B} = 10^{-1}\) und \(\beta = 10^{-3}\) zu untersuchen ===

Elias.S: /* Versuch \(\tau_\text{B} = 10^{3}\) und \(\beta = 10^{-3}\) zu reproduzieren */

2026-08-16T22:31:30Z

Versuch \(\tau_\text{B} = 10^{3}\) und \(\beta = 10^{-3}\) zu reproduzieren

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 ** Parameter wie oben, 1000 Zellen -> nur noch sehr sehr schwache Oszillationen, power law klar erkennbar, Zero-Gradient scheinbar efüllt
 Allerdings: Massenflux steigt linear, kein Steady State erreicht
 === Versuch \(\tau_\text{B} = 10^{-1}\) und \(\beta = 10^{-3}\)  zu untersuchen ===

Elias.S: /* Final Analytical Approximation */

2026-08-16T21:07:56Z

Final Analytical Approximation

← Older revision		Revision as of 23:07, 16 August 2026
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	\[ f_\text{acc} = \left(\frac{\tilde{L}_\infty}{10}\right)^{-\frac{5}{4}}\]		\[ f_\text{acc} = \left(\frac{\tilde{L}_\infty}{10}\right)^{-\frac{5}{4}}\]

	For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B}~~^{-1}~~ \) and \(\tilde{L}_\infty > \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11} \)		For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B} \) and \(\tilde{L}_\infty > \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11} \)
	\[ f_\text{acc} = (\tilde{L}_\infty \tau_\text{B})^{-\frac{5}{8}}\]		\[ f_\text{acc} = (\tilde{L}_\infty \tau_\text{B})^{-\frac{5}{8}}\]

	For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B~~}^{-1~~} \) and \(\tilde{L}_\infty < \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11}\)		For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B} \) and \(\tilde{L}_\infty < \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11}\)
	\[ f_\text{acc} = (10\beta \tau_\text{B}^2)^{-\frac{5}{11}}\]		\[ f_\text{acc} = (10\beta \tau_\text{B}^2)^{-\frac{5}{11}}\]

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	\[ \tilde{L}_\infty = \left(\frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta \tau_\text{B} 10^{\frac{5}{4}}\right)^\frac{4}{9}\]		\[ \tilde{L}_\infty = \left(\frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta \tau_\text{B} 10^{\frac{5}{4}}\right)^\frac{4}{9}\]

	For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B~~}^{-1~~} \) and \(\tilde{L}_\infty > \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11} \)		For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B} \) and \(\tilde{L}_\infty > \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11} \)
	\[ \tilde{L}_\infty = \left(\frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta \tau_\text{B}^\frac{3}{8} \right)^{\frac{8}{13}}\]		\[ \tilde{L}_\infty = \left(\frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta \tau_\text{B}^\frac{3}{8} \right)^{\frac{8}{13}}\]

	For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B~~}^{-1~~} \) and \(\tilde{L}_\infty < \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11}\)		For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B} \) and \(\tilde{L}_\infty < \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11}\)
	\[ \tilde{L}_\infty = \frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta^{\frac{6}{11}} \tau_\text{B}^{\frac{1}{11}} 10^{-\frac{5}{11}}\]		\[ \tilde{L}_\infty = \frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta^{\frac{6}{11}} \tau_\text{B}^{\frac{1}{11}} 10^{-\frac{5}{11}}\]

Elias.S: /* Final Analytical Approximation */

2026-08-16T20:40:20Z

Final Analytical Approximation

← Older revision		Revision as of 22:40, 16 August 2026
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	\[ f_\text{acc} = (\tilde{L}_\infty \tau_\text{B})^{-\frac{5}{8}}\]		\[ f_\text{acc} = (\tilde{L}_\infty \tau_\text{B})^{-\frac{5}{8}}\]

	For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B}^{-1} \) and \(\tilde{L}_\infty > \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11}\)		For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B}^{-1} \) and \(\tilde{L}_\infty < \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11}\)
	\[ f_\text{acc} = (10\beta \tau_\text{B}^2)^{-\frac{5}{11}}\]		\[ f_\text{acc} = (10\beta \tau_\text{B}^2)^{-\frac{5}{11}}\]

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	\[ \tilde{L}_\infty = \left(\frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta \tau_\text{B}^\frac{3}{8} \right)^{\frac{8}{13}}\]		\[ \tilde{L}_\infty = \left(\frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta \tau_\text{B}^\frac{3}{8} \right)^{\frac{8}{13}}\]

	For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B}^{-1} \) and \(\tilde{L}_\infty > \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11}\)		For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B}^{-1} \) and \(\tilde{L}_\infty < \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11}\)
	\[ \tilde{L}_\infty = \frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta^{\frac{6}{11}} \tau_\text{B}^{\frac{1}{11}} 10^{-\frac{5}{11}}\]		\[ \tilde{L}_\infty = \frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta^{\frac{6}{11}} \tau_\text{B}^{\frac{1}{11}} 10^{-\frac{5}{11}}\]

Elias.S: /* Analytical Approximation for \(\tilde{L}_\infty\) */

2026-08-16T20:38:43Z

Analytical Approximation for \(\tilde{L}_\infty\)

← Older revision		Revision as of 22:38, 16 August 2026
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	For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B}^{-1} \) and \(\tilde{L}_\infty > \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11}\)		For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B}^{-1} \) and \(\tilde{L}_\infty > \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11}\)
	\[ \tilde{L}_\infty = \frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta{\frac{6}{11}} \tau_\text{B}^{\frac{1}{11}} 10^{-\frac{5}{11}}\]		\[ \tilde{L}_\infty = \frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta^{\frac{6}{11}} \tau_\text{B}^{\frac{1}{11}} 10^{-\frac{5}{11}}\]

	= das ''Reference-System'' =		= das ''Reference-System'' =

Elias.S: Added formulas Potentially useful for estimating luminosities before run

2026-08-16T20:38:14Z

Added formulas Potentially useful for estimating luminosities before run

← Older revision		Revision as of 22:38, 16 August 2026
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	For \(\tilde{L}_\infty > \text{max}(10, 100\tau_\text{B})\)		For \(\tilde{L}_\infty > \text{max}(10, 100\tau_\text{B})\)
	\[ \tilde{L}_\infty = \frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta \tau_\text{B} \left(\frac{\tilde{L}_\infty}{10}\right)^{-\frac{5}{4}}\]		\[ \tilde{L}_\infty = \frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta \tau_\text{B} \left(\frac{\tilde{L}_\infty}{10}\right)^{-\frac{5}{4}}\]

			\[ \tilde{L}_\infty = \left(\frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta \tau_\text{B} 10^{\frac{5}{4}}\right)^\frac{4}{9}\]

	For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B}^{-1} \) and \(\tilde{L}_\infty > \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11} \)		For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B}^{-1} \) and \(\tilde{L}_\infty > \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11} \)
	\[ \tilde{L}_\infty = \frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta \tau_\text{B} (\~~tilde~~{L}~~_\infty \tau_\text~~{B})^{-\frac{5}{8}}\]		\[ \tilde{L}_\infty = \left(\frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta \tau_\text{B}^\frac{3}{8} \right)^{\frac{8}{13}}\]

	For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B}^{-1} \) and \(\tilde{L}_\infty > \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11}\)		For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B}^{-1} \) and \(\tilde{L}_\infty > \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11}\)
	\[ \tilde{L}_\infty = \frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta \~~tau_\text~~{B} ~~(10\beta~~ \tau_\text{B}^2)^{-\frac{5}{11}}\]		\[ \tilde{L}_\infty = \frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta{\frac{6}{11}} \tau_\text{B}^{\frac{1}{11}} 10^{-\frac{5}{11}}\]

	= das ''Reference-System'' =		= das ''Reference-System'' =

Elias.S: /* Final Analytical Approximation */

2026-08-16T20:29:55Z

Final Analytical Approximation

← Older revision		Revision as of 22:29, 16 August 2026
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	==== Analytical Approximation for \(\tilde{L}_\infty\) ====		==== Analytical Approximation for \(\tilde{L}_\infty\) ====

			\[\tilde{L}_\infty = \frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta \tau_\text{B} f_\text{acc} \]

			For \( \frac{\tilde{L}_\infty}{10 \beta} < \tau_\text{B} < \tilde{L}_\infty^{-1}\)
			\[ \tilde{L}_\infty = \text{No Solution}\]

			For \(10 \tau_\text{B} \beta < \tilde{L}_\infty < \text{min}(10, \tau_\text{B}^{-1})\)
			\[ \tilde{L}_\infty = \frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta \tau_\text{B}\]

			For \(\tilde{L}_\infty > \text{max}(10, 100\tau_\text{B})\)
			\[ \tilde{L}_\infty = \frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta \tau_\text{B} \left(\frac{\tilde{L}_\infty}{10}\right)^{-\frac{5}{4}}\]

			For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B}^{-1} \) and \(\tilde{L}_\infty > \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11} \)
			\[ \tilde{L}_\infty = \frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta \tau_\text{B} (\tilde{L}_\infty \tau_\text{B})^{-\frac{5}{8}}\]

			For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B}^{-1} \) and \(\tilde{L}_\infty > \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11}\)
			\[ \tilde{L}_\infty = \frac{56}{6}\frac{r_\text{B}}{r_\text{s}}\beta \tau_\text{B} (10\beta \tau_\text{B}^2)^{-\frac{5}{11}}\]

	= das ''Reference-System'' =		= das ''Reference-System'' =

Elias.S: /* Final Analytical Approximation */

2026-08-16T20:23:54Z

Final Analytical Approximation

← Older revision		Revision as of 22:23, 16 August 2026
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	==== Analytical Approximation for \(f_\text{acc}\) ====		==== Analytical Approximation for \(f_\text{acc}\) ====
			For \( \frac{\tilde{L}_\infty}{10 \beta} < \tau_\text{B} < \tilde{L}_\infty^{-1}\)
			\[ f_\text{acc} = \text{No Solution}\]

			For \(10 \tau_\text{B} \beta < \tilde{L}_\infty < \text{min}(10, \tau_\text{B}^{-1})\)
			\[ f_\text{acc} = 1\]

			For \(\tilde{L}_\infty > \text{max}(10, 100\tau_\text{B})\)
			\[ f_\text{acc} = \left(\frac{\tilde{L}_\infty}{10}\right)^{-\frac{5}{4}}\]

			For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B}^{-1} \) and \(\tilde{L}_\infty > \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11} \)
			\[ f_\text{acc} = (\tilde{L}_\infty \tau_\text{B})^{-\frac{5}{8}}\]

			For \(\tau_\text{B}^{-1} < \tilde{L}_\infty < 100\tau_\text{B}^{-1} \) and \(\tilde{L}_\infty > \tau_\text{B}^\frac{5}{11} (10\beta)^\frac{8}{11}\)
			\[ f_\text{acc} = (10\beta \tau_\text{B}^2)^{-\frac{5}{11}}\]

	==== Analytical Approximation for \(\tilde{L}_\infty\) ====		==== Analytical Approximation for \(\tilde{L}_\infty\) ====

Elias.S: /* Final Analytical Approximation */

2026-08-16T20:10:14Z

Final Analytical Approximation

← Older revision		Revision as of 22:10, 16 August 2026
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	=== Final Analytical Approximation ===		=== Final Analytical Approximation ===

	==== Analytical Approximation for \[f_\text{acc}\] ====		==== Analytical Approximation for \(f_\text{acc}\) ====


	==== Analytical Approximation for \[\tilde{L}_\infty\] ====		==== Analytical Approximation for \(\tilde{L}_\infty\) ====

	= das ''Reference-System'' =		= das ''Reference-System'' =

Elias.S: /* in PLUTO/belt */

2026-08-16T20:09:39Z

in PLUTO/belt

← Older revision		Revision as of 22:09, 16 August 2026
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	(While the zero gradient conditions do not match theoretical curves they should still be appropriate as the will only lead to local <s>devastation</s>deviations near the respective boundary.)		(While the zero gradient conditions do not match theoretical curves they should still be appropriate as the will only lead to local <s>devastation</s>deviations near the respective boundary.)

			=== Final Analytical Approximation ===

			==== Analytical Approximation for \[f_\text{acc}\] ====


			==== Analytical Approximation for \[\tilde{L}_\infty\] ====

	= das ''Reference-System'' =		= das ''Reference-System'' =