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--- culinary_services [2014/06/02 17:50]
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+++ culinary_services [2014/06/03 18:47]
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 Nathan Parzuchowski (analysis)\\
-**TOPIC** \\
+==== TOPIC ====
 Sensitivity studied of <sup>44</sup>Ti production in in core-collapse supernova environments.
+**[[Scientific Background|Scientific Background]]**
 **Recipe** \\
-Starting with a set parameter space of peak temperatures [T<sub>9</sub> = 4 - 7] and densities [].
+Starting with a set parameter space of peak temperatures [T<sub>9</sub> = 4 - 7] and densities [$\rho$ = 10<sup>5</sup> - 10<sup>7</sup> g/cm<sup>3</sup>].
+We use analytic adiabatic freeze-out trajectories (Hoyle et al. 1964; Fowler & Hoyle 1964) which satisfy the differential equations:
+\begin{equation}
+\frac{dT}{dt} = \frac{-T}{3\tau} \hspace{1cm} \frac{d\rho}{dt} = -\frac{\rho}{\tau}
+\end{equation}
+Where $\tau$ is some static free-fall timescale.
+This **obviously** leads to:
+\begin{equation}
+T(t) = T_0 exp(-t/3\tau) \hspace{1cm} \rho (t) = \rho_0 exp(-t/\tau)
+\end{equation}
+where $T_0$ and $\rho_0$ are the peak temperature and density in the supernova.
+Then you run the code, and it doesn't work.
 **REFERENCES** \\
-[[http://iopscience.iop.org/0067-0049/191/1/66|Trends in 44Ti and 56Ni from Core-Collapse Supernovae]]
+[[http://iopscience.iop.org/0067-0049/191/1/66|Trends in 44Ti and 56Ni from Core-Collapse Supernovae]]\\
+[[http://iopscience.iop.org/0004-637X/504/1/500|Nuclear Reactions Governing the Nucleosynthesis of 44Ti]]\\
+[[http://www.sciencedirect.com/science/article/pii/S1387647303002707|X-ray and gamma-ray observations of Cas A]]

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