deletions | additions       diff --git a/sectionAcknowledgmen.tex b/sectionAcknowledgmen.tex  index 0caa208..bfb46c4 100644  --- a/sectionAcknowledgmen.tex  +++ b/sectionAcknowledgmen.tex 
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\dot{J}_* \sim \bigg[ \frac{\omega_*(r)}{\omega_c} \bigg]^{-a} \dot{J}_0 \sim \bigg[ \frac{A^2 \rho r^5 \omega_c^4}{\lambda^{3/2} N \dot{E}_0} \bigg]^{a/(a+3)} \dot{J}_0 \, .  \end{equation}  During C-shell burning, we find that radiative diffusion damps waves near the shell burning convective zone, while non-linear breaking damps waves near the center of the star. In this case, we first calculate $\omega_*$ and its corresponding energy flux $\dot{E}_*$ via equations \ref{eqn:omstar2} and \ref{eqn:spectrum}. We then substitute the value of $\dot{E}_*$ for $\dot{E}_0$ in equation \ref{eqn:omstarnl}. The appropriate value of $\omega_*$ is then $\omega_* = {\rm max} \big[ {\rm Eqn. \ref{eqn:omstar2}}, Eqn.}$ \ref{eqn:omstar2}$,  {\rm Eqn.\ref{eqn:omstarnl} Eqn.}$\ref{eqn:omstarnl}$  }\big]$. The corresponding AM flux is $\dot{J}_* \sim \Big[ \frac{\omega_*(r)}{\omega_c} \Big]^{-a} \dot{J}_0$. The cores of massive stars nearing death cool primarily through neutrino emission, so it is not unreasonable to think that waves may be damped via neutrino emission. We calculate neutrino energy loss rates in the same manner as \cite{murphy:04}. We find that neutrino damping time scales are always longer than the wave crossing timescale  \begin{equation}