deletions | additions       diff --git a/section_Radiation_Hydrodynamic_Calculations_begin__.tex b/section_Radiation_Hydrodynamic_Calculations_begin__.tex  index 0e7567a..c8fa76e 100644  --- a/section_Radiation_Hydrodynamic_Calculations_begin__.tex  +++ b/section_Radiation_Hydrodynamic_Calculations_begin__.tex 
...
\section{Radiation Hydrodynamic Calculations} \section{Modeling the Supernova Shock-CSM Interaction to Infer Mass-loss History}  \begin{itemize}  \item The variable radio emission from SN Ic encodes but does not directly yield the mass-loss history. To infer the mass-loss hisotry, history,  we must first model the radio emission from a supernova shock overtaking the CSM. \item For relatively simple shock CSM interactions, Chavelier XXX and Chavelier XXX developed analytic solutions and set the language for shock-CSM interactions. However, it is very likely that the mass-loss history is more complicated and requires numerical simulations.  \item In principle, the evolution is radiative and hydrodynamic. However, we will be considering the radio emission from 10 days until 1000 days. During much of this time, one may simply evolve the shock and CSM interaction hydrodynamically, and post-process the radiation.  \item For relatively simple shock CSM interactions, Chavelier XXX and Chavelier XXX developed analytic solutions and set the language for shock-CSM interactions. However, it is very likely that the mass-loss history is more complicated and requires numerical simulations.  \end{itemize}