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Yingjie Wang
2026-04-10 00:08:51 -04:00
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@@ -282,7 +282,7 @@
% \node[draw=none, above=1mm of gh, font=\scriptsize] {full first order}; % \node[draw=none, above=1mm of gh, font=\scriptsize] {full first order};
\end{tikzpicture} \end{tikzpicture}
\caption{Blue: second order systems; Red: first order systems. Solid arrows: direct modifications; Dashed arrows: indirect relation. Bidirectional arrows: equivalence.} \caption{Commenly used systems.\footnote{Blue: second order systems; Red: first order systems. Solid arrows: direct modifications; Dashed arrows: indirect relation. Bidirectional arrows: equivalence.}}
\end{figure} \end{figure}
\begin{itemize} \begin{itemize}
\item Z4 and GH evolve the physical metric, and thus not compatible with the moving puncture method. \item Z4 and GH evolve the physical metric, and thus not compatible with the moving puncture method.
@@ -294,6 +294,10 @@
\end{itemize} \end{itemize}
\end{frame} \end{frame}
\begin{frame}{Searching for a first order Z4c}{Why Z4c?}
\end{frame}
\begin{frame}{Searching for a first order Z4c}{Hyperbolicity of first order systems} \begin{frame}{Searching for a first order Z4c}{Hyperbolicity of first order systems}
\subsection{Hyperbolicity of first order systems} \subsection{Hyperbolicity of first order systems}
Say we have a list of variables $u^I$, and a first order PDE system Say we have a list of variables $u^I$, and a first order PDE system