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Yingjie Wang
2026-04-09 23:43:27 -04:00
parent 04267584fe
commit 6aa2092cd7
1 changed files with 37 additions and 32 deletions
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report.tex
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@@ -240,43 +240,48 @@
\begin{frame}{Searching for a first order Z4c}{Why Z4c?} \begin{frame}{Searching for a first order Z4c}{Why Z4c?}
\section{Searching for a first order Z4c} \section{Searching for a first order Z4c}
\subsection{Why Z4c?} \subsection{Why Z4c?}
\begin{tikzpicture}[ Let's look at the relationship between different formulations of Einstein's equations:
>=Latex, \begin{figure}
node distance=8mm and 10mm, \centering
every node/.style={font=\small}, \begin{tikzpicture}[
sys/.style={ >=Latex,
draw, node distance=8mm and 10mm,
rounded corners, every node/.style={font=\small},
align=center, sys/.style={
minimum width=15mm, draw,
minimum height=7mm, rounded corners,
inner sep=2pt align=center,
}, minimum width=15mm,
std/.style={sys, fill=blue!8}, minimum height=7mm,
fo/.style={sys, fill=red!10, very thick}, inner sep=2pt
rel/.style={->, thick}, },
weak/.style={->, semithick, dashed} std/.style={sys, fill=blue!8},
] fo/.style={sys, fill=red!10, very thick},
rel/.style={->, thick},
weak/.style={->, semithick, dashed}
equv/.style={<->, thick}
]
\node[std] (bssn) {BSSN}; \node[std] (bssn) {BSSN};
\node[std, right=of bssn] (z4) {Z4}; \node[std, right=of bssn] (z4) {Z4};
\node[std, right=of z4] (z4c) {Z4c}; \node[std, right=of z4] (z4c) {Z4c};
\node[std, right=of z4c] (ccz4) {CCZ4}; \node[std, right=of z4c] (ccz4) {CCZ4};
\node[fo, below=10mm of bssn] (fobssn) {FOBSSN}; % \node[fo, below=10mm of bssn] (fobssn) {FOBSSN};
\node[fo, below=10mm of z4c] (gh) {GH}; \node[fo, below=10mm of z4] (gh) {GH};
\node[fo, below=10mm of ccz4] (foccz4) {FOCCZ4}; % \node[fo, below=10mm of ccz4] (foccz4) {FOCCZ4};
\draw[rel] (z4) -- (z4c); \draw[rel] (z4) -- (z4c);
\draw[rel] (z4) to[bend left=18] (ccz4); \draw[rel] (z4) to[bend left=18] (ccz4);
\draw[weak] (bssn) -- (z4c); \draw[weak] (bssn) -- (z4c);
\draw[rel] (bssn) -- (fobssn); % \draw[rel] (bssn) -- (fobssn);
\draw[rel] (ccz4) -- (foccz4); % \draw[rel] (ccz4) -- (foccz4);
\draw[weak] (z4) -- (gh); \draw[rel] (z4) -- (gh);
\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}
\end{figure}
\end{frame} \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}