diff --git a/report.tex b/report.tex index 3ac6f51..f97edfb 100644 --- a/report.tex +++ b/report.tex @@ -240,90 +240,42 @@ \begin{frame}{Searching for a first order Z4c}{Why Z4c?} \section{Searching for a first order Z4c} \subsection{Why Z4c?} - \begin{tikzpicture}[scale=0.5, - font=\small, + \begin{tikzpicture}[ >=Latex, - node distance=12mm and 14mm, + node distance=8mm and 10mm, + every node/.style={font=\small}, sys/.style={ draw, rounded corners, align=center, - minimum width=22mm, - minimum height=9mm, - inner sep=3pt + minimum width=15mm, + minimum height=7mm, + inner sep=2pt }, - second/.style={sys, fill=blue!6}, - first/.style={sys, fill=red!7, very thick}, - note/.style={align=center, font=\footnotesize}, - solidarrow/.style={->, thick}, - dashedarrow/.style={->, thick, dashed}, - influence/.style={->, semithick, dotted} + std/.style={sys, fill=blue!8}, + fo/.style={sys, fill=red!10, very thick}, + rel/.style={->, thick}, + weak/.style={->, semithick, dashed} ] -% ------------------------------------------------- -% upper row: non-fully-first-order / standard forms -% ------------------------------------------------- -\node[second] (bssn) {BSSN}; -\node[second, right=28mm of bssn] (z4) {Z4}; -\node[second, right=22mm of z4] (z4c) {Z4c}; -\node[second, right=22mm of z4c] (ccz4) {CCZ4}; +\node[std] (bssn) {BSSN}; +\node[std, right=of bssn] (z4) {Z4}; +\node[std, right=of z4] (z4c) {Z4c}; +\node[std, right=of z4c] (ccz4) {CCZ4}; -% lower row: fully first-order systems -\node[first, below=22mm of bssn] (fobssn) {FOBSSN}; -\node[first, below=22mm of ccz4] (foccz4) {FOCCZ4}; -\node[first, below=22mm of z4c] (gh) {GH\\(usually first-order)}; +\node[fo, below=10mm of bssn] (fobssn) {FOBSSN}; +\node[fo, below=10mm of z4c] (gh) {GH}; +\node[fo, below=10mm of ccz4] (foccz4) {FOCCZ4}; -% group boxes -\node[ - draw, - rounded corners, - inner sep=6pt, - fit=(bssn)(z4)(z4c)(ccz4), - label={[font=\footnotesize]above:second-order-in-space / standard formulations} -] (upperbox) {}; +\draw[rel] (z4) -- (z4c); +\draw[rel] (z4) to[bend left=18] (ccz4); +\draw[weak] (bssn) -- (z4c); -\node[ - draw=red!70!black, - rounded corners, - very thick, - inner sep=6pt, - fit=(fobssn)(foccz4)(gh), - label={[font=\footnotesize]above:{\textbf{fully first-order systems}}} -] (lowerbox) {}; - -% ------------------------------------------------- -% arrows among upper systems -% ------------------------------------------------- -\draw[solidarrow] (z4) -- node[above, note] {conformal\\reformulation} (z4c); -\draw[solidarrow] (z4) to[bend left=18] node[above, note] {conformal + covariant\\constraint damping} (ccz4); - -% BSSN <-> Z4c relation: not a clean parent/child, so use dotted influence -\draw[influence] (bssn) -- node[above, note] {BSSN-like\\variables} (z4c); - -% ------------------------------------------------- -% arrows to first-order systems -% ------------------------------------------------- -\draw[solidarrow] (bssn) -- node[left, note] {first-order\\reduction} (fobssn); -\draw[solidarrow] (ccz4) -- node[right, note] {first-order\\reduction} (foccz4); - -% GH relation: keep it cautious -\draw[dashedarrow] (z4) -- node[right, note] {closely related\\(principal-part / variable-choice sense)} (gh); - -% optional weak relation from Z4c to FOCCZ4 -\draw[influence] (z4c.south east) to[bend left=18] - node[right, note] {same Z4-family} (foccz4.north west); - -% ------------------------------------------------- -% tiny legend -% ------------------------------------------------- -\node[note, below=8mm of gh] (legend) {% -\begin{tabular}{@{}c l@{}} -\raisebox{0.2ex}{\tikz{\draw[->,thick] (0,0)--(0.7,0);}} & fairly direct reformulation / reduction \\ -\raisebox{0.2ex}{\tikz{\draw[->,thick,dashed] (0,0)--(0.7,0);}} & close relation, but not drawn as a strict descendant \\ -\raisebox{0.2ex}{\tikz{\draw[->,semithick,dotted] (0,0)--(0.7,0);}} & shared variables / family resemblance / influence -\end{tabular} -}; +\draw[rel] (bssn) -- (fobssn); +\draw[rel] (ccz4) -- (foccz4); +\draw[weak] (z4) -- (gh); +\node[draw=none, above=1mm of gh, font=\scriptsize] {full first order}; \end{tikzpicture} \end{frame}