188 lines
7.8 KiB
TeX
188 lines
7.8 KiB
TeX
\begin{frame}{Moteur chimique}
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\begin{columns}
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\column{.7\textwidth}\centering
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\begin{itemize}
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\item \structure{Modèle}
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\begin{itemize}
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\item Réaction-Diffusion-Évaporation à la Turing
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\medskip
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\item EDP couplées
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\begin{equation*}
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\frac{\partial\orr\varphi}{\partial t} =
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\orr{\text{X}}(\orr\varphi) +
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\orr{\text{D}} \cdot
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\nabla^2\orr\varphi
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- \orr{\text{E}} \cdot \orr\varphi
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\end{equation*}
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\end{itemize}
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\item \structure{Simulation}
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\begin{itemize}
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\item Discrétisation de type différences finies sur un automate
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cellulaire 2D
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\medskip
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\item Algorithme Propagation Parallèle à la Margolus (PPM)
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\begin{itemize}
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\item Simuler un automate cellulaire sur un support SIMD
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\item Faire correspondre la segmentation de l'espace aux processus
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\item Éviter les accès concurrents à la même zone mémoire
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\end{itemize}
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\end{itemize}
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\end{itemize}
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\column{.2\textwidth}
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\moteurs[structure!30]
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\end{columns}
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% Animation du «calque» de démonstration de PPM
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\uncover<2->{
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\tikz[overlay,opacity=.95,transform canvas={scale around=.8:(current page.center)}]
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\draw[black,fill=white,rounded corners,ultra thick]
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(current page.south west) rectangle (current page.north east);
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\only<2-7>{
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\tikz[overlay] \node[anchor=center] at (current page.center) {
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\begin{tikzpicture}[
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cell/.style={black,size=1.5mm,circle,inner sep=0pt,font=\TINY},
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neighbor cell/.style={black,size=1.5mm,circle,inner sep=0pt,font=\small},
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center cell/.style={cell,white,fill=black},
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spy using outlines={circle,red,size=58mm,magnification=4,connect spies}]
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\begin{scope}[scale=.5]
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\clip (-27mm,-27mm) rectangle (27mm,27mm);
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% Background
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\only<2,4-6>{%
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\fill[blue!50,shift={(5mm,5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);
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\fill[red!50,shift={(-5mm,-5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);
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}
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\only<3,6->{%
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\fill[red!50,shift={(-5mm,-5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);
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\fill[blue!50,shift={(5mm,5mm)}] (-1cm,-1cm) rectangle (1cm,1cm);
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}
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\only<4-7>{
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\begin{scope}
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\clip (-3mm,-3mm) rectangle (3mm,3mm);
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\draw[very thin] (-5mm,-5mm) grid (5mm,5mm);
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\end{scope}
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}
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\only<4-6>{
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\begin{scope}[shift={(-1cm,0)}]
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\clip (-3mm,-3mm) rectangle (3mm,3mm);
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\draw[very thin] (-5mm,-5mm) grid (5mm,5mm);
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\end{scope}
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\begin{scope}[shift={(-1cm,-1cm)}]
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\clip (-3mm,-3mm) rectangle (3mm,3mm);
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\draw[very thin] (-5mm,-5mm) grid (5mm,5mm);
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\end{scope}
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\begin{scope}[shift={(0cm,-1cm)}]
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\clip (-3mm,-3mm) rectangle (3mm,3mm);
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\draw[very thin] (-5mm,-5mm) grid (5mm,5mm);
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\end{scope}
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}
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\only<2,3>{
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\node[center cell,font=\small] at ( -0mm, -0mm) {$A$};
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\node[cell,font=\small] at (-10mm, -0mm) {$B$};
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\node[cell,font=\small] at (-10mm,-10mm) {$C$};
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\node[cell,font=\small] at ( -0mm,-10mm) {$D$};
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}
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\only<2,3,4>{
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% Voisins
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\node[neighbor cell] at ( 1cm, 0cm) {$v_{A,1}$};
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\node[neighbor cell] at ( 1cm, 1cm) {$v_{A,2}$};
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\node[neighbor cell] at ( 0cm, 1cm) {$v_{A,3}$};
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\node[neighbor cell] at (-1cm, 1cm) {$v_{B,1}$};
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\node[neighbor cell] at (-2cm, 1cm) {$v_{B,2}$};
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\node[neighbor cell] at (-2cm, 0cm) {$v_{B,3}$};
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\node[neighbor cell] at (-2cm,-1cm) {$v_{C,1}$};
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\node[neighbor cell] at (-2cm,-2cm) {$v_{C,2}$};
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\node[neighbor cell] at (-1cm,-2cm) {$v_{C,3}$};
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\node[neighbor cell] at ( 0cm,-2cm) {$v_{D,1}$};
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\node[neighbor cell] at ( 1cm,-2cm) {$v_{D,2}$};
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\node[neighbor cell] at ( 1cm,-1cm) {$v_{D,3}$};
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}
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\only<4>{
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\begin{scope}[scale=0.5,shift={(-5mm,-5mm)}]
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\node[center cell] at ( -0mm, -0mm) {$A$};
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\node[cell] at (-10mm, -0mm) {$B$};
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\node[cell] at (-10mm,-10mm) {$C$};
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\node[cell] at ( -0mm,-10mm) {$D$};
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\node[cell] at ( 1cm, 0cm) {$v_{A,1}$};
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\node[cell] at ( 1cm, 1cm) {$v_{A,2}$};
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\node[cell] at ( 0cm, 1cm) {$v_{A,3}$};
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\node[cell] at (-1cm, 1cm) {$v_{B,1}$};
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\node[cell] at (-2cm, 1cm) {$v_{B,2}$};
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\node[cell] at (-2cm, 0cm) {$v_{B,3}$};
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\node[cell] at (-2cm,-1cm) {$v_{C,1}$};
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\node[cell] at (-2cm,-2cm) {$v_{C,2}$};
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\node[cell] at (-1cm,-2cm) {$v_{C,3}$};
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\node[cell] at ( 0cm,-2cm) {$v_{D,1}$};
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\node[cell] at ( 1cm,-2cm) {$v_{D,2}$};
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\node[cell] at ( 1cm,-1cm) {$v_{D,3}$};
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\end{scope}
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}
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\only<5>{
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\begin{scope}[scale=0.5,shift={(-5mm,-5mm)}]
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\node[center cell] at ( -0mm, -0mm) {$A'$};
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\node[cell] at (-10mm, -0mm) {$B'$};
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\node[cell] at (-10mm,-10mm) {$C'$};
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\node[cell] at ( -0mm,-10mm) {$D'$};
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\end{scope}
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}
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\only<6>{
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\begin{scope}[scale=0.5,shift={(5mm,5mm)}]
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\node[center cell] at ( -0mm, -0mm) {$A'$};
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\node[cell] at (-10mm, -0mm) {$B'$};
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\node[cell] at (-10mm,-10mm) {$C'$};
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\node[cell] at ( -0mm,-10mm) {$D'$};
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\end{scope}
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\begin{scope}[scale=0.5,shift={(-15mm,5mm)}]
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\node[cell] at ( -0mm, -0mm) {$A'$};
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\node[cell] at (-10mm, -0mm) {$B'$};
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\node[cell] at (-10mm,-10mm) {$C'$};
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\node[cell] at ( -0mm,-10mm) {$D'$};
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\end{scope}
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\begin{scope}[scale=0.5,shift={(-15mm,-15mm)}]
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\node[cell] at ( -0mm, -0mm) {$A'$};
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\node[cell] at (-10mm, -0mm) {$B'$};
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\node[cell] at (-10mm,-10mm) {$C'$};
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\node[cell] at ( -0mm,-10mm) {$D'$};
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\end{scope}
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\begin{scope}[scale=0.5,shift={(5mm,-15mm)}]
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\node[cell] at ( -0mm, -0mm) {$A'$};
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\node[cell] at (-10mm, -0mm) {$B'$};
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\node[cell] at (-10mm,-10mm) {$C'$};
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\node[cell] at ( -0mm,-10mm) {$D'$};
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\end{scope}
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}
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\only<7>{
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\begin{scope}[scale=0.5,shift={(5mm,5mm)}]
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\node[center cell] at ( -0mm, -0mm) {$A'$};
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\node[cell] at (-10mm, -0mm) {$B'$};
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\node[cell] at (-10mm,-10mm) {$C'$};
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\node[cell] at ( -0mm,-10mm) {$D'$};
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\end{scope}
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}
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% Grilles:
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\draw[xshift=5mm,yshift=5mm,thin] ( -5cm, -5cm) grid ( 5cm, 5cm);
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\only<2,4-6>{\draw[xshift=5mm,yshift=5mm, step=2cm, thick]%
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( -5cm, -5cm) grid ( 5cm, 5cm);}
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\only<3,7>{\draw[xshift=-5mm,yshift=-5mm, step=2cm, thick]%
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( -5cm, -5cm) grid ( 5cm, 5cm);}
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\only<2,4-6>{
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\coordinate (spyhook) at (-5mm,-5mm);
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}
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\only<3,7>{
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\coordinate (spyhook) at (5mm,5mm);
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}
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\end{scope}
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\spy on (spyhook) in node (zoom) at (5cm,0);
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\end{tikzpicture}
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};
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}
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}
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\end{frame}
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