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Quelle est la rugosit\'e de petites \'echelles\\
\`a la fronti\`ere noyau-manteau?
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\includegraphics[width=\linewidth]{./FIGURE/sy.eps}
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\begin{slide}{La fronti\`ere noyau-manteau}
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\vskip 0.5cm

\hskip -0.5cm $\bullet$ \hskip 0.15cm
R\'eactions chimiques
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{\LemonChiffon
$\longrightarrow$ Dissolution et cristallisation.}

\vskip 0.7cm

\hskip -0.5cm $\bullet$ \hskip 0.15cm
La fronti\`ere Noyau-Manteau
\vskip 0.3cm

{\LemonChiffon 
$\longrightarrow$ Description du mod\`ele.\\
$\longrightarrow$ Une rugosit\'e de petites \'echelles.\\
$\longrightarrow$ Les implications g\'eophysiques.
}

\vskip 0.7cm
\hfill {{\small Narteau et al., {\em PEPI} (2001)}}

\hfill {{\scriptsize {\LemonChiffon {\tt http://www.ipgp.jussieu.fr/$\sim$narteau/TALK/}}}}




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\begin{slide}{Automates cellulaires}
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Syst\`emes compos\'es d'\'el\'ements interagissant les uns avec les autres.

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Interactions de longues port\'ees.

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Interactions de courtes port\'ees.
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Ils permettent d'\'etudier des syst\`emes d'une grande complexit\'e \`a partir de
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$\rightarrow$  la r\'esultante des processus d'auto-organisation
au sein d'un syst\`eme. \\
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ou

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$\rightarrow$ l'\'emergence de structures ma\-cros\-copiques \`a partir des interactions entre les composantes \'el\'ementaires.\\
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\begin{slide}{Un automate cellulaire}
%Un nombre fini d'\'etats et des relations de premiers voisins.
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\begin{slide}{Transitions}
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$\rightarrow$ Une cellule du manteau dissoute sature $n$ \\
{\white $\rightarrow$} cellules de fer liquide du noyau. \\
$\rightarrow$ La gravit\'e est introduite gr\^ace au param\`etre $a$.

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\begin{slide}{Taux de transitions}
Coefficient de diffusion~:
$$D=3 . 10^{-9}\,\,m^2/s$$
Temps caract\'eristique de dissolution~:
$$\tau_l=\frac{d^2\rho_m}{2D(f_{sat}-f_0)\rho_c}$$
Temps caract\'eristique de cristallisation~:
$$\tau_c=\tau_l$$
\end{slide}

