deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index 6382ce5..f5bbf2a 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
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where $\lambda$ and $\mu$ are respectively the first and second Lamé's coefficient, $\alpha$ is the thermal dilatation coefficient and $\delta$ the average depth of laser beam absorption. In the absence of external constraints normal to the surface, the stress across the surface must be zero, i.e. $\sigma_{zz} (z=0) = 0$, so that equation \ref{eq:stressUnidim} can be integrated:  \begin{equation}  u_z = \frac{(3\lambda + 2\mu)}{(\lambda + 2\mu)} \frac{\alpha E \delta}{\rho C S \delta} \approx 3 \alpha E}{\rho C S}   %\label{eq:deplUnidim} % \label{eq:deplUnidim}  \end{equation}  as in a biological soft tissues, $\mu \gg \lambda$. Taking as an order of magnitude $\alpha$ = 70.10$^{-6}$ K$^{-1}$ (water linear thermal dilatation coefficient), $E$ = 200 mJ, $\rho$ = 1000 kg.m$^{-3}$ (water density), $C$ = 4180 kg.m$^{-3}$ (water calorific capacity) and $S$ = 20 mm$^2$, we obtain a displacement $u_z$= 0.5 $\mu$m. This value is still smaller than the typical displacement resolution with ultrasound, of a few micrometers. This unidimensional analysis cannot explain the induction of shear waves, as displacement is curl-free. However, in a tridimensional model, the local expansion acts as dipolar forces parallel to the surface, so displacements along X and Y axis can be higher.  In the ablative regime, the local increase of temperature is so high that the surface of the medium is vaporized. This phenomenon creates a stress $\sigma$ in the medium, given by \cite{scruby1990laser}:  \begin{equation}  \sigma = \frac{1}{\rho}\frac{I^2}{(L+C(T_V-T_0))^2} \label{eq:ablation} %\label{eq:ablation}  \end{equation}  where $L$ is the latent heat required to vaporize the solid, $T_0$ and $T_V$ the initial and vaporization temperatures. 
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