deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index 6b9af36..8aefde2 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
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\sigma_{zz} = (\lambda + \mu) \frac{\partial u_z}{\partial z} - (3\lambda + 2\mu) \frac{\alpha E}{\rho C S \zeta}  \label{eq:stressUnidim}  \end{equation}  where $\lambda$ and $\mu$ are respectively the first and second Lamé's coefficient, $\alpha$ is the thermal dilatation coefficient and $\zeta$ 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, and there is giving  a displacement $u_z$ from the surface: \begin{equation}  u_z = \frac{(3\lambda + 2\mu)}{(\lambda + 2\mu)} \frac{\alpha E \zeta}{\rho C S \zeta}\approx 3 \alpha \frac{E}{\rho C S}  % \label{eq:deplUnidim}  \end{equation}  as As  in a biological soft tissues, $\mu \gg \lambda$. \lambda$, $u_z \approx 3 \alpha \frac{E}{\rho C S}$.  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 slightly smaller than the typical ultrasound resolution of displacement, typically of a few micrometers. In a tridimensional model, displacements along X and Y axis would also occurs, as the local expansion acts as dipolar forces parallel to the surface. 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} 
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