deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index 437209f..36848f4 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 $\delta z$ 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 z}{\rho C S \delta z} \approx 3 \alpha \frac{E}{\rho C S}   %  \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. 
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