deletions | additions       diff --git a/The_absorption_of_the_laser__.tex b/The_absorption_of_the_laser__.tex  index 209536a..8791e04 100644  --- a/The_absorption_of_the_laser__.tex  +++ b/The_absorption_of_the_laser__.tex 
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u_z = \frac{3 \alpha E}{\rho C S}  \label{eq:deplThermoApprox}  \end{equation}  Substituting same experimental parameters as previously and $\alpha$ = 70.10$^{-6}$ K$^{-1}$ (water linear thermal dilatation coefficient), we obtain a displacement $u_z$ = 0.025 $\mu$m. While slightly higher, this value is in good agreement with experimental displacement (about 0.02 $\mu$m). Note that the theory supposed that the displacement is directed outside the medium,which is seen  in agreement with  the experimental images displacements  in the middle of the beam, as indicated by the white circle in the figure Figure  \ref{figElastoPVA}-(A). To calculate the propagation of the displacement along space and time, we have to take into account the transverse dilatation which leads to stronger displacements than along Z. We modeled thus the thermoelastic regime in 2D as two opposite forces directed along Y axis with a depth of 40 $\mu$m and decreasing linearly from 2.5 to 0 mm (respectively -2.5 to 0 mm) \cite{Davies_1993}. The magnitude of the force along space and time is stored in a matrix $H_y^{thermo}(y,z,t)$ (note that X and Z components of the force are supposed null). Propagation as a shear wave along Z axis was calculated using Green operators $G_{yz}$ as calculated by Aki Richards \cite{aki1980quantitative}:  \begin{equation} 
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Displacements along Z are then equal to the convolution between $H_y^{thermo} (y,z,t)$ with $G_{yz}$.  Using a medium density $\rho$ of 1000 kg.m$^{-3}$, a compression wave speed of 1500 m.s$^{-1}$ and a shear wave speed of 5.5 m.s$^{-1}$, we calculated the displacements along space and time. Figure \ref{figGreen}-(A) represents resulting displacement maps along Z axis, 1.0, 1.5, 2.0, 2.5 and 3.0 ms after force application. The normalized displacement maps present many similarities with thelow-energy  experimental results of in  the Figure \ref{Figure2}, \ref{figElastoPVA}-(A),  with a initial central displacement directed outside the medium and the propagation of three half cycles.