deletions | additions       diff --git a/The_absorption_of_the_laser__.tex b/The_absorption_of_the_laser__.tex  index a20443d..209536a 100644  --- a/The_absorption_of_the_laser__.tex  +++ b/The_absorption_of_the_laser__.tex 
...
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 the experimental images in the middle of the beam, as indicated by the white circle in the figure \ref{figElastoPVA}. \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}