deletions | additions       diff --git a/The_absorption_of_the_laser__.tex b/The_absorption_of_the_laser__.tex  index ef59c99..c51a90c 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. This value is slightly higher than the experimental displacement (about 0.02 $\mu$m). Dilatation along X and Y axis also occurs and lead to stronger displacements than along Z. We modeled them thus the thermodilatation  as two opposite forces directed along Y direction with a depth of 50 $\mu$m and decreasing linearly from 2.5 to 0 mm (respectively -2.5 to 0 mm), to simulate an approximate Gaussian shape \cite{Davies_1993}. Propagation as a shear wave along Z axis was calculated using Green operators $G_{yz}$ as calculated by Aki Richards \cite{aki1980quantitative}: \begin{equation}  G_{yz} (r,\theta,z)= \frac{\cos \beta \sin \theta}{4\pi \rho c_p^2 r} \delta_P + \frac{-\sin \theta \cos \theta}{4\pi \rho c_s^2 r} \delta_S + \frac{3\cos \theta \sin \theta}{4\pi \rho r^3} \int_{r/c_p}^{r/c_s}{\tau \delta_{NF}}  \label{eq:Gyz}