deletions | additions       diff --git a/Simu disp maps.tex b/Simu disp maps.tex  index 7c8b789..c04ffe9 100644  --- a/Simu disp maps.tex  +++ b/Simu disp maps.tex 
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  This physical phenomenon was then modeled numerically. The vaporization was modeled as a point force directed along Z direction with a depth of 50 $\mu$m and increasing linearly from -2.5 to 0 mm and decreasing symmetrically from 0 to 2.5 mm, to simulate an approximate Gaussian shape. Propagation as a shear wave was calculated using Green operator as calculated by Aki Richards \cite{aki1980quantitative}:  \begin{equation}  u_z G_1  = \frac{\cos^2 \beta}{4\pi \rho c_p^2 r} \delta_P + \frac{\sin^2 \beta}{4\pi \rho c_s^2 r} \delta_S + \frac{3\cos^2 \beta-1}{4\pi \rho r^3} \tau Rect  G_2 = \frac{\cos \beta \sin \beta}{4\pi \rho c_p^2 r} \delta_P + \frac{-\sin \beta \cos \beta}{4\pi \rho c_s^2 r} \delta_S + \frac{3\cos \beta \sin \beta}{4\pi \rho r^3} \tau  Rect. \label{eq:akirichards}  \end{equation}  then  It used a medium density $\rho$ of 1000 kg.m$^{-3}$, a compression wave speed of 1500 m.s$^{-1}$ and a shear wave speed of 5.75 m.s$^{-1}$. Results are shown on Figure \ref{Figure3} which represents displacement maps along Y and Z axis 0.8, 1.6, 2.4, 3.2 and 4.0 ms after force application. The displacement maps present many similarities with the experimental results of the Figure \ref{Figure2}.