deletions | additions       diff --git a/Simu disp maps.tex b/Simu disp maps.tex  index 845f459..3ae0168 100644  --- a/Simu disp maps.tex  +++ b/Simu disp maps.tex 
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\label{eq:akirichards}  \end{equation}  where $\beta$ is the angle between the applied force and the axis y or z, $\rho$ the medium density, $c_p$ and $c_s$ the compression and shear wave speed respectively, $\delta_S$ and $\delta_P$ Dirac distribution indicating the position of the compression and shear waves along space and time, $\tau$ the time and $Rect$ the near-field term. The three terms correspond respectively to the far-field compression wave, the far-field shear wave and the near-field term.  In our simulation, we used an angle $\beta$ of 0 (force is aligned along Z axis), 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$^{-1}$.   Displacement can then be computed by convoluting $G_y$ and $G_z$ with time and spatial extent of the force:  \begin{equation} 
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\label{eq:akirichards2}  \end{equation}  where H is a 4-D matrix of the applied force along space and time.  We modeled here the vaporization as a point force directed along Z direction (so angle $\beta$ = 0)  during 100 $\mu$s 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 approximate a Gaussian shape). The medium density $\rho$ was taken equal to 1000 kg.m$^{-3}$, the compression wave speed to 1500 m.s$^{-1}$ and the shear wave speed to 5.75 m.s$^{-1}$.  Results are shown on Figure \ref{Figure3} which represents displacement maps between each frame 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}.