deletions | additions       diff --git a/Simu disp maps.tex b/Simu disp maps.tex  index 0d4aba7..1053a38 100644  --- a/Simu disp maps.tex  +++ b/Simu disp maps.tex 
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\end{equation}  Using high-energy experimental parameter, $\zeta \approx \gamma^{-1} = 40 \mu$m (average depth of absorption), $\lambda$ = 2 GPa (first Lamé's coefficient of water), $L$ = 2.2 MJ.kg$^{-1}$ (vaporization latent heat of water) and $T_V-T_0$ = 373-298 = 75 K, we obtain a displacement $u_z$ approximately equal to 2.9 $\mu$m. While slightly higher, this value is in good agreement with experimental displacement (2.5 $\mu$m).  To calculate the propagation of the displacement along space and time, we modeled the ablation regime as a point force directed along Z direction with a depth of 40 $\mu$m during 100 $\mu$s and of constant value from -2.5 to 2.5 mm. The magnitude of the force is stored in a matrix $H_z^{abla}(x,y,z,t)$. $H_z^{abla}(y,z,t)$.  Propagation as a shear wave was calculated using Green operators $G_{zz}$ \cite{aki1980quantitative}: \begin{equation}  G_{zz}(r,\theta,z,t) G_{zz}(r,\theta,t)  = \frac{\cos^2 \theta}{4\pi \rho c_p^2 r} \delta(t-\frac{r}{c_p}) + \frac{\sin^2 \theta}{4\pi \rho c_s^2 r} \delta(t-\frac{r}{c_s}) + \frac{3\cos^2 \theta-1}{4\pi \rho r^3} \int_{r/c_p}^{r/c_s}{\tau f_{NF}(t)dt} \delta(t-\tau)d\tau}  \label{eq:Gzz}  \end{equation}  with same notations as in equation \ref{eq:Gyz}.  Displacements can again be computed by convoluting the applied force 4-D matrix $H_z^{abla}(x,y,z,t)$ $H_z^{abla}(y,z,t)$  with $G_{zz}$. Using same values for the physical quantities as previously, results are illustrated in Figure \ref{figGreen}-(B) which represents displacement maps along Z axis, 1.0, 1.5, 2.0, 2.5 and 3.0 ms after force application. The displacement maps present many similarities with the experimental results of the Figure \ref{Figure2}: initial displacement is directed inside the medium and only two half cycles are propagating.