deletions | additions       diff --git a/Simu disp maps.tex b/Simu disp maps.tex  index dfe6ce4..cbf41b5 100644  --- a/Simu disp maps.tex  +++ b/Simu disp maps.tex 
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u_z = \frac{\zeta}{\rho \lambda}\frac{I^2}{(L+C(T_V-T_0))^2}  \label{eq:deplAblaApprox}  \end{equation}  Using high-energy experimental parameters, $\zeta \approx \gamma^{-1} \gamma^{-1}$  = 40 \mu$m $\mu$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 $u_z$ of 2.9 $\mu$m. Again, this value is inhigh  agreement with the experimentally obtained displacement (2.5 $\mu$m). Both theoretical and experimental displacements are directed towards the inside of the medium (see arrow in the white circle in Figure \ref{figElastoPVA}-(B)). Figures \ref{figElastoPVA}-(B) and \ref{figGreen}-(B)).  To calculate the propagation of the displacement as a function of space and time, we modeled the ablative regime as a point force directed along the Z axis with a depth of 40 $\mu$m and a constant value from -2.5 to 2.5 mm. The magnitude of the force is was  stored in a matrix, $H_z^{abla}(y,z,t)$. Displacements along the Z axis are again equal to the convolution between $H_z^{abla}$ and $G_{zz}$ \cite{aki1980quantitative}: \begin{equation}  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})  \label{eq:Gzz} 
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\end{equation}  with the same notations as presented in equation \ref{eq:Gyz}.  Using the physical quantities quantity  values previously defined, displacement maps along the Z axis were calculated 1.0, 1.5, 2.0, 2.5, and 3.0 ms after force application, as illustrated in Figure \ref{figGreen}-(B). The displacement maps present many similarities to the experimental results of Figure \ref{figElastoPVA}-(B), with initial displacement directed towards the inside of the medium, and propagation of only two half cycles. The ablative regime was also confirmed visually. At high power, a paler colored disk of the same size as the beam diameter appeared at the site of laser impact on the phantom, which is consistent with the theory of partial vaporization of the medium. This was not observed in the low-energy experiments.