deletions | additions       diff --git a/Simu disp maps.tex b/Simu disp maps.tex  index 3b74d7d..acd9b8a 100644  --- a/Simu disp maps.tex  +++ b/Simu disp maps.tex 
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%This affirmation is confirmed by the observation of a disk of paler color of the same size as the beam diameter at the impact location of the laser on the phantom, which could correspond to a vaporization of a fraction of the material.  % This physical phenomenon was then modeled numerically. The thermal dilatation was simulated by calculating the displacement created by two opposite forces decreasing linearly from 2.5 to 0 mm (respectively -2.5 to 0 mm), with a depth of 100 $\mu$m. Propagation as a shear wave was calculated using Green operator \cite{aki1980quantitative}, using a medium density $\rho$ of 1000 kg.m$^{-3}$, a compression wave speed of 1500 m.s$^{-1}$ and a shear wave speed of 4 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}. If enough energy is deposited, the local increase of temperature can also vaporize a part of the surface of the medium \cite{scruby1990laser}.Ejection of particles leads to a displacement inside the medium which can create shear waves: this constitutes the \textit{ablative regime}.  Solving equation \ref{eq:eqChaleurApprox} with same experimental parameters as before but a laser energy of 200 mJ, we find a maximum increase of temperature of 60 K, which leads to a maximum temperature of about 360 K. While slightly below to the vaporization point of our medium, supposed close to 373K (water vaporization temperature), it can be be sufficient to vaporize the medium; Moreover, it has been demonstrated that the presence of small particles like the graphite particles in our medium acts as nucleation sites for vaporization, which facilitate the vaporization of the medium at lower temperature \cite{Alimpiev_1995}. Vaporization of particles leads by reaction to displacements inside the medium, which can create shear waves: this constitutes the \textit{ablative regime}. To describe this vaporization, we suppose the medium as homogeneous and isotropic. The stress $\sigma_{zz}$ is, similarly to the previous section, the sum of the P-wave modulus and a term given by the second law of motion \cite{scruby1990laser}:  \begin{equation}