deletions | additions       diff --git a/Simu disp maps.tex b/Simu disp maps.tex  index 0215ad7..bd764b2 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, of linear amplitude forces decreasing linearly  from0 to  2.5 to 0  mm (respectively0 to  -2.5 to 0  mm), with a depth of  100 $\mu$m in depth. $\mu$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}.