Pol Grasland-Mongrain edited The_two_regimes_have.tex  over 8 years ago

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The two regimes present different displacements patterns \cite{undefined}. As previously described, the thermoelastic regime acts as local dipolar forces parallel to the surface. Thus, the medium stretches locally parallel to the surface, resulting two strong opposite displacements along Y axis (parallel to the surface) and a weak displacement outside the medium along Z axis (normal to the surface). In the ablative regime, the point force in the medium displaces strongly the surface of the medium along Z axis, with weak displacements along Y axis. Initial displacement along Z axis, as seen at $t$=0.8 ms in Figure \ref{Figure2}, is negative, i.e., the displacement is inside the medium along Z axis, and the displacement along Y axis (approx. 1.5 $\mu$m) is quite smaller than the one along Z axis (approx. 3 $\mu$m).  For a comparison with theory, the normalized displacement along space and time created by a force over a disk of 5 mm in diameter and 100 $\mu$m in depth has been represented on Figure \ref{Figure3}. It was calculated in a three-dimensional simulation with spatial steps of 10 $\mu$m and temporal steps of 50 $\mu$m $\mu$s  using Green operator \cite{aki1980quantitative} with a medium density $\rho$ of 1000 kg.m$^{-3}$, a bulk modulus $K$ of 2.3 GPa and a shear modulus $\mu$ of 16 kPa, corresponding to a shear wave speed of 4 m.s$^{-1}$. The displacement maps present many similarities with the experimental results which would agree with the conclusion of an ablative regime. This conclusion 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 melting of a fraction of the material.% From equation \ref{eq:eqTemperature}, with the laser characteristics and an initial temperature $T_0$ of 25 $^o$C, $T$ is higher than 50 $^o$C, approximate phantom melting temperature, over \textcolor{red}{XXX} $\mu$.