deletions | additions       diff --git a/Let_s_describe_the_phenomenon__.tex b/Let_s_describe_the_phenomenon__.tex  index dea3a41..ed3da3b 100644  --- a/Let_s_describe_the_phenomenon__.tex  +++ b/Let_s_describe_the_phenomenon__.tex 
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\end{equation}  where $\lambda + 2 \mu$ is the P-wave modulus and $\lambda + \frac{2}{3}\mu$ the bulk modulus with $\lambda$ and $\mu$ respectively the first and second Lamé's coefficient, $\alpha$ is the thermal dilatation coefficient and $\zeta$ the average depth of laser beam absorption. In the absence of external constraints normal to the surface, the stress across the surface must be zero, i.e. $\sigma_{zz} (z=0) = 0$, so that equation \ref{eq:stressThermo} can be integrated, giving a displacement from the surface $u_z = \frac{(3\lambda + 2\mu)}{(\lambda + 2\mu)} \frac{\alpha E \zeta}{\rho C S \zeta$. As in a biological soft tissues, $\mu \ll \lambda$, the displacement can be approximated as:  \begin{equation}  u_z = \frac{3 \alpha E}{\rho C S} \label{eq:deplThermo}  \end{equation}  Taking as an order of magnitude $\alpha$ = 70.10$^{-6}$ K$^{-1}$ (water linear thermal dilatation coefficient), $E$ = 200 mJ, $\rho$ = 1000 kg.m$^{-3}$ (water density), $C$ = 4180 kg.m$^{-3}$ (water calorific capacity) and $S$ = 20 mm$^2$, we obtain a displacement $u_z$= 0.5 $\mu$m. This value is slightly smaller than the experimental displacement (about 3 $\mu$m). This local displacement can lead to shear waves because of the limited size of the source. In a 3D model, displacements along X and Y axis would also occurs, as the local expansion acts as dipolar forces parallel to the surface, but calculus is beyond the scope of this article.