deletions | additions       diff --git a/The_absorption_of_the_laser__.tex b/The_absorption_of_the_laser__.tex  index 692e967..2590971 100644  --- a/The_absorption_of_the_laser__.tex  +++ b/The_absorption_of_the_laser__.tex 
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\end{equation}  where $\rho$ is the density, $C$ the heat capacity and $\kappa$ the thermal diffusivity. The thermal diffusion path, equal to $\sqrt{4\kappa \tau}$, with $\tau$ = 10 ns the laser emission duration and $\kappa$ = 1.43 10$^{-7}$ m$^2$.s$^{-1}$ for water \cite{Blumm_2003}, is approximately equal here to 80 nm. As $\gamma^{-1} \gg \sqrt{4\kappa t}$, propagation of heat is negligible during laser emission, so that equation \ref{eq:eqChaleur} can be simplified as:  \begin{equation}  \frac{\partial T}{\partial t} = \frac{\gamma I}{\rho C} = \frac{1}{\rho C S} \frac{dE}{dt}  \label{eq:eqChaleurApprox}  \end{equation}  Substituting low-energy experimental parameters ($\gamma^{-1} \approx$ 50 40  $\mu$m$^{-1}$, $S$ = 20 mm$^{2}$, $E$ = 10 mJ, $\rho$ = 1000 kg.m$^{-3}$, $C$ = 4180 J.kg$^{-1}$.K$^{-1}$) lead to a maximum increase of temperature of 3 K. This local increase of temperature gives rise to a local dilatation of the medium. The induced displacements can then lead to shear waves: this constitutes the \textit{thermoelastic regime}. To describe this dilatation, we take a homogeneous and isotropic medium and as the depth of absorption (about 50 $\mu$m) is hundred times smaller than the beam diameter (5 mm), we have adopted a 1D model. The stress $\sigma_{zz}$ is the sum between the axial strain component and the thermal expansion component \cite{scruby1990laser}:  \begin{equation}