deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index 7e7c7cd..d34ea1a 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
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%Even if the sample is mainlyeFor low concentration medium, $\gamma$ is hard to calculate in our case, as the sample is composed of different materials, but the graphite, even in low concentration, absorbate much more than other components, so we can approximate $\gamma \approx \gamma_{graphite}$. For graphite particles of 1.85 $\mu$m at a concentration of 10 g.L$^{-1}$, the order of magnitude of $\gamma$ is 10$^4$ m$^{-1}$, meaning that most of the radiation is absorbed in the first hundred of micrometers of sample.  This is quite higher than metals where the radiation is absorbed within a few nanometres.  The absorption of the laser beam by the medium gives then rise to an absorbed optical energy $q = \gamma I$. Assuming that all the optical energy is converted to heat, a local increase of temperature appears. Temperature distribution $T$ in absence of melting  can be computed using heat equation: \begin{equation}  \frac{\partial T}{\partial t} = \kappa \nabla ^2 T + \frac{q}{\rho C}  \label{eq:eqChaleur}  \end{equation}  where $\rho$ is the density, $C$ the heat capacity and $\kappa$ the thermal diffusivity.  The thermal diffusion path, equal to $\sqrt{4\kappa t}$, with $t$ the laser emission duration (20 ns) and $\kappa$ = 1.43 10$^{-7}$ m$^2$.s$^{-1}$ for water \cite{Blumm_2003}, is equal to 0.1 $\mu$m. As $\gamma^{-1} \gg \sqrt{4\kappa t}$, propagation of heat is negligible during laser emission, and so  term $k \nabla ^2 T$ can be neglected in equation \ref{eq:eqChaleur}. Combination with equation \ref{eq:opticalIntensity} and integration over time lead then allows  to a calculate the  temperature $T$ at the end of the laser emission:  \begin{equation}  T = T_0 + \frac{\gamma}{S \rho C} E \exp(-\gamma r)  \label{eq:eqTemperature}  \end{equation}  where $T_0$ is the initial temperature of the medium. emission (discarding any potential melting effects).  The local increase of temperature can lead to two main effects creating elastic waves: (1) thermoelastic expansion and (2) ablation of medium. In metals, transition from first to second regime occurs approximately about 10$^7$ W.cm$^{-2}$. This is equal to the energy of the laser we used, so the predominant regime in our experiment cannot be determined yet. 
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