deletions | additions       diff --git a/geometry optimization.tex b/geometry optimization.tex  index f3d628f..e0ee9c4 100644  --- a/geometry optimization.tex  +++ b/geometry optimization.tex 
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%  \begin{equation}  \label{eq:velocity_fire}  \vec{\mathrm{v}}(t) \mathrm{\vec{v}}(t)  \rightarrow \vec{\mathrm{V}} \mathrm{\vec{V}}  = (1-\alpha)\vec{\mathrm{v}}(t) (1-\alpha)\mathrm{\vec{v}}(t)  + \alpha |\vec{\mathrm{v}}(t)|\hat{F}(t)\ |\mathrm\vec{{v}}(t)|\hat{F}(t)\  , \end{equation}  %  where $\vec{\mathrm{v}}$ $\mathrm{\vec{v}}$  is the velocity of the atoms, $\alpha$ is an adaptative parameter, and $\hat{F}$ is an unitary vector in the direction of the force $\vec{F}$. By doing this velocity modification, the acceleration of the atoms are given by %  \begin{equation}  \label{eq:acceleration_fire}