deletions | additions       diff --git a/A_snapshots_of_the_distribution__.tex b/A_snapshots_of_the_distribution__.tex  index 7651849..c73dc3a 100644  --- a/A_snapshots_of_the_distribution__.tex  +++ b/A_snapshots_of_the_distribution__.tex 
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A snapshots snapshot  of the distribution of the charge density as a function of time for the simulation using VisIt~\cite{HPV:VisIt} are is  shown in Fig.~\ref{fig:snapshot_copper}. At $t = 0~\text{attoseconds}$ (see Fig.~\ref{fig:snapshot_copper}a)  the $\mathrm{H^+}$ interacts with the neighboring $\mathrm{Cu}$ atoms charge density where some electron density is acquired. As $\mathrm{H^+}$ travels through the $\mathrm{Cu}$ crystal more electron density is acquired from the neighboring atoms as seen at $t = 91.65~\text{attoseconds}$.