deletions | additions       diff --git a/Figure_ref_fig_force_on_proton_shows__.tex b/Figure_ref_fig_force_on_proton_shows__.tex  index 71f9ee8..ebaea27 100644  --- a/Figure_ref_fig_force_on_proton_shows__.tex  +++ b/Figure_ref_fig_force_on_proton_shows__.tex 
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Figure \ref{fig:force_on_proton} shows the force on proton with $v = 1.8 ~\mathrm{a.u.}$ vs. the distance traveled. Note ~\mathrm{a.u.}$. It is noted  that the force in the direction of the velocity (solid green) (dotted line)  does not average to zero, the average (negative) value agrees with the stopping power calculated from the energy increase (Figure \ref{fig:energy_distance}). Note It is important to note  that there is transient effect at first ($\lesssim 5~a_0$), then the projectile reenters in the periodic supercell ($\gtrsim 20.46~a_0$). The A  consistency between energy slope and drag force is discussed in Ref. earlier by Scheife {\emph et. al.}  \cite{Schleife_2015}%