deletions | additions       diff --git a/In_the_low_velocity_cases__.tex b/In_the_low_velocity_cases__.tex  index cef3e08..e0195da 100644  --- a/In_the_low_velocity_cases__.tex  +++ b/In_the_low_velocity_cases__.tex 
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In the low velocity cases extracting a slope becomes more challenging,   first because a longer time simulation is required to sample the crystalline structure and second because the natural oscillations associated with the crystal periodicity becomes relatively larger.   For the channeling cases, we subtract the adiabatic energy from time-dependent energy and we perform an oscillatory fit to the resulting curve.   Fig. \ref{fig:fit_graph} explains how the slopes of Fig. \ref{fig:energy_distance}  are evaluated in these cases. For higher velocities, a linear fit alone is enough to obtain reasonable values with small relative errors.%