deletions | additions       diff --git a/In_the_low_velocity_cases__.tex b/In_the_low_velocity_cases__.tex  index e0195da..629378a 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 rather  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.