deletions | additions       diff --git a/In_the_low_velocities_cases__.tex b/In_the_low_velocities_cases__.tex  index 6911415..b160f8e 100644  --- a/In_the_low_velocities_cases__.tex  +++ b/In_the_low_velocities_cases__.tex 
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In the low velocities 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 energyand  we do and an  oscillatory fit to the resulting curve. Figure \ref{fig:fit_graph} explains how the slopes are evaluated in these cases.   For higher velocities, a linear fit alone is enough to obtain reasonable values with small relative errors. errors.%