deletions | additions       diff --git a/In_the_low_velocities_cases__.tex b/In_the_low_velocities_cases__.tex  index 6bd10ee..3b47dda 100644  --- a/In_the_low_velocities_cases__.tex  +++ b/In_the_low_velocities_cases__.tex 
...
In the low velocities cases extracting a slope becomes more challenging, first because a longer 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 do and oscillatory fit to the resulting curve.  Figure \ref{fig:fit_graph} explains how the slopes of Figure \ref{fig:energy_distance} are evaluated in these cases.   For higher velocities, a linear fit alone is enough to obtain reasonable error values.% values with small relative errors.