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a couple more figure tweaks
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lammps-tutorials.tex

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@@ -3731,7 +3731,8 @@ \subsubsection{Adding water}
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\begin{note}
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{\color{blue}In practice, it is possible to use both \lmpcmd{vashishta} and
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\lmpcmd{lj/cut/tip4p/long} pair styles by employing the \lmpcmd{pair\_style hybrid}
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\lmpcmd{lj/cut/tip4p/long} pair styles at the same time by employing the
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\lmpcmd{pair\_style hybrid}
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command. However, hybridizing force fields should be done with caution, as there
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is no guarantee that the resulting force field will produce meaningful results.}
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\end{note}
@@ -4157,7 +4158,7 @@ \subsubsection{Method 1: Free sampling}
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A \lmpcmd{dump image} command was also added for system visualization.
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{\color{blue} The other commands should also be familiar from previous tutorials.}
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Finally, let us perform an equilibration of 50000 steps,
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\noindent Finally, let us perform an equilibration of 50000 steps,
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using a timestep of $2\,\text{fs}$, corresponding to a total duration of $100\,\text{ps}$:
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\begin{lstlisting}
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timestep 2.0
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\paragraph{Data analysis}
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\begin{figure}
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\centering
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\includegraphics[width=\linewidth]{US-system-unbiased}
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\caption{Snapshot of the system simulated during the free sampling
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step of \hyperref[umbrella-sampling-label]{Tutorial 7}.
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The atoms density is the lowest in the central
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part of the box, \lmpcmd{mymes}. Here,
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$U_0 = 0.36~\text{kcal/mol}$, $\delta = 1.0~\text{\AA{}}$, and $x_0 = 10~\text{\AA{}}$.}
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\label{fig:US-system-unbiased}
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\end{figure}
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Once the simulation is complete, the density profile from \flecmd{free-sampling.dat}
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shows that the density in the center of the box is
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about two orders of magnitude lower than inside the reservoir (Fig.~\ref{fig:US-density}\,a).
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is excellent, despite some noise in the central part, where fewer data points
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are available due to the repulsive potential.
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\begin{figure}
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\centering
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\includegraphics[width=\linewidth]{US-system-unbiased}
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\caption{Snapshot of the system simulated during the free sampling
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step of \hyperref[umbrella-sampling-label]{Tutorial 7}.
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The atoms density is the lowest in the central
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part of the box, \lmpcmd{mymes}. Here,
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$U_0 = 0.36~\text{kcal/mol}$, $\delta = 1.0~\text{\AA{}}$, and $x_0 = 10~\text{\AA{}}$.}
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\label{fig:US-system-unbiased}
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\end{figure}
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\paragraph{The limits of free sampling}
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Increasing the value of $U_0$ reduces the average number of atoms in the central
@@ -4381,6 +4382,17 @@ \subsubsection{Method 2: Umbrella sampling}
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\paragraph{WHAM algorithm}
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\begin{figure}
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\centering
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\includegraphics[width=\linewidth]{US-free-energy}
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\caption{The potential, $U$, as a function of $x$, measured using umbrella
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sampling during \hyperref[umbrella-sampling-label]{Tutorial 7} (blue disks),
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is compared to the imposed potential given in Eq.~\eqref{eq:U}
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(dark line). Parameters are $U_0 = 2.38~\text{kcal/mol}$, $\delta = 1.0~\text{\AA{}}$,
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and $x_0 = 10~\text{\AA{}}$.}
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\label{fig:US-freenergy}
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\end{figure}
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To generate the free energy profile from the particle positions saved in
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the \flecmd{umbrella-sampling.i.dat} files, we use the
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WHAM~\cite{kumar1992weighted,kumar1995multidim} algorithm as implemented
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Achieving similar results through free sampling would require performing extremely
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long and computationally expensive simulations.
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\begin{figure}
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\centering
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\includegraphics[width=\linewidth]{US-free-energy}
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\caption{The potential, $U$, as a function of $x$, measured using umbrella
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sampling during \hyperref[umbrella-sampling-label]{Tutorial 7} (blue disks),
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is compared to the imposed potential given in Eq.~\eqref{eq:U}
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(dark line). Parameters are $U_0 = 2.38~\text{kcal/mol}$, $\delta = 1.0~\text{\AA{}}$,
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and $x_0 = 10~\text{\AA{}}$.}
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\label{fig:US-freenergy}
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\end{figure}
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\subsection{Tutorial 8: Reactive Molecular Dynamics}
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\label{bond-react-label}
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