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\begin{figure} |
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|
\centering |
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\includegraphics[width=\linewidth]{rCutMaxFig.eps} |
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\caption |
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> |
\caption[An explanation of $r_{\text{cut}}$]{The yellow atom has all other images wrapped to itself as the center. If $r_{\text{cut}}=\text{box}/2$, then the distribution is uniform (blue atoms). However, when $r_{\text{cut}}>\text{box}/2$ the corners are disproportionately weighted (green atoms) vs the axial directions (shaded regions).} |
| 513 |
|
\label{introFig:rMax} |
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|
\end{figure} |
| 515 |
|
|
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< |
With the use of an $fix$, however, comes a discontinuity in the |
| 517 |
< |
potential energy curve (Fig.~\ref{fix}). To fix this discontinuity, |
| 518 |
< |
one calculates the potential energy at the $r_{\text{cut}}$, and add |
| 519 |
< |
that value to the potential. This causes the function to go smoothly |
| 520 |
< |
to zero at the cutoff radius. This ensures conservation of energy |
| 521 |
< |
when integrating the Newtonian equations of motion. |
| 516 |
> |
With the use of an $r_{\text{cut}}$, however, comes a discontinuity in |
| 517 |
> |
the potential energy curve (Fig.~\ref{introFig:shiftPot}). To fix this |
| 518 |
> |
discontinuity, one calculates the potential energy at the |
| 519 |
> |
$r_{\text{cut}}$, and adds that value to the potential, causing |
| 520 |
> |
the function to go smoothly to zero at the cutoff radius. This |
| 521 |
> |
shifted potential ensures conservation of energy when integrating the |
| 522 |
> |
Newtonian equations of motion. |
| 523 |
> |
|
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> |
\begin{figure} |
| 525 |
> |
\centering |
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> |
\includegraphics[width=\linewidth]{shiftedPot.eps} |
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> |
\caption[Shifting the Lennard-Jones Potential]{The Lennard-Jones potential is shifted to remove the discontiuity at $r_{\text{cut}}$.} |
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> |
\label{introFig:shiftPot} |
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> |
\end{figure} |
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|
|
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|
The second main simplification used in this research is the Verlet |
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|
neighbor list. \cite{allen87:csl} In the Verlet method, one generates |
