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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).} |
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\label{introFig:rMax} |
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\end{figure} |
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|
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With the use of an $fix$, however, comes a discontinuity in the |
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potential energy curve (Fig.~\ref{fix}). To fix this discontinuity, |
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one calculates the potential energy at the $r_{\text{cut}}$, and add |
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that value to the potential. This causes the function to go smoothly |
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to zero at the cutoff radius. This ensures conservation of energy |
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when integrating the Newtonian equations of motion. |
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With the use of an $r_{\text{cut}}$, however, comes a discontinuity in |
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the potential energy curve (Fig.~\ref{introFig:shiftPot}). To fix this |
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discontinuity, one calculates the potential energy at the |
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$r_{\text{cut}}$, and adds that value to the potential, causing |
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the function to go smoothly to zero at the cutoff radius. This |
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shifted potential ensures conservation of energy when integrating the |
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Newtonian equations of motion. |
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|
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\begin{figure} |
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\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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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 |