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atom in Fig.~\ref{fig:lipidModel}. |
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|
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\begin{figure} |
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< |
\epsfxsize=6in |
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< |
\epsfbox{lipidModel.epsi} |
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> |
\epsfbox{lipidModel.eps} |
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\caption{A representation of the lipid model. $\phi$ is the torsion angle, $\theta$ % |
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is the bend angle, $\mu$ is the dipole moment of the head group, and n is the chain length.} |
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\label{fig:lipidModel} |
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|
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\subsection{\label{sec:eam}Embedded Atom Model} |
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|
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< |
here there be Monsters |
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> |
Several molecular dynamics codes\cite{dynamo86} exist which have the |
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capacity to simulate metallic systems, including some that have |
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> |
parallel computational abilities\cite{plimpton93}. Potentials that |
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describe bonding transition metal |
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systems\cite{Finnis84,Ercolessi88,Chen90,Qi99,Ercolessi02} have a |
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attractive interaction which models the stabilization of ``Embedding'' |
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> |
a positively charged metal ion in an electron density created by the |
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free valance ``sea'' of electrons created by the surrounding atoms in |
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the system. A mostly repulsive pairwise part of the potential |
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> |
describes the interaction of the positively charged metal core ions |
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> |
with one another. A particular potential description called the |
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> |
Embedded Atom Method\cite{Daw84,FBD86,johnson89,Lu97}(EAM) that has |
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particularly wide adoption has been selected for inclusion in OOPSE. A |
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> |
good review of EAM and other metallic potential formulations was done |
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> |
by Voter.\cite{voter} |
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|
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+ |
The {\sc eam} potential has the form: |
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+ |
\begin{eqnarray} |
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V & = & \sum_{i} F_{i}\left[\rho_{i}\right] + \sum_{i} \sum_{j \neq i} |
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+ |
\phi_{ij}({\bf r}_{ij}) \\ |
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+ |
\rho_{i} & = & \sum_{j \neq i} f_{j}({\bf r}_{ij}) |
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+ |
\end{eqnarray} |
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+ |
|
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+ |
where $\phi_{ij}$ is a primarily repulsive pairwise interaction |
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+ |
between atoms $i$ and $j$.In the origional formulation of |
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+ |
EAM\cite{Daw84}, $\phi_{ij}$ was an entirely repulsive term, however |
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+ |
in later refinements to EAM have shown that nonuniqueness between $F$ |
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+ |
and $\phi$ allow for more general forms for $\phi$.\cite{Daw89} The |
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embedding function $F_{i}$ is the energy required to embedded an |
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+ |
positively-charged core ion $i$ into a linear supeposition of |
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+ |
sperically averaged atomic electron densities given by |
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+ |
$\rho_{i}$. There is a cutoff distance, $r_{cut}$, which limits the |
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+ |
summations in the {\sc eam} equation to the few dozen atoms |
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surrounding atom $i$ for both the density $\rho$ and pairwise $\phi$ |
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+ |
interactions. |
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+ |
|
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\subsection{\label{Sec:pbc}Periodic Boundary Conditions} |
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|
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\textit{Periodic boundary conditions} are widely used to simulate truly |
