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\subsection{Extended Systems for other Ensembles} |
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\label{extended} |
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{\sc oopse} implements a |
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\subsubsection{Nose-Hoover Thermostatting} |
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To mimic the effects of being in a constant temperature ({\sc nvt}) |
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ensemble, {\sc oopse} uses the Nose-Hoover extended system |
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approach.\cite{Hoover85} In this method, the equations of motion for |
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the particle positions and velocities are |
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\begin{eqnarray} |
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\dot{{\bf r}} & = & {\bf v} \\ |
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\dot{{\bf v}} & = & \frac{{\bf f}}{m} - \chi {\bf v} |
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\label{eq:nosehoovereom} |
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\end{eqnarray} |
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$\chi$ is an ``extra'' variable included in the extended system, and |
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it is propagated using the first order equation of motion |
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\begin{equation} |
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\dot{\chi} = \frac{1}{\tau_{T}} \left( \frac{T}{T_{target}} - 1 \right) |
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\label{eq:nosehooverext} |
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\end{equation} |
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where $T_{target}$ is the target temperature for the simulation, and |
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$\tau_{T}$ is a time constant for the thermostat. |
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To select the Nose-Hoover {\sc nvt} ensemble, the {\tt ensemble = NVT;} |
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command would be used in the simulation's {\sc bass} file. There is |
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some subtlety in choosing values for $\tau_{T}$, and it is usually set |
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to values of a few ps. Within a {\sc bass} file, $\tau_{T}$ could be |
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set to 1 ps using the {\tt tauThermostat = 1000; } command. |
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