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estimation of friction tensor from hydrodynamics theory into the |
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sophisticated rigid body dynamics. |
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|
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< |
\section{Computational methods{\label{methodSec}}} |
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> |
\section{Computational Methods{\label{methodSec}}} |
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|
|
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\subsection{\label{introSection:frictionTensor}Friction Tensor} |
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Theoretically, the friction kernel can be determined using velocity |
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where $x_OR$, $y_OR$, $z_OR$ are the components of the vector |
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joining center of resistance $R$ and origin $O$. |
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|
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< |
\subsection{Langevin dynamics for rigid particles of arbitrary shape\label{LDRB}} |
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> |
\subsection{Langevin Dynamics for Rigid Particles of Arbitrary Shape\label{LDRB}} |
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|
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Consider a Langevin equation of motions in generalized coordinates |
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\begin{equation} |
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+ \frac{h}{2} {\bf \tau}^b(t + h) . |
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\end{align*} |
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|
518 |
< |
\section{Results and discussion} |
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> |
\section{Results and Discussion} |
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|
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The Langevin algorithm described in previous section has been |
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implemented in {\sc oopse}\cite{Meineke2005} and applied to the |
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studies of kinetics and thermodynamic properties in several systems. |
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|
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< |
\subsection{Temperature control} |
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> |
\subsection{Temperature Control} |
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|
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As shown in Eq.~\ref{randomForce}, random collisions associated with |
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the solvent's thermal motions is controlled by the external |
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\begin{center} |
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\begin{tabular}{|l|l|l|} |
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|
\hline |
549 |
< |
\eta & $\text{T}_{\text{avg}}$ & $\text{T}_{\text{rms}}$ \\ |
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> |
$\eta$ & $\text{T}_{\text{avg}}$ & $\text{T}_{\text{rms}}$ \\ |
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1 & 300.47 & 10.99 \\ |
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0.1 & 301.19 & 11.136 \\ |
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|
0.01 & 303.04 & 11.796 \\ |
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NVE (see green curve in Fig.~\ref{langevin:temperature}) which loses |
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the temperature control ability. |
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|
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– |
|
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\begin{figure} |
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|
\centering |
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|
\includegraphics[width=\linewidth]{temperature.eps} |
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|
temperature fluctuation versus time.} \label{langevin:temperature} |
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|
\end{figure} |
579 |
|
|
580 |
< |
\subsection{Langevin dynamics of banana-shaped molecule} |
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> |
\subsection{Langevin Dynamics of Banana Shaped Molecule} |
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|
|
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+ |
|
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+ |
|
584 |
|
\begin{figure} |
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|
\centering |
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\includegraphics[width=\linewidth]{one_banana.eps} |
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\begin{figure} |
591 |
|
\centering |
592 |
|
\includegraphics[width=\linewidth]{roughShell.eps} |
593 |
< |
\caption[Rough Shell]{Rough Shell.} \label{langevin:roughShell} |
593 |
> |
\caption[Rough shell model for banana shaped molecule]{Rough shell |
594 |
> |
model for banana shaped molecule.} \label{langevin:roughShell} |
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|
\end{figure} |
596 |
|
|
597 |
|
\begin{figure} |
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|
\centering |
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|
\includegraphics[width=\linewidth]{twoBanana.eps} |
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< |
\caption[Two Banana Shaped Molecules]{Two Banana Shaped Molecules.} |
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< |
\label{langevin:twoBanana} |
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> |
\caption[Snapshot from Simulation of Two Banana Shaped Molecules and |
601 |
> |
256 Pentane Molecules]{Snapshot from simulation of two Banana shaped |
602 |
> |
molecules and 256 pentane molecules.} \label{langevin:twoBanana} |
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\end{figure} |
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|
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|
\section{Conclusions} |