98 |
|
estimation of friction tensor from hydrodynamics theory into the |
99 |
|
sophisticated rigid body dynamics. |
100 |
|
|
101 |
< |
\section{Method{\label{methodSec}}} |
101 |
> |
\section{Computational methods{\label{methodSec}}} |
102 |
|
|
103 |
|
\subsection{\label{introSection:frictionTensor}Friction Tensor} |
104 |
|
Theoretically, the friction kernel can be determined using velocity |
360 |
|
where $x_OR$, $y_OR$, $z_OR$ are the components of the vector |
361 |
|
joining center of resistance $R$ and origin $O$. |
362 |
|
|
363 |
< |
\subsection{Langevin dynamics for rigid particles of arbitrary shape} |
363 |
> |
\subsection{Langevin dynamics for rigid particles of arbitrary shape\label{LDRB}} |
364 |
|
|
365 |
|
Consider a Langevin equation of motions in generalized coordinates |
366 |
|
\begin{equation} |
369 |
|
\end{equation} |
370 |
|
where $M_i$ is a $6\times6$ generalized diagonal mass (include mass |
371 |
|
and moment of inertial) matrix and $V_i$ is a generalized velocity, |
372 |
< |
$V_i = V_i(v_i,\omega _i)$. The right side of Eq. |
372 |
> |
$V_i = V_i(v_i,\omega _i)$. The right side of Eq.~ |
373 |
|
(\ref{LDGeneralizedForm}) consists of three generalized forces in |
374 |
|
lab-fixed frame, systematic force $F_{s,i}$, dissipative force |
375 |
|
$F_{f,i}$ and stochastic force $F_{r,i}$. While the evolution of the |
516 |
|
\end{align*} |
517 |
|
|
518 |
|
\section{Results and discussion} |
519 |
+ |
|
520 |
+ |
The Langevin algorithm described in Sec.~\ref{LDRB} has been |
521 |
+ |
implemented in {\sc oopse}\cite{Meineke2005} and applied to several |
522 |
+ |
test systems. |
523 |
+ |
|
524 |
+ |
\subsection{Langevin dynamics of} |
525 |
+ |
|
526 |
+ |
\begin{figure} |
527 |
+ |
\centering |
528 |
+ |
\includegraphics[width=\linewidth]{temperature.eps} |
529 |
+ |
\caption[]{.} \label{langevin:temperature} |
530 |
+ |
\end{figure} |
531 |
|
|
532 |
+ |
\subsection{LD of banana-shaped molecule} |
533 |
+ |
|
534 |
+ |
\begin{figure} |
535 |
+ |
\centering |
536 |
+ |
\includegraphics[width=\linewidth]{one_banana.eps} |
537 |
+ |
\caption[]{.} \label{langevin:banana} |
538 |
+ |
\end{figure} |
539 |
+ |
|
540 |
|
\section{Conclusions} |