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estimation of friction tensor from hydrodynamics theory into the |
| 99 |
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sophisticated rigid body dynamics. |
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|
| 101 |
< |
\section{Method{\label{methodSec}}} |
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> |
\section{Computational methods{\label{methodSec}}} |
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|
| 103 |
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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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|
|
| 363 |
< |
\subsection{Langevin dynamics for rigid particles of arbitrary shape} |
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> |
\subsection{Langevin dynamics for rigid particles of arbitrary shape\label{LDRB}} |
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|
| 365 |
|
Consider a Langevin equation of motions in generalized coordinates |
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\begin{equation} |
| 369 |
|
\end{equation} |
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where $M_i$ is a $6\times6$ generalized diagonal mass (include mass |
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|
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 |
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(\ref{LDGeneralizedForm}) consists of three generalized forces in |
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lab-fixed frame, systematic force $F_{s,i}$, dissipative force |
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$F_{f,i}$ and stochastic force $F_{r,i}$. While the evolution of the |
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\end{align*} |
| 517 |
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|
| 518 |
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\section{Results and discussion} |
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+ |
|
| 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 |
+ |
|
| 535 |
+ |
\begin{figure} |
| 536 |
+ |
\centering |
| 537 |
+ |
\includegraphics[width=\linewidth]{one_banana.eps} |
| 538 |
+ |
\caption[]{.} \label{langevin:banana} |
| 539 |
+ |
\end{figure} |
| 540 |
+ |
|
| 541 |
+ |
\begin{figure} |
| 542 |
+ |
\centering |
| 543 |
+ |
\includegraphics[width=\linewidth]{roughShell.eps} |
| 544 |
+ |
\caption[Rough Shell]{Rough Shell.} \label{langevin:roughShell} |
| 545 |
+ |
\end{figure} |
| 546 |
+ |
|
| 547 |
+ |
|
| 548 |
+ |
\begin{figure} |
| 549 |
+ |
\centering |
| 550 |
+ |
\includegraphics[width=\linewidth]{twoBanana.eps} |
| 551 |
+ |
\caption[Two Banana Shaped Molecules]{Two Banana Shaped Molecules.} |
| 552 |
+ |
\label{langevin:twoBanana} |
| 553 |
+ |
\end{figure} |
| 554 |
+ |
|
| 555 |
|
\section{Conclusions} |
