| 98 |
|
estimation of friction tensor from hydrodynamics theory into the |
| 99 |
|
sophisticated rigid body dynamics. |
| 100 |
|
|
| 101 |
< |
\section{Computational methods{\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\label{LDRB}} |
| 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} |
| 515 |
|
+ \frac{h}{2} {\bf \tau}^b(t + h) . |
| 516 |
|
\end{align*} |
| 517 |
|
|
| 518 |
< |
\section{Results and discussion} |
| 518 |
> |
\section{Results and Discussion} |
| 519 |
|
|
| 520 |
|
The Langevin algorithm described in previous section has been |
| 521 |
|
implemented in {\sc oopse}\cite{Meineke2005} and applied to the |
| 522 |
|
studies of kinetics and thermodynamic properties in several systems. |
| 523 |
|
|
| 524 |
< |
\subsection{Temperature control} |
| 524 |
> |
\subsection{Temperature Control} |
| 525 |
|
|
| 526 |
|
As shown in Eq.~\ref{randomForce}, random collisions associated with |
| 527 |
|
the solvent's thermal motions is controlled by the external |
| 570 |
|
NVE (see green curve in Fig.~\ref{langevin:temperature}) which loses |
| 571 |
|
the temperature control ability. |
| 572 |
|
|
| 573 |
– |
|
| 573 |
|
\begin{figure} |
| 574 |
|
\centering |
| 575 |
|
\includegraphics[width=\linewidth]{temperature.eps} |
| 577 |
|
temperature fluctuation versus time.} \label{langevin:temperature} |
| 578 |
|
\end{figure} |
| 579 |
|
|
| 580 |
< |
\subsection{Langevin dynamics of banana-shaped molecule} |
| 580 |
> |
\subsection{Langevin Dynamics of Banana Shaped Molecule} |
| 581 |
|
|
| 582 |
+ |
|
| 583 |
+ |
|
| 584 |
|
\begin{figure} |
| 585 |
|
\centering |
| 586 |
|
\includegraphics[width=\linewidth]{one_banana.eps} |
| 590 |
|
\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} |
| 595 |
|
\end{figure} |
| 596 |
|
|
| 597 |
|
\begin{figure} |
| 598 |
|
\centering |
| 599 |
|
\includegraphics[width=\linewidth]{twoBanana.eps} |
| 600 |
< |
\caption[Two Banana Shaped Molecules]{Two Banana Shaped Molecules.} |
| 601 |
< |
\label{langevin:twoBanana} |
| 600 |
> |
\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} |
| 603 |
|
\end{figure} |
| 604 |
|
|
| 605 |
|
\section{Conclusions} |
