| 579 |
|
temperature fluctuation versus time.} \label{langevin:temperature} |
| 580 |
|
\end{figure} |
| 581 |
|
|
| 582 |
< |
\subsection{Langevin Dynamics of Banana Shaped Molecule} |
| 582 |
> |
\subsection{Langevin Dynamics of Banana Shaped Molecules} |
| 583 |
|
|
| 584 |
|
In order to verify that Langevin dynamics can mimic the dynamics of |
| 585 |
|
the systems absent of explicit solvents, we carried out two sets of |
| 586 |
|
simulations and compare their dynamic properties. |
| 587 |
– |
|
| 587 |
|
Fig.~\ref{langevin:twoBanana} shows a snapshot of the simulation |
| 588 |
|
made of 256 pentane molecules and two banana shaped molecules at |
| 589 |
|
273~K. It has an equivalent implicit solvent system containing only |
| 591 |
|
calculate the hydrodynamic properties of the banana shaped molecule, |
| 592 |
|
we create a rough shell model (see Fig.~\ref{langevin:roughShell}), |
| 593 |
|
in which the banana shaped molecule is represented as a ``shell'' |
| 594 |
< |
made of 2266 small identical beads with size of 0.3 $\AA$ on the |
| 594 |
> |
made of 2266 small identical beads with size of 0.3 \AA on the |
| 595 |
|
surface. Applying the procedure described in |
| 596 |
|
Sec.~\ref{introEquation:ResistanceTensorArbitraryOrigin}, we |
| 597 |
|
identified the center of resistance at $(0, 0.7482, -0.1988)$, as |
| 606 |
|
0.2057&4.846e-14&1.5036e-14&-3.904e-13&3.219&10.7373\\ |
| 607 |
|
\end{array}} \right). |
| 608 |
|
\] |
| 609 |
< |
|
| 610 |
< |
|
| 609 |
> |
Curves of velocity auto-correlation functions in |
| 610 |
> |
Fig.~\ref{langevin:vacf} were shown to match each other very well. |
| 611 |
> |
However, because of the stochastic nature, simulation using Langevin |
| 612 |
> |
dynamics was shown to decay slightly fast. In order to study the |
| 613 |
> |
rotational motion of the molecules, we also calculated the auto- |
| 614 |
> |
correlation function of the principle axis of the second GB |
| 615 |
> |
particle, $u$. |
| 616 |
|
|
| 617 |
|
\begin{figure} |
| 618 |
|
\centering |
| 632 |
|
\begin{figure} |
| 633 |
|
\centering |
| 634 |
|
\includegraphics[width=\linewidth]{vacf.eps} |
| 635 |
< |
\caption[Plots of Velocity Auto-correlation functions]{Velocity |
| 636 |
< |
Auto-correlation function of NVE (blue) and Langevin dynamics |
| 637 |
< |
(red).} \label{langevin:twoBanana} |
| 635 |
> |
\caption[Plots of Velocity Auto-correlation Functions]{Velocity |
| 636 |
> |
auto-correlation functions in NVE (blue) and Langevin dynamics |
| 637 |
> |
(red).} \label{langevin:vacf} |
| 638 |
|
\end{figure} |
| 639 |
|
|
| 640 |
|
\begin{figure} |
| 641 |
|
\centering |
| 642 |
|
\includegraphics[width=\linewidth]{uacf.eps} |
| 643 |
< |
\caption[Snapshot from Simulation of Two Banana Shaped Molecules and |
| 644 |
< |
256 Pentane Molecules]{Snapshot from simulation of two Banana shaped |
| 645 |
< |
molecules and 256 pentane molecules.} \label{langevin:twoBanana} |
| 643 |
> |
\caption[Auto-correlation functions of the principle axis of the |
| 644 |
> |
middle GB particle]{Auto-correlation functions of the principle axis |
| 645 |
> |
of the middle GB particle in NVE (blue) and Langevin dynamics |
| 646 |
> |
(red).} \label{langevin:twoBanana} |
| 647 |
|
\end{figure} |
| 648 |
|
|
| 649 |
|
\section{Conclusions} |
| 650 |
+ |
|
| 651 |
+ |
We have presented a new Langevin algorithm by incorporating the |
| 652 |
+ |
hydrodynamics properties of arbitrary shaped molecules into an |
| 653 |
+ |
advanced symplectic integration scheme. The temperature control |
| 654 |
+ |
ability of this algorithm was demonstrated by a set of simulations |
| 655 |
+ |
with different viscosities. It was also shown to have significant |
| 656 |
+ |
advantage of producing rapid thermal equilibration over |
| 657 |
+ |
Nos\'{e}-Hoover method. Further studies in systems involving banana |
| 658 |
+ |
shaped molecules illustrated that the dynamic properties could be |
| 659 |
+ |
preserved by using this new algorithm as an implicit solvent model. |
