| 18 |
|
in the microcanonical ensemble have been extensively studied over |
| 19 |
|
the last two decades. Matubayasi developed a |
| 20 |
|
time-reversible integrator for rigid bodies in quaternion |
| 21 |
< |
representation\cite{Matubayasi1999}. Although it is not symplectic, this integrator still |
| 21 |
> |
representation.\cite{Matubayasi1999} Although it is not symplectic, this integrator still |
| 22 |
|
demonstrates a better long-time energy conservation than Euler angle |
| 23 |
|
methods because of the time-reversible nature. Extending the |
| 24 |
|
Trotter-Suzuki factorization to general system with a flat phase |
| 32 |
|
An alternative integration scheme utilizing the rotation matrix |
| 33 |
|
directly proposed by Dullweber, Leimkuhler and McLachlan (DLM) also |
| 34 |
|
preserved the same structural properties of the Hamiltonian |
| 35 |
< |
propagator\cite{Dullweber1997}. In this section, the integration |
| 35 |
> |
propagator.\cite{Dullweber1997} In this section, the integration |
| 36 |
|
scheme of DLM method will be reviewed and extended to other |
| 37 |
|
ensembles. |
| 38 |
|
|
| 581 |
|
|
| 582 |
|
Theoretically, the surface tension $\gamma$ of a stress free |
| 583 |
|
membrane system should be zero since its surface free energy $G$ is |
| 584 |
< |
minimum with respect to surface area $A$, |
| 584 |
> |
minimum with respect to surface area $A$, |
| 585 |
|
\begin{equation} |
| 586 |
|
\gamma = \frac{{\partial G}}{{\partial A}}=0. |
| 587 |
|
\end{equation} |
| 618 |
|
|
| 619 |
|
Based on the fluctuation-dissipation theorem, a force |
| 620 |
|
auto-correlation method was developed by Roux and Karplus to |
| 621 |
< |
investigate the dynamics of ions inside ion channels\cite{Roux1991}. |
| 621 |
> |
investigate the dynamics of ions inside ion channels.\cite{Roux1991} |
| 622 |
|
The time-dependent friction coefficient can be calculated from the |
| 623 |
< |
deviation of the instantaneous force from its mean force. |
| 623 |
> |
deviation of the instantaneous force from its mean force: |
| 624 |
|
\begin{equation} |
| 625 |
|
\xi(z,t)=\langle\delta F(z,t)\delta F(z,0)\rangle/k_{B}T, |
| 626 |
|
\end{equation} |
