| 36 |
|
scheme of DLM method will be reviewed and extended to other |
| 37 |
|
ensembles. |
| 38 |
|
|
| 39 |
< |
\subsection{\label{methodSection:DLM}Integrating the Equations of Motion: the |
| 40 |
< |
DLM method} |
| 39 |
> |
\subsection{\label{methodSection:DLM}Integrating the Equations of Motion: The |
| 40 |
> |
DLM Method} |
| 41 |
|
|
| 42 |
|
The DLM method uses a Trotter factorization of the orientational |
| 43 |
|
propagator. This has three effects: |
| 211 |
|
\chi(t) \right) ,\\ |
| 212 |
|
% |
| 213 |
|
\mathsf{Q}(t + h) &\leftarrow \mathrm{rotate} |
| 214 |
< |
\left(h * {\bf j}(t + h / 2) |
| 214 |
> |
\left(h {\bf j}(t + h / 2) |
| 215 |
|
\overleftrightarrow{\mathsf{I}}^{-1} \right) ,\\ |
| 216 |
|
% |
| 217 |
|
\chi\left(t + h / 2 \right) &\leftarrow \chi(t) |
| 318 |
|
r}_{ij}(t) \otimes {\bf f}_{ij}(t). |
| 319 |
|
\end{equation} |
| 320 |
|
The instantaneous pressure is then simply obtained from the trace of |
| 321 |
< |
the Pressure tensor, |
| 321 |
> |
the pressure tensor, |
| 322 |
|
\begin{equation} |
| 323 |
|
P(t) = \frac{1}{3} \mathrm{Tr} \left( |
| 324 |
|
\overleftrightarrow{\mathsf{P}}(t) \right) . |
| 583 |
|
membrane system should be zero since its surface free energy $G$ is |
| 584 |
|
minimum with respect to surface area $A$, |
| 585 |
|
\begin{equation} |
| 586 |
< |
\gamma = \frac{{\partial G}}{{\partial A}}. |
| 587 |
< |
\end{equation}0 |
| 586 |
> |
\gamma = \frac{{\partial G}}{{\partial A}}=0. |
| 587 |
> |
\end{equation} |
| 588 |
|
However, a surface tension of zero is not |
| 589 |
|
appropriate for relatively small patches of membrane. In order to |
| 590 |
|
eliminate the edge effect of membrane simulations, a special |
| 591 |
< |
ensemble, NP$\gamma$T, has been proposed to maintain the lateral |
| 591 |
> |
ensemble NP$\gamma$T has been proposed to maintain the lateral |
| 592 |
|
surface tension and normal pressure. The equation of motion for the |
| 593 |
|
cell size control tensor, $\eta$, in $NP\gamma T$ is |
| 594 |
|
\begin{equation} |
