| 623 |
|
standard NPT ensemble with a different pressure control strategy |
| 624 |
|
|
| 625 |
|
\begin{equation} |
| 626 |
< |
\.{\overleftrightarrow{{\eta _{\alpha \beta}}}}=\left\{\begin{array}{ll} |
| 626 |
> |
\dot {\overleftrightarrow{\eta}} _{\alpha \beta}=\left\{\begin{array}{ll} |
| 627 |
|
\frac{{V(P_{\alpha \beta } - P_{{\rm{target}}} )}}{{\tau_{\rm{B}}^{\rm{2}} fk_B T_{{\rm{target}}} }} |
| 628 |
< |
& \mbox{if \[ \alpha = \beta = z)$}\\ |
| 628 |
> |
& \mbox{if $ \alpha = \beta = z$}\\ |
| 629 |
|
0 & \mbox{otherwise}\\ |
| 630 |
|
\end{array} |
| 631 |
|
\right. |
| 649 |
|
pressure. The equation of motion for cell size control tensor, |
| 650 |
|
$\eta$, in $NP\gamma T$ is |
| 651 |
|
\begin{equation} |
| 652 |
< |
\.{\overleftrightarrow{{\eta _{\alpha \beta}}}}=\left\{\begin{array}{ll} |
| 652 |
> |
\dot {\overleftrightarrow{\eta}} _{\alpha \beta}=\left\{\begin{array}{ll} |
| 653 |
|
- A_{xy} (\gamma _\alpha - \gamma _{{\rm{target}}} ) & \mbox{$\alpha = \beta = x$ or $\alpha = \beta = y$}\\ |
| 654 |
|
\frac{{V(P_{\alpha \beta } - P_{{\rm{target}}} )}}{{\tau _{\rm{B}}^{\rm{2}} fk_B T_{{\rm{target}}}}} & \mbox{$\alpha = \beta = z$} \\ |
| 655 |
|
0 & \mbox{$\alpha \ne \beta$} \\ |
| 656 |
+ |
\end{array} |
| 657 |
|
\right. |
| 658 |
|
\end{equation} |
| 659 |
|
where $ \gamma _{{\rm{target}}}$ is the external surface tension and |
| 660 |
|
the instantaneous surface tensor $\gamma _\alpha$ is given by |
| 661 |
|
\begin{equation} |
| 662 |
< |
\gamma _\alpha = - h_z |
| 663 |
< |
(\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\leftrightarrow$}} |
| 663 |
< |
\over P} _{\alpha \alpha } - P_{{\rm{target}}} ) |
| 662 |
> |
\gamma _\alpha = - h_z( \overleftrightarrow{P} _{\alpha \alpha } |
| 663 |
> |
- P_{{\rm{target}}} ) |
| 664 |
|
\label{methodEquation:instantaneousSurfaceTensor} |
| 665 |
|
\end{equation} |
| 666 |
|
|
