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 |
|
|