| 276 |
|
arbitrary shape was introduce by Stone\cite{Stone1978} and adopted |
| 277 |
|
by other researchers in liquid crystal studies\cite{Berardi2000}. |
| 278 |
|
|
| 279 |
< |
\begin{equation} |
| 280 |
< |
S_{22}^{220} (r) = \frac{1}{{4\sqrt 5 }}\left\langle {\delta (r - |
| 281 |
< |
r_{ij} )((\hat x_i \cdot \hat x_j )^2 - (\hat x_i \cdot \hat y_j |
| 282 |
< |
)^2 - (\hat y_i \cdot \hat x_j )^2 + (\hat y_i \cdot \hat y_j |
| 283 |
< |
)^2 ) - 2(\hat x_i \cdot \hat y_j )(\hat y_i \cdot \hat x_j ) - |
| 279 |
> |
\begin{eqnarray} |
| 280 |
> |
S_{22}^{220} (r) & = & \frac{1}{{4\sqrt 5 }}\left\langle {\delta (r |
| 281 |
> |
- r_{ij} )((\hat x_i \cdot \hat x_j )^2 - (\hat x_i \cdot \hat |
| 282 |
> |
y_j )^2 - (\hat y_i \cdot \hat x_j )^2 + (\hat y_i \cdot \hat |
| 283 |
> |
y_j )^2 ) \\ |
| 284 |
> |
& & - 2(\hat x_i \cdot \hat y_j )(\hat y_i \cdot \hat x_j ) - |
| 285 |
|
2(\hat x_i \cdot \hat x_j )(\hat y_i \cdot \hat y_j ))} |
| 286 |
|
\right\rangle |
| 287 |
< |
\end{equation} |
| 287 |
> |
\end{eqnarray} |
| 288 |
|
|
| 289 |
|
\begin{equation} |
| 290 |
|
S_{00}^{221} (r) = - \frac{{\sqrt 3 }}{{\sqrt {10} }}\left\langle |
| 291 |
|
{\delta (r - r_{ij} )((\hat z_i \cdot \hat z_j )(\hat z_i \cdot |
| 292 |
< |
\hat z_j \times \hat r_{ij} ))} \right\rangle s\end{equation} |
| 292 |
> |
\hat z_j \times \hat r_{ij} ))} \right\rangle |
| 293 |
> |
\end{equation} |
| 294 |
|
|
| 295 |
|
\section{Results and Conclusion} |
| 296 |
|
\label{sec:results and conclusion} |
