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arbitrary shape was introduce by Stone\cite{Stone1978} and adopted |
277 |
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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 |
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\right\rangle |
287 |
< |
\end{equation} |
287 |
> |
\end{eqnarray} |
288 |
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|
289 |
|
\begin{equation} |
290 |
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S_{00}^{221} (r) = - \frac{{\sqrt 3 }}{{\sqrt {10} }}\left\langle |
291 |
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{\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 |
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|
295 |
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\section{Results and Conclusion} |
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\label{sec:results and conclusion} |