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by other researchers in liquid crystal studies\cite{Berardi2000}. |
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|
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\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 ) - |
284 |
< |
2(\hat x_i \cdot \hat x_j )(\hat y_i \cdot \hat y_j ))} |
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 ) - 2(\hat x_i \cdot \hat y_j )(\hat y_i \cdot \hat x_j ) |
284 |
> |
- 2(\hat x_i \cdot \hat x_j )(\hat y_i \cdot \hat y_j ))} |
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\right\rangle |
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\end{equation} |
287 |
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|
288 |
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\begin{equation} |
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S_{00}^{221} (r) = - \frac{{\sqrt 3 }}{{\sqrt {10} }}\left\langle |
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{\delta (r - r_{ij} )((\hat z_i \cdot \hat z_j )(\hat z_i \cdot |
291 |
< |
\hat z_j \times \hat r_{ij} ))} \right\rangle s\end{equation} |
291 |
> |
\hat z_j \times \hat r_{ij} ))} \right\rangle |
292 |
> |
\end{equation} |
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|
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\section{Results and Conclusion} |
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\label{sec:results and conclusion} |