--- trunk/tengDissertation/LiquidCrystal.tex 2006/06/21 18:28:27 2875 +++ trunk/tengDissertation/LiquidCrystal.tex 2006/06/21 19:46:01 2876 @@ -276,19 +276,21 @@ by other researchers in liquid crystal studies\cite{Be arbitrary shape was introduce by Stone\cite{Stone1978} and adopted by other researchers in liquid crystal studies\cite{Berardi2000}. -\begin{equation} -S_{22}^{220} (r) = \frac{1}{{4\sqrt 5 }}\left\langle {\delta (r - -r_{ij} )((\hat x_i \cdot \hat x_j )^2 - (\hat x_i \cdot \hat y_j -)^2 - (\hat y_i \cdot \hat x_j )^2 + (\hat y_i \cdot \hat y_j -)^2 ) - 2(\hat x_i \cdot \hat y_j )(\hat y_i \cdot \hat x_j ) - +\begin{eqnarray} +S_{22}^{220} (r) & = & \frac{1}{{4\sqrt 5 }}\left\langle {\delta (r +- r_{ij} )((\hat x_i \cdot \hat x_j )^2 - (\hat x_i \cdot \hat +y_j )^2 - (\hat y_i \cdot \hat x_j )^2 + (\hat y_i \cdot \hat +y_j )^2 ) \\ +& & - 2(\hat x_i \cdot \hat y_j )(\hat y_i \cdot \hat x_j ) - 2(\hat x_i \cdot \hat x_j )(\hat y_i \cdot \hat y_j ))} \right\rangle -\end{equation} +\end{eqnarray} \begin{equation} S_{00}^{221} (r) = - \frac{{\sqrt 3 }}{{\sqrt {10} }}\left\langle {\delta (r - r_{ij} )((\hat z_i \cdot \hat z_j )(\hat z_i \cdot -\hat z_j \times \hat r_{ij} ))} \right\rangle s\end{equation} +\hat z_j \times \hat r_{ij} ))} \right\rangle +\end{equation} \section{Results and Conclusion} \label{sec:results and conclusion}