--- trunk/tengDissertation/LiquidCrystal.tex	2006/06/22 05:23:06	2877
+++ trunk/tengDissertation/LiquidCrystal.tex	2006/06/23 21:33:52	2882
@@ -212,8 +212,8 @@ every banana shaped molecule has been represented thre
 
 A series of molecular dynamics simulations were perform to study the
 phase behavior of banana shaped liquid crystals. In each simulation,
-every banana shaped molecule has been represented three GB particles
-which is characterized by $\mu = 1,~ \nu = 2,
+every banana shaped molecule has been represented by three GB
+particles which is characterized by $\mu = 1,~ \nu = 2,
 ~\epsilon_{e}/\epsilon_{s} = 1/5$ and $\sigma_{e}/\sigma_{s} = 3$.
 All of the simulations begin with same equilibrated isotropic
 configuration where 1024 molecules without dipoles were confined in
@@ -276,14 +276,14 @@ 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 )
-- 2(\hat x_i  \cdot \hat x_j )(\hat y_i  \cdot \hat y_j ))}
-\right\rangle
-\end{equation}
+\begin{eqnarray}
+S_{22}^{220} (r) & = & \frac{1}{{4\sqrt 5 }} \left< \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 ) \right. \\
+ & & \left. - 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>
+\end{eqnarray}
 
 \begin{equation}
 S_{00}^{221} (r) =  - \frac{{\sqrt 3 }}{{\sqrt {10} }}\left\langle