--- trunk/xDissertation/md.tex	2008/03/13 22:59:35	3369
+++ trunk/xDissertation/md.tex	2008/03/14 21:38:07	3370
@@ -140,18 +140,17 @@ $\sigma$ and $\epsilon$ parameters,
 Pechukas.\cite{Berne72} The potential is constructed in the familiar
 form of the Lennard-Jones function using orientation-dependent
 $\sigma$ and $\epsilon$ parameters,
-\begin{equation}
-\begin{split}
+\begin{multline}
 V_{ij}({\mathbf{\hat u}_i}, {\mathbf{\hat u}_j}, {\mathbf{\hat
-r}_{ij}}) = & 4\epsilon ({\mathbf{\hat u}_i}, {\mathbf{\hat u}_j},
+r}_{ij}}) = 4\epsilon ({\mathbf{\hat u}_i}, {\mathbf{\hat u}_j},
 {\mathbf{\hat r}_{ij}})\left[ \left(\frac{\sigma_0}{r_{ij}-\sigma({\mathbf{\hat u}_i},
-{\mathbf{\hat u}_j}, {\mathbf{\hat r}_{ij}})+\sigma_0}\right)^{12} \right.\\
- &\left. -\left(\frac{\sigma_0}{r_{ij}-\sigma({\mathbf{\hat u}_i},
+{\mathbf{\hat u}_j}, {\mathbf{\hat r}_{ij}})+\sigma_0}\right)^{12}
+\right. \\
+\left. - \left(\frac{\sigma_0}{r_{ij}-\sigma({\mathbf{\hat u}_i},
  {\mathbf{\hat u}_j}, {\mathbf{\hat
  r}_{ij}})+\sigma_0}\right)^6\right]
-\end{split}
 \label{mdeq:gb}
-\end{equation}
+\end{multline}
 
 The range $(\sigma({\bf \hat{u}}_{i},{\bf \hat{u}}_{j},{\bf
 \hat{r}}_{ij}))$, and strength $(\epsilon({\bf \hat{u}}_{i},{\bf
@@ -172,19 +171,16 @@ calculate the range function,
 where $l$ and $d$ describe the length and width of each uniaxial
 ellipsoid.  These shape anisotropy parameters can then be used to
 calculate the range function,
-\begin{equation}
-\begin{split}
-& \sigma({\bf \hat{u}}_{i},{\bf \hat{u}}_{j},{\bf \hat{r}}_{ij}) =
-\sigma_{0} \times  \\
-& \left[ 1- \left\{ \frac{ \chi \alpha^2 ({\bf \hat{u}}_i \cdot {\bf
+\begin{multline}
+\sigma({\bf \hat{u}}_{i},{\bf \hat{u}}_{j},{\bf \hat{r}}_{ij}) = \\
+\sigma_0 \left[ 1 - \left\{ \frac{ \chi \alpha^2 ({\bf \hat{u}}_i \cdot {\bf
 \hat{r}}_{ij} ) + \chi \alpha^{-2} ({\bf \hat{u}}_j \cdot {\bf
 \hat{r}}_{ij} ) - 2 \chi^2 ({\bf \hat{u}}_i \cdot {\bf
 \hat{r}}_{ij} )({\bf \hat{u}}_j \cdot {\bf
 \hat{r}}_{ij} ) ({\bf \hat{u}}_i \cdot {\bf \hat{u}}_j)}{1 - \chi^2
 \left({\bf \hat{u}}_i \cdot {\bf \hat{u}}_j\right)^2} \right\}
-\right]^{-1/2} 
-\end{split}
-\end{equation}
+\right]^{-1/2}
+\end{multline}
 
 Gay-Berne ellipsoids also have an energy scaling parameter,
 $\epsilon^s$, which describes the well depth for two identical
@@ -211,18 +207,16 @@ The form of the strength function is somewhat complica
 \left[1-\chi^{2}({\bf \hat{u}}_{i}.{\bf
 \hat{u}}_{j})^{2}\right]^{-1/2}
 \end{eqnarray*}
-\begin{equation*}
-\begin{split}
-& \epsilon_{2}({\bf \hat{u}}_{i},{\bf \hat{u}}_{j},{\bf \hat{r}}_{ij})
-= 1 - \\
-& \left\{ \frac{ \chi' \alpha'^2 ({\bf \hat{u}}_i \cdot {\bf
+\begin{multline*}
+\epsilon_{2}({\bf \hat{u}}_{i},{\bf \hat{u}}_{j},{\bf \hat{r}}_{ij})
+=  \\
+1 - \left\{ \frac{ \chi' \alpha'^2 ({\bf \hat{u}}_i \cdot {\bf
 \hat{r}}_{ij} ) + \chi' \alpha'^{-2} ({\bf \hat{u}}_j \cdot {\bf
 \hat{r}}_{ij} ) - 2 \chi'^2 ({\bf \hat{u}}_i \cdot {\bf
 \hat{r}}_{ij} )({\bf \hat{u}}_j \cdot {\bf
 \hat{r}}_{ij} ) ({\bf \hat{u}}_i \cdot {\bf \hat{u}}_j)}{1 - \chi'^2
 \left({\bf \hat{u}}_i \cdot {\bf \hat{u}}_j\right)^2} \right\},
-\end{split}
-\end{equation*}
+\end{multline*}
 although many of the quantities and derivatives are identical with
 those obtained for the range parameter. Ref. \citen{Luckhurst90}
 has a particularly good explanation of the choice of the Gay-Berne
@@ -702,7 +696,9 @@ D = \lim_{t \rightarrow \infty} \frac{1}{6 t} \langle 
 We have computed translational diffusion constants for lipid molecules
 from the mean-square displacement,
 \begin{equation}
-D = \lim_{t \rightarrow \infty} \frac{1}{6 t} \langle {|\left({\bf r}_{i}(t) - {\bf r}_{i}(0) \right)|}^2 \rangle,
+D = \lim_{t \rightarrow \infty} \frac{1}{6 t} \langle {|\left({\bf
+r}_{i}(t) - {\bf r}_{i}(0) \right)|}^2 \rangle,
+\label{mdeq:msdisplacement}
 \end{equation}
 of the lipid bodies. Translational diffusion constants for the
 different head-to-tail size ratios (all at 300 K) are shown in table
