--- trunk/tengDissertation/Langevin.tex	2006/06/16 01:54:28	2865
+++ trunk/tengDissertation/Langevin.tex	2006/06/17 18:43:58	2867
@@ -98,7 +98,7 @@ sophisticated rigid body dynamics.
 estimation of friction tensor from hydrodynamics theory into the
 sophisticated rigid body dynamics.
 
-\section{Computational methods{\label{methodSec}}}
+\section{Computational Methods{\label{methodSec}}}
 
 \subsection{\label{introSection:frictionTensor}Friction Tensor}
 Theoretically, the friction kernel can be determined using velocity
@@ -360,7 +360,7 @@ joining center of resistance $R$ and origin $O$.
 where $x_OR$, $y_OR$, $z_OR$ are the components of the vector
 joining center of resistance $R$ and origin $O$.
 
-\subsection{Langevin dynamics for rigid particles of arbitrary shape\label{LDRB}}
+\subsection{Langevin Dynamics for Rigid Particles of Arbitrary Shape\label{LDRB}}
 
 Consider a Langevin equation of motions in generalized coordinates
 \begin{equation}
@@ -515,13 +515,13 @@ be advanced to the same time value.
     + \frac{h}{2} {\bf \tau}^b(t + h) .
 \end{align*}
 
-\section{Results and discussion}
+\section{Results and Discussion}
 
 The Langevin algorithm described in previous section has been
 implemented in {\sc oopse}\cite{Meineke2005} and applied to the
 studies of kinetics and thermodynamic properties in several systems.
 
-\subsection{Temperature control}
+\subsection{Temperature Control}
 
 As shown in Eq.~\ref{randomForce}, random collisions associated with
 the solvent's thermal motions is controlled by the external
@@ -570,7 +570,6 @@ the temperature control ability.
 NVE (see green curve in Fig.~\ref{langevin:temperature}) which loses
 the temperature control ability.
 
-
 \begin{figure}
 \centering
 \includegraphics[width=\linewidth]{temperature.eps}
@@ -578,8 +577,10 @@ temperature fluctuation versus time.} \label{langevin:
 temperature fluctuation versus time.} \label{langevin:temperature}
 \end{figure}
 
-\subsection{Langevin dynamics of banana-shaped molecule}
+\subsection{Langevin Dynamics of Banana Shaped Molecule}
 
+
+
 \begin{figure}
 \centering
 \includegraphics[width=\linewidth]{one_banana.eps}
@@ -589,14 +590,16 @@ temperature fluctuation versus time.} \label{langevin:
 \begin{figure}
 \centering
 \includegraphics[width=\linewidth]{roughShell.eps}
-\caption[Rough Shell]{Rough Shell.} \label{langevin:roughShell}
+\caption[Rough shell model for banana shaped molecule]{Rough shell
+model for banana shaped molecule.} \label{langevin:roughShell}
 \end{figure}
 
 \begin{figure}
 \centering
 \includegraphics[width=\linewidth]{twoBanana.eps}
-\caption[Two Banana Shaped Molecules]{Two Banana Shaped Molecules.}
-\label{langevin:twoBanana}
+\caption[Snapshot from Simulation of Two Banana Shaped Molecules and
+256 Pentane Molecules]{Snapshot from simulation of two Banana shaped
+molecules and 256 pentane molecules.} \label{langevin:twoBanana}
 \end{figure}
 
 \section{Conclusions}
