--- trunk/fennellDissertation/dissertation.tex	2006/07/03 13:55:25	2918
+++ trunk/fennellDissertation/dissertation.tex	2006/07/03 14:51:28	2920
@@ -720,16 +720,14 @@ respectively.
 in all {\sc spme} calculations, resulting in Ewald coefficients of 0.4200,
 0.3119, and 0.2476\AA$^{-1}$ for cutoff radii of 9, 12, and 15\AA\
 respectively.
-
-
-\section{Discussion on the Pairwise Technique Evaluation}
 
-\subsection{Configuration Energy Differences}\label{sec:EnergyResults}
+\section{Combined Configuration Energy Difference Results}\label{sec:EnergyResults}
 In order to evaluate the performance of the pairwise electrostatic
-summation methods for Monte Carlo simulations, the energy differences
-between configurations were compared to the values obtained when using
-{\sc spme}.  The results for the combined regression analysis of all
-of the systems are shown in figure \ref{fig:delE}.
+summation methods for Monte Carlo (MC) simulations, the energy
+differences between configurations were compared to the values
+obtained when using {\sc spme}.  The results for the combined
+regression analysis of all of the systems are shown in figure
+\ref{fig:delE}.
 
 \begin{figure}
 \centering
@@ -782,10 +780,8 @@ those from an unmodified cutoff.
 systems; although it does provide results that are an improvement over
 those from an unmodified cutoff.
 
-\sub
+\section{Magnitude of the Force and Torque Vector Results}
 
-\subsection{Magnitudes of the Force and Torque Vectors}
-
 Evaluation of pairwise methods for use in Molecular Dynamics
 simulations requires consideration of effects on the forces and
 torques.  Figures \ref{fig:frcMag} and \ref{fig:trqMag} show the
@@ -860,7 +856,7 @@ performs best of all of the methods on molecular torqu
 molecular bodies. Therefore it is not surprising that reaction field
 performs best of all of the methods on molecular torques.
 
-\subsection{Directionality of the Force and Torque Vectors}
+\section{Directionality of the Force and Torque Vector Results}
 
 It is clearly important that a new electrostatic method can reproduce
 the magnitudes of the force and torque vectors obtained via the Ewald
@@ -988,8 +984,34 @@ but damping may be unnecessary when using the {\sc sf}
 observations, empirical damping up to 0.2\AA$^{-1}$ is beneficial,
 but damping may be unnecessary when using the {\sc sf} method.
 
-\subsection{Short-Time Dynamics: Velocity Autocorrelation Functions of NaCl Crystals}
+\section{Individual System Analysis Results}
+
+The combined results of the previous sections show how the pairwise
+methods compare to the Ewald summation in the general sense over all
+of the system types.  It is also useful to consider each of the
+studied systems in an individual fashion, so that we can identify
+conditions that are particularly difficult for a selected pairwise
+method to address. This allows us to further establish the limitations
+of these pairwise techniques.  Below, the energy difference, force
+vector, and torque vector analyses are presented on an individual
+system basis.
 
+\subsection{SPC/E Water Results}
+
+\subsection{SPC/E Ice I$_\textrm{c}$ Results}
+
+\subsection{NaCl Melt Results}
+
+\subsection{NaCl Crystal Results}
+
+\subsection{0.1M NaCl Solution Results}
+
+\subsection{1M NaCl Solution Results}
+
+\subsection{6\AA\ Argon Sphere in SPC/E Water Results}
+
+\section{Short-Time Dynamics: Velocity Autocorrelation Functions of NaCl Crystals}
+
 Zahn {\it et al.} investigated the structure and dynamics of water
 using eqs. (\ref{eq:ZahnPot}) and
 (\ref{eq:WolfForces}).\cite{Zahn02,Kast03} Their results indicated
@@ -1040,7 +1062,7 @@ important.
 constructed out of the damped electrostatic interaction are less
 important.
 
-\subsection{Collective Motion: Power Spectra of NaCl Crystals}
+\section{Collective Motion: Power Spectra of NaCl Crystals}
 
 To evaluate how the differences between the methods affect the
 collective long-time motion, we computed power spectra from long-time
