--- trunk/electrostaticMethodsPaper/electrostaticMethods.tex	2006/03/24 16:54:13	2669
+++ trunk/electrostaticMethodsPaper/electrostaticMethods.tex	2006/04/26 14:20:17	2740
@@ -1,7 +1,7 @@
 %\documentclass[prb,aps,twocolumn,tabularx]{revtex4}
 %\documentclass[aps,prb,preprint]{revtex4}
-\documentclass[11pt]{article}
-\usepackage{endfloat}
+\documentclass[10pt]{article}
+%\usepackage{endfloat}
 \usepackage{amsmath,bm}
 \usepackage{amssymb}
 \usepackage{epsf}
@@ -38,7 +38,7 @@ Notre Dame, Indiana 46556}
 \date{\today}
 
 \maketitle
-\doublespacing
+%\doublespacing
 
 \begin{abstract}
 We investigate pairwise electrostatic interaction methods and show
@@ -106,8 +106,8 @@ or which have one- or two-dimensional periodicity.  Be
 to the direct pairwise sum.  They also lack the added periodicity of
 the Ewald sum, so they can be used for systems which are non-periodic
 or which have one- or two-dimensional periodicity.  Below, these
-methods are evaluated using a variety of model systems to establish
-their usability in molecular simulations.
+methods are evaluated using a variety of model systems to
+establish their usability in molecular simulations.
 
 \subsection{The Ewald Sum}
 The complete accumulation of the electrostatic interactions in a system with
@@ -201,10 +201,11 @@ can prove problematic.  The Ewald sum has been reformu
 interfaces and membranes, the intrinsic three-dimensional periodicity
 can prove problematic.  The Ewald sum has been reformulated to handle
 2D systems,\cite{Parry75,Parry76,Heyes77,deLeeuw79,Rhee89}, but the
-new methods are computationally expensive.\cite{Spohr97,Yeh99}
-Inclusion of a correction term in the Ewald summation is a possible
-direction for handling 2D systems while still enabling the use of the
-modern optimizations.\cite{Yeh99}
+new methods are computationally expensive.\cite{Spohr97,Yeh99} More
+recently, there have been several successful efforts toward reducing
+the computational cost of 2D lattice summations, often enabling the
+use of the mentioned
+optimizations.\cite{Yeh99,Kawata01,Arnold02,deJoannis02,Brodka04}
 
 Several studies have recognized that the inherent periodicity in the
 Ewald sum can also have an effect on three-dimensional
@@ -530,7 +531,7 @@ Fig. \ref{fig:linearFit}.
 
 \begin{figure}
 \centering
-\includegraphics[width = \linewidth]{./dualLinear.pdf}
+\includegraphics[width = 3.25in]{./dualLinear.pdf}
 \caption{Example least squares regressions of the configuration energy
 differences for SPC/E water systems. The upper plot shows a data set
 with a poor correlation coefficient ($R^2$), while the lower plot
@@ -538,11 +539,11 @@ shows a data set with a good correlation coefficient.}
 \label{fig:linearFit} 
 \end{figure}
 
-Each system type (detailed in section \ref{sec:RepSims}) was
-represented using 500 independent configurations.  Additionally, we
-used seven different system types, so each of the alternative
-(non-Ewald) electrostatic summation methods was evaluated using
-873,250 configurational energy differences.
+Each of the seven system types (detailed in section \ref{sec:RepSims})
+were represented using 500 independent configurations.  Thus, each of
+the alternative (non-Ewald) electrostatic summation methods was
+evaluated using an accumulated 873,250 configurational energy
+differences.
 
 Results and discussion for the individual analysis of each of the
 system types appear in the supporting information, while the
@@ -621,14 +622,15 @@ were performed under the microcanonical ensemble, and 
 NaCl crystal is composed of two different atom types, the average of
 the two resulting power spectra was used for comparisons. Simulations
 were performed under the microcanonical ensemble, and velocity
-information was saved every 5 fs over 100 ps trajectories. 
+information was saved every 5~fs over 100~ps trajectories. 
 
 \subsection{Representative Simulations}\label{sec:RepSims}
-A variety of representative simulations were analyzed to determine the
-relative effectiveness of the pairwise summation techniques in
-reproducing the energetics and dynamics exhibited by {\sc spme}.  We wanted
-to span the space of modern simulations (i.e. from liquids of neutral
-molecules to ionic crystals), so the systems studied were:
+A variety of representative molecular simulations were analyzed to
+determine the relative effectiveness of the pairwise summation
+techniques in reproducing the energetics and dynamics exhibited by
+{\sc spme}.  We wanted to span the space of typical molecular
+simulations (i.e. from liquids of neutral molecules to ionic
+crystals), so the systems studied were:
 \begin{enumerate}
 \item liquid water (SPC/E),\cite{Berendsen87}
 \item crystalline water (Ice I$_\textrm{c}$ crystals of SPC/E),
@@ -715,7 +717,7 @@ figure \ref{fig:delE}.
 
 \begin{figure}
 \centering
-\includegraphics[width=5.5in]{./delEplot.pdf}
+\includegraphics[width=3.25in]{./delEplot.pdf}
 \caption{Statistical analysis of the quality of configurational energy
 differences for a given electrostatic method compared with the
 reference Ewald sum.  Results with a value equal to 1 (dashed line)
@@ -775,7 +777,7 @@ accumulation of the statistics from all of the system 
 
 \begin{figure}
 \centering
-\includegraphics[width=5.5in]{./frcMagplot.pdf}
+\includegraphics[width=3.25in]{./frcMagplot.pdf}
 \caption{Statistical analysis of the quality of the force vector 
 magnitudes for a given electrostatic method compared with the
 reference Ewald sum.  Results with a value equal to 1 (dashed line)
@@ -814,7 +816,7 @@ performs more favorably.
 
 \begin{figure}
 \centering
-\includegraphics[width=5.5in]{./trqMagplot.pdf}
+\includegraphics[width=3.25in]{./trqMagplot.pdf}
 \caption{Statistical analysis of the quality of the torque vector 
 magnitudes for a given electrostatic method compared with the
 reference Ewald sum.  Results with a value equal to 1 (dashed line)
@@ -854,7 +856,7 @@ distributions of the combined set over all system type
 
 \begin{figure}
 \centering
-\includegraphics[width=5.5in]{./frcTrqAngplot.pdf}
+\includegraphics[width=3.25in]{./frcTrqAngplot.pdf}
 \caption{Statistical analysis of the width of the angular distribution
 that the force and torque vectors from a given electrostatic method
 make with their counterparts obtained using the reference Ewald sum.
@@ -989,7 +991,7 @@ low-frequency portion of the power spectrum.
 
 \begin{figure}
 \centering
-\includegraphics[width = \linewidth]{./vCorrPlot.pdf}
+\includegraphics[width = 3.25in]{./vCorrPlot.pdf}
 \caption{Velocity autocorrelation functions of NaCl crystals at 
 1000 K using {\sc spme}, {\sc sf} ($\alpha$ = 0.0, 0.1, \& 0.2), and {\sc
 sp} ($\alpha$ = 0.2). The inset is a magnification of the area around
@@ -1029,7 +1031,7 @@ noticeable effect on peak location or magnitude.
 
 \begin{figure}
 \centering
-\includegraphics[width = \linewidth]{./spectraSquare.pdf}
+\includegraphics[width = 3.25in]{./spectraSquare.pdf}
 \caption{Power spectra obtained from the velocity auto-correlation 
 functions of NaCl crystals at 1000 K while using {\sc spme}, {\sc sf}
 ($\alpha$ = 0, 0.1, \& 0.2), and {\sc sp} ($\alpha$ = 0.2).  The inset
@@ -1068,7 +1070,7 @@ cutoff distance.
 
 \begin{figure}
 \centering
-\includegraphics[width = \linewidth]{./increasedDamping.pdf}
+\includegraphics[width = 3.25in]{./increasedDamping.pdf}
 \caption{Effect of damping on the two lowest-frequency phonon modes in
 the NaCl crystal at 1000~K.  The undamped shifted force ({\sc sf})
 method is off by less than 10 cm$^{-1}$, and increasing the
