--- trunk/electrostaticMethodsPaper/electrostaticMethods.tex	2006/03/20 02:00:26	2639
+++ trunk/electrostaticMethodsPaper/electrostaticMethods.tex	2006/03/20 13:31:52	2640
@@ -87,7 +87,7 @@ Ewald summations, interaction shifting or
 classified as implicit methods (i.e., continuum dielectrics, static
 dipolar fields),\cite{Born20,Grossfield00} explicit methods (i.e.,
 Ewald summations, interaction shifting or
-trucation),\cite{Ewald21,Steinbach94} or a mixture of the two (i.e.,
+truncation),\cite{Ewald21,Steinbach94} or a mixture of the two (i.e.,
 reaction field type methods, fast multipole
 methods).\cite{Onsager36,Rokhlin85} The explicit or mixed methods are
 often preferred because they incorporate dynamic solvent molecules in
@@ -106,7 +106,7 @@ a variety of model systems and comparison methodologie
 modification to the direct pairwise sum, and they lack the added
 periodicity of the Ewald sum. Below, these methods are evaluated using
 a variety of model systems and comparison methodologies to establish
-their useability in molecular simulations.
+their usability in molecular simulations.
 
 \subsection{The Ewald Sum}
 The complete accumulation electrostatic interactions in a system with
@@ -126,7 +126,7 @@ case of monopole electrostatics, eq. (\ref{eq:PBCSum})
 $j$, and $\phi$ is Poisson's equation ($\phi(\mathbf{r}_{ij}) = q_i
 q_j |\mathbf{r}_{ij}|^{-1}$ for charge-charge interactions). In the
 case of monopole electrostatics, eq. (\ref{eq:PBCSum}) is
-conditionally convergent and is discontiuous for non-neutral systems.
+conditionally convergent and is discontinuous for non-neutral systems.
 
 This electrostatic summation problem was originally studied by Ewald
 for the case of an infinite crystal.\cite{Ewald21}. The approach he
@@ -176,7 +176,7 @@ real-space or reciprocal space portion of the summatio
 direct and reciprocal-space portions of the summation.  The choice of
 the magnitude of this value allows one to select whether the
 real-space or reciprocal space portion of the summation is an
-$\mathscr{O}(N^2)$ calcualtion (with the other being
+$\mathscr{O}(N^2)$ calculation (with the other being
 $\mathscr{O}(N)$).\cite{Sagui99} With appropriate choice of $\alpha$
 and thoughtful algorithm development, this cost can be brought down to
 $\mathscr{O}(N^{3/2})$.\cite{Perram88} The typical route taken to
@@ -212,7 +212,7 @@ considering the use of the Ewald summation where the i
 artificially stabilized by the periodic replicas introduced by the
 Ewald summation.\cite{Weber00} Thus, care ought to be taken when
 considering the use of the Ewald summation where the intrinsic
-perodicity may negatively affect the system dynamics.
+periodicity may negatively affect the system dynamics.
 
 
 \subsection{The Wolf and Zahn Methods}
@@ -230,7 +230,7 @@ the real-space portion of the Ewald sum) to aid conver
 and a distance-dependent damping function (identical to that seen in
 the real-space portion of the Ewald sum) to aid convergence
 \begin{equation}
-V_{\textrm{Wolf}}(r_{ij})= \frac{q_iq_j \textrm{erfc}(\alpha r_{ij})}{r_{ij}}-\lim_{r_{ij}\rightarrow R_\textrm{c}}\left\{\frac{q_iq_j \textrm{erfc}(\alpha r_{ij})}{r_{ij}}\right\}.
+V_{\textrm{Wolf}}(r_{ij})= \frac{q_i q_j \textrm{erfc}(\alpha r_{ij})}{r_{ij}}-\lim_{r_{ij}\rightarrow R_\textrm{c}}\left\{\frac{q_iq_j \textrm{erfc}(\alpha r_{ij})}{r_{ij}}\right\}.
 \label{eq:WolfPot}
 \end{equation}
 Eq. (\ref{eq:WolfPot}) is essentially the common form of a shifted
@@ -738,7 +738,7 @@ al.},\cite{Wolf99} and this correction indeed improves
 Correcting the resulting charged cutoff sphere is one of the purposes
 of the damped Coulomb summation proposed by Wolf \textit{et
 al.},\cite{Wolf99} and this correction indeed improves the results as
-seen in the Shifted-Potental rows.  While the undamped case of this
+seen in the {\sc sp} rows.  While the undamped case of this
 method is a significant improvement over the pure cutoff, it still
 doesn't correlate that well with SPME.  Inclusion of potential damping
 improves the results, and using an $\alpha$ of 0.2 \AA $^{-1}$ shows
@@ -951,7 +951,7 @@ the point charges for the pairwise summation methods; 
 increased, these peaks are smoothed out, and approach the SPME
 curve. The damping acts as a distance dependent Gaussian screening of
 the point charges for the pairwise summation methods; thus, the
-collisions are more elastic in the undamped {\sc sf} potental, and the
+collisions are more elastic in the undamped {\sc sf} potential, and the
 stiffness of the potential is diminished as the electrostatic
 interactions are softened by the damping function.  With $\alpha$
 values of 0.2 \AA$^{-1}$, the {\sc sf} and {\sc sp} functions are
