X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Fthesis%2Fd_tersoff.tex;h=66abaed4244eb2f648ab13ae766c57ab2b0f09cd;hb=c99f610aabb097a64ddcb1656798fd2d59c958a0;hp=92b421f45876c6ad9a364009353afa1e3c0b2d8d;hpb=a812d191e3b5f031b2227a3bbb40ec3b4be79b3a;p=lectures%2Flatex.git

diff --git a/posic/thesis/d_tersoff.tex b/posic/thesis/d_tersoff.tex
index 92b421f..66abaed 100644
--- a/posic/thesis/d_tersoff.tex
+++ b/posic/thesis/d_tersoff.tex
@@ -3,7 +3,7 @@
 
   \section{Form of the Tersoff potential and its derivative}
 
-The Tersoff potential \cite{tersoff_m} is of the form
+The Tersoff potential~\cite{tersoff_m} is of the form
 \begin{eqnarray}
 E & = & \sum_i E_i = \frac{1}{2} \sum_{i \ne j} V_{ij} \textrm{ ,} \\
 V_{ij} & = & f_C(r_{ij}) [ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) ] \textrm{ .}
@@ -149,7 +149,7 @@ The pair contributions are, thus, easily obtained.
 The contribution of the bond order term is given by:
 \begin{eqnarray}
  \nabla_{{\bf r}_j}\cos\theta_{ijk} &=&
- \nabla_{{\bf r}_j}\Big(\frac{{\bf r}_{ij}{\bf }r_{ik}}{r_{ij}r_{ik}}\Big)
+ \nabla_{{\bf r}_j}\Big(\frac{{\bf r}_{ij}{\bf r}_{ik}}{r_{ij}r_{ik}}\Big)
  \nonumber \\
  &=& \frac{1}{r_{ij}r_{ik}}{\bf r}_{ik} -
      \frac{\cos\theta_{ijk}}{r_{ij}^2}{\bf r}_{ij}
@@ -185,7 +185,7 @@ Concerning $b_{ij}$, in addition to the angular term, the derivative of the cut-
 
   \subsection{Code realization}
 
-The implementation of the force evaluation shown in the following is applied to the potential designed by Erhart and Albe \cite{albe_sic_pot}.
+The implementation of the force evaluation shown in the following is applied to the potential designed by Erhart and Albe~\cite{albe_sic_pot}.
 There are slight differences compared to the original potential by Tersoff:
 \begin{itemize}
  \item Difference in sign of the attractive part.
@@ -220,7 +220,7 @@ LOOP i \{
 	\item
 	\item LOOP k \{
 	      \begin{itemize}
-               \item set $ik$-depending values
+               \item set $ik$-dependent values
                \item calculate: $r_{ik}$, $r_{ik}^2$
 	       \item IF $r_{ik} > S_{ik}$ THEN CONTINUE
 	       \item calculate: $\theta_{ijk}$, $\cos(\theta_{ijk})$,