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cut-off and so on ...
author
hackbard
<hackbard@hackdaworld.org>
Mon, 26 Sep 2011 13:20:07 +0000
(15:20 +0200)
committer
hackbard
<hackbard@hackdaworld.org>
Mon, 26 Sep 2011 13:20:07 +0000
(15:20 +0200)
posic/thesis/basics.tex
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diff --git
a/posic/thesis/basics.tex
b/posic/thesis/basics.tex
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..
c88c6c5
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--- a/
posic/thesis/basics.tex
+++ b/
posic/thesis/basics.tex
@@
-121,7
+121,7
@@
The attractive part is associated with the bonding.
f_R(r_{ij}) & = & A_{ij} \exp (- \lambda_{ij} r_{ij} ) \\
f_A(r_{ij}) & = & -B_{ij} \exp (- \mu_{ij} r_{ij} )
\end{eqnarray}
f_R(r_{ij}) & = & A_{ij} \exp (- \lambda_{ij} r_{ij} ) \\
f_A(r_{ij}) & = & -B_{ij} \exp (- \mu_{ij} r_{ij} )
\end{eqnarray}
-The function $f_C$ is a cutoff function to limit the range of interaction to nearest neighbors.
+The function $f_C$ is a cut
-
off function to limit the range of interaction to nearest neighbors.
It is designed to have a smooth transition of the potential at distances $R_{ij}$ and $S_{ij}$.
\begin{equation}
f_C(r_{ij}) = \left\{
It is designed to have a smooth transition of the potential at distances $R_{ij}$ and $S_{ij}$.
\begin{equation}
f_C(r_{ij}) = \left\{
@@
-133,7
+133,7
@@
f_C(r_{ij}) = \left\{
\label{eq:basics:fc}
\end{equation}
As discussed above, $b_{ij}$ represents a measure of the bond order, monotonously decreasing with the coordination of atoms $i$ and $j$.
\label{eq:basics:fc}
\end{equation}
As discussed above, $b_{ij}$ represents a measure of the bond order, monotonously decreasing with the coordination of atoms $i$ and $j$.
-It is of the form
:
+It is of the form
\begin{eqnarray}
b_{ij} & = & \chi_{ij} (1 + \beta_i^{n_i} \zeta^{n_i}_{ij})^{-1/2n_i} \\
\zeta_{ij} & = & \sum_{k \ne i,j} f_C (r_{ik}) \omega_{ik} g(\theta_{ijk}) \\
\begin{eqnarray}
b_{ij} & = & \chi_{ij} (1 + \beta_i^{n_i} \zeta^{n_i}_{ij})^{-1/2n_i} \\
\zeta_{ij} & = & \sum_{k \ne i,j} f_C (r_{ik}) \omega_{ik} g(\theta_{ijk}) \\