cut-off and so on ...

diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex
index 57f92d4..c88c6c5 100644 (file)
--- 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}) \\