From 515fa83847d7436cf7f08273a8e8ce0aa33b13de Mon Sep 17 00:00:00 2001 From: hackbard Date: Mon, 26 Sep 2011 15:20:07 +0200 Subject: [PATCH] cut-off and so on ... --- posic/thesis/basics.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex index 57f92d4..c88c6c5 100644 --- 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} -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\{ @@ -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 $j$. -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}) \\ -- 2.20.1