From: hackbard <hackbard@tx2.hackdaworld.org>
Date: Sat, 5 Nov 2011 20:47:39 +0000 (+0100)
Subject: formulas ...
X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=d0ff895e76b30891a3fcd4b9a037eada196e9f95;p=lectures%2Flatex.git

formulas ...
---

diff --git a/posic/talks/mpi_app.tex b/posic/talks/mpi_app.tex
index f588e1d..67a4d40 100644
--- a/posic/talks/mpi_app.tex
+++ b/posic/talks/mpi_app.tex
@@ -1008,7 +1008,6 @@ r = \unit[2--4]{nm}
 {\bf Molecular dynamics (MD)}\\
 \scriptsize
 \begin{tabular}{p{4.5cm} p{7.5cm}}
-%\hline
 Basics & Details\\
 \hline
 System of $N$ particles &
@@ -1026,16 +1025,8 @@ E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
     \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
 $\\
 \hline
-%\multicolumn{2}{c}{}\\
 Observables: time/ensemble averages &
 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
-%\begin{itemize}
-%\item Berendsen thermostat:
-%      $\tau_{\text{T}}=100\text{ fs}$
-%\item Berendsen barostat:\\
-%      $\tau_{\text{P}}=100\text{ fs}$,
-%      $\beta^{-1}=100\text{ GPa}$
-%\end{itemize}\\
 \hline
 \end{tabular}
 
@@ -1071,6 +1062,18 @@ $
 \end{itemize}
 \end{minipage}
 \begin{minipage}[t]{6cm}
+
+\[
+\left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
+\]
+\[
+n(r)=\sum_i^N|\Phi_i(r)|^2
+\]
+\[
+V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
+                 +V_{\text{XC}}[n(r)]
+\]
+
 \end{minipage}
 
 \end{slide}