From d2fa687f2ceaf75357f2d1574700820ce9607028 Mon Sep 17 00:00:00 2001
From: hackbard <hackbard>
Date: Wed, 13 Jun 2007 22:59:21 +0000
Subject: [PATCH] potentials missing, some thermo obs missing too

---
 posic/talks/md_simulation_von_silizium.tex | 51 +++++++++++++++++-----
 1 file changed, 41 insertions(+), 10 deletions(-)

diff --git a/posic/talks/md_simulation_von_silizium.tex b/posic/talks/md_simulation_von_silizium.tex
index 47e144a..b78dd11 100644
--- a/posic/talks/md_simulation_von_silizium.tex
+++ b/posic/talks/md_simulation_von_silizium.tex
@@ -38,9 +38,12 @@
 
 \def\slideleftmargin{5.1cm}
 \def\slidetopmargin{-0.6cm}
+\def\slidetopmargin{-0.6cm}
 
 \newcommand{\ham}{\mathcal{H}}
 \newcommand{\pot}{\mathcal{V}}
+\newcommand{\foo}{\mathcal{U}}
+\newcommand{\vir}{\mathcal{W}}
 
 % topic
 
@@ -468,7 +471,7 @@ Simulation von Oberfl"achen:
 \begin{minipage}{4cm}
 \begin{itemize}
  \item Zuf"alliges Hinzuf"ugen von Kohlenstoff\\
-       (schaffrierter Bereich)\\
+       (schraffierter Bereich)\\
        $\Rightarrow$ Energie- und Impulszufuhr in die MD-Zelle
  \item $T$-Skalierung,\\ Kopplung ans W"armebad\\
        (blauer Bereich)\\
@@ -521,24 +524,52 @@ Problemstellung: Finden der Nachbarn f"ur Wechselwirkung
        E = <K> + <U> = < \sum_i \frac{{\bf p}_i^2}{2m_i} > + <U({\bf q})>
        \]
  \item Temperatur/Druck
-       \begin{eqnarray}
-       <p_k \frac{\partial \ham}{\partial p_k}> &=& k_BT \nonumber \\
-       <q_k \frac{\partial \ham}{\partial q_k}> &=& k_BT \nonumber
-       \end{eqnarray}
+       \[
+       <p_k \frac{\partial \ham}{\partial p_k}> = k_BT, \quad
+       <q_k \frac{\partial \ham}{\partial q_k}> = k_BT
+       \]
        \begin{center}
-       "Aquipartitionstheorem
+       {\em "Aquipartitionstheorem}
        \end{center}
        Temperatur:
        \[
-       \sum_i {\bf p}_i \frac{{\bf p}_i}{m_i} = 3Nk_BT \quad
-       \Rightarrow \quad T=\frac{1}{3Nk_B} \sum_i \frac{{\bf p}_i^2}{m_i}
+       <\sum_i {\bf p}_i \frac{{\bf p}_i}{m_i}> = 3Nk_BT \quad
+       \Rightarrow \quad T=\frac{1}{3Nk_B} <\sum_i \frac{{\bf p}_i^2}{m_i}>
        \]
        Druck:
        \[
-       \sum_i {\bf q}_i \nabla_{{\bf q}_i} \pot = 3Nk_BT \quad
+       <\sum_i {\bf q}_i \nabla_{{\bf q}_i} \foo> = 3Nk_BT \quad
        \stackrel{\textrm{kart. Koord.}}{\Rightarrow} \quad 
-       - \sum_i {\bf r}_i \nabla_{{\bf r}_i} \pot = -3Nk_BT \quad
+       - \frac{1}{3} <\sum_i {\bf r}_i \nabla_{{\bf r}_i} \foo> = -Nk_BT
+       \]
+       \begin{center}
+       mit
+       \end{center}
+       \[
+       - \nabla_{{\bf r}_i} \foo = {\bf f}_i^{tot} = {\bf f}_i^{ext} + {\bf f}_i^{int}
+       \]
+       \begin{center}
+       wobei
+       \end{center}
+       \[
+       \frac{1}{3} \sum_i {\bf r}_i {\bf f}_i^{ext}=-pV, \quad
+       \frac{1}{3} \sum_i {\bf r}_i {\bf f}_i^{int}=
+       - \frac{1}{3} \sum_i {\bf r}_i \nabla_{{\bf r}_i} \pot = \vir
        \]
+       \begin{center}
+       folgt
+       \end{center}
+       \[
+       pV = Nk_BT + <\vir>
+       \]
+\end{itemize}
+\end{slide}
+
+\begin{slide}
+{\large\bf
+ Thermodynamische Gr"o"sen
+}
+\begin{itemize}
  \item W"armekapazit"at
  \item Struktur Werte
  \item Diffusion
-- 
2.20.1