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potentials missing, some thermo obs missing too
author
hackbard
<hackbard>
Wed, 13 Jun 2007 22:59:21 +0000
(22:59 +0000)
committer
hackbard
<hackbard>
Wed, 13 Jun 2007 22:59:21 +0000
(22:59 +0000)
posic/talks/md_simulation_von_silizium.tex
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diff --git
a/posic/talks/md_simulation_von_silizium.tex
b/posic/talks/md_simulation_von_silizium.tex
index
47e144a
..
b78dd11
100644
(file)
--- 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\slideleftmargin{5.1cm}
\def\slidetopmargin{-0.6cm}
+\def\slidetopmargin{-0.6cm}
\newcommand{\ham}{\mathcal{H}}
\newcommand{\pot}{\mathcal{V}}
\newcommand{\ham}{\mathcal{H}}
\newcommand{\pot}{\mathcal{V}}
+\newcommand{\foo}{\mathcal{U}}
+\newcommand{\vir}{\mathcal{W}}
% topic
% topic
@@
-468,7
+471,7
@@
Simulation von Oberfl"achen:
\begin{minipage}{4cm}
\begin{itemize}
\item Zuf"alliges Hinzuf"ugen von Kohlenstoff\\
\begin{minipage}{4cm}
\begin{itemize}
\item Zuf"alliges Hinzuf"ugen von Kohlenstoff\\
- (sch
affr
ierter Bereich)\\
+ (sch
raff
ierter Bereich)\\
$\Rightarrow$ Energie- und Impulszufuhr in die MD-Zelle
\item $T$-Skalierung,\\ Kopplung ans W"armebad\\
(blauer 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
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}
\begin{center}
- "Aquipartitionstheorem
+ {\em "Aquipartitionstheorem}
\end{center}
Temperatur:
\[
\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:
\[
\]
Druck:
\[
-
\sum_i {\bf q}_i \nabla_{{\bf q}_i} \pot
= 3Nk_BT \quad
+
<\sum_i {\bf q}_i \nabla_{{\bf q}_i} \foo>
= 3Nk_BT \quad
\stackrel{\textrm{kart. Koord.}}{\Rightarrow} \quad
\stackrel{\textrm{kart. Koord.}}{\Rightarrow} \quad
- - \sum_i {\bf r}_i \nabla_{{\bf r}_i} \pot = -3Nk_BT \quad
+ - \frac{1}{3} <\sum_i {\bf r}_i \nabla_{{\bf r}_i} \foo> = -Nk_BT
+ \]
+ \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
\item W"armekapazit"at
\item Struktur Werte
\item Diffusion