projects
/
lectures
/
latex.git
/ commitdiff
commit
grep
author
committer
pickaxe
?
search:
re
summary
|
shortlog
|
log
|
commit
| commitdiff |
tree
raw
|
patch
|
inline
| side by side (from parent 1:
5d82917
)
potentials, and thermo obs not yet finished
author
hackbard
<hackbard>
Wed, 13 Jun 2007 19:46:07 +0000
(19:46 +0000)
committer
hackbard
<hackbard>
Wed, 13 Jun 2007 19:46:07 +0000
(19:46 +0000)
posic/talks/md_simulation_von_silizium.tex
patch
|
blob
|
history
diff --git
a/posic/talks/md_simulation_von_silizium.tex
b/posic/talks/md_simulation_von_silizium.tex
index
5c8db3b
..
47e144a
100644
(file)
--- a/
posic/talks/md_simulation_von_silizium.tex
+++ b/
posic/talks/md_simulation_von_silizium.tex
@@
-39,6
+39,9
@@
\def\slideleftmargin{5.1cm}
\def\slidetopmargin{-0.6cm}
\def\slideleftmargin{5.1cm}
\def\slidetopmargin{-0.6cm}
+\newcommand{\ham}{\mathcal{H}}
+\newcommand{\pot}{\mathcal{V}}
+
% topic
\begin{slide}
% topic
\begin{slide}
@@
-515,14
+518,27
@@
Problemstellung: Finden der Nachbarn f"ur Wechselwirkung
\begin{itemize}
\item Innere Energie:
\[
\begin{itemize}
\item Innere Energie:
\[
- E = <K> + <U> = < \sum_i \frac{|{\bf p}_i|^2}{2m_i} > + <U({\bf q})>
+ E = <K> + <U> = < \sum_i \frac{{\bf p}_i^2}{2m_i} > + <U({\bf q})>
+ \]
+ \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}
+ \begin{center}
+ "Aquipartitionstheorem
+ \end{center}
+ Temperatur:
+ \[
+ \sum_i {\bf p}_i \frac{{\bf p}_i}{m_i} = 3Nk_BT \quad
+ \Rightarrow \quad T=\frac{1}{3Nk_B} \sum_i \frac{{\bf p}_i^2}{m_i}
\]
\]
-
\item Temperatur
:
+
Druck
:
\[
\[
- E_{kin}=<K>=\frac{3}{2}Nk_BT
- \Rightarrow T=\frac{1}{3Nk_B} \sum_i \frac{|{\bf p}_i|^2}{m_i}
+ \sum_i {\bf q}_i \nabla_{{\bf q}_i} \pot = 3Nk_BT \quad
+ \stackrel{\textrm{kart. Koord.}}{\Rightarrow} \quad
+ - \sum_i {\bf r}_i \nabla_{{\bf r}_i} \pot = -3Nk_BT \quad
\]
\]
- \item Druck
\item W"armekapazit"at
\item Struktur Werte
\item Diffusion
\item W"armekapazit"at
\item Struktur Werte
\item Diffusion
@@
-539,6
+555,7
@@
Problemstellung: Finden der Nachbarn f"ur Wechselwirkung
{\large\bf
EAM
}
{\large\bf
EAM
}
+
\end{slide}
\begin{slide}
\end{slide}
\begin{slide}