Merge pull request #1 from AndreasFMueller/master

update

1 files changed, 89 insertions, 0 deletions

diff --git a/vorlesungen/slides/8/diffusion.tex b/vorlesungen/slides/8/diffusion.tex
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+++ b/vorlesungen/slides/8/diffusion.tex
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+%
+% diffusion.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\begin{frame}[t]
+\frametitle{Diffusion}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+
+\def\r{2.2}
+
+\coordinate (A) at ({\r*cos(0*72)},{\r*sin(0*72)});
+\coordinate (B) at ({\r*cos(1*72)},{\r*sin(1*72)});
+\coordinate (C) at ({\r*cos(2*72)},{\r*sin(2*72)});
+\coordinate (D) at ({\r*cos(3*72)},{\r*sin(3*72)});
+\coordinate (E) at ({\r*cos(4*72)},{\r*sin(4*72)});
+
+\draw[shorten >= 0.3cm,shorten <= 0.3cm] (A) -- (C);
+\draw[color=white,line width=5pt] (B) -- (D);
+\draw[shorten >= 0.3cm,shorten <= 0.3cm] (B) -- (D);
+
+\draw[shorten >= 0.3cm,shorten <= 0.3cm] (A) -- (B);
+\draw[shorten >= 0.3cm,shorten <= 0.3cm] (B) -- (C);
+\draw[shorten >= 0.3cm,shorten <= 0.3cm] (C) -- (D);
+\draw[shorten >= 0.3cm,shorten <= 0.3cm] (D) -- (E);
+\draw[shorten >= 0.3cm,shorten <= 0.3cm] (E) -- (A);
+
+\draw[->,color=darkgreen,line width=8pt,shorten <= 0.25cm,shorten >= 0cm]
+	(A) -- (E);
+\draw[->,color=darkgreen,line width=2pt,shorten <= 0.25cm,shorten >= 0.25cm]
+	(A) -- (B);
+\draw[->,color=darkgreen,line width=4pt,shorten <= 0.25cm,shorten >= 0.15cm]
+	(A) -- (C);
+\draw[->,color=darkgreen,line width=2pt,shorten <= 0.25cm,shorten >= 0.25cm]
+	(B) -- (C);
+\draw[->,color=darkgreen,line width=2pt,shorten <= 0.25cm,shorten >= 0.25cm]
+	(C) -- (D);
+\draw[->,color=darkgreen,line width=2pt,shorten <= 0.25cm,shorten >= 0.25cm]
+	(D) -- (E);
+\draw[->,color=darkgreen,line width=4pt,shorten <= 0.25cm,shorten >= 0.15cm]
+	(B) -- (D);
+
+\fill[color=red] (A) circle[radius=0.3];
+\fill[color=red!50] (B) circle[radius=0.3];
+\fill[color=white] (C) circle[radius=0.3];
+\fill[color=blue!50] (D) circle[radius=0.3];
+\fill[color=blue] (E) circle[radius=0.3];
+
+\draw (A) circle[radius=0.3];
+\draw (B) circle[radius=0.3];
+\draw (C) circle[radius=0.3];
+\draw (D) circle[radius=0.3];
+\draw (E) circle[radius=0.3];
+
+\node at (A) {$1$};
+\node at (B) {$2$};
+\node at (C) {$3$};
+\node at (D) {$4$};
+\node at (E) {$5$};
+\node at (0,0) {$G$};
+
+\end{tikzpicture}
+\end{center}
+\vspace{-10pt}
+\begin{block}{Knotenfunktion}
+$f\colon V\to \mathbb{R}$
+\end{block}
+\end{column}
+\begin{column}{0.48\textwidth}
+\begin{block}{Fluss}
+Je grösser die Differenz zu den Nachbarn, desto grösser der Fluss in 
+den Knoten:
+\begin{align*}
+\frac{df(v)}{dt}
+&=
+\kappa \sum_{\text{$v'$ Nachbar von $v$}} (f(v')-f(v))
+\end{align*}
+``Wärmeleitungsgleichung''
+\end{block}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup