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authorJaron Kent-Dobias <jaron@kent-dobias.com>2019-09-04 20:59:21 -0400
committerJaron Kent-Dobias <jaron@kent-dobias.com>2019-09-04 20:59:21 -0400
commit812fb72add44d14795bd0d5a0a9c36c538c00665 (patch)
tree8b94e0f0f8803993817f054bdeee36b1398eb3ff
parentc74772beba718bdd28d25ee4a8628c7caaa3083d (diff)
downloadaps_mm_2019-master.tar.gz
aps_mm_2019-master.tar.bz2
aps_mm_2019-master.zip
final changesHEADmaster
-rw-r--r--figs/plot-avalanche-aspect.pdfbin0 -> 23619 bytes
-rw-r--r--figs/plot-cluster-ratio.pdfbin0 -> 22549 bytes
-rw-r--r--figs/plot-cluster-x.pdfbin0 -> 22614 bytes
-rw-r--r--figs/plot-cluster-y.pdfbin0 -> 23108 bytes
-rw-r--r--mm_2019.tex67
5 files changed, 46 insertions, 21 deletions
diff --git a/figs/plot-avalanche-aspect.pdf b/figs/plot-avalanche-aspect.pdf
new file mode 100644
index 0000000..648b116
--- /dev/null
+++ b/figs/plot-avalanche-aspect.pdf
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diff --git a/figs/plot-cluster-ratio.pdf b/figs/plot-cluster-ratio.pdf
new file mode 100644
index 0000000..bfb1854
--- /dev/null
+++ b/figs/plot-cluster-ratio.pdf
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diff --git a/figs/plot-cluster-x.pdf b/figs/plot-cluster-x.pdf
new file mode 100644
index 0000000..2b1e945
--- /dev/null
+++ b/figs/plot-cluster-x.pdf
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diff --git a/figs/plot-cluster-y.pdf b/figs/plot-cluster-y.pdf
new file mode 100644
index 0000000..1862880
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+++ b/figs/plot-cluster-y.pdf
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diff --git a/mm_2019.tex b/mm_2019.tex
index fedeace..c512ab9 100644
--- a/mm_2019.tex
+++ b/mm_2019.tex
@@ -77,12 +77,11 @@
\begin{columns}
\begin{column}{0.5\textwidth}
\begin{overprint}
- \onslide<1,3>\includegraphics[width=\textwidth]{figs/plain_square}
- \onslide<2>\includegraphics[width=\textwidth]{figs/uncut_square}
- \onslide<4>\includegraphics[width=\textwidth]{figs/perc_square}
- \onslide<5>\includegraphics[width=\textwidth]{figs/med_square}
- \onslide<6>\includegraphics[width=\textwidth]{figs/nuke_square}
- \onslide<7>\includegraphics[width=\textwidth]{figs/nuke_voronoi}
+ \onslide<1>\includegraphics[width=\textwidth]{figs/plain_square}
+ \onslide<2>\includegraphics[width=\textwidth]{figs/perc_square}
+ \onslide<3>\includegraphics[width=\textwidth]{figs/med_square}
+ \onslide<4>\includegraphics[width=\textwidth]{figs/nuke_square}
+ \onslide<5>\includegraphics[width=\textwidth]{figs/nuke_voronoi}
\end{overprint}
\end{column}
\begin{column}{0.5\textwidth}
@@ -101,15 +100,15 @@
\bigskip
- \alert<4>{Small $\beta$} is disordered, \alert<6->{large $\beta$} ordered
+ \alert<2>{Small $\beta$} is disordered, \alert<4->{large $\beta$} ordered
\medskip
\begin{overprint}
- \onslide<1-3>\includegraphics[width=\textwidth]{figs/dist-all}
- \onslide<4>\includegraphics[width=\textwidth]{figs/dist-small}
- \onslide<5>\includegraphics[width=\textwidth]{figs/dist-med}
- \onslide<6->\includegraphics[width=\textwidth]{figs/dist-large}
+ \onslide<1>\includegraphics[width=\textwidth]{figs/dist-all}
+ \onslide<2>\includegraphics[width=\textwidth]{figs/dist-small}
+ \onslide<3>\includegraphics[width=\textwidth]{figs/dist-med}
+ \onslide<4->\includegraphics[width=\textwidth]{figs/dist-large}
\end{overprint}
\end{column}
\end{columns}
@@ -149,7 +148,7 @@
\begin{frame}
\frametitle{Fixed points}
- \framesubtitle{$\pmb\beta\pmb=\pmb0$ -- percolation}
+ \framesubtitle{$\pmb\beta\pmb=\pmb0$ -- isotropic, self-similar percolation}
\begin{columns}
\begin{column}{0.5\textwidth}
\begin{overprint}
@@ -181,7 +180,7 @@
\begin{frame}
\frametitle{Fixed points}
- \framesubtitle{$\pmb\beta=\infty$ -- nucleation}
+ \framesubtitle{$\pmb\beta=\infty$ -- anisotropic, self-affine nucleation}
\begin{columns}
\begin{column}{0.5\textwidth}
As $L\to\infty$, $\beta\to\infty$, reduces to nucleated crack propagation
@@ -212,13 +211,13 @@
\end{frame}
\begin{frame}
- \frametitle{Self-similarity vs.\ self-affinity}
+ \frametitle{Self-similarity to self-affinity}
Voltage (strain) applied along one direction---we should expect anisotropy!
\bigskip
- Clean cracks are \emph{self-affine}, self-similar under different rescalings of $x$ and $y$
+ Self-affine anisotropy emerges at different scales in different properties, but well within the intermediate microfractured regime.
\begin{overprint}
@@ -232,18 +231,39 @@
\begin{frame}
\frametitle{Scaling theory}
- Old: quantities like moments of $g$ depend on $L\beta^\nu$
+ \begin{columns}
+ \begin{column}{0.5\textwidth}
+ Quantities like moments of $g$ depend on $L_x\beta^{\nu_x}$ and $L_y\beta^{\nu_y}$, no simple ``collapse''
- \bigskip
+ \bigskip
- New: quantities like moments of $g$ depend on $L_x\beta^{\nu_x}$ and $L_y\beta^{\nu_y}$
+ Show expected isotropic percolation scaling in disordered limit, unusual crossover in the intermediate regieme.
- \bigskip
+ \bigskip
- \centering
+ Spatial properties of avalanches remain anisotropic in all regiemes.
+
+ \vspace{18pc}
+ \end{column}
+ \begin{column}{0.5\textwidth}
+ \begin{overprint}
+ \onslide<1>
+ \vspace{-1em}
+
+ \includegraphics[width=\textwidth]{figs/plot-cluster-x}
+
+ \vspace{1em}
+
+ \includegraphics[width=\textwidth]{figs/plot-cluster-y}
+
+ \vspace{1em}
- \huge FIGURE: EXAMPLE SCALING OF $x$ AND $y$ MOMENTS OF $g$ SHOWING DIFFERENT $\nu$
+ \includegraphics[width=\textwidth]{figs/plot-cluster-ratio}
+ \onslide<2>\includegraphics[width=\textwidth]{figs/plot-avalanche-aspect}
+\end{overprint}
+ \end{column}
+\end{columns}
\end{frame}
@@ -273,5 +293,10 @@
\end{frame}
+\begin{frame}
+ \centering
+ \Huge\bf Questions?
+\end{frame}
+
\end{document}