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+%
+%  poster_05.2014.tex - description
+%
+%  Created by  on Tue May 13 12:26:55 PDT 2014.
+%  Copyright (c) 2014 pants productions. All rights reserved.
+%
+\documentclass[portrait]{a0poster}
+
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage[]{amsmath}
+\usepackage{amssymb,latexsym,mathtools,multicol,lipsum,wrapfig}
+\usepackage[font=normalsize,labelfont=bf]{caption}
+\usepackage{tgheros}
+\usepackage[helvet]{sfmath}
+\usepackage[export]{adjustbox}
+\renewcommand*\familydefault{\sfdefault}
+
+\mathtoolsset{showonlyrefs=true}
+
+
+\setlength\textwidth{194pc}
+\begin{document}
+
+\setlength\columnseprule{2pt}
+\setlength\columnsep{5pc}
+\renewenvironment{figure}
+  {\par\medskip\noindent\minipage{\linewidth}}
+    {\endminipage\par\medskip}
+
+    \renewcommand\section[1]{
+    \vspace{3pc}
+    \noindent\huge\textbf{#1}\large
+    \vspace{1.5pc}
+  }
+
+  \newcommand\unit[1]{\hat{\vec{#1}}}
+  \renewcommand\vec[1]{\boldsymbol{\mathbf{#1}}}
+  \newcommand\norm[1]{\|#1\|}
+  \def\rr{\rho}
+  \newcommand\abs[1]{|#1|}
+  \def\dd{\mathrm d}
+  \def\rec{\mathrm{rec}}
+\def\CC{{C\kern-.05em\lower-.4ex\hbox{\cpp +\kern-0.05em+}} }
+\font\cpp=cmr24
+\def\max{\mathrm{max}}
+
+  \noindent\hspace{177pc}\includegraphics[width=18pc]{CULogo-red120px.eps}
+  \vspace{-24.5pc}\\
+  \Huge \textbf{Elastic properties of hidden order in URu$_{\text2}$Si$_{\text2}$ are reproduced by\\ staggered nematic order}
+  \bigskip\\
+  \huge \textbf{Jaron~Kent-Dobias, Michael Matty \& Brad J Ramshaw}
+  \vspace{1pc}
+
+
+  \begin{multicols}{2}
+
+    \section{Introduction}
+    \Large
+
+    \begin{wrapfigure}{r}{.25\textwidth}
+      \centering
+      %\includegraphics[width=0.25\textwidth]{imgs/crack.jpg}
+      \caption{Cracking in concrete.}
+    \end{wrapfigure}
+
+    Understanding material cracking and fracture is necessary for
+    understanding the aging and failure of those materials in our buildings
+    and infrastructure.  In ordinary brittle materials like glass, stress at
+    the tip of a crack causes it to quickly and cleanly propagate through the
+    material.  In ductile materials like metals, this stress is reduced by
+    plastic deformation around the crack tip, forming the crack's
+    \textbf{process zone}.  In quasi- (or disordered) brittle materials like
+    concrete, this stress is reduced by opening a complicated network of
+    microcracks in the process zone.  This makes the structure of the
+    quasibrittle process zone and crack propagation
+    difficult to study by ordinary means.
+
+
+    \section{Fuse Networks}
+
+    \begin{wrapfigure}{l}{.25\textwidth}
+      \centering
+      %\includegraphics[width=0.12\textwidth]{imgs/square_network.pdf}
+      %\includegraphics[width=0.12\textwidth]{imgs/square_high_beta.pdf}\\
+      %\includegraphics[width=0.12\textwidth]{imgs/voronoi_network.pdf}
+      %\includegraphics[width=0.12\textwidth]{imgs/voronoi_high_beta.pdf}
+      \captionof{figure}{Contrasting the square (top) and voronoi (bottom) networks.  {\bf Left:} Unbroken fuse networks. {\bf Right:} A
+    fracture surface in each at low disorder ($\beta=10$).}
+      \label{nets}
+    \end{wrapfigure}
+
+    \Large
+
+    We model quasibrittle cracking and fracture using simulations of fuse
+    networks, which are electrical systems of resistive fuses whose random
+    current thresholds $t$ are cumulatively distributed by $t^\beta$.  $\beta$
+    parameterizes the amount of disorder in the system: large
+    $\beta$ corresponds to vanishing disorder, small $\beta$ to very large
+    disorder.  Fracture is performed adiabatically: the fuse whose ratio of
+    current to threshold is largest breaks, and the current across the
+    networks is recomputed.  In order to reduce lattice effects, which become large for
+    small disorder (see Figure \ref{nets}), we use voronoi meshes for our fuse networks.
+
+
+    \section{Homogeneous Scaling}
+
+    \begin{wrapfigure}{r}{0.25\textwidth}
+      \centering
+      %\includegraphics[width=0.25\textwidth]{imgs/ashivni.png}
+      \captionof{figure}{The `phase diagram' for fracture in homogeneous
+      systems.}
+      \label{ashivni}
+    \end{wrapfigure}
+
+    \Large
+
+    The problem of fracture in fuse networks was unresolved until recently.
+    For low disorder, fracture is nucleation-like, similar to that of ordinary
+    brittle systems.  At large disorder, fracture occurs after a very large
+    amount of uncorrelated damage, and appears percolation-like.
+    Sethna and Shekhawat developed a theory which unifies these behaviors with
+    an {\sc rg} crossover at intermediate disorder characterized by mean-field
+    avalanches.  The percolation-like behavior at high disorder was shown to
+    be unstable under course-graining, and therefore any nonzero $\beta$
+    will cause nucleated fracture at a sufficiently large system size (see
+    Figure \ref{ashivni}).
+
+    In unpublished work, Shekhawat and Sethna found a scaling form for the
+    distribution of network strengths $\sigma_\max$, the largest current
+    applied to the network before it has broken.  It is given by
+    \begin{equation}
+      P(\sigma_\max\mid\beta, L,u)=\sigma_\max^{-\tau_\sigma}\mathcal P(\beta
+      L^{1/\nu_f},\sigma_\max L^\delta,uL^{-\Delta/\nu_f})\label{form}
+    \end{equation}
+    where $\tau_\sigma$, $\nu_f$, $\delta$ and $\Delta$ are universal
+    exponents, $L$ is the system size, and $u$ is an irrelevant scaling
+    variable.  
+
+    \begin{figure}
+      \vspace{1pc}
+      \centering
+      %\includegraphics[width=0.325\textwidth]{imgs/voronoi_homo_big.pdf}
+      %\includegraphics[width=0.325\textwidth]{imgs/voronoi_homo_med.pdf}
+      %\includegraphics[width=0.325\textwidth]{imgs/voronoi_homo_lit.pdf}\\
+      \begin{minipage}[c]{0.325\textwidth}\centering$\pmb{\beta=3}$\end{minipage}
+      \begin{minipage}[c]{0.325\textwidth}\centering$\pmb{\beta=0.5}$\end{minipage}
+      \begin{minipage}[c]{0.325\textwidth}\centering$\pmb{\beta=0.03}$\end{minipage}\\
+      \captionof{figure}{Fractured fuse networks at various $\beta$.  Each colored region shows a
+        contiguous cracked cluster.  The black region shows the surface of
+        the spanning crack.}
+      \label{homo}
+      \vspace{1pc}
+    \end{figure}
+
+
+    \section{Scaling in the Process Zone}
+
+    \begin{figure}
+      \centering
+      %\includegraphics[width=0.245\textwidth]{imgs/sample_16.pdf}
+      %\includegraphics[width=0.245\textwidth]{imgs/sample_32.pdf}
+      %\includegraphics[width=0.245\textwidth]{imgs/sample_64.pdf}
+      %\includegraphics[width=0.245\textwidth]{imgs/sample_128.pdf}\\
+      \begin{minipage}[c]{0.245\textwidth}\centering$\pmb{L=16,\;\beta=1.9}$\end{minipage}
+      \begin{minipage}[c]{0.245\textwidth}\centering$\pmb{L=32,\;\beta=1.2}$\end{minipage}
+      \begin{minipage}[c]{0.245\textwidth}\centering$\pmb{L=64,\;\beta=0.78}$\end{minipage}
+      \begin{minipage}[c]{0.245\textwidth}\centering$\pmb{L=128,\;\beta=0.5}$\end{minipage}\\
+      \captionof{figure}{Notched fuse networks at critical stress.  The
+        disorder for each system is tuned so that $\beta L^{1/\nu_f}$ is
+      constant, and the statistics of each should scale trivially.}
+      \vspace{1pc}
+      \label{notches}
+    \end{figure}
+
+    \Large
+    We have made progress for developing a scaling theory of damage and stress
+    in the process zone of quasibrittle cracks.  We have essentially taken the
+    scaling behavior of \eqref{form} as an ansatz for how the corresponding
+    qualities of a critically semi-cracked network should scale.  We have
+    begun demonstrating the validity of this theory.  Figure \ref{notches}
+    shows critically cracked networks at constant $\beta L^{1/\nu_f}$, an
+    invariant scaling combination under this theory.  As can be seen in Figure
+    \ref{collapse}, the disorder-averaged stress profiles caused by each
+    collapses nicely.
+
+    \begin{figure}
+      \centering
+      %\includegraphics[width=0.5\textwidth]{imgs/legends.pdf}\\
+      \vspace{-.5em}
+      %\includegraphics[width=0.505\textwidth,valign=t]{imgs/sample_collapse_1.pdf}\hfill
+      %\includegraphics[width=0.48\textwidth,valign=t]{imgs/sample_collapse_2.pdf}\\
+      \vspace{-.5em}
+
+      \captionof{figure}{Disorder-averaged stress $\sigma$ as a function of
+        distance $x$ from the tip of a critical crack.  $\beta L^{1/\nu_f}$ is
+        constant for each curve.  \textbf{Left:} The unmodified stress.
+        \textbf{Right:} The stress collapsed.}
+      \label{collapse}
+    \end{figure}
+
+    \section{Next Steps}
+
+    \begin{wrapfigure}{r}{0.25\textwidth}
+      \centering
+      \vspace{-2em}
+      %\includegraphics[width=.25\textwidth]{imgs/voronoi_heir.pdf}
+      \captionof{figure}{A hierarchical voronoi lattice.}
+    \end{wrapfigure}
+
+    \Large
+
+    The voronoi networks we are able to generate allow us great flexibility
+    for future multiscale computational modelling.  Once we have hashed out
+    our scaling theory more thoroughly, we plan on using it to probe much
+    larger systems than previously feasible using networks whose fuse density
+    becomes smaller in regions of less importance.  This should allow us to
+    see cleaner stress and damage scaling and cleanly stitch our discrete system to a
+    continuum approximation.
+
+  \end{multicols}
+\end{document}
+