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authorJaron Kent-Dobias <jaron@kent-dobias.com>2020-01-31 15:01:56 -0500
committerJaron Kent-Dobias <jaron@kent-dobias.com>2020-01-31 15:01:56 -0500
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--- a/poster_aps_mm_2020.tex
+++ b/poster_aps_mm_2020.tex
@@ -1,9 +1,3 @@
-%
-% 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}
@@ -18,7 +12,6 @@
\mathtoolsset{showonlyrefs=true}
-
\setlength\textwidth{194pc}
\begin{document}
@@ -84,134 +77,80 @@
\def\afm{\textsc{afm}} % antiferromagnetism
\def\recip{{\{-1\}}} % functional reciprocal
- \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{Resonant ultrasound spectroscopy}
- \Large
-
- \begin{wrapfigure}{r}{.25\textwidth}
- \centering
- \includegraphics[width=0.25\textwidth]{rus_resonances.jpg}
- \caption{Resonances }
- \end{wrapfigure}
-
- Strain measures the displacement of material from its equilibrium configuration.
-
- \section{Fuse Networks}
-
- \begin{wrapfigure}{l}{.25\textwidth}
- \centering
- \includegraphics[width=0.55\columnwidth]{urusi_modes.png}
- \captionof{figure}{
- The crystal structure of \urusi\ and the influence of irreducible strains on it.
- }
- \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}{}{0.6\columnwidth}
- \centering
- \includegraphics[width=0.6\columnwidth]{paper/phase_diagram_experiments}
-
- \vspace{1em}
-
- \includegraphics[width=0.3\columnwidth]{paper/phases_scalar}\hspace{-0.75em}
- \includegraphics[width=0.3\columnwidth]{paper/phases_vector}
- \captionof{figure}{
- Phase diagrams for (a) \urusi\ from Phys Rev B \textbf{77} 115117 (2008) (b) mean
- field theory of a one-component ($\Bog$ or $\Btg$) Lifshitz point (c) mean
- field theory of a two-component ($\Eg$) Lifshitz point. Solid lines denote
- continuous transitions, while dashed lines denote first order transitions.
- }
- \label{phase_diagram}
- \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=\columnwidth]{paper/fig-stiffnesses.pdf}
- \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}
-
-
- \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.
-
-
- \section{Next Steps}
-
-
- \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}
+\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{Resonant ultrasound spectroscopy}
+ \Large
+
+ \begin{wrapfigure}{R}{.25\textwidth}
+ \centering
+ \includegraphics[width=0.25\textwidth]{rus_resonances.jpg}
+ \caption{Resonances }
+ \end{wrapfigure}
+
+ Strain measures the displacement of material from its equilibrium configuration.
+ \lipsum[1]
+
+ \begin{wrapfigure}{L}{.25\textwidth}
+ \centering
+ \includegraphics[width=0.55\columnwidth]{urusi_modes.png}
+ \captionof{figure}{
+ The crystal structure of \urusi\ and the influence of irreducible strains on it.
+ }
+ \label{nets}
+ \end{wrapfigure}
+
+ \lipsum[2-4]
+
+ \begin{wrapfigure}{R}{0.6\columnwidth}
+ \centering
+ \includegraphics[width=0.6\columnwidth]{paper/phase_diagram_experiments}
+
+ \vspace{1em}
+
+ \includegraphics[width=0.3\columnwidth]{paper/phases_scalar}\hspace{-0.75em}
+ \includegraphics[width=0.3\columnwidth]{paper/phases_vector}
+ \captionof{figure}{
+ Phase diagrams for (a) \urusi\ from Phys Rev B \textbf{77} 115117 (2008) (b) mean
+ field theory of a one-component ($\Bog$ or $\Btg$) Lifshitz point (c) mean
+ field theory of a two-component ($\Eg$) Lifshitz point. Solid lines denote
+ continuous transitions, while dashed lines denote first order transitions.
+ }
+ \label{phase_diagram}
+ \end{wrapfigure}
+
+ \lipsum[4-5]
+
+ \begin{equation}
+ C_\X(0)=C_\X^0\bigg[1+\frac{b^2}{C_\X^0}\big(D_\perp q_*^4+|\Delta\tilde r|\big)^{-1}\bigg]^{-1}.
+ \label{eq:static_modulus}
+ \end{equation}
+
+ \begin{figure}
+ \vspace{1pc}
+ \centering
+ \includegraphics[width=\columnwidth]{paper/fig-stiffnesses.pdf}
+ \captionof{figure}{
+ \Rus\ measurements of the elastic moduli of \urusi\ at ambient pressure
+ as a function of temperature from \texttt{arXiv:1903.00552
+ [cond-mat.str-el]} (blue, solid) alongside fits to theory (magenta,
+ dashed). The solid yellow region shows the location of the \ho\ phase.
+ (a) $\Btg$ modulus data and a fit to the standard form. (b) $\Bog$
+ modulus data and a fit to \eqref{eq:static_modulus}. (c) $\Bog$ modulus
+ data and the fit of the \emph{bare} $\Bog$ modulus. (d) $\Bog$ modulus
+ data and the fit transformed by $[C^0_\Bog(C^0_\Bog/C_\Bog-1)]]^{-1}$,
+ which is predicted from \eqref{eq:static_modulus} to equal $D_\perp
+ q_*^4/b^2+a/b^2|T-T_c|$, e.g., an absolute value function.
+ }
+ \label{homo}
+ \vspace{1pc}
+ \end{figure}
+\end{multicols}
+\end{document}