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diff --git a/poster_aps_mm_2020.tex b/poster_aps_mm_2020.tex index 3fc9316..658d988 100644 --- 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} |