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| -rw-r--r-- | poster_aps_mm_2020.tex | 130 | ||||
| -rw-r--r-- | rus_resonances.jpg | bin | 0 -> 164557 bytes | |||
| -rw-r--r-- | urusi_modes.png | bin | 0 -> 156232 bytes |
3 files changed, 62 insertions, 68 deletions
diff --git a/poster_aps_mm_2020.tex b/poster_aps_mm_2020.tex index 7451fff..3fc9316 100644 --- a/poster_aps_mm_2020.tex +++ b/poster_aps_mm_2020.tex @@ -45,6 +45,45 @@ \font\cpp=cmr24 \def\max{\mathrm{max}} +% Our mysterious boy +\def\urusi{URu$_{\text2}$Si$_{\text2}$} + +\def\e{{\text{\textsc{elastic}}}} % "elastic" +\def\i{{\text{\textsc{int}}}} % "interaction" + +\def\Dfh{D$_{\text{4h}}$} + +% Irreducible representations (use in math mode) +\def\Aog{{\text A_{\text{1g}}}} +\def\Atg{{\text A_{\text{2g}}}} +\def\Bog{{\text B_{\text{1g}}}} +\def\Btg{{\text B_{\text{2g}}}} +\def\Eg {{\text E_{\text g}}} +\def\Aou{{\text A_{\text{1u}}}} +\def\Atu{{\text A_{\text{2u}}}} +\def\Bou{{\text B_{\text{1u}}}} +\def\Btu{{\text B_{\text{2u}}}} +\def\Eu {{\text E_{\text u}}} + +% Variables to represent some representation +\def\X{\text X} +\def\Y{\text Y} + +% Units +\def\J{\text J} +\def\m{\text m} +\def\K{\text K} +\def\GPa{\text{GPa}} +\def\A{\text{\r A}} + +% Other +\def\op{\textsc{op}} % order parameter +\def\ho{\textsc{ho}} % hidden order +\def\rus{\textsc{rus}} % resonant ultrasound spectroscopy +\def\Rus{\textsc{Rus}} % Resonant ultrasound spectroscopy +\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} @@ -55,38 +94,25 @@ \begin{multicols}{2} - \section{Introduction} + \section{Resonant ultrasound spectroscopy} \Large \begin{wrapfigure}{r}{.25\textwidth} \centering - %\includegraphics[width=0.25\textwidth]{imgs/crack.jpg} - \caption{Cracking in concrete.} + \includegraphics[width=0.25\textwidth]{rus_resonances.jpg} + \caption{Resonances } \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. - + Strain measures the displacement of material from its equilibrium configuration. \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 ($\beta=10$).} + \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} @@ -105,12 +131,21 @@ \section{Homogeneous Scaling} - \begin{wrapfigure}{r}{0.25\textwidth} + \begin{wrapfigure}{}{0.6\columnwidth} \centering - %\includegraphics[width=0.25\textwidth]{imgs/ashivni.png} - \captionof{figure}{The `phase diagram' for fracture in homogeneous - systems.} - \label{ashivni} + \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 @@ -140,12 +175,7 @@ \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}\\ + \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.} @@ -156,22 +186,6 @@ \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 @@ -184,29 +198,9 @@ \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 diff --git a/rus_resonances.jpg b/rus_resonances.jpg Binary files differnew file mode 100644 index 0000000..d4f5266 --- /dev/null +++ b/rus_resonances.jpg diff --git a/urusi_modes.png b/urusi_modes.png Binary files differnew file mode 100644 index 0000000..cec7388 --- /dev/null +++ b/urusi_modes.png |
