% vim: set foldmethod=marker foldmarker=<<<,>>>:

\section{Introduction}

\begin{FIframe}{Particulate Flows}{} %<<<

  \begin{columns}
    \column{0.6\textwidth}

      {\bf Applications:}

      \begin{itemize}
        \item Colloidal suspensions, emulsions

        \item Cellular biology, complex fluids

        \item Janus particles, clustering, self-assembly
      \end{itemize}

      % TODO: application
      % TODO: motivation, challenges

    \column{0.4\textwidth}

    \centering
    \includegraphics[width=0.75\textwidth]{figs/colloid}

    \vspace{-0.5em}
    {\footnotesize Source: Wikipedia}

  \end{columns}

  \includegraphics[width=0.25\textwidth]{figs/janus-bilayer}
  \hfill
  \includegraphics[width=0.71\textwidth]{figs/stenosis}

  {\footnotesize Fu, Quaife, Ryham, Young (2021)}
  \hspace{0.23\textwidth}
  {\footnotesize Lu, Rahimian, Zorin (JCP 2017)}

\end{FIframe} %>>>

\begin{FIframe}{Challenges}{} %<<<

  {Example: Sedimenting rings in Stokes flow}
  \begin{columns}
    \begin{column}[T]{0.6\textwidth}
      \centering
      \only<1>{
        \embedvideo{\includegraphics[width=0.99\textwidth]{videos/sed2-top-zoom1}}{videos/sed2-top-zoom1.avi}
      }
      \only<2->{
        \resizebox{0.99\textwidth}{!}{\begin{tikzpicture}%<<<
          \pgfplotsset{
            xmin=0, xmax=250,
            width=12cm, height=7cm,
            xlabel={$T$}, xtick distance=50,
          }
          \begin{axis}[ymin=0, ymax=110, ylabel={$N_{iter}$}, legend style={draw=none,at={(0,1)},anchor=north west}]
            \addplot [thick,color=blue] table [x={t},y={noprecond}] {data/sed2}; \addlegendentry{no-preconditioner};
            \addplot [thick,color=red] table [x={t},y={precond}] {data/sed2}; \addlegendentry{block-preconditioner};
            %\addplot [thick,color=green] table [x={t},y={KSPprecond}] {data/sed2}; \addlegendentry{Krylov-preconditioner};
          \end{axis}

          \begin{axis}[axis y line*=right, ymin=0, ymax=65000, ylabel={$N$}, legend style={draw=none,at={(0.97,0.97)},anchor=north east}]
            \addplot [thick,dashed,color=black] table [x={t},y={N}] {data/sed2}; \addlegendentry{$N$};
          \end{axis}
        \end{tikzpicture}}%>>>
      }
    \end{column}
    \begin{column}[T]{0.347\textwidth}
      \centering
      \only<1>{
        \embedvideo{\includegraphics[width=0.99\textwidth]{videos/sed2-side-color}}{videos/sed2-side-color.mov}
      }
      \only<2->{
        \vspace{0.4em}
        \includegraphics[width=0.99\textwidth]{videos/sed2-side-color_}
      }
    \end{column}
  \end{columns}

  \vspace{0.3em}
  \only<3->{
    {\bf Close interactions:}

    \center
    {\bf $\sim 5\times$ more unknowns, \qquad $\sim 5\times$ more GMRES iterations, \qquad $\sim 5\times$ smaller $\Delta T$}

    \vspace{0.3em}
    {\LARGE \bf\color{red} $>100 \times$ slower!}
  }

\end{FIframe} %>>>

