168 lines
3.6 KiB
TeX
168 lines
3.6 KiB
TeX
\section{Intro}
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\begin{frame}{NAStJA: An MPI Stencil Code Solver}
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\begin{figure}
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\includegraphics[width=0.8\textwidth]{nastja.png}
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\end{figure}
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\begin{itemize}
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\item CiS uses NAStJA under the hood
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\item NAStJA is a massively parallel stencil code solver \\
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$\implies$ CiS extensions should be stencils
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\end{itemize}
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\end{frame}
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\begin{frame}{ECM Viscoelasticity:\\A Factor in Cell Behavior}
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\begin{figure}
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\includegraphics[width=0.48\textwidth]{ecm-cells.png}
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\end{figure}
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\begin{itemize}
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\item Collagen networks in the ECM mechanically restrict cells
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\item Collagen networks are \emph{viscoelastic}
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\item ECM viscoelasticity influences cell behavior
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\end{itemize}
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\end{frame}
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\section{ECM Model}
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\begin{frame}{Modeling ECM Mechanics in CiS}
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How can we model ECM mechanics in CiS?
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\vfill{}
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Two main requirements:
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\begin{itemize}
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\item Model exhibits viscoelastic properties
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\item Model can be implemented as a stencil in NAStJA
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\end{itemize}
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\end{frame}
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\begin{frame}{ECM Models in Literature}
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\begin{figure}
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\includegraphics[width=0.64\textwidth]{models.png}
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\end{figure}
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\begin{itemize}
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\item A host of different ECM models exist
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\item Various foci, e.g. mechanics, growth factors
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\item Various approaches, e.g. FEM, Molecular Dynamics
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\end{itemize}
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\end{frame}
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\begin{frame}{My Approach}
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Two main requirements:
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\begin{itemize}
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\item Model exhibits viscoelastic properties
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\item Model can be implemented as a stencil in NAStJA
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\end{itemize}
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\end{frame}
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\section{Methods}
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\begin{frame}{Lattice Boltzmann Method}
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\begin{figure}
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\includegraphics[width=0.6\textwidth]{lbm.png}
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\end{figure}
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\[
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f_i(\mathbf{x} + \mathbf{c}_i, t + 1) = f_i(\mathbf{x}, t) - \frac{1}{\tau} (f_i(\mathbf{x}, t) - f_i^\text{eq}(\mathbf{x}, t))
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\]
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\begin{itemize}
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\item Discretized particle velocities per lattice site
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\item Update Step: Streaming + Collision
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\item Usually used for hydrodynamics
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\end{itemize}
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\end{frame}
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\begin{frame}{Elastic Lattice Model}
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\begin{columns}
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\column{0.35\textwidth}
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\begin{figure}
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\includegraphics[width=\textwidth]{elm.png}
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\end{figure}
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\column{0.65\textwidth}
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\[
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\mathbf{F}_{ij} = \mathbf{r}_{ij} K_{ij} (\mathbf{u}_{ij} \cdot \mathbf{x}_{ij}) + \frac{c \mathbf{u}_{ij}}{|\mathbf{x}_{ij}|^2} + \eta \mathbf{v}_{ij}
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\]
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\begin{itemize}
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\item A square lattice based discrete particle method
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\item Each lattice site represents a particle
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\item Particles are connected to neighbors by springs
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\end{itemize}
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\end{columns}
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\end{frame}
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\begin{frame}{My Approach}
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Two main requirements:
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\begin{itemize}
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\item Model exhibits viscoelastic properties \checkmark{}
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\item Model can be implemented as a stencil in NAStJA \checkmark{}
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\end{itemize}
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\vfill
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Challenges:
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\begin{itemize}
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\item How do we integrate the model with the CPM?
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\item How can it be implemented in NAStJA?
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\item How do we make it fast?
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\end{itemize}
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\end{frame}
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\begin{comment}
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\section{Intro}
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\subsection{Subsection 1.1}
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\frame{
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\frametitle{Example slide A}
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\begin{itemize}
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\item PCM, Citation: \cite{dh76,kl07} %\language
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\pause
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\item Bullet point 2
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\item \dots
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\end{itemize}
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}
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\subsection{Subsection 1.2}
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\frame{
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\frametitle{Example slide B}
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\begin{block}{Block 1}
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\begin{itemize}
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\item Test: <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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\pause
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\item Bullet point 2
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\item \dots
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\end{itemize}
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\end{block}
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}
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\section{Section 2}
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\frame{
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\frametitle{Example slide C}
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\begin{exampleblock}{Example 1}
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\begin{itemize}
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\item Bullet point 1
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\pause
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\item Bullet point 2
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\item \dots
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\end{itemize}
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\end{exampleblock}
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}
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\frame{
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\frametitle{Example slide D}
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\begin{alertblock}{Alert 1}
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\begin{itemize}
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\item Bullet point 1
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\pause
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\item Bullet point 2
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\item \dots
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\end{itemize}
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\end{alertblock}
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}
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\end{comment}
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