168 lines
		
	
	
		
			3.6 KiB
		
	
	
	
		
			TeX
		
	
	
	
	
	
			
		
		
	
	
			168 lines
		
	
	
		
			3.6 KiB
		
	
	
	
		
			TeX
		
	
	
	
	
	
| \section{Intro}
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| 
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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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| 
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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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| 
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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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| 
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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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| 
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| \section{ECM Model}
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| 
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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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| 
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| \vfill{}
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| 
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| Two main requirements:
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| 
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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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| 
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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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| 
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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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| 
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| \begin{frame}{My Approach}
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| Two main requirements:
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| 
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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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| 
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| \section{Methods}
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| 
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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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| \[
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| f_i(\mathbf{x} + \mathbf{c}_i, t + 1) = f_i(\mathbf{x}, t) - \frac{1}{\tau} (f_i(\mathbf{x}, t) - f_i^\text{eq}(\mathbf{x}, t))
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| \]
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| 
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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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| 
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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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| 
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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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| 
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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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| 
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| \begin{frame}{My Approach}
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| Two main requirements:
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| 
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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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| 
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| \vfill
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| 
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| Challenges:
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| 
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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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| 
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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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