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% temporary preamble |
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%\documentclass[ps,frames,final,nototal,slideColor,colorBG]{prosper} |
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\documentclass{seminar} |
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\usepackage{color} |
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\usepackage{amsmath} |
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\usepackage{amssymb} |
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\usepackage{wrapfig} |
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\usepackage{epsf} |
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\usepackage{jurabib} |
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% ---------------------- |
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% | Title | |
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% ---------------------- |
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\title{A Mezzoscale Model for Phospholipid MD Simulations} |
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|
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\author{Matthew A. Meineke\\ |
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Department of Chemistry and Biochemistry\\ |
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University of Notre Dame\\ |
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Notre Dame, Indiana 46556} |
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\date{\today} |
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%------------------------------------------------------------------- |
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% Begin Document |
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\begin{document} |
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\maketitle |
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\bibliography{canidacy_slides} |
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\bibliographystyle{jurabib} |
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% Slide 1 |
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\begin{slide} {Talk Outline} |
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\begin{itemize} |
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|
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\item Discussion of the research motivation and goals |
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\item Methodology |
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\item Discussion of current research and preliminary results |
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\item Future research |
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\end{itemize} |
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\end{slide} |
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% Slide 2 |
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\begin{slide}{Motivation A: Long Length Scales} |
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\begin{wrapfigure}{r}{45mm} |
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\epsfxsize=45mm |
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\epsfbox{ripple.epsi} |
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\end{wrapfigure} |
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|
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Ripple phase: |
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\begin{itemize} |
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|
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\item |
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The ripple (~$P_{\beta'}$~) phase lies in the transition from the gel |
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to fluid phase. |
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|
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\item |
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periodicity of 100 - 200 $\mbox{\AA}$\footcite{Berne90} |
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|
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\end{itemize} |
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\end{slide} |
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\begin{slide}{Motivation} |
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|
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There is a strong need in phospholipid bilayer simulations for the |
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capability to simulate both long time and length scales. Consider the |
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following: |
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|
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\begin{itemize} |
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|
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\item Drug diffusion |
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\begin{itemize} |
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\item Some drug molecules may spend an appreciable time in the |
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membrane. Long time scale dynamics are needed to observe and |
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characterize their actions. |
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\end{itemize} |
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|
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\item Ripple phase |
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\begin{itemize} |
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\item Between the bilayer gel and fluid phase there exists a ripple |
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phase. This phase has a period of about 100 - 200 $\mbox{\AA}$. |
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\end{itemize} |
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|
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\item Bilayer formation dynamics |
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\begin{itemize} |
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\item Initial simulations show that bilayers can take upwards of |
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20 ns to form completely. |
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\end{itemize} |
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|
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\end{itemize} |
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\end{slide} |
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|
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% Slide 4 |
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|
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\begin{slide}{Length Scale Simplification} |
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\begin{itemize} |
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|
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\item |
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Replace any charged interactions of the system with dipoles. |
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|
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\begin{itemize} |
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\item Allows for computational scaling approximately by $N$ for |
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dipole-dipole interactions. |
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\item In contrast, the Ewald sum scales approximately by $N \log N$. |
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\end{itemize} |
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|
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\item |
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Use unified models for the water and the lipid chain. |
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|
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\begin{itemize} |
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\item Drastically reduces the number of atoms to simulate. |
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\item Number of water interactions alone reduced by $\frac{1}{3}$. |
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\end{itemize} |
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\end{itemize} |
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\end{slide} |
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|
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% Slide 5 |
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|
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\begin{slide}{Time Scale Simplification} |
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\begin{itemize} |
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|
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\item |
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No explicit hydrogens |
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|
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\begin{itemize} |
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\item Hydrogen bond vibration is normally one of the fastest time |
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events in a simulation. |
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\end{itemize} |
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|
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\item |
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Constrain all bonds to be of fixed length. |
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|
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\begin{itemize} |
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\item As with the hydrogens, bond vibrations are the fastest motion in |
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a simulation |
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\end{itemize} |
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|
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\item |
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Allows time steps of up to 3 fs with the current integrator. |
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|
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\end{itemize} |
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\end{slide} |
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|
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% Slide 6 |
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\begin{slide}{Molecular Dynamics} |
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|
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All of our simulations will be carried out using molecular |
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dynamics. This involves solving Newton's equations of motion using |
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the classical \emph{Hamiltonian} as follows: |
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|
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\begin{equation} |
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H(\vec{q},\vec{p}) = T(\vec{p}) + V(\vec{q}) |
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\end{equation} |
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|
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Here $T(\vec{p})$ is the kinetic energy of the system which is a |
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function of momentum. In Cartesian space, $T(\vec{p})$ can be |
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written as: |
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|
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\begin{equation} |
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T(\vec{p}) = \sum_{i=1}^{N} \sum_{\alpha = x,y,z} \frac{p^{2}_{i\alpha}}{2m_{i}} |
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\end{equation} |
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|
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\end{slide} |
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|
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% Slide 7 |
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\begin{slide}{The Potential} |
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|
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The main part of the simulation is then the calculation of forces from |
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the potential energy. |
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|
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\begin{equation} |
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\vec{F}(\vec{q}) = - \nabla V(\vec{q}) |
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\end{equation} |
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|
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The potential itself is made of several parts. |
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|
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\begin{equation} |
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V_{tot} = |
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\overbrace{V_{l} + V_{\theta} + V_{\omega}}^{\mbox{bonded}} + |
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\overbrace{V_{l\!j} + V_{d\!p} + V_{s\!s\!d}}^{\mbox{non-bonded}} |
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\end{equation} |
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|
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Where the bond interactions $V_{l}$, $V_{\theta}$, and $V_{\omega}$ are |
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the bond, bend, and torsion potentials, and the non-bonded |
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interactions $V_{l\!j}$, $V_{d\!p}$, and $V_{s\!p}$ are the |
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lenard-jones, dipole-dipole, and sticky potential interactions. |
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|
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\end{slide} |
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|
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|
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% Slide 8 |
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|
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\begin{slide}{Soft Sticky Dipole Model} |
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|
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The Soft-Sticky model for water is a reduced model. |
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|
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\begin{itemize} |
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|
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\item |
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The model is represented by a single point mass at the water's center |
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of mass. |
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|
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\item |
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The point mass contains a fixed dipole of 2.35 D pointing from the |
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oxygens toward the hydrogens. |
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|
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\end{itemize} |
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|
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It's potential is as follows: |
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|
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\begin{equation} |
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V_{s\!s\!d} = V_{l\!j}(r_{i\!j}) + V_{d\!p}(r_{i\!j},\Omega_{i},\Omega_{j}) |
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+ V_{s\!p}(r_{i\!j},\Omega_{i},\Omega_{j}) |
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\end{equation} |
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\end{slide} |
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|
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% Slide 8b |
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|
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\begin{slide}{SSD Diagram} |
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|
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\begin{center} |
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\begin{figure} |
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\epsfxsize=50mm |
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\epsfbox{ssd.epsi} |
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\end{figure} |
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\end{center} |
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|
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A Diagram of the SSD model. |
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\end{slide} |
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|
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% Slide 9 |
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\begin{slide}{Hydrogen Bonding in SSD} |
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|
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It is important to note that SSD has a potential specifically to |
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recreate the hydrogen bonding network of water. |
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|
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|
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ICE SSD |
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|
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ICE point Dipole |
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|
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|
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The importance of the hydrogen bond network is it's significant |
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contribution to the hydrophobic driving force of bilayer formation. |
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\end{slide} |
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|
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|
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% Slide 10 |
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|
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\begin{slide}{The Lipid Model} |
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|
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To eliminate the need for charge-charge interactions, our lipid model |
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replaces the phospholipid head group with a single large head group |
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atom containing a freely oriented dipole. The tail is a simple alkane chain. |
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|
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Lipid Properties: |
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\begin{itemize} |
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\item $|\vec{\mu}_{\text{HEAD}}| = 20.6\ \text{D}$ |
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\item $m_{\text{HEAD}} = 196\ \text{amu}$ |
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\item Tail atoms are unified CH, $\text{CH}_2$, and $\text{CH}_3$ atoms |
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\begin{itemize} |
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\item Alkane forcefield parameters taken from TraPPE |
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\end{itemize} |
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\end{itemize} |
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|
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\end{slide} |
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|
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% Slide 11 |
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|
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\begin{slide}{Lipid Model} |
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|
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\end{slide} |
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|
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|
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% Slide 12 |
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|
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\begin{slide}{Initial Runs: 25 Lipids in water} |
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|
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\textbf{Simulation Parameters:} |
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|
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\begin{itemize} |
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|
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\item Starting Configuration: |
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\begin{itemize} |
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\item 25 lipid molecules arranged in a 5 x 5 square |
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\item square was surrounded by a sea of 1386 waters |
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\begin{itemize} |
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\item final water to lipid ratio was 55.4:1 |
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\end{itemize} |
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\end{itemize} |
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|
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\item Lipid had only a single saturated chain of 16 carbons |
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|
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\item Box Size: 34.5 $\mbox{\AA}$ x 39.4 $\mbox{\AA}$ x 39.4 $\mbox{\AA}$ |
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|
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\item dt = 2.0 - 3.0 fs |
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|
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\item T = 300 K |
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|
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\item NVE ensemble |
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|
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\item Periodic boundary conditions |
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\end{itemize} |
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|
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\end{slide} |
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|
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|
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% Slide 13 |
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|
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\begin{slide}{5x5: Initial} |
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|
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\begin{center} |
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\begin{figure} |
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\epsfxsize=50mm |
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\epsfbox{5x5-initial.eps} |
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\end{figure} |
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\end{center} |
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|
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The initial configuration |
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|
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\end{slide} |
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|
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\begin{slide}{5x5: Final} |
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|
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\begin{center} |
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\begin{figure} |
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\epsfxsize=60mm |
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\epsfbox{5x5-1.7ns.eps} |
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\end{figure} |
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\end{center} |
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|
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The final configuration at 1.7 ns. |
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|
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\end{slide} |
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|
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|
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% Slide 14 |
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|
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\begin{slide}{5x5: $g(r)$} |
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|
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\begin{center} |
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\begin{figure} |
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\epsfxsize=60mm |
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\epsfbox{all5x5-HEAD-HEAD-gr.eps} |
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\end{figure} |
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\end{center} |
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|
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|
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\end{slide} |
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|
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\begin{slide}{5x5: $g(r)$} |
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|
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\begin{center} |
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\begin{figure} |
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\epsfxsize=60mm |
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\epsfbox{all5x5-HEAD-X-gr.eps} |
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\end{figure} |
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\end{center} |
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|
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|
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\end{slide} |
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|
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|
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% Slide 15 |
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|
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\begin{slide}{5x5: $\cos$ correlations} |
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|
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\begin{center} |
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\begin{figure} |
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\epsfxsize=60mm |
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\epsfbox{all5x5-HEAD-HEAD-cr.eps} |
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\end{figure} |
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\end{center} |
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|
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\end{slide} |
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|
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\begin{slide}{5x5: $\cos$ correlations} |
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|
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\begin{center} |
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\begin{figure} |
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\epsfxsize=60mm |
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\epsfbox{all5x5-HEAD-X-cr.eps} |
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\end{figure} |
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\end{center} |
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|
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\end{slide} |
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|
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|
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% Slide 16 |
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|
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\begin{slide}{Initial Runs: 50 Lipids randomly arranged in water} |
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|
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\textbf{Simulation Parameters:} |
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|
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\begin{itemize} |
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|
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\item Starting Configuration: |
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\begin{itemize} |
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\item 50 lipid molecules arranged randomly in a rectangular box |
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\item The box was then filled with 1384 waters |
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\begin{itemize} |
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\item final water to lipid ratio was 27:1 |
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\end{itemize} |
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\end{itemize} |
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|
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\item Lipid had only a single saturated chain of 16 carbons |
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|
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\item Box Size: 26.6 $\mbox{\AA}$ x 26.6 $\mbox{\AA}$ x 108.4 $\mbox{\AA}$ |
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|
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\item dt = 2.0 - 3.0 fs |
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|
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\item T = 300 K |
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|
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\item NVE ensemble |
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|
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\item Periodic boundary conditions |
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|
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\end{itemize} |
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|
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\end{slide} |
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|
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|
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% Slide 17 |
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|
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\begin{slide}{R-50: Initial} |
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|
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\begin{center} |
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\begin{figure} |
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\epsfxsize=100mm |
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\epsfbox{r50-initial.eps} |
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\end{figure} |
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\end{center} |
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|
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The initial configuration |
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|
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\end{slide} |
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|
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\begin{slide}{R-50: Final} |
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|
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\begin{center} |
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\begin{figure} |
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\epsfxsize=100mm |
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\epsfbox{r50-521ps.eps} |
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\end{figure} |
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\end{center} |
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|
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The fianl configuration at 521 ps |
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|
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\end{slide} |
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|
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|
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% Slide 18 |
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|
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\begin{slide}{R-50: $g(r)$} |
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|
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|
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\begin{center} |
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\begin{figure} |
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\epsfxsize=60mm |
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\epsfbox{r50-HEAD-HEAD-gr.eps} |
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\end{figure} |
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\end{center} |
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|
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\end{slide} |
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|
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|
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\begin{slide}{R-50: $g(r)$} |
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|
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|
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\begin{center} |
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\begin{figure} |
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\epsfxsize=60mm |
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\epsfbox{r50-HEAD-X-gr.eps} |
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\end{figure} |
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\end{center} |
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|
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\end{slide} |
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|
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|
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% Slide 19 |
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|
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\begin{slide}{R-50: $\cos$ correlations} |
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|
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|
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\begin{center} |
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\begin{figure} |
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\epsfxsize=60mm |
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\epsfbox{r50-HEAD-HEAD-cr.eps} |
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\end{figure} |
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\end{center} |
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|
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\end{slide} |
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|
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\begin{slide}{R-50: $\cos$ correlations} |
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|
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|
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\begin{center} |
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\begin{figure} |
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\epsfxsize=60mm |
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\epsfbox{r50-HEAD-X-cr.eps} |
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\end{figure} |
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\end{center} |
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|
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\end{slide} |
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|
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|
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% Slide 20 |
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|
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\begin{slide}{Future Directions} |
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|
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\begin{itemize} |
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|
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\item |
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Simulation of a lipid with 2 chains, or perhaps expand the current |
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unified chain atoms to take up greater steric bulk. |
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|
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\item |
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Incorporate constant pressure and constant temperature into the ensemble. |
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|
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\item |
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Parrellize the code. |
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|
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\end{itemize} |
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\end{slide} |
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|
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|
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% Slide 21 |
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|
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\begin{slide}{Acknowledgements} |
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|
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\begin{itemize} |
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|
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\item Dr. J. Daniel Gezelter |
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\item Christopher Fennel |
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\item Charles Vardeman |
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\item Teng Lin |
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|
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\end{itemize} |
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|
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Funding by: |
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\begin{itemize} |
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\item Dreyfus New Faculty Award |
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\end{itemize} |
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|
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\end{slide} |
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|
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|
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%%%%%%%%%%%%%%%%%%%%%%%%%% END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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|
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\end{document} |