matt_papers/canidacy_talk/canidacy_slides.tex

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% ----------------------
% |      Title         |
% ----------------------

\title{A Mezzoscale Model for Phospholipid MD Simulations}

\author{Matthew A. Meineke\\
Department of Chemistry and Biochemistry\\
University of Notre Dame\\
Notre Dame, Indiana 46556}

\date{\today}

%-------------------------------------------------------------------
%                       Begin Document

\begin{document}

%\maketitle


\nobibliography{canidacy_slides}
\bibliographystyle{jurabib}


% Slide 0 Title slide
\begin{slide}
  \begin{center}
    \bfseries
    \fontsize{24pt}{30pt}\selectfont \color{Black}
    A Mezzoscale Model for Phospholipid MD Simulations  \par
    \fontsize{16pt}{20pt}\selectfont \color{Green3}
     Matthew A. Meineke\par
    \fontsize{12pt}{15pt}\selectfont \color{Purple2}
    Department of Chemistry and Biochemisty \par
    University of Notre Dame \par
    Notre Dame, IN 46556 \par
    \fontsize{12pt}{15pt}\selectfont \color{Red} \date{today} \par
  \end{center}
 \end{slide}


% Slide 1
\begin{slide} {\LARGE Talk Outline}
\begin{itemize}

\item Discussion of the research motivation and goals

\item Methodology

\item Discussion of current research and preliminary results

\item Future research

\end{itemize}
\end{slide}


% Slide 2

\begin{slide}

\centerline{\LARGE Motivation A: Long Length Scales}

\begin{wrapfigure}{r}{60mm}

    \epsfxsize=45mm
    \epsfbox{ripple.epsi}

\end{wrapfigure}

\mbox{}
Ripple phase:
\begin{itemize}

\item
The ripple (~$P_{\beta'}$~) phase lies in the transition from the gel
to fluid phase.

\item
Periodicity of 100 - 200 $\mbox{\AA}$\footcite{Cevc87}

\item
Current simulations have box sizes ranging from 50 - 100 $\mbox{\AA}$
on a side.\footcite{Venable93}\footcite{Heller93}

\end{itemize}
\vspace{10mm}
\end{slide}


\begin{slide}{\LARGE Motivation B: Long Time Scales}

\begin{itemize}

\item
Drug Diffussion
        \begin{itemize}
        \item 
        Some drug molecules may spend appreciable amountsd of time in the
        membrane

        \item
        Long time scale dynamics are need to observe and charecterize their
        actions
        \end{itemize}

\item
Bilayer Formation Dynamics
        \begin{itemize}
        \item
        Current bilayer simulations indicate that lipids can take nearly
        20 ns to form completely.\footcite{Marrink01} 
        \end{itemize}
\end{itemize}
\end{slide}


% Slide 4

\begin{slide}{\LARGE Length Scale Simplification I}


Replace any charged interactions of the system with dipoles.

\begin{itemize}
\item Allows for computational scaling approximately by $N$ for
      dipole-dipole interactions.
        \begin{itemize}
        \item Relatively short range, $\frac{1}{r^3}$, interactions allow
        the application of computational simplification algorithms,
        ie. neighbor lists.
        \end{itemize}

\item In contrast, the Ewald sum, needed for calculating charge - charge 
        interactions, scales approximately by $N \log N$.
\end{itemize}
\end{slide}

\begin{slide}{\LARGE Length Scale Simplification II}

Use unified models for the water and the lipid chain.

\begin{itemize}
\item 
Drastically reduces the number of atoms and interactions to simulate.

\end{itemize}


\begin{figure}
%\epsfxsize=30mm
%\leavevmode
\begin{center}
\includegraphics[width=50mm,angle=-90]{reduction.epsi}
\end{center}
\end{figure}


\end{slide}


% Slide 5

\begin{slide}{Time Scale Simplification}
\begin{itemize}
\item
Constrain all bonds to be of fixed length.

        \begin{itemize}
        \item bond vibrations are the fastest motion in
         a simulation
        \end{itemize}

\item
Allows time steps of up to 3 fs with the current integrator. In
contrast, a time step of 1 fs is usually required for resolving bond
vibration.

\end{itemize}
\end{slide}

% Slide 8

\begin{slide}{Soft Sticky Dipole Model\footcite{Liu96}}

\begin{figure}
\begin{center}
\includegraphics[width=40mm]{ssd.epsi}
\end{center}
\end{figure}


It's potential is as follows:

\begin{equation}
V_{s\!s\!d} = V_{L\!J}(r_{i\!j}) + V_{d\!p}(r_{i\!j},\Omega_{i},\Omega_{j})
        + V_{s\!p}(r_{i\!j},\Omega_{i},\Omega_{j})
\end{equation}
\end{slide}


% Slide 9
\begin{slide}{Hydrogen Bonding in SSD}

The SSD model's $V_{s\!p}(r_{i\!j},\Omega_{i},\Omega_{j})$ recreates
the hydrogen bonding network of water.


\begin{figure}
\begin{center}
\mbox{%
        \subfigure[SSD relaxed on a diamond lattice]{%
                \mbox{\includegraphics[angle=-90,width=55mm]{ssd_ice.epsi}}}%
        \hspace{4mm}
        \subfigure[Stockmayer spheres relaxed on a diamond lattice]{%
                \mbox{\includegraphics[angle=-90,width=55mm]{dipole_ice.epsi}}}%
}

\end{center}
\end{figure}

\end{slide}


% Slide 10

\begin{slide}{The Lipid Model}

\begin{figure}
\begin{center}

\includegraphics[width=40mm,angle=-90]{lipidModel.epsi}

\end{center}
\end{figure}

\begin{equation}
V_{\mbox{lipid}} = \overbrace{%
        V_{\mbox{bend}}(\theta_{ijk}) + V_{\mbox{tors.}}(\phi_{ijkl})%
        }^{bonded}
        + \overbrace{%
        V_{L\!J}(r_{i\!j}) + V_{d\!p}(r_{i\!j},\Omega_{i},\Omega_{j})%
        }^{non-bonded}
\end{equation}

\begin{itemize}
\item 
Tail forcefield parameters taken from TraPPE\footcite{Siepmann1998}
\end{itemize}

\end{slide}


% Slide 12

\begin{slide}{Initial Runs: 25 Lipids in water}

\begin{wrapfigure}{r}{60mm}
        
        \includegraphics[width=55mm]{5x5-initial.eps}

\end{wrapfigure}

\textbf{Simulation Parameters:}

\begin{itemize}

\item $N_{\mbox{lipids}} = 25$

\item $N_{\mbox{H}_{2}\mbox{O}} = 1386$

\item Water to lipid ratio of 55.4:1

\item Lipid had only a single saturated chain of 16 carbons

\item Box Size: 34.5~$\mbox{\AA}$~x~39.4~$\mbox{\AA}$~x~39.4~$\mbox{\AA}$

\item T = 300 K

\item NVE ensemble

\item Periodic boundary conditions
\end{itemize}

\end{slide}

\begin{slide}{5x5: Final}


\begin{figure}
\begin{center}
\includegraphics[width=80mm]{5x5-1.7ns.eps}
\end{center}
\end{figure}

\begin{center}
The final configuration at 1.7 ns.
\end{center}

\end{slide}


% Slide 14

\begin{slide}{5x5: $g(r)$}

\begin{figure}
\includegraphics[width=60mm,angle=-90]{all5x5-HEAD-HEAD-gr.eps}
\end{figure}


\end{slide}

\begin{slide}{5x5: $g(r)$}


\begin{figure}
\includegraphics[width=60mm,angle=-90]{all5x5-HEAD-X-gr.eps}
\end{figure}

\end{slide}


% Slide 15

\begin{slide}{5x5: $\cos$ correlations}

\begin{figure}
\includegraphics[width=60mm,angle=-90]{all5x5-HEAD-HEAD-cr.eps}
\end{figure}

\end{slide}

\begin{slide}{5x5: $\cos$ correlations}

\begin{figure}
\includegraphics[width=60mm,angle=-90]{all5x5-HEAD-X-cr.eps}
\end{figure}

\end{slide}


% Slide 16

\begin{slide}{Initial Runs: 50 Lipids randomly arranged in water}

\begin{wrapfigure}{r}{40mm}

\includegraphics[angle=-90,width=35mm]{r50-initial.eps}

\end{wrapfigure}

\textbf{Simulation Parameters:}

\begin{itemize}

\item $N_{\mbox{lipids}} = 50$

\item $N_{\mbox{H}_{2}\mbox{O}} = 1384$

\item Water to lipid ratio of 27:1

\item Lipid had only a single saturated chain of 16 carbons

\item Box Size: 26.6 $\mbox{\AA}$ x 26.6 $\mbox{\AA}$ x 108.4 $\mbox{\AA}$

\item T = 300 K

\item NVE ensemble

\item Periodic boundary conditions

\end{itemize}

\end{slide}

\begin{slide}{R-50: Final}


\begin{figure}
\begin{center}
\includegraphics[width=120mm]{r50-521ps.eps}
\end{center}
\end{figure}

\begin{center}
The fianl configuration at 521 ps
\end{center}

\end{slide}


% Slide 18

\begin{slide}{R-50: $g(r)$}


\begin{figure}
\includegraphics[width=60mm,angle=-90]{r50-HEAD-HEAD-gr.eps}
\end{figure}

\end{slide}


\begin{slide}{R-50: $g(r)$}


\begin{figure}
\includegraphics[width=60mm,angle=-90]{r50-HEAD-X-gr.eps}
\end{figure}

\end{slide}


% Slide 19

\begin{slide}{R-50: $\cos$ correlations}


\begin{figure}
\includegraphics[width=60mm,angle=-90]{r50-HEAD-HEAD-cr.eps}
\end{figure}

\end{slide}

\begin{slide}{R-50: $\cos$ correlations}

\begin{figure}
\includegraphics[width=60mm,angle=-90]{r50-HEAD-X-cr.eps}
\end{figure}

\end{slide}


% Slide 20

\begin{slide}{Future Directions}

\begin{itemize}

\item
Simulation of a lipid with 2 chains, or perhaps expand the current
unified chain atoms to take up greater steric bulk.

\item
Incorporate constant pressure and constant temperature into the ensemble.

\item
Parrellize the code.

\end{itemize}
\end{slide}


% Slide 21

\begin{slide}{Acknowledgements}

\begin{itemize}

\item Dr. J. Daniel Gezelter
\item Christopher Fennel
\item Charles Vardeman
\item Teng Lin
\item Megan Sprauge
\item Patrick Conforti
\item Dan Combest

\end{itemize}

Funding by:
\begin{itemize}
\item Dreyfus New Faculty Award
\end{itemize}

\end{slide}


%%%%%%%%%%%%%%%%%%%%%%%%%% END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{document}
Revision:	79
Committed:	Thu Aug 15 21:58:43 2002 UTC (22 years, 1 month ago) by mmeineke
Content type:	application/x-tex
File size:	13332 byte(s)
Log Message:	I think I have most of it the way I like it, just need to change the correlation functions, and the final pictures
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176	mmeineke	49	% ----------------------
177			% \| Title \|
178			% ----------------------
179
180	mmeineke	62	\title{A Mezzoscale Model for Phospholipid MD Simulations}
181	mmeineke	49
182			\author{Matthew A. Meineke\\
183	mmeineke	63	Department of Chemistry and Biochemistry\\
184	mmeineke	49	University of Notre Dame\\
185			Notre Dame, Indiana 46556}
186
187			\date{\today}
188
189			%-------------------------------------------------------------------
190			% Begin Document
191
192			\begin{document}
193	mmeineke	62
194	mmeineke	63	%\maketitle
195	mmeineke	49
196
197
198	mmeineke	62
199
200	mmeineke	63	\nobibliography{canidacy_slides}
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202	mmeineke	62
203	mmeineke	63
204			% Slide 0 Title slide
205			\begin{slide}
206			\begin{center}
207			\bfseries
208			\fontsize{24pt}{30pt}\selectfont \color{Black}
209			A Mezzoscale Model for Phospholipid MD Simulations \par
210			\fontsize{16pt}{20pt}\selectfont \color{Green3}
211			Matthew A. Meineke\par
212			\fontsize{12pt}{15pt}\selectfont \color{Purple2}
213			Department of Chemistry and Biochemisty \par
214			University of Notre Dame \par
215			Notre Dame, IN 46556 \par
216			\fontsize{12pt}{15pt}\selectfont \color{Red} \date{today} \par
217			\end{center}
218			\end{slide}
219
220	mmeineke	64
221	mmeineke	49	% Slide 1
222	mmeineke	64	\begin{slide} {\LARGE Talk Outline}
223	mmeineke	49	\begin{itemize}
224
225			\item Discussion of the research motivation and goals
226
227			\item Methodology
228
229			\item Discussion of current research and preliminary results
230
231			\item Future research
232
233			\end{itemize}
234			\end{slide}
235
236
237			% Slide 2
238
239	mmeineke	63	\begin{slide}
240	mmeineke	62
241	mmeineke	64	\centerline{\LARGE Motivation A: Long Length Scales}
242
243	mmeineke	63	\begin{wrapfigure}{r}{60mm}
244	mmeineke	62
245	mmeineke	63	\epsfxsize=45mm
246			\epsfbox{ripple.epsi}
247	mmeineke	62
248	mmeineke	63	\end{wrapfigure}
249	mmeineke	62
250	mmeineke	63	\mbox{}
251	mmeineke	62	Ripple phase:
252			\begin{itemize}
253
254	mmeineke	63	\item
255	mmeineke	62	The ripple (~$P_{\beta'}$~) phase lies in the transition from the gel
256			to fluid phase.
257
258	mmeineke	63	\item
259	mmeineke	64	Periodicity of 100 - 200 $\mbox{\AA}$\footcite{Cevc87}
260	mmeineke	62
261	mmeineke	64	\item
262			Current simulations have box sizes ranging from 50 - 100 $\mbox{\AA}$
263			on a side.\footcite{Venable93}\footcite{Heller93}
264
265	mmeineke	62	\end{itemize}
266	mmeineke	64	\vspace{10mm}
267	mmeineke	62	\end{slide}
268
269
270	mmeineke	64	\begin{slide}{\LARGE Motivation B: Long Time Scales}
271	mmeineke	62
272	mmeineke	64	\begin{itemize}
273	mmeineke	62
274	mmeineke	64	\item
275			Drug Diffussion
276			\begin{itemize}
277			\item
278			Some drug molecules may spend appreciable amountsd of time in the
279			membrane
280	mmeineke	62
281	mmeineke	64	\item
282			Long time scale dynamics are need to observe and charecterize their
283			actions
284			\end{itemize}
285	mmeineke	62
286	mmeineke	64	\item
287			Bilayer Formation Dynamics
288			\begin{itemize}
289			\item
290			Current bilayer simulations indicate that lipids can take nearly
291			20 ns to form completely.\footcite{Marrink01}
292			\end{itemize}
293			\end{itemize}
294			\end{slide}
295	mmeineke	54
296
297	mmeineke	64	% Slide 4
298	mmeineke	49
299	mmeineke	64	\begin{slide}{\LARGE Length Scale Simplification I}
300	mmeineke	49
301
302	mmeineke	64	Replace any charged interactions of the system with dipoles.
303	mmeineke	49
304	mmeineke	64	\begin{itemize}
305			\item Allows for computational scaling approximately by $N$ for
306			dipole-dipole interactions.
307			\begin{itemize}
308			\item Relatively short range, $\frac{1}{r^3}$, interactions allow
309			the application of computational simplification algorithms,
310			ie. neighbor lists.
311			\end{itemize}
312
313			\item In contrast, the Ewald sum, needed for calculating charge - charge
314			interactions, scales approximately by $N \log N$.
315	mmeineke	49	\end{itemize}
316			\end{slide}
317
318	mmeineke	64	\begin{slide}{\LARGE Length Scale Simplification II}
319	mmeineke	49
320	mmeineke	64	Use unified models for the water and the lipid chain.
321	mmeineke	49
322			\begin{itemize}
323	mmeineke	64	\item
324	mmeineke	69	Drastically reduces the number of atoms and interactions to simulate.
325	mmeineke	49
326	mmeineke	64	\end{itemize}
327	mmeineke	49
328
329	mmeineke	69
330	mmeineke	65	\begin{figure}
331	mmeineke	69	%\epsfxsize=30mm
332			%\leavevmode
333			\begin{center}
334			\includegraphics[width=50mm,angle=-90]{reduction.epsi}
335			\end{center}
336	mmeineke	65	\end{figure}
337	mmeineke	64
338	mmeineke	69
339	mmeineke	49	\end{slide}
340
341
342			% Slide 5
343
344			\begin{slide}{Time Scale Simplification}
345			\begin{itemize}
346			\item
347			Constrain all bonds to be of fixed length.
348
349	mmeineke	63	\begin{itemize}
350	mmeineke	69	\item bond vibrations are the fastest motion in
351	mmeineke	63	a simulation
352			\end{itemize}
353	mmeineke	49
354			\item
355	mmeineke	69	Allows time steps of up to 3 fs with the current integrator. In
356			contrast, a time step of 1 fs is usually required for resolving bond
357			vibration.
358	mmeineke	49
359			\end{itemize}
360			\end{slide}
361
362	mmeineke	51	% Slide 8
363	mmeineke	49
364	mmeineke	69	\begin{slide}{Soft Sticky Dipole Model\footcite{Liu96}}
365	mmeineke	49
366	mmeineke	69	\begin{figure}
367			\begin{center}
368			\includegraphics[width=40mm]{ssd.epsi}
369			\end{center}
370			\end{figure}
371	mmeineke	49
372
373	mmeineke	52	It's potential is as follows:
374
375			\begin{equation}
376	mmeineke	69	V_{s\!s\!d} = V_{L\!J}(r_{i\!j}) + V_{d\!p}(r_{i\!j},\Omega_{i},\Omega_{j})
377	mmeineke	63	+ V_{s\!p}(r_{i\!j},\Omega_{i},\Omega_{j})
378	mmeineke	52	\end{equation}
379			\end{slide}
380
381
382			% Slide 9
383			\begin{slide}{Hydrogen Bonding in SSD}
384
385	mmeineke	69	The SSD model's $V_{s\!p}(r_{i\!j},\Omega_{i},\Omega_{j})$ recreates
386			the hydrogen bonding network of water.
387	mmeineke	52
388	mmeineke	54
389	mmeineke	69	\begin{figure}
390			\begin{center}
391			\mbox{%
392			\subfigure[SSD relaxed on a diamond lattice]{%
393			\mbox{\includegraphics[angle=-90,width=55mm]{ssd_ice.epsi}}}%
394			\hspace{4mm}
395			\subfigure[Stockmayer spheres relaxed on a diamond lattice]{%
396			\mbox{\includegraphics[angle=-90,width=55mm]{dipole_ice.epsi}}}%
397			}
398	mmeineke	52
399	mmeineke	69	\end{center}
400			\end{figure}
401	mmeineke	52
402			\end{slide}
403
404
405			% Slide 10
406
407			\begin{slide}{The Lipid Model}
408
409	mmeineke	78	\begin{figure}
410			\begin{center}
411	mmeineke	53
412	mmeineke	78	\includegraphics[width=40mm,angle=-90]{lipidModel.epsi}
413
414			\end{center}
415			\end{figure}
416
417			\begin{equation}
418			V_{\mbox{lipid}} = \overbrace{%
419			V_{\mbox{bend}}(\theta_{ijk}) + V_{\mbox{tors.}}(\phi_{ijkl})%
420			}^{bonded}
421			+ \overbrace{%
422			V_{L\!J}(r_{i\!j}) + V_{d\!p}(r_{i\!j},\Omega_{i},\Omega_{j})%
423			}^{non-bonded}
424			\end{equation}
425
426	mmeineke	53	\begin{itemize}
427	mmeineke	78	\item
428			Tail forcefield parameters taken from TraPPE\footcite{Siepmann1998}
429	mmeineke	53	\end{itemize}
430
431			\end{slide}
432
433
434
435			% Slide 12
436	mmeineke	52
437			\begin{slide}{Initial Runs: 25 Lipids in water}
438
439	mmeineke	76	\begin{wrapfigure}{r}{60mm}
440
441			\includegraphics[width=55mm]{5x5-initial.eps}
442
443			\end{wrapfigure}
444
445	mmeineke	53	\textbf{Simulation Parameters:}
446	mmeineke	52
447	mmeineke	53	\begin{itemize}
448
449	mmeineke	76	\item $N_{\mbox{lipids}} = 25$
450	mmeineke	53
451	mmeineke	76	\item $N_{\mbox{H}_{2}\mbox{O}} = 1386$
452
453			\item Water to lipid ratio of 55.4:1
454
455	mmeineke	53	\item Lipid had only a single saturated chain of 16 carbons
456
457	mmeineke	76	\item Box Size: 34.5~$\mbox{\AA}$~x~39.4~$\mbox{\AA}$~x~39.4~$\mbox{\AA}$
458	mmeineke	53
459			\item T = 300 K
460
461			\item NVE ensemble
462
463			\item Periodic boundary conditions
464			\end{itemize}
465
466	mmeineke	52	\end{slide}
467
468	mmeineke	76	\begin{slide}{5x5: Final}
469	mmeineke	52
470
471	mmeineke	76	\begin{figure}
472	mmeineke	54	\begin{center}
473	mmeineke	76	\includegraphics[width=80mm]{5x5-1.7ns.eps}
474			\end{center}
475	mmeineke	54	\end{figure}
476	mmeineke	52
477	mmeineke	54	\begin{center}
478	mmeineke	76	The final configuration at 1.7 ns.
479	mmeineke	54	\end{center}
480
481			\end{slide}
482
483
484	mmeineke	53	% Slide 14
485	mmeineke	52
486			\begin{slide}{5x5: $g(r)$}
487
488	mmeineke	54	\begin{figure}
489	mmeineke	76	\includegraphics[width=60mm,angle=-90]{all5x5-HEAD-HEAD-gr.eps}
490	mmeineke	54	\end{figure}
491	mmeineke	52
492
493	mmeineke	76
494	mmeineke	54	\end{slide}
495	mmeineke	52
496	mmeineke	54	\begin{slide}{5x5: $g(r)$}
497
498	mmeineke	76
499	mmeineke	54	\begin{figure}
500	mmeineke	76	\includegraphics[width=60mm,angle=-90]{all5x5-HEAD-X-gr.eps}
501	mmeineke	54	\end{figure}
502
503	mmeineke	52	\end{slide}
504
505
506	mmeineke	53	% Slide 15
507	mmeineke	52
508			\begin{slide}{5x5: $\cos$ correlations}
509
510	mmeineke	54	\begin{figure}
511	mmeineke	76	\includegraphics[width=60mm,angle=-90]{all5x5-HEAD-HEAD-cr.eps}
512	mmeineke	54	\end{figure}
513	mmeineke	52
514			\end{slide}
515
516	mmeineke	54	\begin{slide}{5x5: $\cos$ correlations}
517	mmeineke	52
518	mmeineke	54	\begin{figure}
519	mmeineke	76	\includegraphics[width=60mm,angle=-90]{all5x5-HEAD-X-cr.eps}
520	mmeineke	54	\end{figure}
521
522			\end{slide}
523
524
525	mmeineke	53	% Slide 16
526	mmeineke	52
527	mmeineke	53	\begin{slide}{Initial Runs: 50 Lipids randomly arranged in water}
528	mmeineke	52
529	mmeineke	79	\begin{wrapfigure}{r}{40mm}
530	mmeineke	78
531	mmeineke	79	\includegraphics[angle=-90,width=35mm]{r50-initial.eps}
532
533			\end{wrapfigure}
534
535	mmeineke	53	\textbf{Simulation Parameters:}
536	mmeineke	52
537	mmeineke	53	\begin{itemize}
538
539	mmeineke	79	\item $N_{\mbox{lipids}} = 50$
540	mmeineke	53
541	mmeineke	79	\item $N_{\mbox{H}_{2}\mbox{O}} = 1384$
542
543			\item Water to lipid ratio of 27:1
544
545	mmeineke	53	\item Lipid had only a single saturated chain of 16 carbons
546
547			\item Box Size: 26.6 $\mbox{\AA}$ x 26.6 $\mbox{\AA}$ x 108.4 $\mbox{\AA}$
548
549			\item T = 300 K
550
551			\item NVE ensemble
552
553	mmeineke	63	\item Periodic boundary conditions
554	mmeineke	53
555			\end{itemize}
556
557	mmeineke	52	\end{slide}
558
559	mmeineke	79	\begin{slide}{R-50: Final}
560	mmeineke	52
561
562	mmeineke	76	\begin{figure}
563	mmeineke	54	\begin{center}
564	mmeineke	79	\includegraphics[width=120mm]{r50-521ps.eps}
565	mmeineke	76	\end{center}
566	mmeineke	54	\end{figure}
567	mmeineke	52
568	mmeineke	54	\begin{center}
569	mmeineke	79	The fianl configuration at 521 ps
570	mmeineke	54	\end{center}
571
572			\end{slide}
573
574
575	mmeineke	53	% Slide 18
576	mmeineke	52
577			\begin{slide}{R-50: $g(r)$}
578
579
580	mmeineke	54	\begin{figure}
581	mmeineke	76	\includegraphics[width=60mm,angle=-90]{r50-HEAD-HEAD-gr.eps}
582	mmeineke	54	\end{figure}
583	mmeineke	52
584	mmeineke	54	\end{slide}
585	mmeineke	52
586	mmeineke	54
587			\begin{slide}{R-50: $g(r)$}
588
589
590			\begin{figure}
591	mmeineke	76	\includegraphics[width=60mm,angle=-90]{r50-HEAD-X-gr.eps}
592	mmeineke	54	\end{figure}
593
594	mmeineke	52	\end{slide}
595
596
597	mmeineke	53	% Slide 19
598	mmeineke	52
599			\begin{slide}{R-50: $\cos$ correlations}
600
601
602	mmeineke	54	\begin{figure}
603	mmeineke	76	\includegraphics[width=60mm,angle=-90]{r50-HEAD-HEAD-cr.eps}
604	mmeineke	54	\end{figure}
605
606	mmeineke	52	\end{slide}
607
608	mmeineke	54	\begin{slide}{R-50: $\cos$ correlations}
609	mmeineke	52
610	mmeineke	54	\begin{figure}
611	mmeineke	76	\includegraphics[width=60mm,angle=-90]{r50-HEAD-X-cr.eps}
612	mmeineke	54	\end{figure}
613
614			\end{slide}
615
616
617	mmeineke	53	% Slide 20
618	mmeineke	52
619			\begin{slide}{Future Directions}
620
621	mmeineke	53	\begin{itemize}
622	mmeineke	52
623	mmeineke	63	\item
624	mmeineke	53	Simulation of a lipid with 2 chains, or perhaps expand the current
625			unified chain atoms to take up greater steric bulk.
626
627	mmeineke	63	\item
628	mmeineke	53	Incorporate constant pressure and constant temperature into the ensemble.
629
630			\item
631			Parrellize the code.
632
633			\end{itemize}
634	mmeineke	52	\end{slide}
635
636
637	mmeineke	53	% Slide 21
638	mmeineke	52
639			\begin{slide}{Acknowledgements}
640
641	mmeineke	53	\begin{itemize}
642	mmeineke	52
643	mmeineke	53	\item Dr. J. Daniel Gezelter
644			\item Christopher Fennel
645			\item Charles Vardeman
646			\item Teng Lin
647	mmeineke	64	\item Megan Sprauge
648			\item Patrick Conforti
649			\item Dan Combest
650	mmeineke	52
651	mmeineke	53	\end{itemize}
652
653			Funding by:
654			\begin{itemize}
655			\item Dreyfus New Faculty Award
656			\end{itemize}
657
658	mmeineke	52	\end{slide}
659
660
661
662
663
664
665
666
667	mmeineke	49	%%%%%%%%%%%%%%%%%%%%%%%%%% END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
668
669			\end{document}