Révision | 1fc701cae23ea87cedfe9e1697ff025ae601168f (tree) |
---|---|
l'heure | 2008-12-03 01:36:29 |
Auteur | iselllo |
Commiter | iselllo |
I added a code which shows how to create your own personalized beamer style using some templates.
See also the contribution on
given by Eric Rasmusen.
@@ -0,0 +1,515 @@ | ||
1 | +% Copyright 2007 by Till Tantau | |
2 | +% | |
3 | +% This file may be distributed and/or modified | |
4 | +% | |
5 | +% 1. under the LaTeX Project Public License and/or | |
6 | +% 2. under the GNU Public License. | |
7 | +% | |
8 | +% See the file doc/licenses/LICENSE for more details. | |
9 | + | |
10 | + | |
11 | + | |
12 | +\documentclass{beamer} | |
13 | +%\newcommand{\ol}{\overline} | |
14 | +\renewcommand{\i}{\int} | |
15 | +\newcommand{\n}{\nabla} | |
16 | +\newcommand{\x}{\vec x\; } | |
17 | +\renewcommand{\d}{\dag} | |
18 | +\newcommand{\h}{\hat} | |
19 | +\newcommand{\p}{\partial} | |
20 | +\renewcommand{\v}{\vert} | |
21 | +\renewcommand{\l}{\langle} | |
22 | +\renewcommand{\r}{\rangle} | |
23 | +\newcommand{\f}{\frac} | |
24 | +\newcommand{\s}{\sum} | |
25 | +\newcommand{\lm}[1]{\lim_{#1\to\infty}} | |
26 | +% \renewcommand{\in}{\infty} | |
27 | +\newcommand{\rro}{\right)} | |
28 | +\newcommand{\lro}{\left( } | |
29 | +\newcommand{\lsq}{\left[} | |
30 | +\newcommand{\rsq}{\right]} | |
31 | +\newcommand{\rcu}{\right\}} | |
32 | +\newcommand{\lcu}{\left\{} | |
33 | +\newcommand{\be}{\begin{equation}} | |
34 | +\newcommand{\ee}{\end{equation}} | |
35 | +\newcommand{\bi}{\begin{itemize}} | |
36 | +\newcommand{\ei}{\end{itemize}} | |
37 | +\newcommand{\ben}{\begin{enumerate}} | |
38 | +\newcommand{\een}{\end{enumerate}} | |
39 | +\newcommand{\esp}{ESPResSo} | |
40 | + | |
41 | + | |
42 | + | |
43 | +\newcommand{\jc}{{\it Journal of Colloid and Interface Science}} | |
44 | +\newcommand{\jas}{{\it Journal of Aerosol Science}} | |
45 | +\newcommand{\pra}{{\it Physical Review A}} | |
46 | +\newcommand{\prb}{{\it Physical Review B}} | |
47 | +\newcommand{\pre}{{\it Physical Review E}} | |
48 | +\newcommand{\prl}{{\it Physical Review Letters}} | |
49 | + | |
50 | + | |
51 | +%Fine preambolo | |
52 | + | |
53 | + | |
54 | + | |
55 | +\newcommand{\unit}{\hat{\bf n}} | |
56 | +% \newcommand{\pol}{\hat{\bf e}} | |
57 | +\newcommand{\rv}{{\bf r}} | |
58 | +\newcommand{\Ev}{{\bf E}} | |
59 | +\newcommand{\Bv}{{\bf B}} | |
60 | +\newcommand{\Ec}{{\cal E}} | |
61 | +\newcommand{\Rc}{{\cal R}} | |
62 | +\newcommand{\Pc}{{\cal P}} | |
63 | +\newcommand{\Pcv}{\bbox {\cal P}} | |
64 | +\newcommand{\dv}{{\bf d}} | |
65 | +\newcommand{\Dc}{{\cal D}} | |
66 | +\newcommand{\Dcv}{\bbox {\cal D}} | |
67 | +\newcommand{\Hc}{{\cal H}} | |
68 | +\newcommand{\kappav}{\bbox \kappa} | |
69 | +\newcommand{\Dkappav}{\Delta {\bbox\kappa}} | |
70 | +\newcommand{\qv}{{\bf q}} | |
71 | +\newcommand{\kv}{{\bf k}} | |
72 | +\newcommand{\eo}{\epsilon_0} | |
73 | +\newcommand{\ej}{\epsilon_j} | |
74 | +\newcommand{\beq}{\begin{equation}} | |
75 | +\newcommand{\eeq}{\end{equation}} | |
76 | +\newcommand{\bea}{\begin{eqnarray}} | |
77 | +\newcommand{\eea}{\end{eqnarray}} | |
78 | +\newcommand{\up}{\uparrow} | |
79 | +\newcommand{\down}{\downarrow} | |
80 | +\newcommand{\<}{\langle} | |
81 | +\renewcommand{\>}{\rangle} | |
82 | +\renewcommand{\(}{\left(} | |
83 | +\renewcommand{\)}{\right)} | |
84 | +\renewcommand{\[}{\left[} | |
85 | +\renewcommand{\]}{\right]} | |
86 | +\newcommand{\dagg}{d_{\rm{agg}}} | |
87 | +\newcommand{\vagg}{V_{\rm{agg}}} | |
88 | +\newcommand{\nagg}{n_{\rm{agg}}} | |
89 | +\newcommand{\df}{d_{f}} | |
90 | +\newcommand{\ragg}{\rho_{\rm{agg}}} | |
91 | +\newcommand{\reff}{\rho_{\rm{eff}}} | |
92 | +\newcommand{\re}{{\rm{Re}}} | |
93 | +\newcommand{\pr}{{\rm{Pr}}} | |
94 | +\newcommand{\sh}{{\rm{Sh}}} | |
95 | +\newcommand{\Kn}{{\rm{Kn}}} | |
96 | +\newcommand{\ra}{{\rm{Ra}}} | |
97 | +\renewcommand{\sc}{{\rm{Sc}}} | |
98 | +\newcommand{\nusselt}{{\rm{Nu}}} | |
99 | +\newcommand{\magg}{m_{\rm{agg}}} | |
100 | +\newcommand{\tres}{\tau_{\rm{res}}} | |
101 | +\newcommand{\gdif}{{\gamma_{\rm{dif}}}} | |
102 | +\newcommand{\vdep}{{v_{\rm{dep}}}} | |
103 | +\newcommand{\gth}{{\gamma_{\rm{th}}}} | |
104 | +\newcommand{\vth}{{v_{\rm{th}}}} | |
105 | +% \newcommand{\tres}{{\tau_{\rm{res}}}} | |
106 | +\newcommand{\kt}{{K_{\rm{T}}}} | |
107 | +\newcommand{\kair}{{k_{\rm{air}}}} | |
108 | +\newcommand{\vdif}{{v_{\rm{dif}}}} | |
109 | +\newcommand{\kp}{{k_{\rm{p}}}} | |
110 | +\newcommand{\commentout}[1]{{}} | |
111 | +%\newcommand{\half}{\hbox} | |
112 | +% \newcommand{\half}{\hbox{$1\over2$}} | |
113 | +\newcommand{\nv}{{\vec\nabla}} | |
114 | +\renewcommand{\c}{{\cdot}} | |
115 | +\newcommand{\hv}{\harvarditem} | |
116 | +\renewcommand{\baselinestretch}{.9} | |
117 | + | |
118 | + | |
119 | + | |
120 | + | |
121 | + | |
122 | + | |
123 | + | |
124 | +\definecolor{orange}{rgb}{1,0.5,0} | |
125 | +\definecolor{darkgreen}{rgb}{0,0.5,0} | |
126 | + | |
127 | + | |
128 | +\definecolor{mymagenta}{cmyk}{0,1.,0,0.2} | |
129 | + | |
130 | +\definecolor{Brown}{cmyk}{0, 0.8, 1, 0.6} | |
131 | +\definecolor{Yellow}{rgb}{1, 1, 0} | |
132 | +\definecolor{Light}{gray}{.80} | |
133 | +\definecolor{Dark}{gray}{.20} | |
134 | + | |
135 | + | |
136 | + | |
137 | + | |
138 | +% | |
139 | +% DO NOT USE THIS FILE AS A TEMPLATE FOR YOUR OWN TALKS¡!! | |
140 | +% | |
141 | +% Use a file in the directory solutions instead. | |
142 | +% They are much better suited. | |
143 | +% | |
144 | + | |
145 | + | |
146 | + | |
147 | + | |
148 | + | |
149 | + | |
150 | + | |
151 | +% Author, Title, etc. | |
152 | + | |
153 | +\title[Modelling of diesel-engine exhaust nano-particle dynamics] | |
154 | +{% | |
155 | + Modelling of diesel-engine exhaust nanoparticle dynamics | |
156 | +% | |
157 | +} | |
158 | + | |
159 | +\author[Isella, Drossinos] | |
160 | +{ | |
161 | + Lorenzo~Isella\inst{}, | |
162 | + Barouch Giechaskiel\inst{} | |
163 | + and | |
164 | + Yannis~Drossinos\inst{} | |
165 | +} | |
166 | + | |
167 | +\institute[] | |
168 | +{ | |
169 | + \inst{}% | |
170 | + Joint Research Centre, Ispra, Italy | |
171 | +} | |
172 | + | |
173 | +\date{JRC Exploratory Research Symposium, December 2008} | |
174 | + | |
175 | + | |
176 | +%package for movies | |
177 | + | |
178 | +\usepackage{movie15} | |
179 | + | |
180 | + | |
181 | + | |
182 | + | |
183 | +% Setup TikZ | |
184 | + | |
185 | +% \usepackage{tikz} | |
186 | +% \usetikzlibrary{arrows} | |
187 | +% \tikzstyle{block}=[draw opacity=0.7,line width=1.4cm] | |
188 | + | |
189 | + | |
190 | + | |
191 | + | |
192 | +% Standard packages | |
193 | +\usepackage{times} | |
194 | +\usepackage[T1]{fontenc} | |
195 | +\usepackage[english]{babel} | |
196 | +\usepackage[latin1]{inputenc} | |
197 | +\usepackage{verbatim} | |
198 | +\usepackage{epsfig} | |
199 | +\usepackage{amsmath} | |
200 | +\usepackage{amssymb} | |
201 | +\usepackage{amsthm} | |
202 | +\newtheorem{thm}{Theorem}[section] | |
203 | +\setbeamercovered{dynamic} | |
204 | + | |
205 | + | |
206 | + | |
207 | + | |
208 | +% Setup appearance: | |
209 | + | |
210 | + | |
211 | +\usetheme{default} | |
212 | +\usefonttheme[onlylarge]{structurebold} | |
213 | + | |
214 | + | |
215 | + | |
216 | +\setbeamersize{text margin left=.5cm} | |
217 | +\setbeamersize{text margin right=.5cm} | |
218 | +%\setbeamertemplate{headline}{}% | |
219 | +\setbeamertemplate{navigation symbols}{} %gets rid of navigation symbols | |
220 | +%\setbeamertemplate{footline}[page number]{} %gets rid of bottom navigation bars | |
221 | + | |
222 | +\setbeamertemplate{itemize items}[circle] | |
223 | +\setbeamercolor{titlelike}{fg=blue} | |
224 | +\setbeamercolor{item}{fg=blue} | |
225 | + | |
226 | +\setbeamertemplate{frametitle}{ | |
227 | +\vspace{0.7cm} | |
228 | +\begin{centering} | |
229 | +{\Large \textbf{\textmd{\insertframetitle}}} | |
230 | +\par | |
231 | +\end{centering} | |
232 | +} | |
233 | + | |
234 | + | |
235 | + | |
236 | +% The main document | |
237 | + | |
238 | +\begin{document} | |
239 | + | |
240 | + | |
241 | + | |
242 | + | |
243 | + | |
244 | +\usebackgroundtemplate{\includegraphics[width=\paperwidth]{back.pdf}} | |
245 | + | |
246 | + | |
247 | +\begin{frame} | |
248 | + \titlepage | |
249 | +\end{frame} | |
250 | + | |
251 | +% \begin{frame}{Outline} | |
252 | +% \tableofcontents | |
253 | +% \end{frame} | |
254 | + | |
255 | + | |
256 | +\section{Introduction} | |
257 | + | |
258 | +\subsection{Problem Formulation} | |
259 | +%\vspace*{0.3cm} | |
260 | +\begin{frame}[c]{Motivation and Goals} | |
261 | +\vspace*{-0.2cm} | |
262 | + \begin{itemize} | |
263 | +\item \textcolor{red}{Diesel-generated nanoparticles} raise concerns | |
264 | + about their effects on human health and | |
265 | + environment. | |
266 | +\item \textcolor{red}{Legislation} regulating diesel-vehicle particulate \textcolor{red}{mass} | |
267 | + emissions (EURO1,2,3,4,\emph{etc}\dots), but particle number | |
268 | + distributions may be a better metric (especially for health effects). | |
269 | +\item Evaluate \textcolor{red}{effect of sampling and experimental conditions} | |
270 | + on measured particle number distributions emitted from light/heavy duty vehicles $\Rightarrow$ \textcolor{red}{PMP}. | |
271 | +\item Exploratory research as an experimental and theoretical study of the | |
272 | + \textcolor{red}{dynamics of non-volatile (\textcolor{red}{PMP}) particles emitted from diesel | |
273 | + light-duty vehicles} (emphasis on nanoparticle agglomeration). | |
274 | + \item Experiments performed at the \textcolor{red}{Vehicle Emission LAboratories} | |
275 | + (VELA) at Ispra. | |
276 | +% \item Investigation of diesel-nanoparticle aggregate structure, collisions and | |
277 | +% mobility via \textcolor{red}{Langevin} simulations. | |
278 | +% \item Aerosol processes: \textcolor{red}{convection, agglomeration, thermophoretic and | |
279 | +% diffusional transport} | |
280 | +% \item Emitted agglomerates are \textcolor{red}{fractal} objects. How | |
281 | +% to estimate their fractal dimension from limited experimental information? | |
282 | + | |
283 | + | |
284 | + | |
285 | + \end{itemize} | |
286 | +\end{frame} | |
287 | + | |
288 | +\section{Overview of the Experiments} | |
289 | + | |
290 | +\subsection{Exhaust-Particle Measurements} | |
291 | +%\vspace*{0.3cm} | |
292 | +\begin{frame}[t]{Experimental setup} | |
293 | +\vspace*{-.6cm} | |
294 | +\begin{center} | |
295 | +\includegraphics[width=8cm, height=6cm]{figure1.pdf} | |
296 | +\end{center} | |
297 | +\vspace*{-0.2cm} | |
298 | +\begin{itemize} | |
299 | +\item Temperature and particle-size distribution measurements along | |
300 | + \textcolor{red}{whole} experimental manifold (\textcolor{red}{not} | |
301 | + only at legislated position). | |
302 | +\end{itemize} | |
303 | +\end{frame} | |
304 | + | |
305 | + | |
306 | +\subsection{Number Distributions} | |
307 | +%\vspace*{0.3cm} | |
308 | +\begin{frame}[t]{Inlet and outlet experimental | |
309 | + number distributions: \\ { EURO 3 vehicle, 120km/h} } | |
310 | +\vspace*{-0.5cm} | |
311 | +\begin{center} | |
312 | +\rotatebox{90}{\includegraphics[width=5cm, height=8cm]{figure2_b.pdf}} | |
313 | +\end{center} | |
314 | +\vspace*{-0.6cm} | |
315 | +\begin{itemize} | |
316 | +% \item The experimental number distributions can be excellently | |
317 | +% approximated with analytical lognormal distributions. | |
318 | + \item \textcolor{red}{Lognormal} distribution | |
319 | +%\vspace*{-0.3cm} | |
320 | + \beq \nonumber | |
321 | + \begin{split} | |
322 | + dN^{\textrm{fit}} & {} = | |
323 | + \f{N_{\infty}} {\sqrt{2\pi}\log\sigma}\exp\lsq-\f{(\log d_{\rm agg}-\log\mu)^2}{2\log^2\sigma}\rsq d\log d_{\rm agg} \\ | |
324 | +% & {} \equiv n_q (\log d_{\rm agg}) \, d \log d_{\rm agg} | |
325 | + \end{split} | |
326 | + \eeq | |
327 | +\vspace*{-0.2cm} | |
328 | +\item Compact way of representing the data: $N_{\infty}, \mu\;\; {\rm | |
329 | + and}\;\; \sigma $ \textcolor{red}{unambiguously} describe the experimental data. | |
330 | + | |
331 | + | |
332 | +% \item Pressure fluctuations $\Rightarrow$ higher uncertainty on the | |
333 | +% number concentration $N_\infty$ (\textcolor{red}{not} on $\mu$ and $\sigma$) at inlet than outlet. | |
334 | +\end{itemize} | |
335 | +\end{frame} | |
336 | + | |
337 | + | |
338 | + | |
339 | +\section{Dynamics along transfer tube} | |
340 | + | |
341 | +\subsection{1D model for aerosol dynamics} | |
342 | + | |
343 | +%\vspace*{0.3cm} | |
344 | +\begin{frame}[t]{Aerosol in a Tube} | |
345 | +\vspace*{-0.5cm} | |
346 | +\begin{center} | |
347 | +\resizebox{10cm}{3cm}{\input{cylinder.pdf_t}} | |
348 | + | |
349 | +%\includegraphics[width=8cm, height=4cm]{cylinder.pdf} | |
350 | +\end{center} | |
351 | +\begin{itemize} | |
352 | +\vspace*{-0.1cm} | |
353 | +\item Four different aerosol processes: | |
354 | + \textcolor{darkgreen}{agglomeration}, | |
355 | + \textcolor{mymagenta}{diffusion}, | |
356 | +\textcolor{Brown}{thermophoresis} and \textcolor{blue}{convection}. | |
357 | +%\vspace*{-0.1cm} | |
358 | +\item 1D model neglecting turbulence-induced local particle density | |
359 | + inhomogeneities. | |
360 | + \item \textcolor{red}{$n_q$} (flux-averaged axial aggregate | |
361 | + concentration of size $d_q$ [$q$-mer]) | |
362 | + along tube as function | |
363 | + of \textcolor{red}{residence time} \textcolor{blue}{$\tau$} | |
364 | +\end{itemize} | |
365 | +\vspace*{-0.1cm} | |
366 | + \beq\nonumber | |
367 | + \;\;\,\f{d n_q(\textcolor{blue}{\tau})}{d\textcolor{blue}{\tau}}=-\f{2(\textcolor{mymagenta}{v_{\rm dif}}+\textcolor{Brown}{v_{\rm th}})}{ | |
368 | + R}n_q(\textcolor{blue}{\tau})+ | |
369 | +\f{1}{2}\sum_{i+j=q}\textcolor{darkgreen}{\mathcal{K}_{ij}}n_i(\textcolor{blue}{\tau})n_j(\textcolor{blue}{\tau}) - n_q(\textcolor{blue}{\tau})\sum_i\textcolor{darkgreen}{\mathcal{K}_{iq}}n_i(\textcolor{blue}{\tau}). | |
370 | + \eeq | |
371 | + | |
372 | +% \item $n_q$ the mean (flux-averaged) axial aggregate concentration of size $d_q$ | |
373 | + | |
374 | + | |
375 | + | |
376 | +\end{frame} | |
377 | + | |
378 | +%\vspace*{0.3cm} | |
379 | +\begin{frame}[t]{Time-Scales and Approximations} | |
380 | +%\vspace*{-0.45cm} | |
381 | + \begin{itemize} | |
382 | + \item Time-scales for each process: $\tau_{\rm agg}\simeq 2$s, | |
383 | + $\tau_{\rm dif}\simeq 10^{3}$s, $\tau_{\rm th}\simeq 30s$ and | |
384 | + $\tau_{\rm conv}\simeq 2$s. | |
385 | + \end{itemize} | |
386 | +\vspace*{-0.5cm} | |
387 | +\begin{center} | |
388 | +\includegraphics[width=8cm, height=5.5cm]{figure7_b.pdf} | |
389 | +\end{center} | |
390 | +\vspace*{-0.5cm} | |
391 | +\begin{itemize} | |
392 | +\item Effect of the transfer tube length on number concentration: | |
393 | + important for experiment \textcolor{red}{reproducibility}. | |
394 | +\item Different $\tau_{\rm agg}$ for a \textcolor{red}{light-duty} Euro4-5 diesel engine. | |
395 | +\end{itemize} | |
396 | + | |
397 | + | |
398 | +\end{frame} | |
399 | + | |
400 | + | |
401 | +\section{Simulation of soot aggregate formation} | |
402 | +\subsection{Model for Monomer Dynamics} | |
403 | +%\vspace*{0.3cm} | |
404 | +\begin{frame}[t]{Langevin Equation for Mesoscopic Systems} | |
405 | +\vspace*{-0.5cm} | |
406 | +\begin{center} | |
407 | +\resizebox{7cm}{4.5cm}{\input{brownian.pdf_t}} | |
408 | + | |
409 | +%\includegraphics[width=8cm, height=4cm]{cylinder.pdf} | |
410 | +\end{center} | |
411 | +%\vspace*{-0.15cm} | |
412 | +\begin{itemize} | |
413 | +\item \textcolor{red}{3D} system of interacting monomers, each | |
414 | + obeying | |
415 | +%\vspace*{-0.2cm} | |
416 | +\begin{equation} | |
417 | + \label{eq:Langevin} \nonumber | |
418 | + m_1\ddot{\bf r}_i=\textcolor{red}{{\bf F}_i}-\beta_1 m_1\dot{\bf r}_i+ | |
419 | + {\bf W}_i(t). | |
420 | +\end{equation} | |
421 | +\vspace*{-0.55cm} | |
422 | +\item Force acting on i-th monomer from \textcolor{red}{pairwise} monomer-monomer interaction potential | |
423 | +\vspace*{-0.25cm} | |
424 | +\begin{equation} \nonumber | |
425 | + \label{eq:potential_pairwise} | |
426 | + {\bf F}_i=-\nabla_{{\bf r}_i} U_i=-\f{\nabla_{{\bf r}_i}}{2}\lro\s_{j\neq i}u(r_{ij})\rro. | |
427 | +\end{equation} | |
428 | +\end{itemize} | |
429 | +\end{frame} | |
430 | + | |
431 | + | |
432 | + | |
433 | +\subsection{Interaction Potential} | |
434 | +%\vspace*{0.3cm} | |
435 | +\begin{frame}[t]{Monomer-Monomer Interaction Potential} | |
436 | +%\vspace*{-0.5cm} | |
437 | +% \begin{block}{General Features} | |
438 | +%\vspace*{-0.4cm} | |
439 | + \begin{itemize} | |
440 | + \item \textcolor{red}{Repulsion} at short separations $r\le\sigma$ | |
441 | + (hard-core repulsion) and \textcolor{red}{attraction} for separations above | |
442 | + $\sigma$ | |
443 | + (sticking upon collision). | |
444 | +\item Simulations performed with two \textcolor{red}{radial} interaction potentials: integrated Lennard-Jones | |
445 | + potential (model for the attractive part of \textcolor{red}{Van der Waals} | |
446 | + interaction between two spheres, $\sim r^{-6}$ for $r\gg\sigma$) and with a short-ranged | |
447 | + \textcolor{red}{model potential}. | |
448 | +%\begin{itemize} | |
449 | +%\item Potential used in the simulations: | |
450 | +\end{itemize} | |
451 | +\vspace*{-.5cm} | |
452 | +\begin{figure} | |
453 | +\includegraphics[height=5cm, width=9cm]{presentation_potential.pdf} | |
454 | +%\caption{show an example picture} | |
455 | +\end{figure} | |
456 | + | |
457 | + | |
458 | + | |
459 | +\end{frame} | |
460 | + | |
461 | + | |
462 | + | |
463 | + | |
464 | + | |
465 | +%\vspace*{0.3cm} | |
466 | +\begin{frame}[t]{Distribution of Aggregate Morphologies} | |
467 | +\vspace*{-0.5cm} | |
468 | +\begin{figure} | |
469 | +\includegraphics[height=3.5cm, width=0.43\columnwidth]{final2.png} | |
470 | +\vspace*{0.1cm} | |
471 | +\includegraphics[height=3.5cm, width=0.43\columnwidth]{50_monomers_neighbor1_bis.png} | |
472 | +%\caption{show an example picture} | |
473 | +\end{figure} | |
474 | + | |
475 | +\vspace{-0.5cm} | |
476 | + | |
477 | +\begin{figure} | |
478 | +\includegraphics[height=3.5cm, width=0.43\columnwidth]{50_monomers_neighbor2_bis.png} | |
479 | +\vspace*{0.1cm} | |
480 | +\includegraphics[height=3.5cm, width=0.43\columnwidth]{50_monomers_neighbor3_bis.png} | |
481 | +%\caption{show an example picture} | |
482 | +\end{figure} | |
483 | +\end{frame} | |
484 | + | |
485 | + | |
486 | + | |
487 | + | |
488 | +\subsection{Determination of the Fractal Dimension} | |
489 | +\begin{frame} | |
490 | +\begin{figure} | |
491 | +\includegraphics[height=5cm, width=5cm]{camera.jpeg} | |
492 | +%\caption{show an example picture} | |
493 | +\end{figure} | |
494 | +\end{frame} | |
495 | + | |
496 | + | |
497 | +\section{Conclusions} | |
498 | +%\vspace*{0.3cm} | |
499 | +\begin{frame}[t]{Final Remarks} | |
500 | + \begin{itemize} | |
501 | + \item Simplified 1D model for soot solid nanoparticles (PMP | |
502 | + recommendation) $\Rightarrow$ runs on any up-to-date PC within hours. | |
503 | +\item Determination of characteristic time-scales. | |
504 | +\item Different role of agglomeration for Euro4-5 vehicles. | |
505 | +\item Modelling complements the experimental information on soot | |
506 | + aggregates $\Rightarrow$ theoretical investigation on aggregate | |
507 | + structure, mobility and collisional properties. | |
508 | + \end{itemize} | |
509 | +\end{frame} | |
510 | + | |
511 | + | |
512 | + | |
513 | +\end{document} | |
514 | + | |
515 | + |