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Lecture_repo / Lectures_my / NumMet / 2016 / Lecture11 / mchrzasz.tex
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  53. \usepackage{cancel} % For "SUSY-breaking" symbol
  54. \usepackage{slashed} % for slashed characters in math mode
  55. \usepackage{bbm} % for \mathbbm{1} (unit matrix)
  56. \usepackage{amsthm} % For theorem environment
  57. \usepackage{multirow} % For multi row cells in table
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  80. % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
  81. \usepackage{tikzfeynman} % For Feynman diagrams
  82. \usetikzlibrary{arrows,shapes}
  83. \usetikzlibrary{trees}
  84. \usetikzlibrary{matrix,arrows} % For commutative diagram
  85. % http://www.felixl.de/commu.pdf
  86. \usetikzlibrary{positioning} % For "above of=" commands
  87. \usetikzlibrary{calc,through} % For coordinates
  88. \usetikzlibrary{decorations.pathreplacing} % For curly braces
  89. % http://www.math.ucla.edu/~getreuer/tikz.html
  90. \usepackage{pgffor} % For repeating patterns
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  92. \usetikzlibrary{decorations.pathmorphing} % For Feynman Diagrams
  93. \usetikzlibrary{decorations.markings}
  94. \tikzset{
  95. % >=stealth', %% Uncomment for more conventional arrows
  96. vector/.style={decorate, decoration={snake}, draw},
  97. provector/.style={decorate, decoration={snake,amplitude=2.5pt}, draw},
  98. antivector/.style={decorate, decoration={snake,amplitude=-2.5pt}, draw},
  99. fermion/.style={draw=gray, postaction={decorate},
  100. decoration={markings,mark=at position .55 with {\arrow[draw=gray]{>}}}},
  101. fermionbar/.style={draw=gray, postaction={decorate},
  102. decoration={markings,mark=at position .55 with {\arrow[draw=gray]{<}}}},
  103. fermionnoarrow/.style={draw=gray},
  104. gluon/.style={decorate, draw=black,
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  106. scalar/.style={dashed,draw=black, postaction={decorate},
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  108. scalarbar/.style={dashed,draw=black, postaction={decorate},
  109. decoration={markings,mark=at position .55 with {\arrow[draw=black]{<}}}},
  110. scalarnoarrow/.style={dashed,draw=black},
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  112. decoration={markings,mark=at position .55 with {\arrow[draw=black]{>}}}},
  113. bigvector/.style={decorate, decoration={snake,amplitude=4pt}, draw},
  114. }
  115.  
  116. % TIKZ - for block diagrams,
  117. % from http://www.texample.net/tikz/examples/control-system-principles/
  118. % \usetikzlibrary{shapes,arrows}
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  136. % SOME COMMANDS THAT I FIND HANDY
  137. % \renewcommand{\tilde}{\widetilde} % dinky tildes look silly, dosn't work with fontspec
  138. \newcommand{\comment}[1]{\textcolor{comment}{\footnotesize{#1}\normalsize}} % comment mild
  139. \newcommand{\Comment}[1]{\textcolor{Comment}{\footnotesize{#1}\normalsize}} % comment bold
  140. \newcommand{\COMMENT}[1]{\textcolor{COMMENT}{\footnotesize{#1}\normalsize}} % comment crazy bold
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  172. % For shapo's formulas:
  173. \def\lsi{\raise0.3ex\hbox{$<$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}}
  174. \def\gsi{\raise0.3ex\hbox{$>$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}}
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  182. \newcommand{\vev}[1]{\rm{$\langle #1 \rangle$}}
  183. \newcommand{\abs}[1]{\rm{$\left| #1 \right|$}}
  184. \newcommand{\eV}{\rm{eV}}
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  189. \def\be{\begin{equation}}
  190. \def\ee{\end{equation}}
  191. \def\ba{\begin{eqnarray}}
  192. \def\ea{\end{eqnarray}}
  193. \def\d{\partial}
  194. \def\l{\left(}
  195. \def\r{\right)}
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  198. \def\e{{\rm e}}
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  200. \def\fixme{{\color{red} FIXME!}}
  201. \def\mc{{\color{Magenta}{MC}}\xspace}
  202. \def\pdf{{\rm p.d.f.}}
  203. \def\ARROW{{\color{JungleGreen}{$\Rrightarrow$}}\xspace}
  204. \def\ARROWR{{\color{WildStrawberry}{$\Rrightarrow$}}\xspace}
  205.  
  206. \author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz, Danny van Dyk} (UZH)}
  207. \institute{UZH}
  208. \title[Linear equation systems: exact methods]{Linear equation systems:exact methods}
  209. \date{21 September 2016}
  210.  
  211.  
  212. \begin{document}
  213. \tikzstyle{every picture}+=[remember picture]
  214.  
  215. {
  216. \setbeamertemplate{sidebar right}{\llap{\includegraphics[width=\paperwidth,height=\paperheight]{bubble2}}}
  217. \begin{frame}[c]%{\phantom{title page}}
  218. \begin{center}
  219. \begin{center}
  220. \begin{columns}
  221. \begin{column}{0.9\textwidth}
  222. \flushright\fontspec{Trebuchet MS}\bfseries \Huge {Chaos in ODEs}
  223. \end{column}
  224. \begin{column}{0.2\textwidth}
  225. %\includegraphics[width=\textwidth]{SHiP-2}
  226. \end{column}
  227. \end{columns}
  228. \end{center}
  229. \quad
  230. \vspace{3em}
  231. \begin{columns}
  232. \begin{column}{0.6\textwidth}
  233. \flushright \vspace{-1.8em} {\fontspec{Trebuchet MS} \large Marcin Chrząszcz, Danny van Dyk\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}, \href{mailto:dany.van.dyk@gmail.com}{danny.van.dyk@gmail.com}}
  234.  
  235. \end{column}
  236. \begin{column}{0.4\textwidth}
  237. \includegraphics[height=1.3cm]{uzh-transp}
  238. \end{column}
  239. \end{columns}
  240.  
  241. \vspace{1em}
  242. % \footnotesize\textcolor{gray}{With N. Serra, B. Storaci\\Thanks to the theory support from M. Shaposhnikov, D. Gorbunov}\normalsize\\
  243. \vspace{0.5em}
  244. \textcolor{normal text.fg!50!Comment}{Numerical Methods, \\ 16 November, 2016}
  245. \end{center}
  246. \end{frame}
  247. }
  248.  
  249.  
  250. \begin{frame}\frametitle{Classical mechanics formulation}
  251.  
  252. \ARROW This you should know by heart:\\{~}\\
  253. \begin{columns}
  254. \column{0.33\textwidth}
  255. \ARROW Newton:
  256. \begin{align*}
  257. \overrightarrow{F} = \frac{d \overrightarrow{p}}{dt}
  258. \end{align*}
  259. \column{0.33\textwidth}
  260. \ARROW Lagrange:
  261. \begin{align*}
  262. \mathcal{L}=T-V\\
  263. \frac{\partial \mathcal{L} }{ \partial x} - \frac{d}{dt} \frac{\partial \mathcal{L}}{\partial \dot{x}}=0
  264. \end{align*}
  265. \column{0.33\textwidth}
  266. \ARROW Hamilton:
  267. \begin{align*}
  268. \mathcal{H}=T+ V\\
  269. \frac{d p}{d t}=-\frac{\partial \mathcal{H}}{\partial x}\\
  270. \frac{d x }{d t}= \frac{\partial \mathcal{H}}{\partial p}
  271. \end{align*}
  272.  
  273. \end{columns}
  274.  
  275. \ARROW Now what are advantages of each one?
  276.  
  277. \end{frame}
  278.  
  279.  
  280.  
  281.  
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  284. \begin{frame}\frametitle{Backup}
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  286.  
  287. \end{frame}
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  294.  
  295. \backupend
  296. \end{document}