Commit cfb50e15 authored by Quentin Aristote's avatar Quentin Aristote
Browse files

continued presentation

parent a1c6e6c5
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......@@ -22,11 +22,12 @@
\usepackage{float}
\usepackage{mwe}
\usepackage{array}
\usepackage{pst-solides3d}
\usepackage{multimedia}
\usepackage{hyperref}
\usepackage[sorting = none, backend = biber]{biblatex}
\addbibresource{rapport.bib}
\usepackage[normalem]{ulem}
% ------------------------------ Theorems ------------------------------
......@@ -313,4 +314,36 @@
% theorie de la relat generale : metrique déformée par la présence d'une masse
% proba importante => 1-3 (= puit)
% proba petite => 3-1 (enlève le puit)
\section{Étude du marcheur}
% couplage défini -> l'étudier
% marche intéressante ?
% comportement cohérent avec théorie de la relat générale ?
\begin{frame}{1ères simulations}
\pause
Complexité d'un pas : $\mathcal{O}(\#\mathrm{triangles}) = \mathcal{O}(t^2)$
\pause
\vspace{20pt}
Résultats :
\begin{itemize}
\item \movie[externalviewer]{\uline{$\alpha = \beta = 1$ (réseau plat)}}{graphics/evolution_alpha_1.gif}
\item \movie[externalviewer]{\uline{$\alpha = \beta = 0.1$}}{graphics/evolution_alpha_.1.gif}
\item \movie[externalviewer]{\uline{$\alpha = \beta = 0.01$}}{graphics/evolution_alpha_.01.gif}
\end{itemize}
\end{frame}
% 1ères sim pour conjectures
% implémentation en Python, couteux
% condition initiale : équiprobabilité triangle centre
% gifs : évolution distrib
% alpha = 1 : reseau plat -> hexagone
% alpha = 0.1 -> hexagone moche (réseau redevient plat)
% alpha = 0.01 -> étoile (3-1 pms) puis boule (plus de pm -> réseau plat ?)
\end{document}
\ No newline at end of file
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[graphics,tightpage,active]{preview}
\PreviewEnvironment{tikzpicture}
\PreviewEnvironment{equation}
\PreviewEnvironment{equation*}
\newlength{\imagewidth}
\newlength{\imagescale}
\pagestyle{empty}
\thispagestyle{empty}
\tikzstyle{vertex} = [circle, fill = white, draw = black]
\newcommand{\up}{\uparrow}
\newcommand{\down}{\downarrow}
\begin{document}
\begin{tikzpicture}
\pgftransformcm{-1}{0}{0}{sqrt(3)/2}{\pgfpoint{0cm}{0cm}}
\draw (0,0) -- (1,2) node[left] {} -- (2,4) -- (3,2) node[right] {} -- (4,0) -- (2,0) node[below] {} -- (0,0) ;
\node[below] at (2,0) {$\mathrm{rg} \psi = 6$} ;
\draw[<-] (5,2) -- (6,2) ;
\draw (7 + 0, 0) -- (7 + 1,2) node[left] {} -- (7 + 2,4) -- (7 + 3,2) node[right] {} -- (7 + 4,0) -- (7 + 2,0) node[below] {} -- (7 + 0,0) ;
\draw[very thick] (7 + 0, 0) -- (7 + 1,2/3) node[above] {} -- (7 + 2, 4/3) ;
\draw[very thick] (7 + 2, 4) -- (7 + 2,8/3) node[left] {} -- (7 + 2, 4/3) ;
\draw[very thick] (7 + 4, 0)-- (7 + 3,2/3) node[above] {} -- (7 + 2, 4/3) ;
\node[below] at (9,0) {$\mathrm{rg} \psi = 12$} ;
% \draw (1, .75) node[below left] {$\widetilde{\psi}(t,v,2)$} -- (2, 1.5);
% \draw (3, .75) node[below right] {$\widetilde{\psi}(t,v,3)$} -- (2, 1.5);
% \draw (2, 2.75) node[above] {$\widetilde{\psi}(t,v,1)$} -- (2, 1.5);
% \node [vertex] at (2, 1.5) {$\down\down\down$} ;
% \draw[->] (4,1.5) -- (6,1.5) ;
% \draw (7 + 0, 0) -- (7 - 1, -.75) node[below left] {$\widetilde{\psi}(t,v,2)$} ;
% \draw (7 + 4, 0) -- (7 + 5, -.75) node[below right] {$\widetilde{\psi}(t,v,3)$} ;
% \draw (7 + 2, 4) -- (7 + 2, 5.25) node[above] {$\widetilde{\psi}(t,v,1)$} ;
% \draw (7 + 0, 0) -- (7 + 1, 2) node[above left] {$\vec{0}$} -- (7 + 2, 4) -- (7 + 3, 2) node[above right] {$\vec{0}$} -- (7 + 4, 0) -- (7 + 2, 0) node[below] {$\vec{0}$} -- cycle ;
% \node [vertex] at (7 + 0, 0) {$\down\down\up$} ;
% \node [vertex] at (7 + 4, 0) {$\up\up\down$} ;
% \node [vertex] at (7 + 2, 4) {$\down\down\down$} ;
\end{tikzpicture}
\end{document}
\ No newline at end of file
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[graphics,tightpage,active]{preview}
\PreviewEnvironment{tikzpicture}
\PreviewEnvironment{equation}
\PreviewEnvironment{equation*}
\newlength{\imagewidth}
\newlength{\imagescale}
\pagestyle{empty}
\thispagestyle{empty}
\tikzstyle{vertex} = [circle, fill = white, draw = black]
\newcommand{\up}{\uparrow}
\newcommand{\down}{\downarrow}
\begin{document}
\begin{tikzpicture}
\pgftransformcm{1}{0}{1}{sqrt(3)/2}{\pgfpoint{0cm}{0cm}}
\clip (0,1) rectangle (5,5) ;
\draw[fill = gray!5] (0,1) rectangle (5,5) ;
\draw[fill = gray!30, draw = gray] (2,3) -- (3,3) -- (2,4) -- cycle ;
\draw[dashed, very thick, fill = gray!30] (2,3) -- (2.9,2.8) -- (3,3) ;
\draw[dashed, very thick] (2.9,2.8) -- (2,4) ;
\draw[gray, fill = gray] (-3,0) grid (8,6) ;
\pgftransformcm{1}{0}{-2/sqrt(3)}{2/sqrt(3)}{\pgfpoint{0cm}{0cm}}
\shade[ball color = blue!40] (5.675,2.7) circle (.2);
\pgftransformcm{1}{0}{0}{-sqrt(3)/2}{\pgfpoint{0cm}{0cm}}
%\draw[gray, fill = gray] (-3,0) grid (14,-6) ;
\draw[very thick] (6,-3) -- (5,-3) -- (6, -4) -- cycle ;
\end{tikzpicture}
\end{document}
\ No newline at end of file
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[graphics,tightpage,active]{preview}
\PreviewEnvironment{tikzpicture}
\PreviewEnvironment{equation}
\PreviewEnvironment{equation*}
\newlength{\imagewidth}
\newlength{\imagescale}
\pagestyle{empty}
\thispagestyle{empty}
\tikzstyle{vertex} = [circle, fill = white, draw = black]
\newcommand{\up}{\uparrow}
\newcommand{\down}{\downarrow}
\begin{document}
\begin{tikzpicture}
\pgftransformcm{0}{1}{-sqrt(3)/2}{1/2}{\pgfpoint{0cm}{0cm}}
\draw[->, blue] (.6, 1.5) to [out = 90, in = -50] (-.9, 5.5) ;
\draw[->, blue] (-1.1, 5.5) to [out = 130, in = -50] (-1.9, 9.5) ;
\draw (0, 0) -- (-.5, -.5) node[below right] {1} ;
\draw (2, 0) -- (3, -.5) node[above right] {2} ;
\draw (-1, 4) -- (-2,5) node[below left] {2} ;
\draw (-1, 6) -- (0, 5) node[above right] {2} ;
\draw (-2, 8) -- (-3, 9) node[below left] {2} ;
\draw (0, 2) -- (-.5, 3) node[above] {0} -- (-1, 4) node[vertex] {$w$} -- (-1, 5) node[below] {1} -- (-1, 6) node[vertex] {} -- (-1.5, 7) node[above] {0} -- (-2, 8) node[vertex] {} -- (-2, 9) node[above left] {1} ;
\draw (0, 0) node[vertex] {} -- (1,0) node[right] {0} -- (2, 0) node[vertex] {} -- (1, 1) node[above] {1} -- (0, 2) node[vertex] {$v$} -- (0, 1) node[below] {2} -- cycle ;
\end{tikzpicture}
\end{document}
\ No newline at end of file
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