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diff --git a/langfassung/docs/1_kurzfassung.tex b/langfassung/docs/1_kurzfassung.tex new file mode 100644 index 0000000..b4aee7d --- /dev/null +++ b/langfassung/docs/1_kurzfassung.tex @@ -0,0 +1 @@ +Kurzfassung diff --git a/langfassung/docs/2_einleitung.tex b/langfassung/docs/2_einleitung.tex new file mode 100644 index 0000000..806c214 --- /dev/null +++ b/langfassung/docs/2_einleitung.tex @@ -0,0 +1,19 @@ +Einleitung + +\subsection{Themen} + +\begin{itemize} + \item Heidelberg bla + \item Galaxy Foo bla + \item Stauchen / Strecken bla + \item Problem: Geschwindigkeit bla + \item Benchmarks: + \begin{itemize} + \item 10000 Sterne - 1 Stern + \item ... + \end{itemize} +\end{itemize} + +\subsection{Motivation} + +Motivations blah diff --git a/langfassung/docs/3_hauptteil.tex b/langfassung/docs/3_hauptteil.tex new file mode 100644 index 0000000..eab3897 --- /dev/null +++ b/langfassung/docs/3_hauptteil.tex @@ -0,0 +1,65 @@ +\subsection{Navarro–Frenk–White profile} + +Das Navarro-Frenk-White profil (NFW-profil) ist im grunde genommen eine Funktion +die einem die Warscheinlichkeit das ein Stern an einer bestimmten position ist +liefert. +Die Funktion ist im allgemeinen wie folgt aufgebaut: + +\begin{equation} + \rho = \frac{ 1 }{ \sqrt{ 2 \pi } \cdot \sigma } \cdot + \exp \left( \frac{ -\phi(r) }{ \sigma^{ 2 } } \right) +\end{equation} + +\begin{equation} + \phi_{NFW}(r) = \frac{ 4\pi \cdot G \cdot f_{0} \cdot R_{s}^3 }{ r } \cdot + ln{ \left( 1 + \frac{ r }{ R_{s} } \right) } +\end{equation} + +Sieht kompliziert aus, ist es aber nicht: Um zu gucken ob ein zufälliger Stern +bei \( x_1 \), \( y_1 \) und \( z_1 \) generiert werden kann wird wie folgt +vorgegangen: Aus den Koordinaten wird der Wert \( r \) mithilfe des Satz des +Phtargoras berechnet, dieser gibt +an wie weit der jeweilige Stern vom Zentrum der Galaxie entfernt ist. Um zu +prüfen ob der Stern generiert wird, wird dieser \( r \)-wert in die Funktion +\( \phi \) eingesetzt. Der entstehende Wert gibt an wie warscheinlich es ist, +das ein Stern in der Entfernung zum Ursprung generiert wird. +\par +Um herrauszufinden ob der Stern generiert wird, wird ein weiterer zufälliger +Wert \( x \) im bereich \( [\phi_{max}; \phi_{min}] \) generiert. Liegt dieser +Wert über dem Wert aus der Funktion \( \phi \) wird kein Stern generiert. +Liegt dieser Stern jedoch unter dem wert aus der \( \phi \) funktion wird +ein Stern an den Koordinaten \( x_1 \), \( y_1 \) und \( z_1 \) generiert. + +\subsection{Einasto profile} + +\begin{equation} + \gamma(r) = \frac{ d \ln(\rho(r)) }{ d \ln(\rho) } \propto r^{\alpha} +\end{equation} + +\subsection{Blender + Python} + +Blender is Awesome, Python is Awesome and together they are +\bold{SUPER AWESOME!!!} + +\subsection{Making things faster} + +Kicking out to many Stars, 1 out of 10000 is just to much... + +\subsection{Spiral Galaxies} + +The previous Galaxy models where all using a completely spherical model, generating +a spiral galaxy is just not possible using these models. + +\subsubsection{N-Körper problem} + +Kurze Beschreibung des N-Körper Problems + +\subsubsection{Hilbert Spiral} + +Beschreibung der Hilbert Spirale + +\subsection{Größeneinheiten} + +\begin{equation} + 3.086 \cdot 10^{36} m +\end{equation} diff --git a/langfassung/docs/4_ergebnisse.tex b/langfassung/docs/4_ergebnisse.tex new file mode 100644 index 0000000..abd806d --- /dev/null +++ b/langfassung/docs/4_ergebnisse.tex @@ -0,0 +1,27 @@ +Ergebnisse + +\subsection{Simulation Speed} + +Nach mergen des speed-branches sind folgende Ergebnisse zusammengekommen: + +\begin{tabular}{l | l | l} + +Sterne & Zeit Vorher & Zeit Nachher \\ \hline\hline +1e5 & 2.93 sek. & k.A. \\ +1e6 & 29.38 sek. & k.A. \\ +1e7 & 315.67 sek. & k.A. \\ +1e9 & 9h & k.A. \\ + +\end{tabular} + +Aus 1e9 Sternen werden vorher letztendlich 45000 Sterne generiert. + +Pro MegaByte können die Koordinaten von 10000 Sternen gespeichert werden. + +\subsection{Spiral Galaxies} + +Die generierung von Spiralgalaxien gestaltet sich schweiriger als erwartet. + +\subsection{Distortion of Galaxies} + +Galaxien verformen dinge diff --git a/langfassung/docs/5_quellen.tex b/langfassung/docs/5_quellen.tex new file mode 100644 index 0000000..17bb702 --- /dev/null +++ b/langfassung/docs/5_quellen.tex @@ -0,0 +1,24 @@ +Quellen + +\begin{center} + \textbf{ + Das Python-Programm sowie die Blender Darstellungen wurden vollständig ohne fremde Hilfe selber erstellt. + } +\end{center} +\par Einen Großteil der Formeln fand ich durch eine Wikipedia Recherche, jedoch wurden auch Informationen aus dem 'SPACETRACK REPORT' von Felix R. Hoots und Ronald L. Roerich, +No. 3 (Dec. 1980) entnommen. +\par Das Programieren in der Programiersprache Python habe ich wärend des Projektes mithilfe der Python-Documentation gelernt. Mit dem Umgang des 3D-Programms Blender +bin ich schon vertraut gewesen. Die Grundlagen für \LaTeX, in dem diese Langfassung geschrieben wurde, erlernte ich durch das Studieren diverser Beiträge in Foren und der Einsicht +in das Jugend Forscht Projekt von Konstantin Bosbach, Tilman Hoffbauer und Steffen Ritsche aus dem vorherigem Jahr (2016, Underwater Accoustic Communication). +\par Da es das erste Mal war, dass ich Python mit Blender kombiniert habe, musste ich mich in diesen Bereich ebenfalls einarbeiten. +Dabei war die Blender API Documentation (www.blender.org/api) von großer Hilfe. + + +\raggedleft +\section*{Dank gilt...} +\paragraph{Herrn Jörg Thar} meinem Betreuer +\paragraph{Konstantin Bosbach} welcher mir eine Möglichkeit gab für 2 Wochen in Heidelberg zu wohnen. +\paragraph{Tilman Hoffbauer} + +\centering +\vspace{0.5cm} \textbf{Außerdem gilt mein Dank allen, die mich auf jede nur erdenkliche Weise unterstützt haben.} diff --git a/langfassung/figs/Jugend_forscht.jpg b/langfassung/figs/Jugend_forscht.jpg new file mode 100644 index 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b/langfassung/master.pdf new file mode 100644 index 0000000..c39170c --- /dev/null +++ b/langfassung/master.pdf Binary files differdiff --git a/langfassung/master.synctex.gz b/langfassung/master.synctex.gz new file mode 100644 index 0000000..2d05754 --- /dev/null +++ b/langfassung/master.synctex.gz Binary files differdiff --git a/langfassung/master.tex b/langfassung/master.tex new file mode 100644 index 0000000..aa34893 --- /dev/null +++ b/langfassung/master.tex @@ -0,0 +1,139 @@ +\documentclass[a4paper,12pt]{scrartcl} +\usepackage[top=1cm, bottom=2.5cm, left=1cm, right=1cm]{geometry} +\usepackage[utf8]{inputenc} +\usepackage[english,ngerman]{babel} +\usepackage{amsmath} +\usepackage{tabularx} +\usepackage[hidelinks]{hyperref} + +\usepackage{graphicx} +\usepackage{caption} +\usepackage{lmodern} +\usepackage{textcomp} + +\usepackage{tikz} + +\usepackage{hyperref} +\hypersetup{ +colorlinks, +citecolor=black, +filecolor=black, +linkcolor=black, +urlcolor=black +} + +\newcommand{\bold}{\textbf} +\renewcommand{\arraystretch}{1.5} +\newcommand{ \rarrow }{\( \rightarrow \)} + +\setlength\parindent{0pt} +\setlength\parskip{10pt} +\setlength{\footskip}{30pt} +\setcounter{tocdepth}{3} + +%%% MAIN DOCUMENT BEGINS HERE %%% + +\begin{document} + +\title{Galaxy Stuff} +\subtitle{Jugend Forscht \the\year} +\author{ Emile Hansmaennel \texttt{ emile.hansmaennel@gmail.com }} +\date{\today} + +\maketitle + +\input{docs/1_kurzfassung} + +\thispagestyle{empty} +\clearpage +\newpage +\setcounter{page}{1} + +\tableofcontents +\newpage + +\section{Einleitung} \label{Einleitung} +\input{docs/2_einleitung} +\newpage + +\section{Hauptteil} \label{Hauptteil} +\subsection{Notes} + +\subsubsection{Todo} + +\begin{itemize} + \item Find a better way to kick out stars using a more efficient method + \item Find a way to generate a spiral with a curvature y of the arms + \item Compare the generated galaxies with real galaxies to find out if they + are legit + \item Generate the dark-matter, link the galaxies to the dark matter and watch + how the dark matter affects the galaxy while deforming the dark matter. +\end{itemize} + +\subsubsection{Generally building a galaxy} + +\begin{enumerate} + \item Generate the galaxy-data using the NFW-Profile or the Einasto-profile + \item Display the data in Blender and create an image using the OpenGL-renderer + \item Train a Neural Network (NN) to classify galaxies + \item Let the NN modify the galaxy to generate a perfect galaxy +\end{enumerate} + +\subsubsection{Spiral Galaxy} + +\begin{itemize} + \item Generate the coordinates independently from each other: + + \item Generate the spiral on the x/y plane: + \begin{itemize} + \item x / y: generate a spiral using the Polar coordinate system + \item z: generate the according z-value inddependently using the pythargoras + theorem to calculate the distance of a possible star from the center of the + galaxy, then continue by using the generated value inside of the NFW-profile + to find out if the star should be generated or not + \end{itemize} + \item Use the function to adapt the arms to real conditions +\end{itemize} + +\subsubsection{Important aspects of spiral galaxies} + +\begin{itemize} + \item Thickness of the galaxy at the bulge in the middle + \item Radius + \begin{itemize} + \item of the entire galaxy + \item of the bulge in the middle + \end{itemize} + \item Number of arms + \item Density + \begin{itemize} + \item of the spiral arms + \item of the bulge in the middle + \end{itemize} +\end{itemize} + +\subsubsection{Speed} + +\begin{itemize} + \item Manipulat the NFW-Profile (don't kick out so many stars!) + \item lookup-table for the random numbers + \item Amazon-Web-Services (AWS)? + \item PyPy + \item generally try to generate less galaxies further away ftom the center + so kicking out as many stars doesn't become problematic anymore. + (start with a linear function above the NFW-profile and kick out the remaining + stars to enhance the profile) +\end{itemize} + + +\input{docs/3_hauptteil} +\newpage + +\section{Ergebnisse} \label{ergebnisse} +\input{docs/4_ergebnisse} +\newpage + +\section{Quellen und Hilfen} \label{quellen} +\input{docs/5_quellen} + +\end{document} diff --git a/langfassung/master.toc b/langfassung/master.toc new file mode 100644 index 0000000..11af2a8 --- /dev/null +++ b/langfassung/master.toc @@ -0,0 +1,27 @@ +\select@language {ngerman} +\contentsline {section}{\numberline {1}Einleitung}{2}{section.1} +\contentsline {subsection}{\numberline {1.1}Themen}{2}{subsection.1.1} +\contentsline {subsection}{\numberline {1.2}Motivation}{2}{subsection.1.2} +\contentsline {section}{\numberline {2}Hauptteil}{3}{section.2} +\contentsline {subsection}{\numberline {2.1}Notes}{3}{subsection.2.1} +\contentsline {subsubsection}{\numberline {2.1.1}Todo}{3}{subsubsection.2.1.1} +\contentsline {subsubsection}{\numberline {2.1.2}Generally building a galaxy}{3}{subsubsection.2.1.2} +\contentsline {subsubsection}{\numberline {2.1.3}Spiral Galaxy}{3}{subsubsection.2.1.3} +\contentsline {subsubsection}{\numberline {2.1.4}Important aspects of spiral galaxies}{3}{subsubsection.2.1.4} +\contentsline {subsubsection}{\numberline {2.1.5}Speed}{4}{subsubsection.2.1.5} +\contentsline {subsection}{\numberline {2.2}Navarro\IeC {\textendash }Frenk\IeC {\textendash }White profile}{4}{subsection.2.2} +\contentsline {subsection}{\numberline {2.3}Einasto profile}{4}{subsection.2.3} +\contentsline {subsection}{\numberline {2.4}Blender + Python}{4}{subsection.2.4} +\contentsline {subsection}{\numberline {2.5}Making things faster}{5}{subsection.2.5} +\contentsline {subsection}{\numberline {2.6}Spiral Galaxies}{5}{subsection.2.6} +\contentsline {subsubsection}{\numberline {2.6.1}N-K\IeC {\"o}rper problem}{5}{subsubsection.2.6.1} +\contentsline {subsubsection}{\numberline {2.6.2}Hilbert Spiral}{5}{subsubsection.2.6.2} +\contentsline {subsection}{\numberline {2.7}Gr\IeC {\"o}\IeC {\ss }eneinheiten}{5}{subsection.2.7} +\contentsline {section}{\numberline {3}Ergebnisse}{6}{section.3} +\contentsline {subsection}{\numberline {3.1}Simulation Speed}{6}{subsection.3.1} +\contentsline {subsection}{\numberline {3.2}Spiral Galaxies}{6}{subsection.3.2} +\contentsline {subsection}{\numberline {3.3}Distortion of Galaxies}{6}{subsection.3.3} +\contentsline {section}{\numberline {4}Quellen und Hilfen}{7}{section.4} +\contentsline {paragraph}{\nonumberline Herrn J\IeC {\"o}rg Thar}{7}{section*.3} +\contentsline {paragraph}{\nonumberline Konstantin Bosbach}{7}{section*.4} +\contentsline {paragraph}{\nonumberline Tilman Hoffbauer}{7}{section*.5} diff --git a/langfassung/references/dissSchwarzmeier.pdf b/langfassung/references/dissSchwarzmeier.pdf new file mode 100644 index 0000000..b1b5d2b --- /dev/null +++ b/langfassung/references/dissSchwarzmeier.pdf Binary files differdiff --git a/langfassung/references/master(2).pdf b/langfassung/references/master(2).pdf new file mode 100644 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