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\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}
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