added a folder for storing the so called langfassung

author: hanemile <emile.hansmaennel@gmail.com> 2017-12-03 13:30:43 +0100
committer: hanemile <emile.hansmaennel@gmail.com> 2017-12-03 13:30:43 +0100
commit: b031dc7d5e97d209d2e461b958e44e7aa6e7e855 (patch)
tree: 4b173d40e1d59c86827ab32f02d224c6eb5f8ab0 /langfassung
parent: cc5da556b93f5105faa7243cd0b3b509c9ac98e3 (diff)
17 files changed, 2243 insertions, 0 deletions
diff --git a/langfassung/docs/1_kurzfassung.tex b/langfassung/docs/1_kurzfassung.tex
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+++ 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 0000000..6d23e96
--- /dev/null
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index 0000000..41ce740
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+\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Blender + Python}{4}{subsection.2.4}}
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+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.6.1}N-K\IeC {\"o}rper problem}{5}{subsubsection.2.6.1}}
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+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Herrn J\IeC {\"o}rg Thar}{7}{section*.3}}
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+   defining Unicode char U+00A0 (decimal 160)
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+   defining Unicode char U+00A3 (decimal 163)
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+   defining Unicode char U+00C2 (decimal 194)
+   defining Unicode char U+00C3 (decimal 195)
+   defining Unicode char U+00C4 (decimal 196)
+   defining Unicode char U+00C5 (decimal 197)
+   defining Unicode char U+00C6 (decimal 198)
+   defining Unicode char U+00C7 (decimal 199)
+   defining Unicode char U+00C8 (decimal 200)
+   defining Unicode char U+00C9 (decimal 201)
+   defining Unicode char U+00CA (decimal 202)
+   defining Unicode char U+00CB (decimal 203)
+   defining Unicode char U+00CC (decimal 204)
+   defining Unicode char U+00CD (decimal 205)
+   defining Unicode char U+00CE (decimal 206)
+   defining Unicode char U+00CF (decimal 207)
+   defining Unicode char U+00D0 (decimal 208)
+   defining Unicode char U+00D1 (decimal 209)
+   defining Unicode char U+00D2 (decimal 210)
+   defining Unicode char U+00D3 (decimal 211)
+   defining Unicode char U+00D4 (decimal 212)
+   defining Unicode char U+00D5 (decimal 213)
+   defining Unicode char U+00D6 (decimal 214)
+   defining Unicode char U+00D8 (decimal 216)
+   defining Unicode char U+00D9 (decimal 217)
+   defining Unicode char U+00DA (decimal 218)
+   defining Unicode char U+00DB (decimal 219)
+   defining Unicode char U+00DC (decimal 220)
+   defining Unicode char U+00DD (decimal 221)
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+   defining Unicode char U+00DF (decimal 223)
+   defining Unicode char U+00E0 (decimal 224)
+   defining Unicode char U+00E1 (decimal 225)
+   defining Unicode char U+00E2 (decimal 226)
+   defining Unicode char U+00E3 (decimal 227)
+   defining Unicode char U+00E4 (decimal 228)
+   defining Unicode char U+00E5 (decimal 229)
+   defining Unicode char U+00E6 (decimal 230)
+   defining Unicode char U+00E7 (decimal 231)
+   defining Unicode char U+00E8 (decimal 232)
+   defining Unicode char U+00E9 (decimal 233)
+   defining Unicode char U+00EA (decimal 234)
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+   defining Unicode char U+00ED (decimal 237)
+   defining Unicode char U+00EE (decimal 238)
+   defining Unicode char U+00EF (decimal 239)
+   defining Unicode char U+00F0 (decimal 240)
+   defining Unicode char U+00F1 (decimal 241)
+   defining Unicode char U+00F2 (decimal 242)
+   defining Unicode char U+00F3 (decimal 243)
+   defining Unicode char U+00F4 (decimal 244)
+   defining Unicode char U+00F5 (decimal 245)
+   defining Unicode char U+00F6 (decimal 246)
+   defining Unicode char U+00F8 (decimal 248)
+   defining Unicode char U+00F9 (decimal 249)
+   defining Unicode char U+00FA (decimal 250)
+   defining Unicode char U+00FB (decimal 251)
+   defining Unicode char U+00FC (decimal 252)
+   defining Unicode char U+00FD (decimal 253)
+   defining Unicode char U+00FE (decimal 254)
+   defining Unicode char U+00FF (decimal 255)
+   defining Unicode char U+0100 (decimal 256)
+   defining Unicode char U+0101 (decimal 257)
+   defining Unicode char U+0102 (decimal 258)
+   defining Unicode char U+0103 (decimal 259)
+   defining Unicode char U+0104 (decimal 260)
+   defining Unicode char U+0105 (decimal 261)
+   defining Unicode char U+0106 (decimal 262)
+   defining Unicode char U+0107 (decimal 263)
+   defining Unicode char U+0108 (decimal 264)
+   defining Unicode char U+0109 (decimal 265)
+   defining Unicode char U+010A (decimal 266)
+   defining Unicode char U+010B (decimal 267)
+   defining Unicode char U+010C (decimal 268)
+   defining Unicode char U+010D (decimal 269)
+   defining Unicode char U+010E (decimal 270)
+   defining Unicode char U+010F (decimal 271)
+   defining Unicode char U+0110 (decimal 272)
+   defining Unicode char U+0111 (decimal 273)
+   defining Unicode char U+0112 (decimal 274)
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+   defining Unicode char U+0114 (decimal 276)
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+   defining Unicode char U+0117 (decimal 279)
+   defining Unicode char U+0118 (decimal 280)
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+   defining Unicode char U+011B (decimal 283)
+   defining Unicode char U+011C (decimal 284)
+   defining Unicode char U+011D (decimal 285)
+   defining Unicode char U+011E (decimal 286)
+   defining Unicode char U+011F (decimal 287)
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+   defining Unicode char U+0122 (decimal 290)
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+   defining Unicode char U+0125 (decimal 293)
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+   defining Unicode char U+0129 (decimal 297)
+   defining Unicode char U+012A (decimal 298)
+   defining Unicode char U+012B (decimal 299)
+   defining Unicode char U+012C (decimal 300)
+   defining Unicode char U+012D (decimal 301)
+   defining Unicode char U+012E (decimal 302)
+   defining Unicode char U+012F (decimal 303)
+   defining Unicode char U+0130 (decimal 304)
+   defining Unicode char U+0131 (decimal 305)
+   defining Unicode char U+0132 (decimal 306)
+   defining Unicode char U+0133 (decimal 307)
+   defining Unicode char U+0134 (decimal 308)
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+   defining Unicode char U+013B (decimal 315)
+   defining Unicode char U+013C (decimal 316)
+   defining Unicode char U+013D (decimal 317)
+   defining Unicode char U+013E (decimal 318)
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+   defining Unicode char U+0142 (decimal 322)
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+   defining Unicode char U+014D (decimal 333)
+   defining Unicode char U+014E (decimal 334)
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+   defining Unicode char U+0152 (decimal 338)
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+   defining Unicode char U+0159 (decimal 345)
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+   defining Unicode char U+015B (decimal 347)
+   defining Unicode char U+015C (decimal 348)
+   defining Unicode char U+015D (decimal 349)
+   defining Unicode char U+015E (decimal 350)
+   defining Unicode char U+015F (decimal 351)
+   defining Unicode char U+0160 (decimal 352)
+   defining Unicode char U+0161 (decimal 353)
+   defining Unicode char U+0162 (decimal 354)
+   defining Unicode char U+0163 (decimal 355)
+   defining Unicode char U+0164 (decimal 356)
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+   defining Unicode char U+0169 (decimal 361)
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+   defining Unicode char U+016B (decimal 363)
+   defining Unicode char U+016C (decimal 364)
+   defining Unicode char U+016D (decimal 365)
+   defining Unicode char U+016E (decimal 366)
+   defining Unicode char U+016F (decimal 367)
+   defining Unicode char U+0170 (decimal 368)
+   defining Unicode char U+0171 (decimal 369)
+   defining Unicode char U+0172 (decimal 370)
+   defining Unicode char U+0173 (decimal 371)
+   defining Unicode char U+0174 (decimal 372)
+   defining Unicode char U+0175 (decimal 373)
+   defining Unicode char U+0176 (decimal 374)
+   defining Unicode char U+0177 (decimal 375)
+   defining Unicode char U+0178 (decimal 376)
+   defining Unicode char U+0179 (decimal 377)
+   defining Unicode char U+017A (decimal 378)
+   defining Unicode char U+017B (decimal 379)
+   defining Unicode char U+017C (decimal 380)
+   defining Unicode char U+017D (decimal 381)
+   defining Unicode char U+017E (decimal 382)
+   defining Unicode char U+01CD (decimal 461)
+   defining Unicode char U+01CE (decimal 462)
+   defining Unicode char U+01CF (decimal 463)
+   defining Unicode char U+01D0 (decimal 464)
+   defining Unicode char U+01D1 (decimal 465)
+   defining Unicode char U+01D2 (decimal 466)
+   defining Unicode char U+01D3 (decimal 467)
+   defining Unicode char U+01D4 (decimal 468)
+   defining Unicode char U+01E2 (decimal 482)
+   defining Unicode char U+01E3 (decimal 483)
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+   defining Unicode char U+01E9 (decimal 489)
+   defining Unicode char U+01EA (decimal 490)
+   defining Unicode char U+01EB (decimal 491)
+   defining Unicode char U+01F0 (decimal 496)
+   defining Unicode char U+01F4 (decimal 500)
+   defining Unicode char U+01F5 (decimal 501)
+   defining Unicode char U+0218 (decimal 536)
+   defining Unicode char U+0219 (decimal 537)
+   defining Unicode char U+021A (decimal 538)
+   defining Unicode char U+021B (decimal 539)
+   defining Unicode char U+0232 (decimal 562)
+   defining Unicode char U+0233 (decimal 563)
+   defining Unicode char U+1E02 (decimal 7682)
+   defining Unicode char U+1E03 (decimal 7683)
+   defining Unicode char U+200C (decimal 8204)
+   defining Unicode char U+2010 (decimal 8208)
+   defining Unicode char U+2011 (decimal 8209)
+   defining Unicode char U+2012 (decimal 8210)
+   defining Unicode char U+2013 (decimal 8211)
+   defining Unicode char U+2014 (decimal 8212)
+   defining Unicode char U+2015 (decimal 8213)
+   defining Unicode char U+2018 (decimal 8216)
+   defining Unicode char U+2019 (decimal 8217)
+   defining Unicode char U+201A (decimal 8218)
+   defining Unicode char U+201C (decimal 8220)
+   defining Unicode char U+201D (decimal 8221)
+   defining Unicode char U+201E (decimal 8222)
+   defining Unicode char U+2030 (decimal 8240)
+   defining Unicode char U+2031 (decimal 8241)
+   defining Unicode char U+2039 (decimal 8249)
+   defining Unicode char U+203A (decimal 8250)
+   defining Unicode char U+2423 (decimal 9251)
+   defining Unicode char U+1E20 (decimal 7712)
+   defining Unicode char U+1E21 (decimal 7713)
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+   defining Unicode char U+00A3 (decimal 163)
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+   defining Unicode char U+00BF (decimal 191)
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+   defining Unicode char U+00C6 (decimal 198)
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+   defining Unicode char U+00E6 (decimal 230)
+   defining Unicode char U+00EC (decimal 236)
+   defining Unicode char U+00ED (decimal 237)
+   defining Unicode char U+00EE (decimal 238)
+   defining Unicode char U+00EF (decimal 239)
+   defining Unicode char U+00F8 (decimal 248)
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+   defining Unicode char U+2014 (decimal 8212)
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+\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
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+++ 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
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author	hanemile <emile.hansmaennel@gmail.com>	2017-12-03 13:30:43 +0100
committer	hanemile <emile.hansmaennel@gmail.com>	2017-12-03 13:30:43 +0100
commit	b031dc7d5e97d209d2e461b958e44e7aa6e7e855 (patch)
tree	4b173d40e1d59c86827ab32f02d224c6eb5f8ab0 /langfassung
parent	cc5da556b93f5105faa7243cd0b3b509c9ac98e3 (diff)