diff options
Diffstat (limited to 'langfassung')
-rw-r--r-- | langfassung/docs/2_einleitung.tex | 47 | ||||
-rw-r--r-- | langfassung/docs/3_hauptteil.tex | 49 | ||||
-rw-r--r-- | langfassung/docs/4_ergebnisse.tex | 26 | ||||
-rw-r--r-- | langfassung/master.aux | 20 | ||||
-rw-r--r-- | langfassung/master.fdb_latexmk | 36 | ||||
-rw-r--r-- | langfassung/master.fls | 15 | ||||
-rw-r--r-- | langfassung/master.log | 313 | ||||
-rw-r--r-- | langfassung/master.out | 7 | ||||
-rw-r--r-- | langfassung/master.pdf | bin | 189951 -> 223308 bytes | |||
-rw-r--r-- | langfassung/master.synctex.gz | bin | 38015 -> 49962 bytes | |||
-rw-r--r-- | langfassung/master.tex | 3 | ||||
-rw-r--r-- | langfassung/master.toc | 18 | ||||
-rw-r--r-- | langfassung/master.x.gnuplot | 2 |
13 files changed, 369 insertions, 167 deletions
diff --git a/langfassung/docs/2_einleitung.tex b/langfassung/docs/2_einleitung.tex index 806c214..bce9ec8 100644 --- a/langfassung/docs/2_einleitung.tex +++ b/langfassung/docs/2_einleitung.tex @@ -1,3 +1,4 @@ +op Einleitung \subsection{Themen} @@ -16,4 +17,50 @@ Einleitung \subsection{Motivation} +\paragraph{ \( \Phi \) } + +\begin{equation} + \Phi(r) = - \frac{4\pi G \rho_0 R_s^3}{r} \ln ( 1+ \frac{r}{R_s} ) +\end{equation} + +with the limits + +\begin{equation} + \lim_{r\to \infty} \Phi=0 +\end{equation} + +and + +\begin{equation} + \lim_{r\to 0} \Phi=-4\pi G\rho_0 R_s^2 +\end{equation} + +\paragraph{ \( \rho \) } + +\begin{equation} + \rho(r) = \frac{1}{\sqrt{2 \cdot \pi} \cdot \sigma} \cdot + e^{\left( - \frac{(\Phi(r)}{\sigma^{2}} \right)} +\end{equation} + +\paragraph{\( \rho_{new} \rightarrow (deriviation) \) } + +\begin{equation} + \rho(r) \cdot 1-\frac{1}{(2 \cdot sigma^{2} )} \cdot + ( Mxx \cdot x^{2} + 2 \cdot Mxy \cdot xy + Myy \cdot y^{2} )) +\end{equation} + +% def rho_new(x, y, z): +% a = (1 - ((1) / (2 * (sigma ** 2))) * ( Mxx * x**2 + 2 * Mxy * x * y + Myy * y**2 ) ) +% return rho(x, y, z) * a +% +% # phi function +% def phi(x): +% if x == 0: +% return -4 * pi * f_0 * G * R_s**2 +% +% a = - ( 4 * pi * G * f_0 * R_s ** 3 ) / x +% b = np.log(1. + (x / R_s) ) +% c = a * b +% return c + Motivations blah diff --git a/langfassung/docs/3_hauptteil.tex b/langfassung/docs/3_hauptteil.tex index eab3897..5174f08 100644 --- a/langfassung/docs/3_hauptteil.tex +++ b/langfassung/docs/3_hauptteil.tex @@ -43,14 +43,59 @@ Blender is Awesome, Python is Awesome and together they are \subsection{Making things faster} -Kicking out to many Stars, 1 out of 10000 is just to much... +\paragraph{ Kicking out to many Stars, 1 out of 10000 is just to much... } +~\\ + +\begin{itemize} + \item Use a custom Density function for each Axis + \begin{itemize} + \item \( \phi(r_x)\), \( \phi(r_y) \) and \( \phi(r_z) \) + \item more controll + \end{itemize} +\end{itemize} + +\begin{tikzpicture} +\begin{scope} + + \node[draw] (H) at (0,-2) + {\( \phi(x_1) > rand_x \)}; + \node[draw] (I) at (5,-2) + {\( \phi(y_1) > rand_y \)}; + \node[draw] (J) at (10,-2) + {\( \phi(z_1) > rand_z \)}; + + \node[draw] (K) at (10, -4) {true}; + \node[draw] (L) at (0, -4) {false}; + + \node[draw] (M) at (10, -6) {write data to data.csv}; + + \node[draw] (N) at (0, -6) {generate new random coordinates}; + +\end{scope} + +\begin{scope} [every node/.style={fill=white,circle}, + every edge/.style={draw=red,very thick}] + + \path[->] (H) edge (K); + \path[->] (I) edge (K); + \path[->] (J) edge (K); + \path[->] (H) edge (L); + \path[->] (I) edge (L); + \path[->] (J) edge (L); + + \path[->] (K) edge (M); + \path[->] (L) edge (N); + +\end{scope} + +\end{tikzpicture} \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} +\subsubsection{N-body problem} Kurze Beschreibung des N-Körper Problems diff --git a/langfassung/docs/4_ergebnisse.tex b/langfassung/docs/4_ergebnisse.tex index abd806d..088b13e 100644 --- a/langfassung/docs/4_ergebnisse.tex +++ b/langfassung/docs/4_ergebnisse.tex @@ -22,6 +22,32 @@ Pro MegaByte können die Koordinaten von 10000 Sternen gespeichert werden. Die generierung von Spiralgalaxien gestaltet sich schweiriger als erwartet. +\subsection{Lookup-Table Speed} + +\begin{tabular}{l | l | l} +rho-values & step & time (in seconds) \\ \hline\hline +1500000 & 1 & 8.07 \\ +750000 & 2 & 4.4 \\ +375000 & 4 & 2.26 \\ +187500 & 8 & 1.35 \\ +93750 & 16 & 0.76 \\ +\end{tabular} + +The correlation between the number of stars generated and the time needed ist +clearly linear. + +\paragraph{Python script} ~\\ +\lstset{language=Python} +\begin{lstlisting}[frame = single] +import matplotlib.pyplot as plt + +list_time = [8.07, 4.4, 2.26, 1.35, 0.76] +list_rho_values = [1500000, 750000, 375000, 187500, 93750] + +plt.plot(list_time, list_rho_values, '-ro') +plt.show() +\end{lstlisting} + \subsection{Distortion of Galaxies} Galaxien verformen dinge diff --git a/langfassung/master.aux b/langfassung/master.aux index 41ce740..65d8f03 100644 --- a/langfassung/master.aux +++ b/langfassung/master.aux @@ -26,6 +26,9 @@ 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{subsection}{\numberline {2.5}Making things faster}{5}{subsection.2.5}} +\@writefile{toc}{\contentsline {paragraph}{\nonumberline Kicking out to many Stars, 1 out of 10000 is just to much...}{5}{section*.5}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.6}Spiral Galaxies}{5}{subsection.2.6}} -\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.6.1}N-K\IeC {\"o}rper problem}{5}{subsubsection.2.6.1}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.6.1}N-body problem}{5}{subsubsection.2.6.1}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {2.6.2}Hilbert Spiral}{5}{subsubsection.2.6.2}} \@writefile{toc}{\contentsline {subsection}{\numberline {2.7}Gr\IeC {\"o}\IeC {\ss }eneinheiten}{5}{subsection.2.7}} \@writefile{toc}{\contentsline {section}{\numberline {3}Ergebnisse}{6}{section.3}} \newlabel{ergebnisse}{{3}{6}{Ergebnisse}{section.3}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Simulation Speed}{6}{subsection.3.1}} 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PDF statistics: - 234 PDF objects out of 1000 (max. 8388607) - 211 compressed objects within 3 object streams - 44 named destinations out of 1000 (max. 500000) - 197 words of extra memory for PDF output out of 10000 (max. 10000000) + 276 PDF objects out of 1000 (max. 8388607) + 249 compressed objects within 3 object streams + 64 named destinations out of 1000 (max. 500000) + 205 words of extra memory for PDF output out of 10000 (max. 10000000) diff --git a/langfassung/master.out b/langfassung/master.out index ebce7ca..c2573b4 100644 --- a/langfassung/master.out +++ b/langfassung/master.out @@ -13,11 +13,12 @@ \BOOKMARK [2][-]{subsection.2.4}{Blender + Python}{section.2}% 13 \BOOKMARK [2][-]{subsection.2.5}{Making things faster}{section.2}% 14 \BOOKMARK [2][-]{subsection.2.6}{Spiral Galaxies}{section.2}% 15 -\BOOKMARK [3][-]{subsubsection.2.6.1}{N-K\366rper problem}{subsection.2.6}% 16 +\BOOKMARK [3][-]{subsubsection.2.6.1}{N-body problem}{subsection.2.6}% 16 \BOOKMARK [3][-]{subsubsection.2.6.2}{Hilbert Spiral}{subsection.2.6}% 17 \BOOKMARK [2][-]{subsection.2.7}{Gr\366\337eneinheiten}{section.2}% 18 \BOOKMARK [1][-]{section.3}{Ergebnisse}{}% 19 \BOOKMARK [2][-]{subsection.3.1}{Simulation Speed}{section.3}% 20 \BOOKMARK [2][-]{subsection.3.2}{Spiral Galaxies}{section.3}% 21 -\BOOKMARK [2][-]{subsection.3.3}{Distortion of Galaxies}{section.3}% 22 -\BOOKMARK [1][-]{section.4}{Quellen und Hilfen}{}% 23 +\BOOKMARK [2][-]{subsection.3.3}{Lookup-Table Speed}{section.3}% 22 +\BOOKMARK [2][-]{subsection.3.4}{Distortion of Galaxies}{section.3}% 23 +\BOOKMARK [1][-]{section.4}{Quellen und Hilfen}{}% 24 diff --git a/langfassung/master.pdf b/langfassung/master.pdf index c39170c..d61dfc8 100644 --- a/langfassung/master.pdf +++ b/langfassung/master.pdf Binary files differdiff --git a/langfassung/master.synctex.gz b/langfassung/master.synctex.gz index 2d05754..f9ed4ad 100644 --- a/langfassung/master.synctex.gz +++ b/langfassung/master.synctex.gz Binary files differdiff --git a/langfassung/master.tex b/langfassung/master.tex index aa34893..b248c7e 100644 --- a/langfassung/master.tex +++ b/langfassung/master.tex @@ -12,6 +12,7 @@ \usepackage{textcomp} \usepackage{tikz} +\usepackage{listings} \usepackage{hyperref} \hypersetup{ @@ -67,7 +68,7 @@ urlcolor=black \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. + how the dark matter affects the galaxy while deforming the dark matter. \end{itemize} \subsubsection{Generally building a galaxy} diff --git a/langfassung/master.toc b/langfassung/master.toc index 11af2a8..dce2f87 100644 --- a/langfassung/master.toc +++ b/langfassung/master.toc @@ -2,6 +2,9 @@ \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 {paragraph}{\nonumberline \( \Phi \)}{2}{section*.2} +\contentsline {paragraph}{\nonumberline \( \rho \)}{2}{section*.3} +\contentsline {paragraph}{\nonumberline \( \rho _{new} \rightarrow (deriviation) \)}{2}{section*.4} \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} @@ -13,15 +16,18 @@ \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 {paragraph}{\nonumberline Kicking out to many Stars, 1 out of 10000 is just to much...}{5}{section*.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 {2.6.1}N-body 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} +\contentsline {subsection}{\numberline {3.3}Lookup-Table Speed}{6}{subsection.3.3} +\contentsline {paragraph}{\nonumberline Python script}{6}{section*.6} +\contentsline {subsection}{\numberline {3.4}Distortion of Galaxies}{7}{subsection.3.4} +\contentsline {section}{\numberline {4}Quellen und Hilfen}{8}{section.4} +\contentsline {paragraph}{\nonumberline Herrn J\IeC {\"o}rg Thar}{8}{section*.8} +\contentsline {paragraph}{\nonumberline Konstantin Bosbach}{8}{section*.9} +\contentsline {paragraph}{\nonumberline Tilman Hoffbauer}{8}{section*.10} diff --git a/langfassung/master.x.gnuplot b/langfassung/master.x.gnuplot new file mode 100644 index 0000000..84fcd41 --- /dev/null +++ b/langfassung/master.x.gnuplot @@ -0,0 +1,2 @@ +set table "master.x.table"; set format "%.5f" +set samples 25; plot [x=-5:5] x*x |