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diff --git a/langfassung/docs/1_kurzfassung.tex b/langfassung/docs/1_kurzfassung.tex index b4aee7d..e9aea85 100644 --- a/langfassung/docs/1_kurzfassung.tex +++ b/langfassung/docs/1_kurzfassung.tex @@ -1 +1,12 @@ -Kurzfassung +\begin{abstract} +\large +Ziel meines Projektes war es, Galaxien zu generieren und diese mit den Modellen +von echten Galaxien zu vergleichen um mit der Zeit immer bessere Simulationen +zu generieren. Dies gelang mir im Verlauf des letzten Jahres immer besser, wobei +ich zurzeit (\today) auf meinem Laptop ca. 1000 neue Sterne in 1.5 Stunden +generieren kann. +Zu dem Projekt bin ich während meines Praktikum im Zentrum für Astronomie in +Heidelberg (ZAH) gekommen bei dem ich von Tim Tugendhat eine Einführung in das +NFW-Profil bekommen habe, welches genutzt wird um Galaxien zu generieren. + +\end{abstract} diff --git a/langfassung/docs/2_einleitung.tex b/langfassung/docs/2_einleitung.tex index bce9ec8..a204783 100644 --- a/langfassung/docs/2_einleitung.tex +++ b/langfassung/docs/2_einleitung.tex @@ -1,66 +1,40 @@ -op -Einleitung +Nach meinem letzten Jugend-Forscht Projekt ergab sich die Möglichkeit ein +Praktikum im Zentrum für Astronomie in Heidelberg zu absolvieren. Über die +social-media Platform Reddit stellte ich den kontakt mit Tim Tugendkat her +der zurzeit seinen PhD. in Physik an der Universität in Heidelberg macht. +Dieser ermöglichte es mir, die Physikalische Fakultät an einer Uni mal genauer +zu sehen und das täglich leben eines Physikers mitzuerleben. +\par +Während des Praktikums stellte ich fest das ich die im letzten Jahr erlerne Fähigkeit mit +Python\footnote{Programmiersprache} zu Programmieren und mit +Blender\footnote{3D Software Suite} umzugehen nutzen konnte um Galaxien +darzustellen. +Dies war insgesamt unglaublich Interessant und zeigte mir zum wiederholten mal: +Projekte sind sehr dazu geeignet um sich in neues einzuarbeiten oder neues +zu lernen und bieten einem ein Ziel welches man erreichen möchte was einem +immer genügend motivation bietet weiterzumachen. +\par +Eine frage die ich mir öfters gestellt habe war warum man eigentlich Galaxien +simuliert? Wäre es nicht einfacher einfach in den Himmel zu gucken und +die bereits bestehenden Galaxien zu beobachten? +Nach kurzer recherche lag die Antwort auf der Hand: Galaxien brauchen mehrere +Millionen Jahre um sich zu entwickeln, also kann man ihre Entwicklung als +normaler Mensch nicht in dem Umfang beobachten, um dann daraus schlüsse zu +ziehen. Daher simuliert man die Galaxien und kann dann somit vorhersagen oder +herrausfinden wie die Galaxien entstanden sind bzw. was mit ihnen passieren +wird. \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} + \item Generierung von Elliptischen Galaxien + \item Generierung von einem Dark-Matter Halo um die Elliptische Galaxie + \item Stauchung und Streckung des Dark-Matter mit beinflussung der eigentlichen Galaxie + \item Beschleunigung des generierungsprozesses mithilfe einer sogennanten ''lookup-table`` + \item Aufbau eines neuronalen Netzes für die unbeaufsichtigte Generation von Galaxien + \item Generation von Spiralgalaxien \end{itemize} \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 +Ich habs einfach mal getan... diff --git a/langfassung/docs/3_hauptteil.tex b/langfassung/docs/3_hauptteil.tex index 5174f08..617e4f9 100644 --- a/langfassung/docs/3_hauptteil.tex +++ b/langfassung/docs/3_hauptteil.tex @@ -1,107 +1,303 @@ -\subsection{Navarro–Frenk–White profile} + +% \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 +% + + +\subsection{Generierung der Elliptischen Galaxien} +\subsubsection{Das Navarro-Frenk-White Profil} 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 +\begin{equation} \label{eq:NFW_profile} + \rho_{NFW}(r) = \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 +\begin{equation*} + \phi(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} +\end{equation*} -Sieht kompliziert aus, ist es aber nicht: Um zu gucken ob ein zufälliger Stern +Um die Formel (\ref{eq:NFW_profile}) einfach zu beschreiben kann man sie sich +wie folgt vorstellen: +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 +Pytargoras berechnet ( \( r = \sqrt{{x_1}^2 + {x_2}^2 + {x_3}^2} \) ) , 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, +\( \rho_{NFW} \) 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 + +\subsubsection{Random Sampling} + +Die sogennante ''Random Sampling`` Methode wird genutzt um herrauszufinden ob +ein Stern generiert wird oder nicht.Es wird dazu ein zufälliger +Wert \( x \) im bereich \( [~\rho_{max}~;~\rho_{min}~] \) generiert. Liegt dieser +Wert über dem Wert aus der Funktion \( \rho \) wird kein Stern generiert. +Liegt dieser Stern jedoch unter dem wert aus der \( \rho \) Funktion wird ein Stern an den Koordinaten \( x_1 \), \( y_1 \) und \( z_1 \) generiert. -\subsection{Einasto profile} +Um das generieren zu Beschleunigen wird eine sogenneante ''lookuptable`` +verwendet. (\( \rightarrow \) \ref{subsec:lookuptable}) + +Generiert man ein paar Sterne mithilfe des NFW-Profils hat man theoretisch +schon eine Galaxie, jedoch ist diese nicht klar definiert. Um eine klare +definition zu erreichen müssen mehrere hundert Sterne generiert werden. + +% \subsubsection{Das Einasto Profil} +% +% \begin{equation} +% \gamma(r) = \frac{ d \ln(\rho(r)) }{ d \ln(\rho) } \propto r^{\alpha} +% \end{equation} + +% \subsubsection{Blender + Python} +% +% Blender is Awesome, Python is Awesome and together they are +% \bold{SUPER AWESOME!!!} +% +% \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} + + +\subsection{Generierung eines Dunkle-Materie Halos} + +Das sogennannte ''Dunkle-Materie Halo`` ist eine art Kugel die eine Galaxie +umspannt: Duch dieses Halo ist die Dichte der Dunklen Materie welches sich um die +Galaxie herum befindet definiert. Problematisch ist jedoch, dass wir dieses +Halo nicht sehen können weshalb wir nur aufgrund anderer phänomäne welche durch +die Halos verursacht werden auf die Eigenschaften des Halos schließen können. +\par +Um diese Halos darzustellen wird das NFW-Profil~(\ref{eq:NFW_profile}) +abgewandelt und quasi mit dem Profil für Elliptische Galaxien verbunden. + +... + +\subsubsection{Anpassung des NFW-Profils} \begin{equation} - \gamma(r) = \frac{ d \ln(\rho(r)) }{ d \ln(\rho) } \propto r^{\alpha} + \rho(r) = \frac{1}{\sqrt{2 \cdot \pi} \cdot \sigma} \cdot + e^{\left( - \frac{(\Phi(r)}{\sigma^{2}} \right)} \end{equation} -\subsection{Blender + Python} +\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} -Blender is Awesome, Python is Awesome and together they are -\bold{SUPER AWESOME!!!} +\begin{lstlisting} -\subsection{Making things faster} +# new rho function +def rho_new(x, y, z): + a = (1 - ((1) / (2 * (sigma ** 2))) + b = ( Mxx * x**2 + 2 * Mxy * x * y + Myy * y**2 ) ) + c = a * b +return rho(x, y, z) * c -\paragraph{ Kicking out to many Stars, 1 out of 10000 is just to much... } -~\\ +# phi function +def phi(x): + if x == 0: + return -4 * pi * f_0 * G * R_s**2 -\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} + a = - ( 4 * pi * G * f_0 * R_s ** 3 ) / x + b = np.log(1. + (x / R_s) ) + c = a * b + return c -\begin{tikzpicture} -\begin{scope} +\end{lstlisting} - \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}; +\subsection{Stauchung und Streckung der Galaxie} - \node[draw] (M) at (10, -6) {write data to data.csv}; +Wird eine Galaxie gestreckt oder gestaucht kann das an der umliegenden Dunklen +Materie liegen. Um solch eine Streckung darzustellen wird wie folgt vorgegangen: +Die Position eines Sternes an einer Achse muss mit einem Skalar multipliziert +bzw. dividiert werden. +Dies ist relativ einfach machbar da die Koordinaten der jeweiligen Sterne +in einer Datei nach dem Format \( [x, y, z] \) gespeichert sind. +Um die Galaxie vertikal zu strecken wird z.B. für jeden Stern die z-Koordinate +mit dem skalar \( s \) multipliziert. Da gestaucht werden soll liegt dieser +Wert im Intervall \( 0 < s < 1 \). Die neue Koordinate für einen Stern ist also +\( [x, y, z \cdot s] \). Möchte man die Galaxie strecken muss das Skalar \( s \) +im Intervall \( 1 < s < \infty \) liegen. - \node[draw] (N) at (0, -6) {generate new random coordinates}; +\subsection{Beschleunigung der Generierung} -\end{scope} +Die Sterne schnell zu generieren ist natürlich energieeffizienter aber auch +wichtig damit das neuronale netzt in unserer lebzeit fertig wird. -\begin{scope} [every node/.style={fill=white,circle}, - every edge/.style={draw=red,very thick}] +Es gibt ein paar Aktionen die umgebaut werden können um das generieren zu +beschleunigen: - \path[->] (H) edge (K); - \path[->] (I) edge (K); - \path[->] (J) edge (K); - \path[->] (H) edge (L); - \path[->] (I) edge (L); - \path[->] (J) edge (L); +\subsubsection{n-Sterne} - \path[->] (K) edge (M); - \path[->] (L) edge (N); +Statt am Anfang mehrere Millionen Sterne zu generieren wird wenn eine +neue Koordinate benötigt wird eine neue erstellt. So erstellt man auf keinen +Fall zu viele Koordinaten was Zeit spaart. +Dem programm kann also gesagt werden, dass es genau \( n_1 \) Sterne aus +\( m_1 \) potentiellen Sternen generieren soll, andernfalls werden \( n_2 \) +Sterne aus \( m_2 > m_1 \) potentiellen Sternen generiert. -\end{scope} +\subsubsection{Lookuptable} \label{subsec:lookuptable} -\end{tikzpicture} +Eine Weitere Möglichkeit für meherere Berechnungen Zeit zu Spaaren ist, den +Entsprechenden Wert aus dem NFW-Profil (Formel \ref{eq:NFW_profile}) vorher zu +berechnen und in eine Tabelle zu schreiben. +Dies kann für z.B. \( 2e8 \) Werte getan werden was zwar eine 6 GB große Datei +erzeugt, diese kann jedoch innerhalb weniger Sekunden eingelesen werden. + +\subsubsection{Weitere Optimierungen} + +\paragraph{Nichts in der Konsole ausgeben:} + +Eine Vorgang der erstaunlicherweise sehr viel Rechenleistung erfordert, ist +der Vorgang beim ausgeben von Text in die Konsole. Gibt man jede potentielle +Koordinate in die Konsole aus, stürtzt das Programm aufgund von Überlast ab. +Um dies zu umgehen kann z.B. nur jeder 100.000 Wert in die Konsole ausgegeben +werden. + +\paragraph{...} + +\newpage +\subsection{Nutzung eines Neuronalen Netzes zum unbeaufsichtigeten generieren} +\subsubsection{Aufbau des Neuronalen Netzes} + +Ein Neuronales Netz ist wie folgt aufgebaut: -\subsection{Spiral Galaxies} +\bigskip -The previous Galaxy models where all using a completely spherical model, generating -a spiral galaxy is just not possible using these models. +\hrule -\subsubsection{N-body problem} +\bigskip -Kurze Beschreibung des N-Körper Problems +\tikzset{% + every neuron/.style={ + circle, + draw, + minimum size=1cm + }, + neuron missing/.style={ + draw=none, + scale=2, + text height=0.333cm, + execute at begin node=\color{black}$\vdots$ + }, +} -\subsubsection{Hilbert Spiral} +\begin{center} + \begin{tikzpicture}[x=2cm, y=1.5cm, >=stealth] + + \foreach \m/\l [count=\y] in {1,2,3,missing,4} + \node [every neuron/.try, neuron \m/.try] (input-\m) at (0,2.5-\y) {}; + + \foreach \m [count=\y] in {1,missing,2} + \node [every neuron/.try, neuron \m/.try ] (hidden-\m) at (2,2-\y*1.25) {}; + + \foreach \m [count=\y] in {1,missing,2} + \node [every neuron/.try, neuron \m/.try ] (output-\m) at (4,1.5-\y) {}; + + \foreach \l [count=\i] in {1,2,3,n} + \draw [<-] (input-\i) -- ++(-1,0) + node [above, midway] {$I_\l$}; + + \foreach \l [count=\i] in {1,n} + \node [above] at (hidden-\i.north) {$H_\l$}; + + \foreach \l [count=\i] in {1,n} + \draw [->] (output-\i) -- ++(1,0) + node [above, midway] {$O_\l$}; + + \foreach \i in {1,...,4} + \foreach \j in {1,...,2} + \draw [->] (input-\i) -- (hidden-\j); + + \foreach \i in {1,...,2} + \foreach \j in {1,...,2} + \draw [->] (hidden-\i) -- (output-\j); + + \foreach \l [count=\x from 0] in {Eingabe, Versteckte, Ausgabe} + \node [align=center, above] at (\x*2,2) {\l \\ ebene}; + + \end{tikzpicture} +\end{center} +\bigskip + +\hrule + +\bigskip + +Das \textbf{Neuronale Netz} besitze mehrere Ebenen: die \textbf{Eingabe ebene}, +die \textbf{Versteckte Ebene(n)} und die \textbf{Ausgabe Ebene}. +Diese Ebenen bestehen aus sogennanten \textbf{Neuronen} die wie im Menschlichen +Gehirn Informationen aufnehmen und weitergeben. Die Eingabe kann verschieden +gewichtet sein, es kann also sein das eine Eingabe eine Gewichtung von +\( 10\% \) hat und eine andere eine Gewichtung von \( 90\% \). +Die Eingabe Ebene ist dazu da eine Eingabe inform einer Matrix an die +verschiedenen Neuronen in der Versteckten Ebene weiterzuleiten. +Die Versteckte Ebene verarbeitet die Information aus der Matrix und leitet +diese an die Ausgabe Ebene weiter die die Information ausgibt. +\par +Das sogennante ''Trainieren`` ist der Prozess, bei dem die Gewichtung der +Neuronen so Verändert wird, damit ein gewünschtes Ergebnis herrauskommt. +Beispiel: man möchte ein Neuronales Netz darauf Trainieren eine Galaxie zu +Identifizieren, dann werden ganz viele positiv Beispiele durch das Netz gejagt +welche die Gewichtung immer weiter anpassen. In der Ausgangs Ebene wird dann +mithilfe zweier Neuronen entweder dargestellt das das eingegebene Bild eine +Galaxie ist oder das das eingegebene Bild eben keine Galaxie ist. + +\subsubsection{Nutzung eines Neuronalen Netztes zur verbesserung von Galaxien Simulationen} + +Möchte man mithilfe eines Neuronalen Netztes vorhandene Galaxiensimulationen +verbessern, wird wie im folgenden Diagramm zusehen vorgegangen: + +\begin{tikzpicture} +[node distance = 4cm, auto, ->, on grid] + +\node [draw, minimum width=3cm, text depth = 1cm] (galaxy) {Galaxie}; +\node [draw, right of=galaxy] (neural_net) {Neuralonales Netz}; + +\node [draw] (yes) [right of=neural_net] {Ja} +node [right=3cm of yes, align=center] {Galaxie ist eine Galaxie}; + +\node [draw] (no) [below=2cm of neural_net] {Nein} +node [right=3.5cm of no, align=center] {Galaxie ist keine Galaxie \\ +\( \rightarrow \) ändere parameter und \\generiere eine neue Galaxie}; + + +\draw[->, line width=0.25mm] (galaxy) -- (neural_net) +node [above=1cm of neural_net, align=center] {Testet ob die Eingabe \\eine +Galaxie ist oder nicht}; + +\node[draw, yshift=5mm] (paramter) at (galaxy.south) {paramter}; + +\draw[->, line width=0.25mm] (neural_net) -- (yes); +\draw[->, line width=0.25mm] (neural_net) -- (no); + +\path[line width=0.25mm] (no) edge [bend left] node {} (paramter); + +\end{tikzpicture} -Beschreibung der Hilbert Spirale +\subsection{Spiralgalaxien} +\subsubsection{Das n-Körper Problem} \subsection{Größeneinheiten} diff --git a/langfassung/docs/5_quellen.tex b/langfassung/docs/5_quellen.tex index 17bb702..f928fa3 100644 --- a/langfassung/docs/5_quellen.tex +++ b/langfassung/docs/5_quellen.tex @@ -5,20 +5,16 @@ Quellen 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 +\par Einen Großteil der Formeln fand ich durch eine Wikipedia Recherche. +\par Das Programieren in der Programiersprache Python habe ich während meines Jugen-Forscht Projektes im letztem Jahr (2017) 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. - +in das Jugend Forscht Projekt von Konstantin Bosbach, Tilman Hoffbauer und Steffen Ritsche (2016, Underwater Accoustic Communication). \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} +\paragraph{Tilman Hoffbauer} der bei problemen bereit war Licht ins Dunkle zu bringen. \centering \vspace{0.5cm} \textbf{Außerdem gilt mein Dank allen, die mich auf jede nur erdenkliche Weise unterstützt haben.} diff --git a/langfassung/figs/2017-12-05-164935_374x65_scrot.png b/langfassung/figs/2017-12-05-164935_374x65_scrot.png new file mode 100644 index 0000000..9a95146 --- /dev/null +++ b/langfassung/figs/2017-12-05-164935_374x65_scrot.png Binary files differdiff --git a/langfassung/master.aux b/langfassung/master.aux index 65d8f03..d6dac0e 100644 --- a/langfassung/master.aux +++ b/langfassung/master.aux @@ -26,38 +26,40 @@ \newlabel{Einleitung}{{1}{2}{Einleitung}{section.1}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Themen}{2}{subsection.1.1}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Motivation}{2}{subsection.1.2}} -\@writefile{toc}{\contentsline {paragraph}{\nonumberline \( \Phi \)}{2}{section*.2}} -\@writefile{toc}{\contentsline {paragraph}{\nonumberline \( \rho \)}{2}{section*.3}} -\@writefile{toc}{\contentsline {paragraph}{\nonumberline \( \rho 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((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 diff --git a/langfassung/master.synctex.gz b/langfassung/master.synctex.gz index f9ed4ad..5baf9cf 100644 --- a/langfassung/master.synctex.gz +++ b/langfassung/master.synctex.gz Binary files differdiff --git a/langfassung/master.tex b/langfassung/master.tex index b248c7e..c3ed027 100644 --- a/langfassung/master.tex +++ b/langfassung/master.tex @@ -10,9 +10,18 @@ \usepackage{caption} \usepackage{lmodern} \usepackage{textcomp} +\usepackage[onehalfspacing]{setspace} \usepackage{tikz} +\usetikzlibrary{positioning} + \usepackage{listings} +\lstset{ % + frame=single, % adds a frame around the code + language=Python, % the language of the code + numbers=left, % where to put the line-numbers; possible values are (none, left, right) + stepnumber=1, % the step between two line-numbers. If it's 1, each line will be numbered +} \usepackage{hyperref} \hypersetup{ @@ -36,7 +45,7 @@ urlcolor=black \begin{document} -\title{Galaxy Stuff} +\title{Galaxy Generation} \subtitle{Jugend Forscht \the\year} \author{ Emile Hansmaennel \texttt{ emile.hansmaennel@gmail.com }} \date{\today} @@ -58,75 +67,6 @@ urlcolor=black \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 diff --git a/langfassung/master.toc b/langfassung/master.toc index dce2f87..0c43803 100644 --- a/langfassung/master.toc +++ b/langfassung/master.toc @@ -2,32 +2,32 @@ \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} -\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 {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-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}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} +\contentsline {subsection}{\numberline {2.1}Generierung der Elliptischen Galaxien}{3}{subsection.2.1} +\contentsline {subsubsection}{\numberline {2.1.1}Das Navarro-Frenk-White Profil}{3}{subsubsection.2.1.1} +\contentsline {subsubsection}{\numberline {2.1.2}Random Sampling}{3}{subsubsection.2.1.2} +\contentsline {subsection}{\numberline {2.2}Generierung eines Dunkle-Materie Halos}{3}{subsection.2.2} +\contentsline {subsubsection}{\numberline {2.2.1}Anpassung des NFW-Profils}{4}{subsubsection.2.2.1} +\contentsline {subsection}{\numberline {2.3}Stauchung und Streckung der Galaxie}{4}{subsection.2.3} +\contentsline {subsection}{\numberline {2.4}Beschleunigung der Generierung}{5}{subsection.2.4} +\contentsline {subsubsection}{\numberline {2.4.1}n-Sterne}{5}{subsubsection.2.4.1} +\contentsline {subsubsection}{\numberline {2.4.2}Lookuptable}{5}{subsubsection.2.4.2} +\contentsline {subsubsection}{\numberline {2.4.3}Weitere Optimierungen}{5}{subsubsection.2.4.3} +\contentsline {paragraph}{\nonumberline Nichts in der Konsole ausgeben:}{5}{section*.2} +\contentsline {paragraph}{\nonumberline ...}{5}{section*.3} +\contentsline {subsection}{\numberline {2.5}Nutzung eines Neuronalen Netzes zum unbeaufsichtigeten generieren}{6}{subsection.2.5} +\contentsline {subsubsection}{\numberline {2.5.1}Aufbau des Neuronalen Netzes}{6}{subsubsection.2.5.1} +\contentsline {subsubsection}{\numberline {2.5.2}Nutzung eines Neuronalen Netztes zur verbesserung von Galaxien Simulationen}{6}{subsubsection.2.5.2} +\contentsline {subsection}{\numberline {2.6}Spiralgalaxien}{7}{subsection.2.6} +\contentsline {subsubsection}{\numberline {2.6.1}Das n-K\IeC {\"o}rper Problem}{7}{subsubsection.2.6.1} +\contentsline {subsection}{\numberline {2.7}Gr\IeC {\"o}\IeC {\ss }eneinheiten}{7}{subsection.2.7} +\contentsline {section}{\numberline {3}Ergebnisse}{8}{section.3} +\contentsline {subsection}{\numberline {3.1}Simulation Speed}{8}{subsection.3.1} +\contentsline {subsection}{\numberline {3.2}Spiral Galaxies}{8}{subsection.3.2} +\contentsline {subsection}{\numberline {3.3}Lookup-Table Speed}{8}{subsection.3.3} +\contentsline {paragraph}{\nonumberline Python script}{8}{section*.4} +\contentsline {subsection}{\numberline {3.4}Distortion of Galaxies}{9}{subsection.3.4} +\contentsline {section}{\numberline {4}Quellen und Hilfen}{10}{section.4} +\contentsline {paragraph}{\nonumberline Herrn J\IeC {\"o}rg Thar}{10}{section*.6} +\contentsline {paragraph}{\nonumberline Konstantin Bosbach}{10}{section*.7} +\contentsline {paragraph}{\nonumberline Tilman Hoffbauer}{10}{section*.8} |
