# tikz_tikz

folder: /Users/saeta/Documents/Courses/p23/2015/rec
filename: rec01-stud.tex
modified: 2015-08-18 20:44:30
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \fill[fill=blue!10!white] (-2,0) rectangle (5,3);
    \draw[dashed, color=gray] (0,3) -- (0,0.2) -- (3,0.2);
    \draw[<->,color=DarkGreen] (-1.5,0) --node[anchor=east]{$D$} ++(90:3);
    \draw[<->,color=DarkGreen]  (0,-0.3) -- node[anchor=north]{$D$} ++(0:3);
    \draw[vel] (1.5,1.5) -- ++ (0:1) node[anchor=south]{$V_{0}$};
    \draw[vel] (0,0.2)--++(0:1) node[anchor=south]{$A$};
    \draw[vel] (0,0.2)--++(90:1) node[anchor=east]{$B$};
    \fill[fill=DarkRed] (0,-0.1) circle[radius=0.08] (0,3.1) circle[radius=0.08]
    (3.1,-0.1) circle[radius=0.08];

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/rec
filename: rec01-stud.tex
modified: 2015-08-18 20:44:30
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \fill[fill=gray!20!white] (-1,-1) rectangle (1,4.5);
    \draw[line width=3pt, color=SlateGray] (-0.25,-0.25) rectangle (0.25,4.25);
    \filldraw[fill=gray] (0,1) circle[radius=0.2];
    \draw[vel] (0,1.3) -- ++(90:1) node[anchor=south]{$U$};
    \filldraw[dashed,fill=gray!30!white] (0,0) circle[radius=0.2] (0,4)
    circle[radius=0.2];
    \draw[<->,color=DarkGreen] (-0.65,0) -- node[fill=gray!20!white]{$D$}
    ++(90:4);

    \draw[dashed] (1.5,-1) -- (1.5,4.5);

    \begin{scope}[shift={(3,0)}]
      \fill[fill=gray!20!white] (-1,-1) rectangle (1.5,4.5);
      \draw[line width=3pt, color=SlateGray] (-0.25,-0.25) rectangle (0.25,4.25);
      \filldraw[fill=gray] (0,1) circle[radius=0.2];
      \draw[vel] (0.6,2) -- node[anchor=north]{$V$} ++(0:1);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/rec
filename: rec01-prof.tex
modified: 2015-08-18 20:44:28
domain: p23
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[->,color=blue!40!white,line width=1.5pt] (0,0) -- node[anchor=north]{$V_{0}$} (4,0);
    \draw[->,color=red!50!white,line width=1.5pt] (4,0) -- node[anchor=south west]{$v_{\rm s}$} (0,3);
    \draw[vel,line width=2.5pt] (0,0) -- node[anchor=east]{$v$} (0,3);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/rec
filename: rec01-prof.tex
modified: 2015-08-18 20:44:28
domain: p23
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[vel,color=blue!40!white] (0,0) -- node[anchor=north]{$V$} ++(0:3);
    \draw[vel,color=blue!40!white] (3,0) -- node[anchor=east]{$U$} ++(90:4);
    \draw[vel] (0,0) --node[anchor=south east]{$v$} (3,4);
    \draw (0.75,0) arc (0:53.1:0.75);
    \node at (26.5:1.4) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/rec
filename: rec01-prof.tex
modified: 2015-08-18 20:44:28
domain: p23
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[dashed] (0,0) --node[anchor=south east]{$\ell$} (3,4) -- (6,0) -- (0,0);
    \draw (0.75,0) arc (0:53.1:0.75);
    \node at (26.5:1.4){$\theta$};
    \draw[coord,<->] (3,0) --node[anchor=east]{$D$} (3,4);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/exam
filename: p23-2015-story-key.tex
modified: 2015-09-29 22:53:42
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    % Earth
    \filldraw[fill=blue!30!white,draw=Brown,line width=2] (0,0.3) circle[radius=0.6]
    node{E};
    \draw[<->] (0,-0.5) -- node[fill=white]{$d$} ++(0:12);
    \begin{scope}[shift={(-0.5,-1.6)}]
      % Ship C
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(0:1)
      -- ++(0.2,-0.2) -- ++(-0.2,-0.2) --++(180:1) -- cycle;
      \node at (0.5,0){\sCC};
      \draw[vel] (1.3,0) -- ++(0:0.65) node[anchor=south]{$v_{2} = \vC$};
    \end{scope}

    \begin{scope}[shift={(0.5,-1)}]
      % Ship A
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(180:1)
      -- ++(-0.2,-0.2) -- ++(0.2,-0.2) --++(0:1) -- cycle;
      \node at (-0.5,0){\sAA};
      \draw[vel] (-1.3,0) -- ++(180:0.65) node[anchor=south]{$v_{1} = \vA$};
    \end{scope}

    \begin{scope}[shift={(12.5,-1)}]
      % Ship B
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(180:1)
      -- ++(-0.2,-0.2) -- ++(0.2,-0.2) --++(0:1) -- cycle;
      \node at (-0.5,0){\sBB};
      \draw[vel] (-1.3,0) -- ++(180:0.65) node[anchor=south]{$v_{1} =\vA$};
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/exam
filename: p23-2015-story-key.tex
modified: 2015-09-29 22:53:42
domain: p23
source:
  \begin{tikzpicture}[scale=0.5,font=\tiny]
    \node[font=\normalsize] at (-10,0) {$t_{0}$};
    % Earth
    \filldraw[fill=blue!30!white,draw=Brown,line width=1] (10,0) circle[radius=0.6]
    node{E};
    \rship{(9.5,-1.6)}{S}{\myfrac{4}{5}\,c} % Sally
    \lship{(10.5,-1)}{T}{\myfrac{3}{5}\,c} % Trump
    \lship{(17.5,-1)}{H}{\myfrac{3}{5}\,c} % Harry

    \draw[color=SlateGray] (-10,-2.5) -- ++(0:28);
    % time 1
    \begin{scope}[shift={(0,-4)}]
      \node[font=\normalsize] at (-10, 0){$ t_{1}$};
      \filldraw[fill=blue!30!white,draw=Brown,line width=1] (10,0) circle[radius=0.6]
      node{E};
      \rship{(13.5,-1.9)}{S}{\myfrac{4}{5}\,c} % Sally
      \lship{(7.5,-1)}{T}{\myfrac{3}{5}\,c} % Trump
      \lship{(14.5,-1)}{H}{\myfrac{3}{5}\,c} % Harry
      \bship{(14.,-1.5)}{B}{v_B} % Bernie
    \end{scope}

    \draw[color=SlateGray] (-10,-6.5) -- ++(0:28);
    % time 2
    \begin{scope}[shift={(0,-8)}]
      \node[font=\normalsize] at (-10, 0){$ t_{2}$};
      \filldraw[fill=blue!30!white,draw=Brown,line width=1] (10,0) circle[radius=0.6]
      node{E};
      %  \rship{(13.5,-1.9)}{S}{\myfrac{4}{5}\,c} % Sally
      \lship{(-6.5,-1)}{T}{\myfrac{3}{5}\,c} % Trump
      \lship{(3.5,-1)}{H}{\myfrac{3}{5}\,c} % Harry
      \bship{(-6.,-1.5)}{B}{v_B} % Bernie
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/exam
filename: p23-2015-story-key.tex
modified: 2015-09-29 22:53:42
domain: p23
source:
  \begin{tikzpicture}[scale=0.5,font=\tiny]
    \node[font=\normalsize] at (-8,0) {$T_{0}$};
    % Earth
    \filldraw[fill=blue!30!white,draw=Brown,line width=1] (-6,0) circle[radius=0.6]
    node{E};
    \draw[vel,line width=1pt] (-5,0) -- ++(0:0.6) node[anchor=west]{$\myfrac{3}{5}\,c$};
    \rship{(-6.5,-1.6)}{S}{v_S} % Sally
    \lship{(-5.5,-1)}{T}{} % Trump
    \lship{(17.5,-1)}{H}{} % Harry

    \draw[color=SlateGray] (-8,-2.5) -- ++(0:26);
    % time 1
    \begin{scope}[shift={(0,-4)}]
      \node[font=\normalsize] at (-8, 0){$ T_{1}$};
      \filldraw[fill=blue!30!white,draw=Brown,line width=1] (10,0) circle[radius=0.6]
      node{E};
      \draw[vel,line width=1pt] (11,0) -- ++(0:0.6) node[anchor=west]{$\myfrac{3}{5}\,c$};
      \rship{(16.5,-2)}{S}{v_S} % Sally
      \lship{(-5.5,-1)}{T}{} % Trump
      \lship{(17.5,-1)}{H}{} % Harry
      \bship{(17,-1.5)}{B}{\myfrac{4}{5}\,c} % Bernie
    \end{scope}

    \draw[color=SlateGray] (-8,-6.5) -- ++(0:26);
    % time 2
    % time 1
    \begin{scope}[shift={(0,-8)}]
      \node[font=\normalsize] at (-8, 0){$ T_{2}$};
      \lship{(-5.5,-1)}{T}{} % Trump
      \lship{(17.5,-1)}{H}{} % Harry
      \bship{(-6,-1.5)}{B}{\myfrac{4}{5}\,c} % Bernie
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/exam
filename: p23-2015-story-v1.tex
modified: 2015-09-09 18:52:45
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    % Earth
    \filldraw[fill=blue!30!white,draw=Brown,line width=2] (0,0) circle[radius=0.6]
    node{E};
    \begin{scope}[shift={(-0.5,-1.6)}]
      % Ship C
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(0:1)
      -- ++(0.2,-0.2) -- ++(-0.2,-0.2) --++(180:1) -- cycle;
      \node at (0.5,0){\sCC};
      \draw[vel] (1.3,0) -- ++(0:0.65) node[anchor=south]{$v_{2} = \vC$};
    \end{scope}

    \begin{scope}[shift={(0.5,-1)}]
      % Ship A
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(180:1)
      -- ++(-0.2,-0.2) -- ++(0.2,-0.2) --++(0:1) -- cycle;
      \node at (-0.5,0){\sAA};
      \draw[vel] (-1.3,0) -- ++(180:0.65) node[anchor=south]{$v_{1} = \vA$};
    \end{scope}

    \begin{scope}[shift={(12.5,-1)}]
      % Ship B
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(180:1)
      -- ++(-0.2,-0.2) -- ++(0.2,-0.2) --++(0:1) -- cycle;
      \node at (-0.5,0){\sBB};
      \draw[vel] (-1.3,0) -- ++(180:0.65) node[anchor=south]{$v_{1} =\vA$};
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/exam
filename: p23-2015-story-v1.tex
modified: 2015-09-09 18:52:45
domain: p23
source:
  \begin{tikzpicture}[scale=0.5,font=\tiny]
    % Earth
    \filldraw[fill=blue!30!white,draw=Brown,line width=2] (0,0) circle[radius=0.6]
    node{E};
    \begin{scope}[shift={(-0.5,-1.6)}]
      % Ship C
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(0:1)
      -- ++(0.2,-0.2) -- ++(-0.2,-0.2) --++(180:1) -- cycle;
      \node at (0.5,0){\sCC};
      \draw[vel,line width=1pt] (1.3,0) -- ++(0:0.65) node[anchor=south]{$\vC$};
    \end{scope}

    \begin{scope}[shift={(0.5,-1)}]
      % Ship A
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(180:1)
      -- ++(-0.2,-0.2) -- ++(0.2,-0.2) --++(0:1) -- cycle;
      \node at (-0.5,0){\sAA};
      \draw[vel,line width=1pt] (-1.3,0) -- ++(180:0.65) node[anchor=south]{$\vA$};
    \end{scope}

    \begin{scope}[shift={(8.5,-1)}]
      % Ship B
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(180:1)
      -- ++(-0.2,-0.2) -- ++(0.2,-0.2) --++(0:1) -- cycle;
      \node at (-0.5,0){\sBB};
      \draw[vel,line width=1pt] (-1.3,0) -- ++(180:0.65) node[anchor=south]{$\vA$};
    \end{scope}
    %    \draw[color=white] (0,2) -- (0,2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/exam
filename: p23-2015-story-v3.tex
modified: 2015-09-16 22:30:12
domain: p23
source:
  \begin{tikzpicture}[scale=0.5,font=\tiny]
    % Earth
    \filldraw[fill=blue!30!white,draw=Brown,line width=1] (0,0) circle[radius=0.6]
    node{E};
    \begin{scope}[shift={(-0.5,-1.6)}]
      % Ship C
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(0:1)
      -- ++(0.2,-0.2) -- ++(-0.2,-0.2) --++(180:1) -- cycle;
      \node at (0.5,0){\sCC};
      \draw[vel,line width=1pt] (1.3,0) -- ++(0:0.65) node[anchor=south]{$\vC$};
    \end{scope}

    \begin{scope}[shift={(0.5,-1)}]
      % Ship A
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(180:1)
      -- ++(-0.2,-0.2) -- ++(0.2,-0.2) --++(0:1) -- cycle;
      \node at (-0.5,0){\sAA};
      \draw[vel,line width=1pt] (-1.3,0) -- ++(180:0.65) node[anchor=south]{$\vA$};
    \end{scope}

    \begin{scope}[shift={(8.5,-1)}]
      % Ship B
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(180:1)
      -- ++(-0.2,-0.2) -- ++(0.2,-0.2) --++(0:1) -- cycle;
      \node at (-0.5,0){\sBB};
      \draw[vel,line width=1pt] (-1.3,0) -- ++(180:0.65) node[anchor=south]{$\vA$};
    \end{scope}
    %    \draw[color=white] (0,2) -- (0,2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/exam
filename: Final2015A.tex
modified: 2015-10-15 19:03:29
domain: p23
source:
  \begin{tikzpicture}[scale=0.75,line width=1.5pt]
    \draw (0,2) circle[radius=0.8];
    \draw[->] (0,2) -- ++(90:0.7);
    \draw[->] (1.25,2) --node[anchor=south]{$\displaystyle \frac{4}{5} c$} ++(0:1.5);
    \draw (0,0) circle[radius=0.8];
    \draw[->] (0,0) -- ++(90:0.7);
    \node at (-1.25,0){A};
    \node at (-1.25,2){C};
    \draw (15,0) circle[radius=0.8];
    \draw[->] (15,0) -- ++(90:0.7);
    \node at (16.25,0){B};
    \draw[<->] (0,-1.25) -- node[fill=white] {$20\; c\;\mathrm{min}$} ++(0:15);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/exam
filename: Final2015A.tex
modified: 2015-10-15 19:03:29
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!10!white] (0,0) -- ++(90:0.3*\rocketlength)
    --++(0:\rocketlength)
    -- ++(0.3*\rocketlength,-0.3*\rocketlength)
    -- ++(-0.3*\rocketlength,-0.3*\rocketlength)
    --++(180:\rocketlength) -- cycle;
    \draw[color=DarkGreen,->,line width=1.25pt] (0,0)
    ++(1.4*\rocketlength,0) node[anchor=south west]{$\displaystyle
        \frac{3}{5} c$} -- ++(0:0.6*\rocketlength);
    \begin{scope}[shift={(0.3*\rocketlength,0)}]
      \filldraw[fill=white] (0,0) circle[radius=0.2*\rocketlength];
      \draw[->] (0,0) -- ++(90:0.2*\rocketlength);
      \node at (0.5*\rocketlength,0){A};
    \end{scope}

    \draw[<->] (1,-1) --node[fill=white]{$80\; c$-min} (14,-1);

    \begin{scope}[shift={(15,0)}]
      \filldraw[fill=gray!10!white]
      (0,0) -- ++(90:0.3*\rocketlength)
      --++(180:\rocketlength)
      -- ++(-0.3*\rocketlength,-0.3*\rocketlength)
      -- ++(0.3*\rocketlength,-0.3*\rocketlength)
      --++(0:\rocketlength) -- cycle;
      \draw[color=DarkGreen,->,line width=1.25pt] (0,0)
      ++(-1.4*\rocketlength,0) node[anchor=south east]{$\displaystyle
          \frac{3}{5} c$} -- ++(180:0.6*\rocketlength);

      \begin{scope}[shift={(-0.3*\rocketlength,0)}]
        \filldraw[fill=white] (0,0) circle[radius=0.2*\rocketlength];
        \draw[->] (0,0) -- ++(90:0.2*\rocketlength);
        \node at (-0.5*\rocketlength,0){B};
      \end{scope}

    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/exam
filename: p23-collisions-2015-q1.tex
modified: 2015-09-30 18:48:25
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \node at (1.5,1){\textsf{before}};
    \node at (10,1){\textsf{after}};
    \filldraw (0,0) circle[radius=.1] (5,0) circle[radius=0.1];
    \node at (0,0.5){$m$};
    \node at (5,0.5){$m$};
    \draw[vel] (0.5,0) --node[anchor=south]{$p = mc$} ++(0:2) ;
    \draw[dashed] (6,1) -- (6,-1);
    \begin{scope}[shift={(10,0)}]
      \draw[photon,->] (-.2,0) --node[anchor=south]{$E_{1}$} ++(180:1.5);
      \draw[photon,->] (.2,0) --node[anchor=south]{$E_{2}$} ++(0:2);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2015/exam
filename: p23-collisions-2015a-v3.tex
modified: 2015-10-06 03:08:48
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \node at (2.5,1.5){\textsf{before}};
    \node at (10,1.5){\textsf{after}};
    \filldraw (0,0) circle[radius=.1] (5,0) circle[radius=0.1];
    \node at (0,0.5){$m$};
    \node at (0,-0.5){$e^{+}$};
    \node at (5,0.5){$m$};
    \node at (5,-0.5){$e^{-}$};
    \draw[vel] (0.5,0) --node[anchor=south]{$p = mc$} ++(0:2) ;
    \draw[dashed] (6,1) -- (6,-1);
    \begin{scope}[shift={(10,0)}]
      \draw[photon,->] (-.2,0) --node[anchor=south]{$E_{1}$} ++(180:1.5);
      \draw[photon,->] (.2,0) --node[anchor=south]{$E_{2}$} ++(0:2);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/physics-23/p23_pns/prob
filename: Puck.tex
modified: 2020-08-09 21:58:42
domain: p23
source:
  \begin{tikzpicture}[scale=0.9]
    \def\rad{0.18}
    \node at (1.5,5) {\textsf{top view}};
    \fill[fill=gray!20!white] (-1,-1) rectangle (1,4.5);
    \draw[line width=3pt, color=SlateGray] (-0.25,-0.25) rectangle (0.25,4.25);
    \filldraw[fill=gray] (0,1) circle[radius=\rad];
    \draw[vel] (0,1.3) -- ++(90:1) node[anchor=south]{$U$};
    \filldraw[dashed,fill=gray!30!white] (0,0) circle[radius=\rad] (0,4)
    circle[radius=\rad];
    \draw[<->,color=DarkGreen] (-0.65,0) -- node[fill=gray!20!white]{$D$}
    ++(90:4);

    \draw[dashed] (1.5,-1) -- (1.5,4.5);

    \begin{scope}[shift={(3,0)}]
      \fill[fill=gray!20!white] (-1,-1) rectangle (2,4.5);
      \draw[line width=3pt, color=SlateGray] (-0.25,-0.25) rectangle (0.25,4.25);
      \filldraw[fill=gray] (0,1) circle[radius=\rad];
      \draw[vel] (0.6,2) -- node[anchor=north]{$V$} ++(0:1.25);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/physics-23/p23_pns/prob
filename: CatchMe.tex
modified: 2020-09-14 14:39:10
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \rocket[label={A}]

    \draw[vel] (0.25,0) -- node[anchor=south]{$\myfrac{4}{5}c$}
    ++(0:1.25);
    \rocket[label={B},pos={(5,0)}]
    \draw[vel] (5.5,0) -- node[anchor=south]{$\myfrac{3}{5}c$}
    ++(0:1.);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/physics-23/p23_pns/prob
filename: CatchMe.tex
modified: 2020-09-14 14:39:10
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \rocket[label={A}]

    \draw[vel] (0.25,0) -- node[anchor=south]{$\myfrac{4}{5}c$}
    ++(0:1.25);
    \rocket[label={C},pos={(5,0.5)},rotate=180]
    \draw[vel] (4.5,0.5) -- node[anchor=south]{$\myfrac{3}{5}c$}
    ++(180:1.);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/physics-23/p23_pns/prob
filename: Swimming.tex
modified: 2021-06-07 00:21:27
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \fill[fill=blue!10!white] (-2,0) rectangle (5,3);
    \draw[dashed, color=gray] (0,3) -- (0,0.2) -- (3,0.2);
    \draw[<->,color=DarkGreen] (-1.5,0) --node[anchor=east]{$D$} ++(90:3);
    \draw[<->,color=DarkGreen]  (0,-0.3) -- node[anchor=north]{$D$} ++(0:3);
    \draw[vel] (1.5,1.5) -- ++ (0:1) node[anchor=south]{$V_{0}$};
    \draw[vel] (0,0.2)--++(0:1) node[anchor=south]{$A$};
    \draw[vel] (0,0.2)--++(90:1) node[anchor=east]{$B$};
    \fill[fill=DarkRed] (0,-0.1) circle[radius=0.08] (0,3.1) circle[radius=0.08]
    (3.1,-0.1) circle[radius=0.08];
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/physics-23/p23_pns/sol
filename: LongitudinalLightClock.tex
modified: 2020-09-01 16:32:50
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    % event 0
    \node[anchor=east] at (-1,0.5) {$t_{0} = 0$};
    \def\d{4}
    \fill[gray!50] (0,0) rectangle (-0.1,1) (\d,0) rectangle ++(0.1,1);
    \draw (0,0) -- ++(90:1) (\d,0) -- ++(90:1);
    \dimline[start={(0,-0.2)},end={(\d,-0.2)}, label={$d$}]
    \draw[photon] (0,0.5) -- ++(0:1);
    \draw[vel] (\d+0.2,0.5) -- ++(0:1) node[anchor=south]{$V$};

    \node[anchor=east] at (-1,-1.5) {$t_{1}$};
    \begin{scope}[shift={(2,-2)}]
      \fill[gray!50] (0,0) rectangle (-0.1,1) (\d,0) rectangle ++(0.1,1);
      \draw (0,0) -- ++(90:1) (\d,0) -- ++(90:1);
      \draw[photon] (\d,0.5) -- ++(180:1);
      \draw[vel] (\d+0.2,0.5) -- ++(0:1) node[anchor=south]{$V$};
    \end{scope}

    \node[anchor=east] at (-1,-3.5) {$t_{2}$};
    \begin{scope}[shift={(3,-4)}]
      \fill[gray!50] (0,0) rectangle (-0.1,1) (\d,0) rectangle ++(0.1,1);
      \draw (0,0) -- ++(90:1) (\d,0) -- ++(90:1);
      \draw[photon] (0,0.5) -- ++(0:1);
      \draw[vel] (\d+0.2,0.5) -- ++(0:1) node[anchor=south]{$V$};
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/physics-23/p23_pns/sol
filename: Invasion.tex
modified: 2020-10-07 03:58:52
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \def\wid{12}
    \foreach \y in {0,-1,-2,-3} {
        \node[gray,fill=yellow,circle,draw]  at (0,\y) {S};
        \Star[pos={(\wid, \y)}]
      }
    \node[anchor=east] at (-0.5,0) {$t_1 = 0$};
    \node[anchor=east] at (-0.5,-1) {$t_2$};
    \node[anchor=east] at (-0.5,-2) {$t_3$};
    \node[anchor=east] at (-0.5,-3) {$t_4$};
    \rocket[pos={(0.5,0)},aspect=0.5,size=0.5]
    \clock[center={(0.5,0)},second=0,size=0.125cm]
    \draw[->] (1,0) --  node[anchor=south]{$v$} ++(0.6,0);
    \rocket[pos={(5.5,-1)},aspect=0.5,size=0.5]
    \draw[photon] (\wid-0.5,-1) -- ++(-1,0);
    \rocket[pos={(8,-2)},aspect=0.5,size=0.5]
    \clock[center={(8,-2)},second=30,size=0.125cm]
    \draw[photon] (9.35,-2) -- ++(-1,0);
    \rocket[pos={(11.25,-3)},aspect=0.5,size=0.5]
    \clock[center={(11.2,-3)},second=45,size=0.125cm]
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/physics-23/p23_pns/sol
filename: Puck.tex
modified: 2020-08-09 21:51:27
domain: p23
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[dashed,line width=1.5] (0,0) --node[anchor=south east]{$\ell$} (3,4)
    -- (6,0);
    \draw[SlateGray] (0,0) --node[anchor=north]{$\qty(\frac{3}{4}U)
        \qty(\frac{D}{U} )$} (3,0) -- (6,0);
    \draw (0.75,0) arc (0:53.1:0.75);
    \node at (26.5:1.4){$\theta$};
    \draw[coord,<->] (3,0) --node[anchor=east]{$D$} (3,4);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/physics-23/Helliwell/sol
filename: H0802.tex
modified: 2020-09-07 23:07:48
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \SPFrame
    \begin{scope}[opacity=0.75]
      \clock[second=0]
      \clock[center={(2,0)}]
    \end{scope}
    \node[anchor=north] at (2,-0.25) {$\SI{1}{m}$};
    \draw[vel] (0,1.5) -- node[anchor=south]{$v=\myfrac{3}{5}c$}++ (0:1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/physics-23/Helliwell/sol
filename: H0611.tex
modified: 2020-08-31 14:22:45
domain: p23
source:
  \begin{tikzpicture}[scale=0.8]
    \def\rocketlength{0.5}
    \def\earth{0.3}
    \begin{scope} % this is the Sun Frame
      \node at (2,2){\large Sun Frame};
      % Earth
      \filldraw[fill=blue!30!white,draw=brown,line width=1]
      (0,0.5) circle[radius=\earth] node{E};
      % draw the rocket leaving
      \Rocket[\frac{4}{5}c]{(0,0)};
      \node at (-1.5,0){$t = 0$};
    \end{scope}

    \begin{scope}[shift={(0,-1.5)}] % this is the Sun Frame
      % Earth
      \shade[shading=radial] (0,0) circle[radius=0.6];
      \Rocket[ ]{(1.5,0)};
      \draw[photon,->] (0,0) -- ++(0:0.75);
      \node at (-1.5,0){$t = t_{\rm E}$};
    \end{scope}

    \begin{scope}[shift={(0,-3)}] % this is the Sun Frame
      % Earth
      \shade[shading=radial] (0,0) circle[radius=0.3,opacity=0.5];
      \Rocket[ ]{(4.5,0)};
      \node at (-1.5,0){$t = t_{\rm A}$};
      \draw[photon,->] (4,0) -- ++(0:0.75);
    \end{scope}

    \draw[dashed,color=gray] (6,2) -- ++(0,-5);

    % Now handle the ship frame
    \begin{scope}[shift={(7,0)}]
      \node at (2,2){\large Ship Frame};
      % Earth
      \filldraw[fill=blue!30!white,draw=brown,line width=1]
      (5,0.5) circle[radius=\earth] node{E};
      \draw[color=DarkGreen,line width=1.5,->] (4.5,0.5) -- ++(180:0.4)
      node[anchor=south] {$\frac{4}{5} c$};
      % draw the rocket leaving
      \Rocket{(5,0)};
      \node[anchor=west] at (6,0){$t' = 0$};

      \begin{scope}[shift={(0,-1.5)}] % this is the Sun Frame
        % Earth
        \shade[shading=radial] (2.5,0) circle[radius=0.6];
        \Rocket{(5,0)};
        \draw[photon,->] (2.5,0) -- ++(0:0.75);
        \draw[color=DarkGreen,line width=1.5,->] (2.,0) -- ++(180:0.4);
        \node[anchor=west] at (6,0){$t'_{\rm E}$};
      \end{scope}

      \begin{scope}[shift={(0,-3)}] % final event
        % Earth
        \shade[shading=radial] (0,0) circle[radius=0.3,opacity=0.5];
        \draw[color=DarkGreen,line width=1.5,->] (-0.3,0) -- ++(180:0.4);
        \Rocket{(5,0)};
        \node[anchor=west] at (6,0){$t'_{\rm A}$};
        \draw[photon,->] (4.5,0) -- ++(0:0.75);
      \end{scope}
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/physics-23/Helliwell/sol
filename: H0610.tex
modified: 2020-09-07 20:40:23
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \node[anchor=west] at (-5,0) {$t'_{\rm D} = 0$};
    \node[anchor=west] at (-5,-1.5) {$t'_{\rm E}$};
    \node[anchor=west] at (-5,-3) {$t'_{\rm A}$};

    \foreach \y in {0.5, -1, -2.5} {\rocket[pos={(0,\y)}]}
    \node[circle,fill=yellow,font=\tiny] at (0,0) {Sun};
    \foreach \x in {-0.5, 3.5}{
        \draw[vel] (\x,0) -- node[anchor=south]{$\frac{4}{5} c$} ++ (180:1);
      }
    \Star[pos={(4,0)}]

    \dimline[start={(0,-0.5)}, end={(4,-0.5)},label={$d$}]

    \begin{scope}[shift={(-2.25,-1.5)}]
      \node[starburst, fill=yellow, draw=red, font=\scriptsize] at (0,0) {};
      \Star[pos={(4,0)}]
      \draw[vel] (3.5,0) -- node[anchor=south]{$\frac{4}{5} c$} ++ (180:1);
      \draw[photon] (0,0) -- ++(0:1) node[anchor=south]{$c$};
    \end{scope}
    \begin{scope}[shift={(-4,-3)}]
      \node[starburst, fill=yellow, draw=red, font=\scriptsize,opacity=0.5] at (0,0) {};
      \Star[pos={(4,0)}]
      \draw[vel] (3.5,0) -- node[anchor=south]{$\frac{4}{5} c$} ++ (180:1);
      \draw[photon] (3.75,-0) -- ++(0:1);
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec02.tex
modified: 2021-06-17 04:10:16
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \node at  (0,0)
    {\includegraphics[width=0.4\columnwidth]{Einstein-1905}};
    \node[cloud callout, cloud puffs=15, aspect=2.5, cloud puff arc=120,
      shading=ball, ball color=Gold, text=white, text width=2.5cm] at (-1.7,3) {Newton, please forgive me.};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec01.tex
modified: 2021-06-16 01:07:32
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \node[anchor=south] at (3,0) {\includegraphics[width=2.5cm]{saeta}};
    \node[anchor=north] at (3,0) {Peter Saeta};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec01.tex
modified: 2021-06-16 01:07:32
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \onslide<2->{
      \shade[ball color=blue] (3,2,1) coordinate (b) circle[radius=0.125];
    }

    \onslide<3|handout:0>{
      \refframe[4]{x}{y}{z};
      \draw[vector] (0,0,0) --node[anchor=south]{$\vb{r}$} (b);
    }
    \onslide<4->{
      \refframe[4]{x}{y}{z};
      \draw[vector] (0,0,0)
      --node[anchor=south,shift={(180:0.1)}]{$\vb{r}(t)$} (b);
    }
    \onslide<5>{
      \begin{scope}[shift=(b),shift={(0,0.5)}]{
          \clock[second=7,bgcolor=gray!10];
          % \filldraw[fill=gray!15] (0,0) circle[radius=0.25];
          % \foreach \q in {0,30,...,330} {
          %   \draw[gray] (\q:0.2) -- (\q:0.25);
          %   \draw[line width=1] (0,0) -- (45:0.225) (0,0) -- (255:0.15);
        }
      \end{scope}
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec01.tex
modified: 2021-06-16 01:07:32
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \only<handout>{
      \foreach \c in {0,1.5,...,7.5}{
          \ruler[length=1.45,pos={(\c,-0.75)}]
          \clock[center={(\c,0)}, second=0,size=0.25cm]
        }
      \clock[center={(9,0)},second=0,size=0.25cm]
    }
    \only<beamer>{
      \foreach \n in {1, 2,3}{
          \foreach \c in {0,1.5,...,7.5}{
              \ruler[length=1.45,pos={(\c,-0.75)}]
            }
          \onslide<\n>{
            \foreach \c in {0,1,...,5}{
                \pgfmathsetmacro{\x}{\c*1.5}
                \pgfmathsetmacro{\s}{5*(\n-1)}
                \clock[center={(\x,0)}, second={\s},size=0.35cm]
              }
            \shade[ball color=DarkRed] (\n*1.5-1.5,0.75) coordinate (c)
            circle[radius=0.125];
            \begin{scope}[shift=(c),SlateGray]
              \foreach \y in {-0.05,0,0.05}{\draw (-0.25,\y) -- ++(180:0.2);}
            \end{scope}
          }
        }
      \def\news{-1.5}
      \onslide<1|handout:0>{
        \node[anchor=west] at (0,\news) {Event 0: at $t = 0$, the ball is at $x = 0$};
      }
      \onslide<2|handout:0>{
        \node[anchor=west] at (1.5,\news) {Event 1: at $t = \SI{5}{s}$, the ball is at $x =
            \SI{1}{m}$};
      }
      \onslide<3>{
        \node[anchor=west] at (3,\news) {Event 2: at $t = \SI{10}{s}$, the ball is at $x =
            \SI{2}{m}$};

        \node[DarkRed,text width=8cm,anchor=north,draw,rounded corners,
          fill=gray!5] at (4.25,-3){
          \textit{To measure velocity, we can use synchronized clocks separated by
            known distances. Observers next to each clock read it when the
            object
            passes by and then get together to compare notes.}
        };
      }
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec01.tex
modified: 2021-06-16 01:07:32
domain: p23
source:
  \begin{tikzpicture}[scale=0.85]
    \fill[gray!10] (-0.75,-0.25) rectangle (2.25,6.25);
    \fill[gray!50] (0,0) rectangle (2,-0.1) (0,6) rectangle ++(2,0.1);
    \draw (0,0) -- ++(0:2) (0,6) -- ++(0:2);
    \draw[coord,<->] (-0.25,0) -- node[anchor=east]{$D$} ++(90:6);

    \onslide<2> { \event{(1,0)}{Event 0} }
    \onslide<3> { \event{(1,6)}{Event 1} }
    \onslide<4> { \event{(1,0)}{Event 2} }

    \onslide<2,4>{\draw[photon,->,line width=1] (1,0) -- ++(90:1.5)
      node[anchor=west]{$c$};}
    \onslide<3>{\draw[photon,->,line width=1] (1,6) -- ++(-90:1.5);}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec01.tex
modified: 2021-06-16 01:07:32
domain: p23
source:
  \begin{tikzpicture}[scale=0.75]
    \def\fram{0.75}
    % unprimed frame
    \draw[coord,<->] (-1,-1)  ++(\fram,0) -- ++(-\fram,0) --
    ++(0,\fram) node[anchor=south]{$S$};

    % gray backgrounds behind mirrors
    \onslide<1>{
      \fill[gray!10] (-0.25,-0.25) rectangle (2.2,6.25);
      % primed frame
      \draw[coord,<->] (0,0.25)  ++(\fram,0) -- ++(-\fram,0) --
      ++(0,\fram) node[anchor=south]{$S'$};
    }

    % clock at t = 1
    \onslide<2>{
      \fill[gray!10] (3.75,-0.25) rectangle ++(2.4,6.5);
      \draw[coord,<->] (4,0.25)  ++(\fram,0) -- ++(-\fram,0) --
      ++(0,\fram) node[anchor=south]{$S'$};
    }

    % clock at t = 2
    \onslide<3>{
      \fill[gray!10] (7.75,-0.25) rectangle ++(2.4,6.5);

      \draw[coord,<->] (8,0.25)  ++(\fram,0) -- ++(-\fram,0) --
      ++(0,\fram) node[anchor=south]{$S'$};
    }
    \draw[coord,<->] (-0.5,0) --node[anchor=east]{$D$} ++(90:6);

    \begin{scope}[shift={(0,0)}]
      \fill[gray!50] (0,0) rectangle (2,-0.1) (0,6) rectangle ++(2,0.1);
      \draw (0,0) -- ++(0:2) (0,6) -- ++(0:2);
      \draw[vel] (0.5,6.5) -- ++(0:1) node[anchor=west]{$V$};
      \onslide<1|handout:1>{
        \clock[center={(1,-1)},second=0]
      }
      \onslide<1|handout:0>{
        \node at (1,-1.5){$t = 0$};
      }
    \end{scope}

    \onslide<2->{
      \begin{scope}[shift={(4,0)}]
        \fill[gray!50] (0,0) rectangle (2,-0.1) (0,6) rectangle ++(2,0.1);
        \draw (0,0) -- ++(0:2) (0,6) -- ++(0:2);
        \draw[vel] (0.5,6.5) -- ++(0:1) node[anchor=west]{$V$};
      \end{scope}
    }

    \onslide<2|handout:0>{
      \clock[center={(1,-1)},second=10]
      \clock[center={(5,-1)},second=10]
    }
    \only<handout>{
      \clock[center={(5,-1)}]
    }

    \onslide<3->{
      \begin{scope}[shift={(8,0)}]
        \fill[gray!50] (0,0) rectangle (2,-0.1) (0,6) rectangle ++(2,0.1);
        \draw (0,0) -- ++(0:2) (0,6) -- ++(0:2);
        \draw[vel] (0.5,6.5) -- ++(0:1) node[anchor=west]{$V$};
      \end{scope}
    }

    \onslide<1>{
      \event{(1,0)}{Event 0}
      \only<beamer>{\draw[photon] (1,0) -- ++(1,1.5);}
    }
    \onslide<2>{
      \event{(5,6)}{Event 1}
      \only<beamer>{\draw[photon] (5,6) -- ++(1,-1.5);}
    }
    \onslide<2|handout:0>{
      \node at (5,-1.5){$t = t_{1}$};
    }
    \onslide<3>{
      \event{(9,0)}{Event 2}
      \only<beamer>{\draw[photon] (9,0) -- ++(1,1.5);}
    }
    \onslide<3|handout:0>{
      \foreach \x in {1,5,9}{
          \clock[center={(\x,-1)},second=20]
        }
      \node at (9,-1.5){$t = t_{2}$};
    }
    \onslide<beamer:0|handout:1>{
      \clock[center={(9,-1)}]
    }

    % Now show the paths and the lengths
    \onslide<4-|handout:0>{
      \draw[dashed,DarkRed] (1,0) --node[rotate=56.3, anchor=south,]{$d = c
          t_{1}$}  (5,6) -- (9,0);
      \draw[dotted] (5,6) --node[anchor=west]{$D$} (5,0)
      -- (1,0);
      \draw[coord,<->] (1,-0.5) -- node[anchor=north]{$V t_{1}$} (5,-0.5);
    }

    \onslide<5|handout:0>{
      \node[message] at (5,-2) {The light must travel a distance $2d > 2D$. Therefore\ldots?};
    }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec01.tex
modified: 2021-06-16 01:07:32
domain: p23
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[line width=1.5] (0,0) -- node[rotate=56.3,anchor=south]{$d=ct_{1}$}
    (4,6) -- node[anchor=west]{$D = c\tau_{1}$} (4,0) --
    node[anchor=north]{$V t_{1}$} cycle;
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec01.tex
modified: 2021-06-16 01:07:32
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \node at (0,0) {$V^{2} t_{1}^{2} + c^{2} \tau_{1}^{2} = c^{2} t_{1}^{2}$};
    \node at (0, -1){$c^{2}\tau_{1}^{2} = \qty(c^{2} - V^{2}) t_{1}^{2} $};
    \node at (0,-2){$ \tau_{1}^{2} = \qty(1 - \frac{V^{2}}{c^{2}}) t_{1}^{2}$};
    \node at (0,-3){$\tau_{1} = \sqrt{1 - \frac{V^{2}}{c^{2}} } t_{1} $};
    \filldraw[DarkRed,fill=gray!10] (-4.5,-5.5) rectangle (4.5,-3.5);

    \node at (0,-4){$\Delta\tau = \sqrt{1 - \frac{V^{2}}{c^{2}} } \Delta t
      $};
    \draw[<-,DarkRed] (-1.35,-4.25) -- ++(215:1) node[anchor=north]{time
      on ``moving'' clock};
    \draw[<-,DarkRed] (1.35,-4.25) -- ++(-35:1) node[anchor=north]{time on
      ``our'' clock};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec01.tex
modified: 2021-06-16 01:07:32
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \shade[inner color=yellow,outer color=white] (0,0) circle[radius=0.5];
    \node[anchor=west] at (0.5,0){Sun};
    \shade[inner color=red,outer color=white] (8,0) circle[radius=0.3];
    \node[anchor=east] at (7.7,0) {Proxima Centauri};
    \draw[coord,<->] (0,-0.6) -- node[anchor=north]{$D = 4\cy$} ++(8,0);
    \filldraw[SlateBlue,fill=SlateBlue!50] (-0.5,1) --
    ++(0.5,0) -- ++(0.1,0.1) coordinate (t) -- ++(-0.1,0.1) -- ++(-0.5,0)
    --cycle;
    \draw[vel] (t) ++(0.1,0) -- ++(1,0) node[anchor=west] {$V = \frac{4}{5}
        c$};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec01.tex
modified: 2021-06-16 01:07:32
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \def\D{10}
    \shade[inner color=yellow,outer color=white] (0,0) circle[radius=0.15];
    \shade[inner color=red,outer color=white] (\D,0) coordinate (alpha) circle[radius=0.1];

    \node at (-1,0) {$t_{\rm D} = 0$};
    \dimline[start={(0,-0.3)}, end={(\D,-0.3)}, label={$D = 4\cy$}]

    \rocket[pos={(0,0.35)}]
    \draw[vel] (0.5,0.35) -- node[anchor=south]{$V = \frac{4}{5}c$} ++(1,0);
    \clock[center={(0,0.45)},second=0,size=0.125]

    % separate frames

    \draw[SlateGray] (-1.5,-0.75) -- ++(\D+3,0);

    \begin{scope}[shift={(0,-1.5)}]
      \shade[inner color=yellow,outer color=white] (0,0) circle[radius=0.15];
      \shade[inner color=red,outer color=white] (\D,0) coordinate (alpha) circle[radius=0.1];
      \rocket[pos={(\D,0.35)}]
      \draw[vel] (\D+0.5,0.35) -- ++(1,0);
      \clock[center={(\D,0.45)},second=15,size=0.125]
      \node at (-1, 0) {$t_{\rm A} = \SI{5}{y}$};
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec01.tex
modified: 2021-06-16 01:07:32
domain: p23
source:
  \begin{tikzpicture}[scale=0.65]
    \draw[vel,line width=1] (0,0) --node[anchor=east]{$c$} (6,6) coordinate (A);
    \draw[vel,line width=1] (0,0) --node[anchor=north]{$V$} (6,0) coordinate (B);
    \draw[vel,line width=1] (B) -- node[anchor=west]{$c\srF$} (A);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec04.tex
modified: 2021-06-24 04:48:36
domain: p23
source:
  \begin{tikzpicture}[scale=1.5,
    ]
    \pgfmathsetmacro{\len}{3}
    \pgfmathsetmacro{\ang}{60}
    \draw[vel,line width=3] (0,0) -- node[anchor=south east]{$A$} ++(\ang:\len);
    \coordinate (Ax) at ($3*cos(60)*(1,0)$);
    \onslide<2-3>{
      \SFrame
      \draw[component] (0,0) --node[anchor=north]{$A_{x}$} (Ax);
      \draw[component] (Ax) -- node[anchor=east]{$A_{y}$} (\ang:\len);
    }

    \onslide<3>{
      \draw (0.5,0) arc(0:\ang:0.5);
      \node at (\ang/2:0.65){$\varphi$};
    }

    \onslide<4->{
      % draw the old stuff with transparency
      \begin{scope}[opacity=0.2]
        \SFrame[3.5]
        \draw[component] (0,0) --node[anchor=north]{$A_{x}$} (Ax);
        \draw[component] (Ax) -- node[anchor=east]{$A_{y}$} (\ang:\len);
      \end{scope}

      \def\frot{15}
      \draw (0.75,0) arc(0:\frot:0.75);
      \node[font=\tiny] at (\frot/2:0.85) {$\theta$};
      \draw (\frot:0.35) arc(\frot : \ang : 0.35);
      \node[font=\tiny] at (\frot/2 + \ang/2:0.55) {$\varphi-\theta$};

      \begin{scope}[rotate=\frot]
        \SPFrame[3.5]
        \coordinate (Apx) at ($3*cos(\ang-\frot)*(1,0)$);
        \draw[component] (0,0) --node[anchor=south]{$A'_{x}$} (Apx);
        \draw[component] (Apx) -- node[anchor=west]{$A'_{y}$} (\ang-\frot:\len);
      \end{scope}
    }

    \onslide<5>{
      \begin{scope}[shift={(1,3)}, rotate=0]
        \fill[fill=yellow!15!white] (0,-0.2) rectangle (2.5,0.6);
        \node[anchor=west] at (0,.4) {$A'_{x} = A_{x} \cos\theta + A_{y}
          \sin\theta$};
        \node[anchor=west] at (0,0) {$A'_{y} = -A_{x}\sin\theta + A_{y}\cos\theta$};
      \end{scope}

    }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec04.tex
modified: 2021-06-24 04:48:36
domain: p23
source:
  \begin{tikzpicture}[scale=1.25]
    \refframe{z}{x}{y}
    \filldraw[fill=red] (1,1) coordinate (p1) circle[radius=0.05];
    \node[anchor=north,font=\tiny] at (p1) {$(ct,x,y,z)$};
    \onslide<2->{
      \filldraw[fill=red] (2,2) coordinate (p2) circle[radius=0.05];
      \node[anchor=south,font=\tiny] at (p2) {$(c(t+\Delta t),x+\Delta
          x,y+\Delta y,z+\Delta z)$};
    }
    \onslide<3->{
      \draw[->,DarkRed] (p1) -- node[anchor=north
        west,font=\tiny]{$\Delta s=(c\Delta t, \Delta x, \Delta y, \Delta z)$} (p2);
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec04.tex
modified: 2021-06-24 04:48:36
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \onslide<3->{
      \RFrame[5]{x}{ct}
      \event[pos={(1,1)},label=A]
      \event[pos={(4,1)},label=B]
      \foreach \x/\y in {1/25, 4/125}{
          \draw[DarkGreen] (\x,0) -- ++(0,0.2);
          \node[anchor=north,font=\small] at (\x,0) {\y\ km};
        }
    }

    \onslide<5->{
      \node at (2.5,4.5) {$\Delta s = (0, \SI{100}{km}, 0, 0)$};
    }
    \onslide<6->{
    \node at (2.5,3.5) {$(\Delta s)^{2} = 10^{4}\,\si{km^{2}} > 0$};
      \node[rounded corners,DarkRed,draw,fill=yellow!25!white,
        font=\scriptsize\sffamily\bfseries,text width=3.75cm] at (2.5,2.25) {
        Events that are spacelike separated in one frame are spacelike
        separated in all frames. We can find an inertial frame in which
        they are simultaneous.};
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec04.tex
modified: 2021-06-24 04:48:36
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \onslide<2->{
      \RFrame[5]{x}{ct}
      \event[pos={(2,1)},label={A}]
      \event[pos={(2,3)},label={B}]
      \foreach \y/\t in {1/1, 3/2}{
          \draw[DarkGreen] (0,\y) -- ++(0.2,0);
          \node[anchor=east,font=\small] at (0,\y) {$t_{\t}$};
        }
    }

    \onslide<3->{
      \node at (2.5,4) {$(\Delta s)^{2} = -(1 c\,\si{s})^{2}$};
    }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec04.tex
modified: 2021-06-24 04:48:36
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \def\dim{3.25}
    \coordinate (f1) at (45:1.25*\dim);
    \coordinate (f2) at (135:1.25*\dim);
    \coordinate (p1) at (-45:1.25*\dim);
    \coordinate (p2) at (-135:1.25*\dim);
    \coordinate (A) at (0.75,1.75);
    \coordinate (B) at (2, 0.5);
    \coordinate (message) at (-1.5*\dim,\dim);




    \onslide<1>{
      \mess{An explosion takes place at the origin of our
        coordinate system and at time $t = 0$.}
    }

    % forward light cone
    \onslide<4->{
      \fill[gray!25!white] (0,0) -- (f1) -- (f2) -- cycle;
      \node[anchor=north east,font={\tiny\sffamily},DarkRed,shift={(-0.25,0)}] at (f1)
      {future light cone};
    }

    % past light cone
    \onslide<6-|handout:0>{
      \fill[gray!25!white] (0,0) -- (p1) -- (p2) -- cycle;
      \node[anchor=south east,font={\tiny\sffamily},DarkRed,shift={(-0.25,0)}]
      at (p1) {past light cone};
      \draw[->,red] (p1) -- (0.2,-0.2);
      \draw[->,red] (p2) -- (-0.2,-0.2);
      \event[pos={(-2,-1)},label=C]
      \event[pos={(1,-2)},label=D]
      \mess{The mirror image of the \term{future light cone}---which is the locus of points
        in spacetime that could be influenced by the event \textsf{E}---is the \term{past
          light cone}, which is the locus of points in spacetime that \emph{could}
        influence event \textsf{E}. In principle, event \textsf{D} could have caused the
        explosion, but event \textsf{C} could not.}
    }

    \onslide<2->{
      \draw[->,red] (0,0) -- (f1) node[anchor=south west]{$c$};
      \draw[->,red] (0,0) -- (f2) node[anchor=south east]{$c$};
    }
    \onslide<2|handout:0>{ \mess{Light beams head out in all directions, forming a
        spherical surface that expands at the speed
        of light, centered on the explosion. On our spacetime diagram that
        shows only $x$ and $ct$, the expanding looks like diagonal lines with
        slope 1 and $-1$.}
    }

    \onslide<3|handout:0>{
      \mess{If we include one more spatial dimension, the expanding sphere
        looks like a cone, so we typically call it the light cone, even when
        we don't draw the extra dimension.}

      \fill[left color=gray!50!black,
        right color=gray!50!black,
        middle color=gray!50,
        shading=axis,
        opacity=0.25] (0,0) -- ($0.9*(f1)$) -- ($0.9*(f2)$) -- cycle;

      \fill[gray!25]
      (0,0.8*\dim) circle[x radius=0.79*\dim, y radius=0.1 * \dim];
    }

    \draw[coord] (-\dim,0) -- (\dim,0) node[anchor=north]{$x$};
    \draw[coord] (0,-\dim) -- (0,\dim) node[anchor=east]{$ct$};
    \event[label=E]

    \onslide<4-|handout:0>{ \event[label=A,pos={(A)}] }
    \onslide<4|handout:0>{ \mess{Suppose
        another event---perhaps a piece of shrapnel pierces my left
        bicep---happens where I have shown event \textsf{A}. Could the
        explosion have caused my injury?};
      \draw[dashed,line width=2,SlateGray] ($(0,0)!0.15!(A)$) -- ($(0,0)!0.85!(A)$);
    }

    \onslide<5-|handout:0>{ \event[label=B,pos={(B)}] }
    \onslide<5|handout:0>{
      \mess{It turns out that a president who shall not be named tweeted a message at event
        \textsf{B}. Could that message be a response to the explosion?}
    }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec04.tex
modified: 2021-06-24 04:48:36
domain: p23
source:
  \begin{tikzpicture}[scale=1.25]
    \refframe{z}{x}{y}
    \filldraw[fill=red] (1,1) coordinate (p1) circle[radius=0.05];
    \node[anchor=north,font=\tiny] at (p1) {$(ct,x,y,z)$};
    \filldraw[fill=red] (2,2) coordinate (p2) circle[radius=0.05];
    \node[anchor=south,font=\tiny] at (p2) {$(c(t+\Delta t),x+\Delta
        x,y+\Delta y,z+\Delta z)$};

    \draw[->,DarkRed] (p1) -- node[anchor=north
      west,font=\tiny]{$\Delta s=(c\Delta t, \Delta x, \Delta y, \Delta z)$} (p2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec04.tex
modified: 2021-06-24 04:48:36
domain: p23
source:
  \begin{tikzpicture}[scale=1.25]
    \refframe{z}{x}{y}
    \filldraw[fill=red] (1,1) coordinate (p1) circle[radius=0.05];
    \node[anchor=north,font=\tiny] at (p1) {$(ct,x,y,z)$};
    \filldraw[fill=red] (2,2) coordinate (p2) circle[radius=0.05];
    \node[anchor=south,font=\tiny] at (p2) {$(c(t+\Delta t),x+\Delta
        x,y+\Delta y,z+\Delta z)$};

    \draw[->,DarkRed] (p1) -- node[anchor=north
      west,font=\tiny]{$\Delta s=(c\Delta t, \Delta x, \Delta y, \Delta
        z)$} (p2);

    \node[message, text width=5cm] at (2,-1) {What is the invariant square of the 4-velocity $u_{\mu}$?};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec04.tex
modified: 2021-06-24 04:48:36
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \def\ymax{4}
    \begin{axis}[
        xmin=0, xmax=1.1, ymin=0, ymax=\ymax, enlargelimits=false,
        width=3in, height=2.25in,
        xlabel={$v$}, ylabel={$|\VEC{p}| = \gamma_{v} m v$}, ytick={}, xtick={0, 0.5, 1},
        xticklabels={0, $\frac{c}{2}$, $c$}, yticklabel=\empty,
        % axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[red, domain=0:0.99, samples=100, line width=2pt,]
      {x / sqrt(1 -x*x)};
      \draw[dashed, SlateGray] (1,0) -- (1,\ymax);
      \draw[dashed,line width=1.25,DarkGreen] (0,0) -- (1.1,1.1);
      \node[anchor=north,DarkGreen] at (0.8,0.8) {$mv$};
      \node[rotate=-90,anchor=south,SlateGray,font=\sffamily\scriptsize] at
      (1,3){speed limit};
    \end{axis}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec04.tex
modified: 2021-06-24 04:48:36
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \node[rounded corners, draw, DarkSlateGray,anchor=south west]
    at (8.5,1) {$\VEC{p} = \gamma_{v} m \VEC{v}$};
    \fill[SlateGray] (0,0) circle[radius=0.25];
    \node[font=\sffamily] at (0,1.5) {before};
    \draw[dashed,SlateGray] (2,2) -- (2,-1);
    \begin{scope}[shift={(6,0)}]
      \node[font=\sffamily] at (0,1.5) {after};
      \begin{scope}[DarkGreen]
        \fill[DarkGreen] (-1,0) coordinate (M) circle[radius=0.25];
        \draw[->] (-1.4,0) --node[anchor=south]{$v_{M}=\frac{5}{13} c$}
        ++(-1,0);
        \draw (M) ++(0,-0.3) node[anchor=north]{$M$};
      \end{scope}

      \begin{scope}[DarkRed]
        \fill[DarkRed] (1,0) coordinate (m) circle[radius=0.25];
        \draw[->] (1.4,0) --node[anchor=south]{$v_{m}=\frac{12}{13} c$}
        ++(1,0);
        \draw (m) ++(0,-0.3) node[anchor=north]{$m$};
      \end{scope}
    \end{scope}
    \node[message] at (2,-2) {Solve for $\frac{m}{M}$};
    \node at (2,-5) { };
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec04.tex
modified: 2021-06-24 04:48:36
domain: p23
source:
  \begin{tikzpicture}[scale=1,font=\Large]
    \node at (0,0) {$c p_{t} = \textcolor{DarkRed}{m c^{2}} +
        \textcolor{DarkGreen}{\underbrace{\frac{1}{2} m v^{2} +
            \cdots}_{\text{energy of motion}}}$};
    \draw[DarkRed,<-,font=\normalsize] (-1,0) -- ++(225:0.5) node[anchor=north]{rest
      energy};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec04.tex
modified: 2021-06-24 04:48:36
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) node[draw]{$E^{2} = m^{2} c^{4} + p^{2} c^{2}$};
    \draw[<-,DarkRed] (-1.75,0) -- ++ (-1,0) node[anchor=east]{Total energy of
      the particle};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec04.tex
modified: 2021-06-24 04:48:36
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \def\rad{0.3}
    \filldraw[fill=\Acol!33!white] (-3,0) coordinate (A) circle[radius=\rad] node{A};
    \draw[\Acol,line width=2,->] (A) ++ (0.5,0) -- ++(1,0)
    node[anchor=south]{$v$};
    \draw[\Acol] (A) ++ (0,\rad) node[anchor=south]{$m$};
    \draw[dashed,SlateGray,->,line width=1.5] (-1.5,0) -- (-\rad,0) arc(270:360:\rad) -- (0,2);
    \filldraw[fill=\Acol,opacity=0.33] (0,2.5) circle[radius=\rad];
    \filldraw[fill=green!33!white] (3,0) coordinate (B) circle[radius=\rad] node{B};
    \draw[\Bcol] (B) ++ (0,\rad) node[anchor=south]{$m$};
    \draw[\Bcol,line width=2,->] (B) ++ (-0.5,0)
    -- ++ (-1,0) node[anchor=south]{$v$};
    \draw[dashed,SlateGray,->,line width=1.5] (1.5,0) -- (\rad,0) arc(90:180:\rad) -- (0,-2);
    \filldraw[fill=\Bcol,opacity=0.33] (0,-2.5) circle[radius=\rad];

    \onslide<2->{
      \begin{scope}[shift={(-3.5,-0.5)},opacity=0.5]
        \SFrame[2]
      \end{scope}
      \begin{scope}[shift={(-3,-0.4)}, opacity=0.5]
        \SPFrame[2]
        \draw[->,SlateGray] (0,1.25) -- node[anchor=south]{$V$} ++(1,0);
      \end{scope}
    }

    \onslide<3>{ \node[message,text width=3.5cm] at (-4,-2) {If we use
        $\VEC{p} = m \VEC{v}$, momentum is \textbf{not conserved}, but if we
        use $\VEC{p} = \gamma_{v} m \VEC{v}$, it is!}; }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec04.tex
modified: 2021-06-24 04:48:36
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \def\rad{0.2}
    \def\ang{30}
    % Put the velocity transform equations in the top right corner
    \begin{scope}[shift={(5,3)}]
      \filldraw[draw=\Acol,fill=\Acol!20!white,rounded corners] (0,-0.5) rectangle (4.5,0.5);
      \node[anchor=west] at (0,0) {$v'_{x} = \frac{v_{x}-V}{1 - \frac{v_{x}V}{c^{2}}} $};
      \node[anchor=west] at (2,0) {$v'_{y} = \frac{ v_{y}\srF}{1
          -\frac{v_{x}V}{c^{2}}}$};
    \end{scope}

    \begin{scope}[shift={(5,0)}, rotate=0]
      \coordinate (A) at (0,0);
      \coordinate (B) at (5,0);

      % B's trajectory
      \draw[dashed, SlateGray,->,line width=1.5] (2.75, 0) --
      (0.5,0) arc(90:90+\ang:0.5) -- ++(180+\ang:2.75) coordinate (Bf);
      % A's trajectory
      \draw[dashed, SlateGray,->,line width=1.5] (A) ++(150:0.4) -- ++(150:2)
      coordinate (Af);
      \filldraw[fill=\Acol,opacity=0.33] (Af) ++ (180-\ang:0.4)
      circle[radius=\rad];
      \filldraw[fill=\Bcol,opacity=0.33] (Bf) ++ (180+\ang:0.4)
      circle[radius=\rad];

      \filldraw[fill=\Acol!33!white] (0,0) coordinate (A) circle[radius=\rad] node{A};
      \filldraw[fill=\Bcol!33!white] (5,0) coordinate (B) circle[radius=\rad]
      node{B};
      \draw[\Bcol,line width=2,->] (B) ++ (-0.5,0)
      -- node[anchor=north]{$v'_{B,\initial}$} ++ (-1.5,0) ;

      % show the final velocities

      \draw[->,line width=1.5,\Bcol] (Bf) ++(180+\ang:0.8) --
      node[anchor=north west] {$v'_{B,\final}$} ++(180+\ang:1.5);
      \draw[->,line width=1.5,\Acol] (Af) ++(180-\ang:0.8) --
      node[anchor=south west]{$v'_{A,\final}$} ++(180-\ang:1.5);
    \end{scope}

    % The initial and final coordinates in S

    \begin{scope}[shift={(-4,2.5)}, rotate=0]
      \filldraw[rounded corners, fill=\Acol!15!white] (0,0) rectangle (1.75,1);
      \node[anchor=west] at (0,0.7) {$\VEC{v}_{A,\initial} = v\,\ux$};
      \node[anchor=west] at (0,0.3) {$\VEC{v}_{A,\final} = v\, \uy$};

      \filldraw[rounded corners,fill=\Bcol!15!white] (2.2,0) rectangle (4,1);
      \node[anchor=west] at (2.2,0.7) {$\VEC{v}_{B,\initial} = -v\, \ux$};
      \node[anchor=west] at (2.2,0.3) {$\VEC{v}_{B,\final} = -v\, \uy$};
    \end{scope}

    \onslide<2-|handout:0>{
    \draw[\Bcol] (B) ++ (-1,0.15) node[anchor=south] {$\frac{-2v}{1+v^{2}/c^{2}} $};
    }

    \onslide<3-|handout:0>{
      \draw[\Acol,->] (A) ++ (-0.35,0) --node[anchor=north] {$v$} ++(-3.7,0)
      coordinate (x);
    }
    \onslide<4-|handout:0>{
      \draw[\Acol,->] (x) -- node[anchor=east] {$v\sqrt{1-\frac{v^{2}}{c^{2}}}$} ++(90:2.35);
    }
    \onslide<5-|handout:0>{
    \node[rotate=-30,\Acol] at (2.5,1) {$v\sqrt{2 - v^{2}/c^{2}}$};
    }

    \onslide<6|handout:0>{
    \node[message, text width=4cm,anchor=north east] at (-1,2) {If
    we assume the wrong definition of momentum,
    $\VEC{p} = m \VEC{v}$, we have
    $$\VEC{p}_{\initial} = - \frac{2 m v}{1+v^{2}/c^{2}} \ux $$
    and
    $$\VEC{p}_{\final} = -2 m v \,\ux$$
    $\VEC{p}=m\VEC{v}$ \textbf{is not conserved in the collision}
    };
    }

    \onslide<7|handout:0>{
      \node[message, text width=4cm,anchor=north east] at (-1,2)
      {We need to compute each particle's $\gamma$ to use the correct
        definition, $\VEC{p}  = \gamma m \VEC{v}$. What is it for the
        incident proton (B)?};
    }
    \onslide<8-|handout:0>{
    \draw (B) ++ (0,-0.75) node[draw,anchor=north east,\Bcol]
    {$\gamma_{B,\initial} = \frac{1+v^{2}/c^{2}}{1-v^{2}/c^{2}} $};
    }
    \onslide<8|handout:0>{
      \node[message, text width=4cm,anchor=north east] at (-1,2)
      {Now calculate $\gamma$ for the outgoing particles.};
    }
    \onslide<9-|handout:0>{
    \draw (Af) ++ (-0.4,0.75) node[draw,\Acol,rotate=-30,anchor=south west]
    {$\gamma_{A,\final} = \frac{1}{1-v^{2}/c^{2}} $};
    \node[message, text width=4cm,anchor=north east] at (-1,2)
    {So, is momentum $\VEC{p} = \gamma m \VEC{v}$ conserved?};
    }
    \onslide<10-|handout:0>{
      \node[message,text width=4cm,anchor=north east] at (-1,1)
      {In the $x'$ direction,
        \begin{align*}
          p'_{x,\initial} & = \frac{-2mv}{1-v^{2}/c^{2}}                   \\
          p'_{x,\final}   & = 2 m \frac{-v}{1-v^{2}/c^{2}} \quad\checkmark
        \end{align*}
      };
    }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec04.tex
modified: 2021-06-24 04:48:36
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \def\rad{0.3}
    \begin{scope}[shift={(-3.5,-0.5)},opacity=0.5]
      \SFrame[2]
    \end{scope}
    \begin{scope}[shift={(-3,-0.4)}, opacity=0.5]
      \SPFrame[2]
      \draw[->,SlateGray] (0,1.25) -- node[anchor=south]{$V$} ++(1,0);
    \end{scope}


    % incident A
    \filldraw[fill=\Acol!33!white] (-3,0) coordinate (A) circle[radius=\rad] node{A};
    \draw[\Acol,line width=2,->] (A) ++ (0.5,0) -- ++(1,0)
    node[anchor=south]{$v$};
    \draw[\Acol] (A) ++ (0,\rad) node[anchor=south]{$m$};

    \draw[dashed,SlateGray,->,line width=1.5] (-1.5,0) -- (-\rad,0)
    arc(270:360:\rad) -- (0,2);

    % at end
    \filldraw[gray,fill=\Acol,opacity=0.25] (0,2.5) coordinate (Af)
    circle[radius=\rad];

    % incident B
    \filldraw[fill=green!33!white] (3,0) coordinate (B) circle[radius=\rad] node{B};
    \draw[\Bcol] (B) ++ (0,\rad) node[anchor=south]{$m$};
    \draw[\Bcol,line width=2,->] (B) ++ (-0.5,0)
    -- ++ (-1,0) node[anchor=south]{$v$};
    \draw[dashed,SlateGray,->,line width=1.5] (1.5,0) -- (\rad,0)
    arc(90:180:\rad) -- (0,-2);

    % at end
    \filldraw[gray,fill=\Bcol,opacity=0.25] (0,-2.5) coordinate (Bf) circle[radius=\rad];


    \draw[\Acol] (A) ++ (0,-1) node[draw,rounded corners,
    anchor=north,fill=\Acol!15!white] {$p'_{A} = (mc, 0, 0, 0)$};

    \onslide<3>{
    \draw[\Bcol] (B) ++ (-0.8,0.65) node[draw,rounded corners,
    anchor=south,fill=\Bcol!15!white] {$p'_{B} =
      \frac{\qty(mc(1+\frac{v^{2}}{c^{2}}), -2mv, 0, 0)}{1-v^{2}/c^{2}}$};
    }


  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec04.tex
modified: 2021-06-24 04:48:36
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \def\rad{0.3}
    % reference frames
    \begin{scope}[shift={(-3.5,-0.5)},opacity=0.5]
      \SFrame[2]
    \end{scope}
    \begin{scope}[shift={(-3,-0.4)}, opacity=0.5]
      \SPFrame[2]
      \draw[->,SlateGray] (0,1.25) -- node[anchor=south]{$V$} ++(1,0);
    \end{scope}


    % incident A
    \filldraw[fill=\Acol!33!white] (-3,0) coordinate (A) circle[radius=\rad] node{A};
    \draw[\Acol,line width=2,->] (A) ++ (0.5,0) -- ++(1,0)
    node[anchor=south]{$v$};
    \draw[\Acol] (A) ++ (0,\rad) node[anchor=south]{$m$};

    \draw[dashed,SlateGray,->,line width=1.5] (-1.5,0) -- (-\rad,0)
    arc(270:360:\rad) -- (0,2);

    % at end
    \filldraw[gray,fill=\Acol,opacity=0.25] (0,2.5) coordinate (Af)
    circle[radius=\rad];

    % incident B
    \filldraw[fill=green!33!white] (3,0) coordinate (B) circle[radius=\rad] node{B};
    \draw[\Bcol] (B) ++ (0,\rad) node[anchor=south]{$m$};
    \draw[\Bcol,line width=2,->] (B) ++ (-0.5,0)
    -- ++ (-1,0) node[anchor=south]{$v$};
    \draw[dashed,SlateGray,->,line width=1.5] (1.5,0) -- (\rad,0)
    arc(90:180:\rad) -- (0,-2);

    % at end
    \filldraw[gray,fill=\Bcol,opacity=0.25] (0,-2.5) coordinate (Bf) circle[radius=\rad];


    \onslide<5->{
    \draw (Af) ++ (0,0.65) node[draw,rounded corners,
    anchor=south,fill=red!15!white] {$p'_{A,\final} =
      \gamma_{v}m(\Gamma c, -\Gamma v, v, 0)$};
    }

    \onslide<5->{
    \draw (Bf) ++ (-0.5,0) node[draw,rounded corners,
    anchor=east,fill=red!15!white] {$p'_{B,\final} =
      \gamma_{v}m(\Gamma c, -\Gamma v, -v, 0)$};
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: lec04.tex
modified: 2021-06-24 04:48:36
domain: p23
source:
  \begin{tikzpicture}[scale=0.8]
    \def\rad{0.3}


    % incident A
    \filldraw[fill=\Acol!33!white] (-3,0) coordinate (A) circle[radius=\rad] node{A};
    \draw[\Acol,line width=2,->] (A) ++ (0.5,0) -- ++(1,0)
    node[anchor=south]{$v$};
    \draw[\Acol] (A) ++ (0,\rad) node[anchor=south]{$m$};

    \draw[dashed,SlateGray,->,line width=1.5] (-1.5,0) -- (-\rad,0)
    arc(270:360:\rad) -- (0,2);

    % at end
    \filldraw[gray,fill=\Acol,opacity=0.25] (0,2.5) coordinate (Af)
    circle[radius=\rad];

    % incident B
    \filldraw[fill=green!33!white] (3,0) coordinate (B) circle[radius=\rad] node{B};
    \draw[\Bcol] (B) ++ (0,\rad) node[anchor=south]{$m$};
    \draw[\Bcol,line width=2,->] (B) ++ (-0.5,0)
    -- ++ (-1,0) node[anchor=south]{$v$};
    \draw[dashed,SlateGray,->,line width=1.5] (1.5,0) -- (\rad,0)
    arc(90:180:\rad) -- (0,-2);

    % at end
    \filldraw[gray,fill=\Bcol,opacity=0.25] (0,-2.5) coordinate (Bf) circle[radius=\rad];

    % initial momentum of A
    \draw[\Acol] (A) ++ (0,-0.5) node[draw,rounded corners,
    anchor=north,fill=\Acol!15!white] {$p'_{A} = (mc, 0, 0, 0)$};

    % initial momentum of B
    \draw[\Bcol] (B) ++ (0,0.65) node[draw,rounded corners,
    anchor=south,fill=\Bcol!15!white] {$p'_{B} =
      \frac{\qty(mc(1+\frac{v^{2}}{c^{2}}), -2mv, 0, 0)}{1-v^{2}/c^{2}}$};


    % final momentum of A
    \draw (Af) ++ (0,0.65) node[draw,rounded corners,
    anchor=south,fill=red!15!white] {$p'_{A,\final} =
      \gamma_{v}m(\Gamma c, -\Gamma v, v, 0) =
      \frac{m}{1-\frac{v^{2}}{c^{2}}} \qty( c , -v, v\sqrt{1-v^{2}/c^{2}}, 0)$};

    % final momentum of B
    \draw (Bf) ++ (0,-0.5) node[draw,rounded corners,
    anchor=north,fill=red!15!white] {$p'_{B,\final} =
      \gamma_{v}m(\Gamma c, -\Gamma v, -v, 0)
      =        \frac{m}{1-\frac{v^{2}}{c^{2}}} \qty( c , -v, -v\sqrt{1-v^{2}/c^{2}}, 0)$};


    \onslide<2->{
    \node[text width=3cm] at (-8,2) {
    Initial momentum $p'_{\rm tot, i} = p'_{A} + p'_{B}$
    $= 2mc (1, -\frac{v/c}{1-v^{2}/c^{2}}, 0 , 0) $
    };
    }

    \onslide<3>{
    \node[text width=3cm] at (-8,-2) {
    Final momentum $p'_{\rm tot, f} = p'_{A,\final} + p'_{B,\final}$
    $= 2mc (1, -\frac{v/c}{1-v^{2}/c^{2}}, 0 , 0) $
    };

    }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/lec
filename: scrap.tex
modified: 2021-06-17 03:22:24
domain: p23
source:
  \begin{tikzpicture}[scale=1, info/.style={anchor=west,text
          width=5cm,DarkGreen}]
    \def\sep{3}
    \def\dA{3}
    \def\ysep{0.25}
    \begin{scope}[shift={(0,0)}]
      \rocket[pos={(0,\ysep)}, label=A]
      \draw[vel] (0.75,\ysep) -- node[anchor=south]{$V$} ++(1,0);

      \onslide<3->{
        \begin{scope}[opacity=0.33]
          \rocket[pos={(\sep,\ysep)}, label={A2}]
          \draw[vel] (0.75+\sep,\ysep) -- node[anchor=south]{$V$} ++(1,0);
        \end{scope}
      }
      \rocket[pos={(0,-\ysep)},label=B]
      \draw[vel] (0.75,-\ysep) --  node[anchor=north]{$v$} ++(1.25,0);
      \node[anchor=west,DarkRed] at (-2,0) {$t = 0$};

      \node[info] at (8,0) {At $t = 0$ on our clocks the two ships head out
        from $x = 0$.};

    \end{scope}

    \begin{scope}[shift={(0,-1.5)}]
      \onslide<2->{
        \draw[dashed,gray!50] (0,0.8) -- ++(5,0);
        \rocket[pos={(2,\ysep)}, label=A]
        \onslide<3->{
          \begin{scope}[opacity=0.5]
            \rocket[pos={(2+\sep,\ysep)}, label={A2}]
            \draw[vel] (2.75+\sep,\ysep) -- node[anchor=south]{$V$} ++(1,0);
          \end{scope}
        }
        \draw[vel] (2.75,\ysep) -- node[anchor=south]{$V$} ++(1,0);
        \rocket[pos={(\sep+2,-\ysep)},label=B]
        \draw[vel] (\sep+2.75,-\ysep) --  node[anchor=north]{$v$} ++(1.25,0);

        \node[anchor=west,DarkRed] at (-2,0) {$t=\Delta t$};

        \dimline[start={(1.5,-0.75)}, end={(1.5+\sep,-0.75)},label={$\Delta x$},fraction=0.7];
      }

      \onslide<2>{
        \node[info] at (8,0) {At $t = \Delta t$ on our clocks, what is the distance
          $\Delta x$ that separates the two ships in our frame?};
      }

      \onslide<3>{
        \node[info] at (8,0) {What does the clock on \ship{A} read when our
          clock reads $\Delta t$?};
      }

      \onslide<4>{
        \node[info] at (8,0) {What does the clock on \ship{A2} read when our
          clock reads $\Delta t$? Why do we care about this reading?};
      }

      \onslide<5->{
        \node[info] at (8,0) {From \ship{A}'s perspective, what
          is the distance $\Delta x'$ between it and \ship{A2}?};
      }
      \onslide<6>{
      \node[info] at (8,-2) {In terms of $\Delta x'$ and $t'_{\ship{A2}}$, what is
      \ship{B}'s velocity according to \ship{A}?}
      }

    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/rec
filename: rec01slides.tex
modified: 2021-06-15 14:27:54
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \foreach \n in {1, 2, 3, 4} {
        \onslide<\n>{
          \coordinate (face) at (5+\n,0.7);
          \face
          \node[anchor=west] at (\n*2,0) {\includegraphics[width=8cm]{bus}};
        }
      }
    \onslide<5>{
      \face
      \node[anchor=west] at (8,0) {\includegraphics[width=8cm]{bus}};
      \coordinate (o) at (2,-1.25);
      \draw[DarkBlue!33!white, line width=2, ->] (o) -- node[anchor=south]{\Large$\vb{R}$} (8.2,-1.25) coordinate (bb);
      \draw[coord] (o) -- ++(0,2) node[anchor=east]{$y$};
      \draw[coord] (o) -- ++(2,0) node[anchor=north]{$x$};

      \draw[DarkRed,line width=2,->] (bb) -- node[anchor=south
        east,fill=white]{\Large$r'$} (face);
      \node[text width=5in,anchor=west,DarkGreen] at (2,-3) {We can express the position
        of the passenger with respect to the ground by first walking $\vb{R}$ to
        the back of the bus from a fixed point on the ground, and then walking
        $\vb{r'}$ from the back of the bus to
        the passenger: $\vb{r} = \vb{R} + \vb{r'}$};
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/rec
filename: rec01slides.tex
modified: 2021-06-15 14:27:54
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \draw[vector] (0,0) --node[anchor=south east]{$\vb{C}$} ++(30:3) ;
    \onslide<2-3|handout:0>{
      \draw[accel] (0,0) --node[anchor=north]{$\vb{A}$} (4,-1) coordinate
      (A);
      \draw[accel] (A) -- node[anchor=west]{$\vb{B}$} (30:3);
    }
    \onslide<2|handout:0>{
      \node at (2,-1.5){$\vb{A + B = C}$};
    }
    \onslide<3|handout:0>{
      \node at (2,-1.5){$|\vb{C}| = C \ne A + B$};
    }
    \onslide<4->{
      \draw[coord,->] (0,-0.5) -- ++(90:2.5) node[anchor=east]{$y$};
      \draw[coord,->] (-0.5,0) -- (0:3.25) node[anchor=north]{$x$};
      \draw[component] (0,0) -- node[anchor=north]{$C_{x}$} (2.598076211,0)
      coordinate (B);
      \draw[component] (B) -- node[anchor=west]{$C_{y}$} (30:3);

      \node at (2,-1.5) {$\vb{C} = C_{x}\ux + C_{y} \uy$};
    }

    \onslide<5->{
      \node[component] at (2,-2.5) {
        $C_{x} = \vb{C} \vdot \ux$};
      \node[component] at (2,-3) {
        $C_{y} = \vb{C} \vdot \uy$};
    }

    \onslide<6>{
      \node[DarkGreen,
        text width=4cm,
        anchor=north,
        rounded corners,
        draw,
        fill=yellow!15] at (2,-4)
      {Is $C_{x}$ the magnitude of the $x$ component
        of $\vb{C}$?};
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/rec
filename: rec01slides.tex
modified: 2021-06-15 14:27:54
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \xyzframe
    \def\brad{0.125}
    \onslide<2->{
      \shade[ball color=DarkRed!50] (2.5,1.5,1.5) coordinate (b) circle[radius=\brad];
    }

    \onslide<3->{
      \draw[vel,DarkRed,line width=1.5] (0,0,0) -- node[anchor=south]{$\vb{r}$} (b);
    }

    \onslide<4>{
      \shade[ball color=DarkRed!25,opacity=0.75] (3,0,1) coordinate (c) circle[radius=\brad];
      \draw[vel,DarkRed!50!white,line width=1.5] (0,0,0)
      --node[anchor=north]{$\vb{r}(t+\Delta t)$} (c);
      \draw[vector] (b) --node[anchor=south west]{$\vb{v} \Delta t$} (c);
    }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/rec
filename: rec01slides.tex
modified: 2021-06-15 14:27:54
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \sframe
    \coordinate (o) at (2,0.2,0);
    \begin{scope}[shift={(o)}]
      \pframe
      \draw[vel] (0,2,0) -- ++(0:1) node[anchor=west]{$\vb{V} = \dv{\vb{R}}{t}$};
      \onslide<2->{\draw[vector] (0,0) -- node[anchor=south]{$\vb{r}'$} (2,1) coordinate
        (p);
        \fill[DarkRed] (p) circle[radius=0.05];}
    \end{scope}
    \draw[vector] (0,0,0) -- node[anchor=north]{$\vb{R}(t)$} (o);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/exams
filename: collisions-2021.tex
modified: 2021-06-28 22:07:13
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \node at (1.5,1){\textsf{before}};
    \node at (10,1){\textsf{after}};
    \filldraw (0,0) circle[radius=.1] (5,0) circle[radius=0.1];
    \node at (0,0.5){$m$};
    \node at (5,0.5){$m$};
    \draw[vel] (0.5,0) --node[anchor=south]{$p$} ++(0:2) ;
    \draw[dashed] (6,1) -- (6,-1);
    \begin{scope}[shift={(10,0)}]
      \draw[photon,->] (-.2,0) --node[anchor=south,shift={(0,0.05)}]{$E_{1}$} ++(180:1.5);
      \draw[photon,->] (.2,0) --node[anchor=south,shift={(0,0.05)}]{$E_{2}$} ++(0:2);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/exams
filename: p23-2021-story-v1.tex
modified: 2021-06-19 19:12:24
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    % Earth
    \node at (0,0.3) {\includegraphics[width=1cm]{earth}};
    %  \filldraw[fill=blue!20!white,draw=Brown,line width=2] (0,0.3) circle[radius=0.4] node{E};
    \draw[<->] (0,-0.5) -- node[fill=white]{$d$} ++(0:12);
    \begin{scope}[shift={(-0.5,-1.6)}]
      % Ship C
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(0:1)
      -- ++(0.2,-0.2) -- ++(-0.2,-0.2) --++(180:1) -- cycle;
      \node at (0.5,0){\sCC};
      \draw[vel] (1.3,0) -- ++(0:0.65) node[anchor=south]{$v_{2} = \vC$};
    \end{scope}

    \begin{scope}[shift={(0.5,-1)}]
      % Ship A
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(180:1)
      -- ++(-0.2,-0.2) -- ++(0.2,-0.2) --++(0:1) -- cycle;
      \node at (-0.5,0){\sAA};
      \draw[vel] (-1.3,0) -- ++(180:0.65) node[anchor=south]{$v_{1} = \vA$};
    \end{scope}

    \begin{scope}[shift={(12.5,-1)}]
      % Ship B
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(180:1)
      -- ++(-0.2,-0.2) -- ++(0.2,-0.2) --++(0:1) -- cycle;
      \node at (-0.5,0){\sBB};
      \draw[vel] (-1.3,0) -- ++(180:0.65) node[anchor=south]{$v_{1} =\vA$};
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/exams
filename: p23-2021-final-v1.tex
modified: 2021-07-01 02:39:27
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!10!white] (0,0) -- ++(90:0.3*\rocketlength)
    --++(0:\rocketlength)
    -- ++(0.3*\rocketlength,-0.3*\rocketlength)
    -- ++(-0.3*\rocketlength,-0.3*\rocketlength)
    --++(180:\rocketlength) -- cycle;
    \draw[color=DarkGreen,->,line width=1.25pt] (0,0)
    ++(1.4*\rocketlength,0) node[anchor=south west]{$\displaystyle
        \frac{3}{5} c$} -- ++(0:0.6*\rocketlength);
    \begin{scope}[shift={(0.3*\rocketlength,0)}]
      \filldraw[fill=white] (0,0) circle[radius=0.2*\rocketlength];
      \draw[->] (0,0) -- ++(90:0.2*\rocketlength);
      \node at (0.5*\rocketlength,0){A};
    \end{scope}

    \draw[<->] (1,-1) --node[fill=white]{$d = 80\; c$ s} (14,-1);

    \begin{scope}[shift={(15,0)}]
      \filldraw[fill=gray!10!white]
      (0,0) -- ++(90:0.3*\rocketlength)
      --++(180:\rocketlength)
      -- ++(-0.3*\rocketlength,-0.3*\rocketlength)
      -- ++(0.3*\rocketlength,-0.3*\rocketlength)
      --++(0:\rocketlength) -- cycle;
      \draw[color=DarkGreen,->,line width=1.25pt] (0,0)
      ++(-1.4*\rocketlength,0) node[anchor=south east]{$\displaystyle
          \frac{3}{5} c$} -- ++(180:0.6*\rocketlength);

      \begin{scope}[shift={(-0.3*\rocketlength,0)}]
        \filldraw[fill=white] (0,0) circle[radius=0.2*\rocketlength];
        \draw[->] (0,0) -- ++(90:0.2*\rocketlength);
        \node at (-0.5*\rocketlength,0){B};
      \end{scope}

    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/exams
filename: p23-2021-final-v1.tex
modified: 2021-07-01 02:39:27
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) .. controls (0.5,0) and (2,0.15) .. (\ww,0.25) -- ++ (0,\hh)
    .. controls (2,0.15+\hh) and (0.5,\hh) .. (0,\hh) -- cycle;
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/exams
filename: p23-2021-final-v1.tex
modified: 2021-07-01 02:39:27
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) .. controls (0.5,0) and (2,-0.15) .. (\ww,-0.25) -- ++ (0,\hh)
    .. controls (2,-0.15+\hh) and (0.5,\hh) .. (0,\hh) -- cycle;
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2021/exams
filename: p23-2021-final-v1.tex
modified: 2021-07-01 02:39:27
domain: p23
source:
  \begin{tikzpicture}[scale=0.75,line width=1.5pt]
    \draw (0,2) circle[radius=0.8];
    \draw[->] (0,2) -- ++(90:0.7);
    \draw[->] (1.25,2) --node[anchor=south]{$\myfrac{4}{5} c$} ++(0:2);
    \draw (0,0) circle[radius=0.8];
    \draw[->] (0,0) -- ++(90:0.7);
    \node at (-1.25,0){A};
    \node at (-1.25,2){C};
    \draw (15,0) circle[radius=0.8];
    \draw[->] (15,0) -- ++(90:0.7);
    \node at (16.25,0){B};
    \draw[<->] (0,-1.25) -- node[fill=white] {$20\; c\;\mathrm{min}$} ++(0:15);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2020/First Half
filename: LT.tex
modified: 2020-09-15 21:38:42
domain: p23
source:
  \begin{tikzpicture}[scale=#1]
    \begin{scope}[shift={(-4,-2)}, rotate=0]
      \SFrame[4]
    \end{scope}
    \begin{scope}[shift={(-3.5,-1.98)}, rotate=0]
      \SPFrame[4]
      \draw[vel] (0,0.5) --node[anchor=south]{$V$} ++(0:1);
    \end{scope}

    \filldraw[SlateGray,fill=gray!10] (1.25,0.25) rectangle (9,2.75);
    \node[anchor=west,font=\scriptsize\sffamily] at (1.4,2.45)
    {Lorentz Transformation};
    \node[] at (7,2.35) {$\gamma = \frac{1}{\srF} $};

    \filldraw[DarkGreen,fill=green!10] (1.25,-3) rectangle (9,0);
    \node[anchor=west,font=\scriptsize\sffamily] at (1.4,-0.25)
    {Lorentz Velocity Transformation};

    \def\x{3}
    \node at (\x,1.5) {$  t' = \gamma\qty(t - x V/c^{2})$};
    \node at (\x,1) {$x' = \gamma(x - V t)$};
    \node at (\x,0.5) {$y' = y$};

    \node at (\x,-1) {$\displaystyle v'_{x} = \frac{v_{x}-V}{1 -
        \frac{v_{x}V}{c^{2}}} $};
    \node at (\x, -2.25) {$\displaystyle v'_{y} = \frac{ v_{y}\srF}{1 -
        \frac{v_{x}V}{c^{2}}}$};

    \def\x{7}
    \node at (\x,1.5) {$t = \gamma\qty(t' + x' V/c^{2})$};
    \node at (\x,1) {$x = \gamma(x' + V t')$};

    \node at (\x,0.5) {$z = z'$};
    \node at (\x,-1) {$\displaystyle v_{x} = \frac{v'_{x}+V}{1 +
      \frac{v'_{x}V}{c^{2}}} $};
    \node at (\x, -2.25) {$\displaystyle v_{y} = \frac{ v'_{y}\srF}{1 +
      \frac{v'_{x}V}{c^{2}}}$};

    %    \node at (8,1) {Lorentz transformation};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2020/First Half/lec
filename: lec02.tex
modified: 2020-09-03 20:12:00
domain: p23
source:
  \begin{tikzpicture}[scale=0.7]
    \def\wid{2.cm}
    \node[anchor=south] at (0,0)  {\includegraphics[width=\wid]{connolly}};
    \node[anchor=north] at (0,0) {Liz Connolly};
    \node[anchor=south] at (3,0) {\includegraphics[width=\wid]{saeta}};
    \node[anchor=north] at (3,0) {Peter Saeta};
    \node[anchor=south] at (6,0) {\includegraphics[width=\wid]{shuve}};
    \node[anchor=north] at (6,0) {Brian Shuve};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2020/First Half/lec
filename: lec01.tex
modified: 2020-08-25 03:22:47
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \node[anchor=south] at (0,0)  {\includegraphics[width=2.5cm]{connolly}};
    \node[anchor=north] at (0,0) {Liz Connolly};
    \node[anchor=south] at (3,0) {\includegraphics[width=2.5cm]{saeta}};
    \node[anchor=north] at (3,0) {Peter Saeta};
    \node[anchor=south] at (6,0) {\includegraphics[width=2.5cm]{shuve}};
    \node[anchor=north] at (6,0) {Brian Shuve};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2020/First Half/lec
filename: lec01.tex
modified: 2020-08-25 03:22:47
domain: p23
source:
  \begin{tikzpicture}[scale=0.65]
    \draw[vel,line width=1] (0,0) --node[anchor=east]{$c$} (6,6) coordinate (A);
    \draw[vel,line width=1] (0,0) --node[anchor=north]{$V$} (6,0) coordinate (B);
    \draw[vel,line width=1] (B) -- node[anchor=west]{$\srF$} (A);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2020/First Half/lec
filename: lec04.tex
modified: 2020-09-17 20:12:21
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \def\rad{0.3}
    \filldraw[fill=\Acol!33!white] (-3,0) coordinate (A) circle[radius=\rad] node{A};
    \draw[\Acol,line width=2,->] (A) ++ (0.5,0) -- ++(1,0)
    node[anchor=south]{$v$};
    \draw[\Acol] (A) ++ (0,\rad) node[anchor=south]{$m$};
    \draw[dashed,SlateGray,->,line width=1.5] (-1.5,0) -- (-\rad,0) arc(270:360:\rad) -- (0,2);
    \filldraw[fill=\Acol,opacity=0.33] (0,2.5) circle[radius=\rad];
    \filldraw[fill=green!33!white] (3,0) coordinate (B) circle[radius=\rad] node{B};
    \draw[\Bcol] (B) ++ (0,\rad) node[anchor=south]{$m$};
    \draw[\Bcol,line width=2,->] (B) ++ (-0.5,0)
    -- ++ (-1,0) node[anchor=south]{$v$};
    \draw[dashed,SlateGray,->,line width=1.5] (1.5,0) -- (\rad,0) arc(90:180:\rad) -- (0,-2);
    \filldraw[fill=\Bcol,opacity=0.33] (0,-2.5) circle[radius=\rad];

    \onslide<2->{
      \begin{scope}[shift={(-3.5,-0.5)},opacity=0.5]
        \SFrame[2]
      \end{scope}
      \begin{scope}[shift={(-3,-0.4)}, opacity=0.5]
        \SPFrame[2]
        \draw[->,SlateGray] (0,1.25) -- node[anchor=south]{$V$} ++(1,0);
      \end{scope}
    }

    \onslide<3>{
      \node[message,text width=3.5cm] at (-4,-2)
      {If we use $\VEC{p} = m \VEC{v}$, it is \textbf{not conserved}, but if we
        use $\VEC{p} = \gamma_{v} m \VEC{v}$, it is!};
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2020/First Half/rec
filename: rec02slides.tex
modified: 2020-08-25 00:52:46
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \refframe{z}{x}{y}
    \coordinate (o) at (2,0,0);
    \begin{scope}[shift={(o)}]
      \refframe{z'}{x'}{y'}
      \draw[vel] (0,2,0) -- ++(0:1) node[anchor=west]{$\vb{V} = \dv{\vb{R}}{t}$};
      \onslide<2->{\draw[vector] (0,0) -- node[anchor=south]{$\vb{r}'$} (2,1) coordinate
        (p);
        \fill[DarkRed] (p) circle[radius=0.05];}
    \end{scope}
    \draw[vector] (0,0,0) -- node[anchor=north]{$\vb{R}(t)$} (o);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2020/First Half/rec
filename: rec02slides.tex
modified: 2020-08-25 00:52:46
domain: p23
source:
  \begin{tikzpicture}[scale=0.9]
    \fill[fill=blue!10!white] (-2,0) rectangle (5,3);
    \draw[dashed, color=gray] (0,3) -- (0,0.2) -- (3,0.2);
    \draw[<->,color=DarkGreen] (-1.5,0) --node[anchor=east]{$D$} ++(90:3);
    \draw[<->,color=DarkGreen]  (0,-0.3) -- node[anchor=north]{$D$} ++(0:3);
    \draw[vel] (1.5,1.5) -- ++ (0:1) node[anchor=south]{$V_{0}$};
    \draw[vel] (0,0.2)--++(0:1) node[anchor=south]{$A$};
    \draw[vel] (0,0.2)--++(90:1) node[anchor=east]{$B$};
    \fill[fill=DarkRed] (0,-0.1) circle[radius=0.08] (0,3.1) circle[radius=0.08]
    (3.1,-0.1) circle[radius=0.08];

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2020/First Half/rec
filename: rec01slides.tex
modified: 2020-08-23 16:40:34
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    \foreach \n in {1, 2, 3, 4} {
        \onslide<\n>{
          \filldraw[DarkRed,line width=1.25,fill=Gold] (5+\n,0.7) circle[radius=0.2];
          \node[anchor=west] at (\n*2,0) {\includegraphics[width=8cm]{bus}};
        }
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p23/2020/First Half/exams
filename: p23-2020-story-v2.tex
modified: 2020-09-08 18:37:48
domain: p23
source:
  \begin{tikzpicture}[scale=1]
    % Earth
    \node at (0,0.3) {\includegraphics[width=1cm]{earth}};
    %  \filldraw[fill=blue!20!white,draw=Brown,line width=2] (0,0.3) circle[radius=0.4]
    node{E};
    \draw[<->] (0,-0.5) -- node[fill=white]{$d$} ++(0:12);
    \begin{scope}[shift={(-0.5,-1.6)}]
      % Ship C
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(0:1)
      -- ++(0.2,-0.2) -- ++(-0.2,-0.2) --++(180:1) -- cycle;
      \node at (0.5,0){\sCC};
      \draw[vel] (1.3,0) -- ++(0:0.65) node[anchor=south]{$v_{2} = \vC$};
    \end{scope}

    \begin{scope}[shift={(0.5,-1)}]
      % Ship A
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(180:1)
      -- ++(-0.2,-0.2) -- ++(0.2,-0.2) --++(0:1) -- cycle;
      \node at (-0.5,0){\sAA};
      \draw[vel] (-1.3,0) -- ++(180:0.65) node[anchor=south]{$v_{1} = \vA$};
    \end{scope}

    \begin{scope}[shift={(12.5,-1)}]
      % Ship B
      \filldraw[fill=gray!20!white] (0,0) -- ++(90:0.2) --++(180:1)
      -- ++(-0.2,-0.2) -- ++(0.2,-0.2) --++(0:1) -- cycle;
      \node at (-0.5,0){\sBB};
      \draw[vel] (-1.3,0) -- ++(180:0.65) node[anchor=south]{$v_{1} =\vA$};
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p161/pns/prob
filename: OhWell.tex
modified: 2019-10-02 15:49:30
domain: p161
source:
  \begin{tikzpicture}[scale=1]
    \draw[->] (0,-4) -- (0,2) node[anchor=east]{$V$};
    \draw[->] (0,0) -- (6,0) node[anchor=north]{$r$};
    \draw (2,0.1) -- (2,-0.1) node[anchor=north west]{$a$};
    \draw (4,0.1) -- (4,-0.1) node[anchor=north west]{$2a$};
    \draw[DarkRed,line width=2] (0,-3) -- (2,-3) -- (2, 1) -- (4,1) --
    (4,0)--(5,0);
    \node[anchor=east] at (0,0) {$0$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p161/pns/prob
filename: DeltaTrouble.tex
modified: 2018-10-03 17:36:21
domain: p161
source:
  \begin{tikzpicture}[scale=1]
    \draw[->] (0,-3) -- (0,3) node[anchor=east]{$V$};
    \draw[->] (0,0) -- (6,0) node[anchor=north]{$r$};
    \draw (4.5,0.1) -- (4.5,-0.1) node[anchor=north west]{$a$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p161/pns/sol
filename: DeltaTrouble.tex
modified: 2018-10-17 20:37:13
domain: p161
source:
  \begin{tikzpicture}[scale=1]
    \draw[->] (0,-3) -- (0,3) node[anchor=east]{$V$};
    \draw[->] (0,0) -- (6,0) node[anchor=north]{$r$};
    \draw (4.5,0.1) -- (4.5,-0.1) node[anchor=north west]{$a$};

    \begin{scope}[
        color=DarkRed,
        line width=2]
      \draw (0,-2) node[anchor=east]{$-\frac{\hb^{2}Q^{2}}{2\mu} $}-- (4.5, -2) -- (4.5,0) -- (5.5,0);
      \draw[line width=1,->] (4.5,0) -- ++(90:2.5) node[anchor=west]{$\gamma \delta(r-a)$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p161/pns/sol
filename: DeltaTrouble.tex
modified: 2018-10-17 20:37:13
domain: p161
source:
  \begin{tikzpicture}
    \begin{axis}[
        xmin=0,
        xmax=5,
        ymin=-2,
        ymax=6,
        enlargelimits=false,
        width=2.5in, height=2in,
        xlabel={$x = Qa$},
        ylabel={},
        xtick={0,pi/2,pi,1.5*pi},
        xticklabels={0, $\frac{\pi}{2}$, $\pi$, $\frac{3\pi}{2}$},
        %ytick={0,1}, xtick={0,1},
        % xticklabel=\empty, xticklabels{0,,$a$,,a$},
        % axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkGreen, domain=0:1.5, samples=30, line width=2pt,] {tan(x
        * 180/pi)};
      \addplot[DarkGreen, domain=1.7:4.7, samples=30, line width=2pt,] {tan(x * 180/pi)};
      \addplot[DarkRed, domain=0:5, samples=2,line width=2pt]{x};
      \node[anchor=south east,DarkRed] at (3,3) {$x$};
      \node[anchor=west,DarkGreen] at (1.5,5) {$\tan x$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p161/pns/sol
filename: DeltaTrouble.tex
modified: 2018-10-17 20:37:13
domain: p161
source:
  \begin{tikzpicture}
    \begin{axis}[
        xmin=0,
        xmax=2,
        ymin=-2.5,
        ymax=2.5,
        enlargelimits=false,
        width=2.5in, height=2in,
        xlabel={$r$},
        ylabel={},
        yticklabels={},
        xtick={0,1,2},
        xticklabels={0, $a$,$2a$},
        %ytick={0,1}, xtick={0,1},
        % xticklabel=\empty, xticklabels{0,,$a$,,a$},
        % axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \draw[dashed] (0,0) -- (2,0);
      \draw[dashed] (1,0) -- (1,2.5);
      \addplot[line width=2,DarkBlue,opacity=0.5] {2*sin(10*x)};
      \addplot[line width=2,DarkBlue,opacity=1,dashed,domain=1:2,samples=30]
      {2*cos(10*(x-1))};
      \draw[line width=2,DarkRed] (0,-2) -- (1,-2) -- (1,0) -- (2,0);
      \addplot[DarkGreen, domain=0:1, samples=30, line width=2pt,]
      {2*sin(x * 90)};
    \end{axis}
    \begin{scope}[shift={(2.1in,0.75in)}, line width=2]
      \draw[color=DarkGreen] (0,0.6) --++(0:1) node[anchor=west]{$u(r)$ in
        the well};
      \draw[color=DarkBlue,dashed] (0,0.2) -- ++ (0:1) node[anchor=west]{$u(r)$
        outside the well};
      \draw[color=DarkBlue,opacity=0.5] (0,-0.2) -- ++ (0:1) node[anchor=west]{$u(r)$
        with no well};
      \draw[color=DarkRed] (0,-0.6) -- ++(0:1) node[anchor=west]{$V(r)$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p51/2014
filename: test.tex
modified: 2014-10-06 03:13:57
domain: p51
source:
  \begin{tikzpicture}[scale=1,line width=1.25]
    \draw[decorate,
      decoration={zigzag,
          segment length=3mm,
          amplitude=2mm}] (-0.75,0) -- (0.75,0);
    \draw (0.75,0) -- (1.5,0) -- (1.5,0.75);
    \draw[line width=1.5] (1.2,0.75) -- (1.8,0.75);
    \draw[line width=1.5] (1.2,0.9) -- (1.8,0.9);
    \draw (1.5,0.9) -- (1.5,1.5) -- (0.1,1.5)
    (-0.1,1.5) -- (-1.5,1.5) -- (-1.5,0) -- (-0.75,0);
    \draw[line width=1.5] (-0.1,1.3) -- (-0.1,1.7);
    \draw (0.1,1.1) -- (0.1,1.9);
    \node at (0,2.2){$\mathscr{E}$};
    \node at (0.3, 1.8) {\small{+}};
    \node at (2,0.75){$C$};
    \node at (0,0.5){$R$};
    \draw[line width=0.75] (-1.25,0.5) -- (-1.25,0.75) arc(180:90:0.5);
    \draw[->,line width=0.75] (-0.75,1.25) -- ++(0:0.25);
    \node at (-0.5,1){$i$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p51/2014/exams
filename: mt1-2014-v2.tex
modified: 2014-09-26 20:59:03
domain: p51
source:
  \begin{tikzpicture}[scale=1.5]
    \draw[dashed] (-45:2) -- (0,0) -- (45:2);
    \draw[line width=3,color=gray] (-45:2) arc(-45:45:2) ;
    \draw (-45:0.5) arc (-45:45:0.5);
    \node at (15:0.7){$\theta_{0}$};
    \node at (30:2.3) {$\lambda$};
    \fill (0,0) circle (0.05) node[anchor=east]{P};
    \draw[->] (0,0) -- (2.5,0) node[anchor=north]{$x$};
    \draw[->] (0,0) -- (0,1.5) node[anchor=east]{$y$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p51/2014/exams
filename: mt1-2014-v2.tex
modified: 2014-09-26 20:59:03
domain: p51
source:
  \begin{tikzpicture}[scale=1]
    \shade[shading=axis,
      top color=gray,
      bottom color=gray,
      middle color=white] (-5,-2) rectangle (5,2) ;
    \draw[dashed] (-5,0) -- (5,0);
    \draw[->] (0,0) -- node[anchor=west]{$x$} (0,1);
    \draw[<->] (-6,-2) -- node[anchor=east]{$d$} (-6,2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p51/2014/exams
filename: mt1-2014-v2.tex
modified: 2014-09-26 20:59:03
domain: p51
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!60!white] (0,0) circle(2);
    \filldraw[fill=white] (0,0) circle(1.8);
    \filldraw[fill=gray!50!white] (0,0) circle(0.75);
    \draw[->] (0,0) -- node[anchor=east]{$a$} (45:0.75);
    \draw[->] (0,0) -- node[anchor=north]{$b$} (-45:1.75);
    \node at (225:0.375) {$\scriptsize +Q$};
    %\draw[<-] (135:0.75) -- ++(135:0.4) node[anchor=south]{$+q$};
    \node at (135:1.2) {$\scriptsize -Q$};
    \draw[<-] (135:1.8) -- +(-45:0.5);
    \draw[->] (0,0) -- (15:2) node[anchor=west]{$c$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p51/2014/exams
filename: mt1-2014-v1.tex
modified: 2014-09-16 21:51:09
domain: p51
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!60!white] (0,0) circle(2);
    \filldraw[fill=white] (0,0) circle(1.75);
    \filldraw[fill=gray!50!white] (0,0) circle(0.75);
    \draw[->] (0,0) -- node[anchor=east]{$a$} (45:0.75);
    \draw[->] (0,0) -- node[anchor=north]{$b$} (-45:1.75);
    \node at (225:0.375) {$\scriptsize +q$};
    %\draw[<-] (135:0.75) -- ++(135:0.4) node[anchor=south]{$+q$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p51/p51_prob_src/prob/hrk/ch30
filename: 30E37.tex
modified: 2014-09-23 14:30:25
domain: p51
source:
  \begin{tikzpicture}[scale=1,>=Stealth]
    \filldraw[fill=red!10!white, draw=red!50!white] (-2,-0.25) rectangle (2,0.25);
    \node at (0,0) {\textsf{Copper}};
    \draw (-2.75,0.25) -- (-2.1,0.25) (-2.75,-0.25) -- (-2.1,-0.25);
    \node at (-2.6,0) {$b$};
    \draw[<-] (-2.6,0.25) -- +(90:0.5);
    \draw[<-] (-2.6,-0.25) -- +(-90:0.5);
    \draw[line width=1.2] (-1.75,-0.5) -- (1.75,-0.5) (-1.75,0.5) -- (1.75,0.5);
    \node at (0.4,0.75){$A$};
    \draw (0,0.5) -- +(90:0.5) (0,-0.5) -- +(-90:0.5);
    \draw (1.85,0.5) -- +(0:0.75) (1.85,-0.5) -- +(0:0.75);
    \draw[<->] (2.5,-0.5) -- node[fill=white]{$d$} (2.5,0.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p51/p51_prob_src/prob/hrk/ch28
filename: 28E02.tex
modified: 2014-09-13 02:22:21
domain: p51
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) rectangle (2,2);
    \shade[ball color=gray] (0,0) circle(0.2) node[anchor=north]{$-q$};
    \shade[ball color=gray] (2,0) circle(0.2) node[anchor=north]{$+q$};
    \shade[ball color=gray] (0,2) circle(0.2) node[anchor=south]{$-q$};
    \shade[ball color=gray] (2,2) circle(0.2) node[anchor=south]{$+q$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p51/p51_prob_src/prob/hrk/ch28
filename: 28P12.tex
modified: 2014-09-18 16:03:48
domain: p51
source:
  \begin{tikzpicture}[scale=1,>=Stealth]
    \filldraw (0,0) circle (0.05) node[anchor=west] {$P$};
    \draw[dashed] (0,0) -- (-1.25,0)
    (0,-2) -- ++(180:1.25)
    (0,-5) -- ++(180:1.25);
    \draw[<->] (-1,0) -- node[fill=white]{$y$} (-1,-2);
    \draw[<->] (-1,-2) -- node[fill=white]{$L$} (-1,-5);
    \filldraw[fill=red!20!white,draw=red!50!white] (-0.05,-2) rectangle
    (0.05,-5);
    \node at (0.3,-3.5){$\lambda$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Old Courses/p22
filename: circuits.tex
modified: 2015-04-10 05:20:36
domain: p22
source:
  \begin{tikzpicture}[scale=1,
      line width=1.5,
      circuit ee IEC,
      set resistor graphic = var resistor IEC graphic]
    \draw (0,0) to [resistor] (0,2) ;
    \node at (0.35, 1){$R$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Old Courses/p22
filename: circuits.tex
modified: 2015-04-10 05:20:36
domain: p22
source:
  \begin{tikzpicture}[scale=1,
      line width=1.5,
      circuit ee IEC  ]
    \draw (0,0) to [capacitor] (0,2) ;
    \node at (0.35,1.35) {$C$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Old Courses/p22
filename: circuits.tex
modified: 2015-04-10 05:20:36
domain: p22
source:
  \begin{tikzpicture}[scale=1,
      line width=1.5,
      circuit ee IEC]
    \draw (0,0) to [inductor] (0,2) ;
    \node at (0.35, 1) {$L$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p50
filename: SolarCells.tex
modified: 2018-07-28 20:04:47
domain: p50
source:
  \begin{tikzpicture}[scale=1.25,
      every info/.style={font=\footnotesize}
    ]
    \def\dy{2}
    \def\dx{2}
    \draw (0,0) -- (0,\dy) -- (\dx,\dy) -- node[circle, draw, fill=white]{$A$}
    (\dx,0) -- cycle;
    \begin{scope}[shift={(-0.4,0.4)}]
      \filldraw[fill=gray!20] (0,0) rectangle (0.8,1.2);
      \foreach \x in {0.1,0.3,0.5} {
          \foreach \y in {0.1,0.2,...,1} {
              \fill[fill=gray!50] (\x+0.02,\y) rectangle (\x+0.18,\y+0.08);
            }
        }
    \end{scope}
    \foreach \y in {0,\dy} {
        \filldraw (0,\y) circle[radius=0.05];
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p50
filename: SolarCells.tex
modified: 2018-07-28 20:04:47
domain: p50
source:
  \begin{tikzpicture}[scale=1.25,
      every info/.style={font=\footnotesize}
    ]
    \def\dy{2}
    \def\dx{2}
    \draw (0,0) -- (0,\dy) -- (\dx,\dy) -- node[circle, draw, fill=white]{$V$}
    (\dx,0) -- cycle;
    \begin{scope}[shift={(-0.4,0.4)}]
      \filldraw[fill=gray!20] (0,0) rectangle (0.8,1.2);
      \foreach \x in {0.1,0.3,0.5} {
          \foreach \y in {0.1,0.2,...,1} {
              \fill[fill=gray!50] (\x+0.02,\y) rectangle (\x+0.18,\y+0.08);
            }
        }
    \end{scope}
    \foreach \y in {0,\dy} {
        \filldraw (0,\y) circle[radius=0.05];
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p50
filename: SolarCells.tex
modified: 2018-07-28 20:04:47
domain: p50
source:
  \begin{tikzpicture}[
      every info/.style={font=\footnotesize},
      decoration={zigzag,amplitude=0.15cm,segment length=0.4cm}
    ]
    \def\dy{2.5}
    \def\dx{2}
    % Outline
    \draw (0,0) -- (0,\dy) -- (2*\dx,\dy) --
    node[circle, draw, fill=white]{$V$} (2*\dx,0)
    -- (\dx,0) -- node[circle, draw, fill=white]{$A$} -- cycle;
    \draw (\dx,0) -- (\dx,0.25*\dy);
    \draw (\dx,0.75*\dy) -- (\dx,\dy);
    \draw[decorate] (\dx,0.25*\dy) -- (\dx,0.75*\dy); % the resistor
    \draw[->,line width=1.25] (\dx-0.35,\dy*0.5-0.35) -- (\dx+0.35,\dy*0.5+0.35)
    node[anchor=north west] {$R$};

    \begin{scope}[shift={(-0.4,0.6)}]
      \filldraw[fill=gray!20] (0,0) rectangle (0.8,1.2);
      \foreach \x in {0.1,0.3,0.5} {
          \foreach \y in {0.1,0.2,...,1} {
              \fill[fill=gray!50] (\x+0.02,\y) rectangle (\x+0.18,\y+0.08);
            }
        }
    \end{scope}
    \foreach \x/\y in {0/0,\dx/0,\dx/\dy} {
        \filldraw (\x,\y) circle[radius=0.05];
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p50
filename: SolarCells.tex
modified: 2018-07-28 20:04:47
domain: p50
source:
  \begin{tikzpicture}[
      every info/.style={font=\footnotesize}
    ]
    \def\dy{2}
    \def\dx{2}
    \draw (0,0) -- node[circle, draw, fill=white]{$A$}  (\dx,0)
    -- (2*\dx,0) -- node[circle,draw,fill=white]{$V$}  (2*\dx,\dy)
    -- (0,\dy) -- node[circle,draw,fill=white]{} -- cycle;
    \node at (-0.2,0.5*\dy+0.3){+};
    \node at (-0.4,0.5*\dy){$V$};
    \draw (\dx,0) -- (\dx,\dy);
    \draw[line width=1.25,->] (-0.25,0.5*\dy-0.25) -- ++(45:0.8);
    \begin{scope}[shift={(\dx-0.4,0.4)}]
      \filldraw[fill=gray!20] (0,0) rectangle (0.8,1.2);
      \foreach \x in {0.1,0.3,0.5} {
          \foreach \y in {0.1,0.2,...,1} {
              \fill[fill=gray!50] (\x+0.02,\y) rectangle (\x+0.18,\y+0.08);
            }
        }
      \fill[fill=gray,opacity=0.6] (-0.3,-0.3) rectangle (1.2,1.7);
    \end{scope}
    \foreach \y in {0,\dy} {
        \filldraw (\dx,\y) circle[radius=0.05];
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p50
filename: SolarCells.tex
modified: 2018-07-28 20:04:47
domain: p50
source:
  \begin{tikzpicture}[
      circuit ee IEC,
      x=3cm,
      y=2cm,
      semithick,
      every info/.style={font=\footnotesize},
      small circuit symbols,
      set resistor graphic=var resistor IEC graphic
    ]

    \foreach \contact/\y in {1/1,2/2,3/3.5} {
        \node [contact] (left contact \contact) at (0,\y) {};
        \node [contact] (right contact \contact) at (1,\y) {}; }
    \draw (right contact 1) -- (right contact 2) -- (right contact 3);
    \draw (left contact 1) to [diode] ++(down:1)
    to [voltage source={near start, direction info={volt={3\,}}},
      resistor={near end,ohm={3\,}}] ++(right:1)
    to (right contact 1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p50
filename: SolarCells.tex
modified: 2018-07-28 20:04:47
domain: p50
source:
  \begin{tikzpicture}[
      every info/.style={font=\footnotesize}
    ]
    \def\dy{2}
    \def\dx{2}
    \draw (0,0) -- (0,\dy) -- (\dx,\dy) -- node[circle, draw, fill=white]{$A$}
    (\dx,0) -- cycle;
    \begin{scope}[shift={(-0.4,0.4)}]
      \filldraw[fill=gray!20] (0,0) rectangle (0.8,1.2);
      \foreach \x in {0.1,0.3,0.5} {
          \foreach \y in {0.1,0.2,...,1} {
              \fill[fill=gray!50] (\x+0.02,\y) rectangle (\x+0.18,\y+0.08);
            }
        }
    \end{scope}
    \foreach \y in {0,\dy} {
        \filldraw (0,\y) circle[radius=0.05];
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p50
filename: SolarCells.tex
modified: 2018-07-28 20:04:47
domain: p50
source:
  \begin{tikzpicture}[
      every info/.style={font=\footnotesize},
      decoration={zigzag,amplitude=0.15cm,segment length=0.4cm}
    ]
    \def\dy{2}
    \def\dx{2}
    % Outline
    \draw (0,0) -- (0,\dy) -- (2*\dx,\dy) --
    node[circle, draw, fill=white]{$V$} (2*\dx,0)
    -- (\dx,0) -- node[circle, draw, fill=white]{$A$} -- cycle;
    \draw (\dx,0) -- (\dx,0.25*\dy);
    \draw (\dx,0.75*\dy) -- (\dx,\dy);
    \draw[decorate] (\dx,0.25*\dy) -- (\dx,0.75*\dy); % the resistor
    \draw[->,line width=1.25] (\dx-0.25,\dy*0.5-0.25) -- (\dx+0.25,\dy*0.5+0.25)
    node[anchor=north west] {$R$};
    \begin{scope}[shift={(-0.4,0.4)}]
      \filldraw[fill=gray!20] (0,0) rectangle (0.8,1.2);
      \foreach \x in {0.1,0.3,0.5} {
          \foreach \y in {0.1,0.2,...,1} {
              \fill[fill=gray!50] (\x+0.02,\y) rectangle (\x+0.18,\y+0.08);
            }
        }
    \end{scope}
    \foreach \x/\y in {0/0,\dx/0,\dx/\dy} {
        \filldraw (\x,\y) circle[radius=0.05];
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/MSECS/2021
filename: SolidState.tex
modified: 2021-09-13 21:57:24
domain: MSECS
source:
  \begin{tikzpicture}[scale=1,
      german/.style={DarkGreen,font={\large\itshape}},
    ]

    \draw (11,4.5) node[anchor=west] {\includegraphics[width=2cm]{Pauli}}
    node[anchor=east,german] {Noch einmal!};

    \onslide<2->{
      \draw (0,0) node[anchor=south] {\includegraphics[width=2cm]{god}}
      node[anchor=north,german] {Gott schuf};
    }

    \onslide<3->{
      \draw (3,0) node[anchor=south] {\includegraphics[width=3.5cm]{xtal}}
      node[anchor=north,german] {das Volumen,};
    }

    \onslide<4->{
      \draw (6,0) node[anchor=south] {\includegraphics[width=2cm]{devil}}
      node[anchor=north,german] {der Teufel};
    }

    \onslide<5->{
    \draw (10.5,0) node[anchor=south] {\includegraphics[width=6cm]{surface}};
    \draw (10.5,0) node[german,anchor=north] {die Oberfl\"{a}che!};
    }

    \onslide<6>{
      \draw (3, 4.5) node[anchor=west,font=\Huge\itshape,DarkRed]{Warum?};
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/MSECS/2021
filename: SolidState.tex
modified: 2021-09-13 21:57:24
domain: MSECS
source:
  \begin{tikzpicture}[scale=1]
    \def\scl{2.5}
    \draw[DarkGreen,->] (-\scl,0) -- (\scl,0) node[anchor=north]{$k$};
    \draw[DarkGreen,->] (0,0) -- (0,\scl) node[anchor=east]{$E$};
    \draw[DarkRed,line width=1.5] (0,0) parabola (\scl,\scl) (0,0) parabola (-\scl,\scl);
    \node[anchor=east,DarkRed] at (\scl,\scl) {$E = \frac{\hb^{2}k^{2}}{2m}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/MSECS/2021
filename: SolidState.tex
modified: 2021-09-13 21:57:24
domain: MSECS
source:
  \begin{tikzpicture}[scale=3,
      Ga/.style={ball color=blue, opacity=0.5},
      As/.style={ball color=red=opacity=0.5},
      edges/.style={DarkGreen,opacity=0.5},
      bond/.style={black,line width=1,opacity=0.5},
      z={-0.2cm},
    ]
    \def\radius{0.05}

    \draw[edges] (0, 0, 0)
    -- (1, 0, 0)
    -- (1, 1, 0)
    -- (0, 1, 0)
    -- (0, 0, 0)
    -- (0, 0, 1)
    -- (1, 0, 1)
    -- (1, 0, 0)
    -- (1, 0, 1)
    -- (1, 1, 1)
    -- (1, 1, 0)
    -- (1, 1, 1)
    -- (0, 1, 1)
    -- (0, 1, 0)
    -- (0, 1, 1)
    -- (0, 0, 1)
    ;
    \bond{(0.0, 0.0, 0.0)}{(0.25, 0.25, 0.25)}
    \bond{(0.0, 0.5, 0.5)}{(0.25, 0.25, 0.25)}
    \bond{(0.0, 0.5, 0.5)}{(0.25, 0.75, 0.75)}
    \bond{(0.0, 1.0, 1.0)}{(0.25, 0.75, 0.75)}
    \bond{(0.5, 0.0, 0.5)}{(0.25, 0.25, 0.25)}
    \bond{(0.5, 0.0, 0.5)}{(0.75, 0.25, 0.75)}
    \bond{(0.5, 0.5, 0.0)}{(0.25, 0.25, 0.25)}
    \bond{(0.5, 0.5, 0.0)}{(0.75, 0.75, 0.25)}
    \bond{(0.5, 0.5, 1.0)}{(0.25, 0.75, 0.75)}
    \bond{(0.5, 0.5, 1.0)}{(0.75, 0.25, 0.75)}
    \bond{(0.5, 1.0, 0.5)}{(0.25, 0.75, 0.75)}
    \bond{(0.5, 1.0, 0.5)}{(0.75, 0.75, 0.25)}
    \bond{(1.0, 0.0, 1.0)}{(0.75, 0.25, 0.75)}
    \bond{(1.0, 0.5, 0.5)}{(0.75, 0.25, 0.75)}
    \bond{(1.0, 0.5, 0.5)}{(0.75, 0.75, 0.25)}
    \bond{(1.0, 1.0, 0.0)}{(0.75, 0.75, 0.25)}
    \Ga{(0.0, 0.0, 0.0)}{1}
    \Ga{(0.0, 0.0, 1.0)}{1.8}
    \Ga{(0.0, 0.5, 0.5)}{1.4}
    \Ga{(0.0, 1.0, 0.0)}{1}
    \Ga{(0.0, 1.0, 1.0)}{1.8}
    \Ga{(0.5, 0.0, 0.5)}{1.5}
    \Ga{(0.5, 0.5, 0.0)}{1.1}
    \Ga{(0.5, 0.5, 1.0)}{1.9}
    \Ga{(0.5, 1.0, 0.5)}{1.5}
    \Ga{(1.0, 0.0, 0.0)}{1.2}
    \Ga{(1.0, 0.0, 1.0)}{2}
    \Ga{(1.0, 0.5, 0.5)}{1.6}
    \Ga{(1.0, 1.0, 0.0)}{1.2}
    \Ga{(1.0, 1.0, 1.0)}{2}
    \As{(0.25, 0.25, 0.25)}{1.25}
    \As{(0.25, 0.75, 0.75)}{1.65}
    \As{(0.75, 0.25, 0.75)}{1.75}
    \As{(0.75, 0.75, 0.25)}{1.35}
    \node[anchor=north,SlateGray,font=\sffamily] at (0.5,-0.3) {real
      space};

    \begin{scope}[shift={(2,0)}]
      \node[anchor=south] at (0,-0.25) {\includegraphics[width=0.4\columnwidth]{kfcc}};
      \node[anchor=north,SlateGray,font=\sffamily] at (0,-0.3) {momentum space};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/MSECS/2021
filename: SolidState.tex
modified: 2021-09-13 21:57:24
domain: MSECS
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) node[anchor=south west]
    {\includegraphics[width=11cm]{GaAs-phonons}};
    \node at (6,-0.25) {$k / k_{\rm max}$};
    \node[DarkRed,font=\small,anchor=east] at (0.9, 5.75) {$\SI{37}{meV}$};

    \begin{scope}[SlateGray]
      \node[anchor=west] at (-3,5) {L = longitudinal};
      \node[anchor=west] at (-3,4.6) {T = transverse};

      \node[anchor=west] at (-3,3.8) {A = acoustic};
      \node[anchor=west] at (-3,3.4) {O = optical};
    \end{scope}

    \node[text width=3.cm,font=\small,DarkGreen,anchor=south west] at
    (-3,0) {Acoustic phonons satisfy $\omega \propto k$ near zone center; the energy of
      optical phonons has almost no dependence on $k$.};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/MSECS/2021
filename: SolidState.tex
modified: 2021-09-13 21:57:24
domain: MSECS
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) node {\includegraphics[width=0.8\columnwidth]{GaAs}};
    \node[anchor=north,DarkGreen] at (0,-3) {$k$};
    \node[anchor=south,DarkGreen,rotate=90] at (-3,0) {$E\; (\mathrm{eV})$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/MSECS/2021
filename: SolidState.tex
modified: 2021-09-13 21:57:24
domain: MSECS
source:
  \begin{tikzpicture}[scale=1,
      band/.style={line width=1.5,SlateGray},
      axes/.style={gray!50!white},
    ]

    % \node at (0,0) {\includegraphics[height=6cm]{silicon}};
    \draw[axes,->] (-2,0) -- (2,0) node[anchor=north]{$k$};
    \draw[axes,->] (0,-2) -- (0,4) node[anchor=south]{$E=\hb \omega$};

    \draw[band] (0,0) parabola (2, -2) (0,0) parabola (-2,-2);
    \draw[band] (0,2) parabola (1,4) (0,2) parabola (-1, 4);


    \only<2>{\absorb{(0,0)}{(0,2)}{DarkRed}}
    \only<3>{\absorb{(0.806,-0.3)}{(0.806,3.3)}{DarkGreen}}
    \only<4>{
      \draw[photon, DarkGreen!25!white,->] (0.806,-0.3) -- (0.806,3.3);
      \fill[DarkGreen!30!white] (0.806,3.3) circle[radius=\eradius];
      \ecascade{(0.80623, 3.30000)}{(0.65828,2.86667)}{DarkGreen!50!white}
      \ecascade{(0.65828, 2.86667)}{(0.46547,2.43333)}{DarkGreen!70!white}
      \ecascade{(0.46547, 2.43333)}{(0.00000,2.00000)}{DarkGreen}

      \filldraw[DarkGreen!30!white,fill=white,opacity=0.5] (0.806,-0.325) circle[radius=\eradius];
      \hcascade{(0.80623, -0.32500)}{(0.57009,-0.16250)}{DarkGreen}
      \hcascade{(0.57009, -0.16250)}{(-0.00000,0.00000)}{DarkGreen}
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/MSECS/2021
filename: SolidState.tex
modified: 2021-09-13 21:57:24
domain: MSECS
source:
  \begin{tikzpicture}[scale=1,
      band/.style={line width=1.5,SlateGray},
      axes/.style={gray!50!white},
    ]

    % \node at (0,0) {\includegraphics[height=6cm]{silicon}};
    \draw[axes,->] (-2,0) -- (2,0) node[anchor=north]{$k$};
    \draw[axes,->] (0,-2) -- (0,4) node[anchor=south]{$E=\hb \omega$};

    \draw[band] (0,0) parabola (2, -2) (0,0) parabola (-2,-2);
    \draw[band] (0,2) parabola (1,4) (0,2) parabola (-1, 4);

    \only<1-2>{\absorb{(0,2)}{(0,0)}{DarkRed}}
    \only<2>{\node at (-1,1) {\includegraphics[width=1.5cm]{god}};}
    \only<3>{
      \begin{scope}[DarkRed]
        \draw[dashed] (-2,1) -- (2,1);
        \fill (0,2) coordinate (p) circle[radius=\eradius];
        \filldraw[fill=DarkRed!50!white] (0,1) coordinate (q)
        circle[radius=\eradius] (0,0) coordinate (h) circle[radius=\eradius];
        \draw[->] (p) to[out=-30,in=60] (q);
        \draw[->] (q) to[out=210,in=120] (h);
        \node at (2.5,1) {\includegraphics[width=2cm]{devil}};
      \end{scope}
    }

    \only<4>{
      \begin{scope}[shift={(2,1)},yellow, line width=3]
        \node at (0,0) {\includegraphics[width=2.5cm]{devil}};
        \draw[line width=7pt] (1.25,-1.5) -- (-1.25, 1.5) (1.25,1.5) -- (-1.25,-1.5);
        \draw[DarkRed] (1.25,-1.5) -- (-1.25, 1.5) (1.25,1.5) -- (-1.25,-1.5);
      \end{scope}
    }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/MSECS/2021
filename: SolidState.tex
modified: 2021-09-13 21:57:24
domain: MSECS
source:
  \begin{tikzpicture}[scale=1,
      band/.style={line width=1.5,SlateGray},
      axes/.style={gray!50!white},
    ]
    \only<2-3>{

      % \node at (0,0) {\includegraphics[height=6cm]{silicon}};
      \draw[axes,->] (-2,0) -- (2,0) node[anchor=north]{$k$};
      \draw[axes,->] (0,-2) -- (0,4) node[anchor=south]{$E=\hb \omega$};

      \draw[band] (0,0) parabola (2, -2) (0,0) parabola (-2,-2);
      \draw[band] (0,2) parabola (1,4) (0,2) parabola (-1, 4);

      \absorb{(0.806,-0.3)}{(0.806,3.3)}{DarkGreen}

      \only<3>{
        \draw[photon, DarkGreen!25!white,->] (0.806,-0.3) -- (0.806,3.3);
        \fill[DarkGreen!30!white] (0.806,3.3) circle[radius=\eradius];
        \ecascade{(0.80623, 3.30000)}{(0.65828,2.86667)}{DarkGreen!50!white}
        \ecascade{(0.65828, 2.86667)}{(0.46547,2.43333)}{DarkGreen!70!white}
        \ecascade{(0.46547, 2.43333)}{(0.00000,2.00000)}{DarkGreen}

        \filldraw[DarkGreen!30!white,fill=white,opacity=0.5] (0.806,-0.325) circle[radius=\eradius];
        \hcascade{(0.80623, -0.32500)}{(0.57009,-0.16250)}{DarkGreen}
        \hcascade{(0.57009, -0.16250)}{(-0.00000,0.00000)}{DarkGreen}
      }
    }
    \only<4-5|handout: 0>{
      \node at (0,0){ \includegraphics[width=\columnwidth]{band-bending}};
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Core179A
filename: tmp.tex
modified: 2022-01-08 03:20:38.457354
domain: Core179A
source:
  \begin{tikzpicture}[scale=1]
    %  \fill [red,even odd rule] (0,0) circle[radius=2cm] circle[radius=1cm];
    \fill[\colsun,path fading=fade out,even odd rule] (0,0) circle[radius=3] (0,0) circle[radius=4];
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Core179A
filename: radioactivity.tex
modified: 2022-01-29 20:51:33.263437
domain: Core179A
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=2.25, ymin=0, ymax=1.2, enlargelimits=false,
        width=2.5in, height=1.75in,
        xlabel={$t$}, ylabel={$N$}, ytick={0,1}, xtick={0,1,2},
        xticklabels={0,$\gamma^{-1}$,$2\gamma^{-1}$},
        yticklabels={0,$N_{0}$},
        axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkGreen, domain=0:2, samples=100, line width=2pt,]
      {exp(-x)};
      \draw[dashed,DarkRed] (0,0.5) coordinate(A)  -- (0.693,0.5) -- (0.693,0)
      coordinate(B);
    \end{axis}
    %\draw (A) ++(-90:0.2) {$t_{1/2}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Core179A
filename: radioactivity.tex
modified: 2022-01-29 20:51:33.263437
domain: Core179A
source:
  \begin{tikzpicture}[scale=0.75,
      func/.style={line width=1.25,gray},
      coord/.style={line width=0.5, DarkGreen, ->},
    ]
    \draw[coord] (0,-1.25) -- (0,1.25) node[anchor=east]{$V$};
    \draw[coord] (-3.25,-0.02) -- (3.25,-0.02) node[anchor=north]{$r$};
    \draw[func] (0,-1) -- ++(1,0) -- ++(0,2) .. controls (1.5,0) and (1.6,0) .. (3,0);
    \draw[func] (0,-1) -- ++(-1,0) -- ++(0,2) .. controls (-1.5,0) and (-1.6,0) .. (-3,0);
    \draw[dashed, DarkRed] (-3,0.25) -- ++(6,0) node[anchor=south]{$E$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Core179A
filename: radioactivity.tex
modified: 2022-01-29 20:51:33.263437
domain: Core179A
source:
  \begin{tikzpicture}[scale=1]
    \node at (0,0) { \includegraphics[width=0.85\columnwidth]{be}};
    \onslide<2>{\node[anchor=west,DarkRed] at (-2,0) {Fusion releases more energy};
      \node[anchor=west,DarkRed] at (-2,-0.5) {Fission yields a range of
        daughter nuclei};
      \node[anchor=west,DarkRed] at (-1.5,-0.8) {and a variable number of
        neutrons};
      \node[anchor=west,DarkRed] at (-2,-1.5) {Fission releases 10 million
        times};
      \node[anchor=west,DarkRed] at (-1.5,-1.9) {more energy than chemical
        reactions};}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Core179A
filename: radioactivity.tex
modified: 2022-01-29 20:51:33.263437
domain: Core179A
source:
  \begin{tikzpicture}[scale=1]
    \def\len{1.5}
    \draw[gray,ball color=gray!10!white] (-\len,\len) coordinate (n) circle[radius=0.25]
    node[anchor=south,shift={(0,0.3)}] {$n$};
    \ISO{(0,2*\len)}{U}{238}{92}
    %\draw[->, DarkGreen,line width=2] ($(n)!0.25!(U)$) -- ($(n)!0.75!(U)$);
    \ARROW{n}{U}{}
    \ISO{(\len,\len)}{U}{239}{92}
    \ARROW{0,2*\len}{U}{}
    \BETA{U}

    \ISO{(2*\len,0)}{Np}{239}{93}
    \BETA{Np}
    \ARROW{U}{Np}{$\tau\shalf=\SI{23.5}{min}$}
    \ISO{(3*\len,-\len)}{Pu}{239}{94}
    \ARROW{Np}{Pu}{$\tau\shalf=\SI{2.35}{days}$}
    \draw[DarkGreen] (Pu) ++(0.75,0) node[anchor=west] {$\tau\shalf = \SI{2.44e4}{y}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Core179A/logo
filename: logo3.tex
modified: 2022-04-21 01:36:42.346020
domain: Core179A
source:
  \begin{tikzpicture}[mindmap]
    \fill[gray!15] (-10,-6) rectangle (10,6);
    %  \fill[black!55!white] (0,0) circle[radius=3];
    %  \fill[black,path fading=fade out,even odd rule] (0,0) circle[radius=6] (0,0)
    %  circle[radius=3];
    \fill[black,path fading=fade out] (0,0) circle[radius=6];
    \begin{scope}[
        every node/.style={concept, circular drop shadow,execute at begin
            node=\hskip0pt},
        root concept/.append style={
            concept color=black, fill=gray!20!white, line width=1ex, text=black, font=\large\scshape},
        text=white,
        core/.style={concept color=\cola,faded/.style={concept color=red!50}},
        creativity/.style={concept color=\colb,faded/.style={concept color=red!50}},
        communication/.style={concept color=\colc,faded/.style={concept color=blue!50}},
        collaboration/.style={concept color=\cold,faded/.style={concept color=orange!50}},
        context/.style={concept color=\colb,faded/.style={concept
                color=green!50!black!50}},
        grow cyclic,
        level 1/.append style={level distance=4.5cm,sibling angle=90,font=\scshape},
        level 2/.append style={level distance=3cm,sibling angle=45,font=\scriptsize}]

      \node [root concept] {\huge Climate\\[.1in]Change} % root
      child[grow=45,core] {node {Core}}
      child[grow=135,collaboration] {node {Collaboration}}
      child[grow=225,communication] {node {Communication}}
      child[grow=-45,context] {node {Context}};
      %  child[core] {node {Core}};
    \end{scope}

    \draw[decoration={
    text along path,
    text format delimiters={[}{]},
    text = {[\huge\color{white}\sc]Critical},
    text align={center},
    raise=0.2cm},decorate]
    (120:3) arc(120:60:3);

    \draw[decoration={
    text along path,
    text format delimiters={[}{]},
    text = {[\huge\color{white}\sc]Analysis},
    text align={center},
    raise=0.2cm},decorate]
    (210:3) arc(210:150:3);

    \draw[decoration={
    text along path,
    text format delimiters={[}{]},
    text = {[\huge\color{white}\sc]Critical},
    text align={center},
    raise=0.2cm},decorate]
    (300:3) arc(300:240:3);

    \draw[decoration={
    text along path,
    text format delimiters={[}{]},
    text = {[\huge\color{white}\sc]Analysis},
    text align={center},
    raise=0.2cm},decorate]
    (30:3) arc(30:-30:3);

    % Other cs
    % creativity, complexity, crisis, caring, cancer, consensus,
    % 
    \begin{scope}[shift={(-1.25,0)},every extra concept/.append style={minimum
            size=2.5cm,
            circular drop shadow}]
      \def\rad{9}
      \def\angs{25}
      \node [extra concept,anchor=west,white,fill=\colc] at (\angs:\rad) {\sc Nuclear Power?};
      \node [extra concept,anchor=west,white,fill=\cola] at (180+\angs:\rad) {\sc Geo\-engineering};
      \node [extra concept,anchor=west,white,fill=\colb] at (180-\angs:\rad)
      {\sc Policy};
      \node [extra concept,anchor=west,white,fill=\cold] at (-\angs:\rad) {\sc Eco-feminism};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Core179A/logo
filename: logo.tex
modified: 2022-01-04 02:56:29.274414
domain: Core179A
source:
  \begin{tikzpicture}[mindmap]
    \fill[blue,path fading=fade out] (0,0) circle[radius=6.5];
    \begin{scope}[
        every node/.style={concept, circular drop shadow,execute at begin
            node=\hskip0pt},
        root concept/.append style={
            concept color=black, fill=gray!20!white, line width=1ex, text=black, font=\large\scshape},
        text=white,
        core/.style={concept color=\cola,faded/.style={concept color=red!50}},
        creativity/.style={concept color=\colb,faded/.style={concept color=red!50}},
        communication/.style={concept color=\colc,faded/.style={concept color=blue!50}},
        collaboration/.style={concept color=\cold,faded/.style={concept color=orange!50}},
        context/.style={concept color=green!70!black,faded/.style={concept
                color=green!50!black!50}},
        grow cyclic,
        level 1/.append style={level distance=4.5cm,sibling angle=90,font=\scshape},
        level 2/.append style={level distance=3cm,sibling angle=45,font=\scriptsize}]

      \node [root concept] {Climate\\Change} % root
      child[grow=45,core] {node {Core}}
      child[grow=135,collaboration] {node {Collaboration}}
      child[grow=225,communication] {node {Communication}}
      child[grow=-45,context] {node {Context}};
      %  child[core] {node {Core}};
    \end{scope}

    \draw[decoration={
    text along path,
    text format delimiters={[}{]},
    text = {[\huge\color{white}\sc]Critical},
    text align={center},
    raise=0.2cm},decorate]
    (120:3) arc(120:60:3);

    \draw[decoration={
    text along path,
    text format delimiters={[}{]},
    text = {[\huge\color{white}\sc]Analysis},
    text align={center},
    raise=0.2cm},decorate]
    (210:3) arc(210:150:3);

    \draw[decoration={
    text along path,
    text format delimiters={[}{]},
    text = {[\huge\color{white}\sc]Critical},
    text align={center},
    raise=0.2cm},decorate]
    (300:3) arc(300:240:3);

    \draw[decoration={
    text along path,
    text format delimiters={[}{]},
    text = {[\huge\color{white}\sc]Analysis},
    text align={center},
    raise=0.2cm},decorate]
    (30:3) arc(30:-30:3);

    % Other cs
    % creativity, complexity, crisis, caring, cancer, consensus,
    % 
    \begin{scope}[shift={(-1.25,0)},every extra concept/.append style={minimum
            size=2.5cm,
            circular drop shadow}]
      \def\rad{9}
      \def\angs{25}
      \node [extra concept,anchor=west,white,fill=blue] at (\angs:\rad) {\sc Nuclear Power?};
      \node [extra concept,anchor=west,white,fill=yellow] at (180+\angs:\rad) {\sc Geo\-engineering};
      \node [extra concept,anchor=west,white,fill=green!50!black] at (180-\angs:\rad)
      {\sc Policy};
      \node [extra concept,anchor=west,white,fill=red] at (-\angs:\rad) {\sc Eco-feminism};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/math/SP14/Lecture Notes
filename: RLCcircuit.tex
modified: 2012-12-26 19:23:12
domain: math
source:
  \begin{tikzpicture}[scale=2.54]
    % dpic version 2011.01.05 option -g for TikZ and PGF 1.01
    \ifx\dpiclw\undefined\newdimen\dpiclw\fi
    \global\def\dpicdraw{\draw[line width=\dpiclw]}
    \global\def\dpicstop{;}
    \dpiclw=0.8bp
    \dpiclw=0.8bp
    \psset{linewidth=0.8pt}%
    \makeatletter\@ifundefined{ifPst@noCurrentPoint}%
    {\@ifundefined{MPS@Patch}{\gdef\MPS@Patch{}%
        \typeout{ Dpic -p: patching psbezier in pstricks.tex (some versions) }%
        \def\psbezier@ii{\addto@pscode{%
            \ifshowpoints true \else false \fi\tx@OpenBezier%
            \ifshowpoints\tx@BezierShowPoints\fi}\end@OpenObj}}{}}%
    {\@ifundefined{MPS@PatchMsg}{\gdef\MPS@PatchMsg{}%
        \typeout{ Dpic -p: Setting noCurrentPoint to use all coord pairs }}{}%
      \psset{noCurrentPoint}}\makeatother%
    \psset{arrowsize=1.1pt 4,arrowlength=1.64,arrowinset=0}%
    \dpicdraw (0,0)
    --(0,0.5)\dpicstop
    \dpicdraw (0,0.5)
    --(0.15,0.5)
    --(0.170833,0.541667)
    --(0.2125,0.458333)
    --(0.254167,0.541667)
    --(0.295833,0.458333)
    --(0.3375,0.541667)
    --(0.379167,0.458333)
    --(0.4,0.5)
    --(0.55,0.5)\dpicstop
    \dpicdraw (0.55,0.5)
    --(0.7,0.5)\dpicstop
    \dpicdraw (0.7,0.5)
    --(0.7,0.494444)\dpicstop
    \dpicdraw (0.7,0.5)
    ..controls (0.7,0.517259) and (0.713991,0.53125)
    ..(0.73125,0.53125)
    ..controls (0.748509,0.53125) and (0.7625,0.517259)
    ..(0.7625,0.5)\dpicstop
    \dpicdraw (0.7625,0.5)
    --(0.7625,0.494444)\dpicstop
    \dpicdraw (0.7625,0.5)
    ..controls (0.7625,0.517259) and (0.776491,0.53125)
    ..(0.79375,0.53125)
    ..controls (0.811009,0.53125) and (0.825,0.517259)
    ..(0.825,0.5)\dpicstop
    \dpicdraw (0.825,0.5)
    --(0.825,0.494444)\dpicstop
    \dpicdraw (0.825,0.5)
    ..controls (0.825,0.517259) and (0.838991,0.53125)
    ..(0.85625,0.53125)
    ..controls (0.873509,0.53125) and (0.8875,0.517259)
    ..(0.8875,0.5)\dpicstop
    \dpicdraw (0.8875,0.5)
    --(0.8875,0.494444)\dpicstop
    \dpicdraw (0.8875,0.5)
    ..controls (0.8875,0.517259) and (0.901491,0.53125)
    ..(0.91875,0.53125)
    ..controls (0.936009,0.53125) and (0.95,0.517259)
    ..(0.95,0.5)\dpicstop
    \dpicdraw (0.95,0.5)
    --(0.95,0.494444)\dpicstop
    \dpicdraw (0.95,0.5)
    --(1.1,0.5)\dpicstop
    \dpicdraw (1.1,0.5)
    --(1.35,0.5)\dpicstop
    \dpicdraw (1.35,0.416667)
    --(1.35,0.583333)\dpicstop
    \dpicdraw (1.4,0.416667)
    --(1.4,0.583333)\dpicstop
    \dpicdraw (1.4,0.5)
    --(1.65,0.5)\dpicstop
    \dpicdraw (1.65,0.5)
    --(1.65,0)\dpicstop
    \dpicdraw (1.65,0)
    --(1.15,0)\dpicstop
    \dpicdraw (1.15,0)
    --(1,0)\dpicstop
    \dpicdraw (0.875,0) circle (0.049213in)\dpicstop
    \draw (0.9375,0) node{$-$};
    \draw (0.8125,0) node{$+$};
    \dpicdraw (0.75,0)
    --(0.6,0)\dpicstop
    \dpicdraw (0.6,0)
    --(0,0)\dpicstop
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019
filename: p134defs.tex
modified: 2019-03-04 01:45:04
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,-.3ex) node[fill=blue!10!white,draw,rounded corners] {\textsf{\textbf{#1}}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019
filename: p134defs.tex
modified: 2019-03-04 01:45:04
domain: p134
source:
  \begin{tikzpicture}[execute at end picture=%
        {
          \begin{pgfonlayer}{background}
            \path[fill=blue!10!white]
            (current bounding box.south west) rectangle
            (current bounding box.north east);
          \end{pgfonlayer}
        }]
    \ifthenelse{\equal{}{#1}}
    {\draw(0,0) rectangle (0.3,0.3);
      \draw (0,0) -- (0.3,0.3) (0,0.3) -- (0.3,0);
    }
    {
      \draw (0.15,0.15) circle[radius=0.125];
      \fill (0.15,0.15) circle[radius=0.05];
    }
    \draw (0.4,0.15) node[anchor=west] {\textsf{#2}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019
filename: p134.tex
modified: 2019-01-15 03:19:26
domain: p134
source:
  \begin{tikzpicture}[scale=1]%
    \draw (0,-.3ex) node[fill=blue!10!white,draw,rounded corners] {\textsf{\textbf{#1}}};%
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019
filename: p134.tex
modified: 2019-01-15 03:19:26
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,-.3ex) node[fill=gray!10,draw,rounded corners] {\textsf{\textbf{\scriptsize #1}}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec17.tex
modified: 2020-03-02 06:08:00
domain: p134
source:
  \begin{tikzpicture}[scale=0.5, font=\small]
    \fill (-4,1,0) coordinate (S) circle[radius=0.04] node[anchor=south east]{$S(x_{s}, y_{s}, z_{s})$};
    \filldraw[fill=gray!5] (0,-1.5,-1.5) -- (0,1.5,-1.5) -- (0,1.5,1.5) --
    (0,-1.5,1.5) -- cycle;
    \filldraw[fill=white] (0,0,0) circle[x radius=0.3, y radius = 1];
    \draw[DarkGreen,->] (0,0,0) -- (6,0,0) node[anchor=north] {$z$ };
    \begin{scope}[shift={(4,0)}]
      \filldraw[fill=gray!10,opacity=0.75] (0,-1.5,-1.5) -- (0,1.5,-1.5) -- (0,1.5,1.5) --
      (0,-1.5,1.5) -- cycle;
    \end{scope}

    \draw[DarkGreen,->] (0,0,0) -- (0,2,0) node[anchor=south] {$x$ };
    \draw[DarkGreen,->] (0,0,0) -- (0,0,2) node[anchor=north] {$y$ };
    \draw[DarkGreen,->] (4,0,0) -- (6,0,0) node[anchor=north] {$z$ };

    \draw[DarkBlue,->] (S) -- node[anchor=north] {$\vb{s}_{0}$} (0,0);
    \fill (4,0.75,-0.75) coordinate (P) circle[radius=0.04];
    \draw[DarkBlue,->] (0,0) -- node[anchor=north] {$\vb{r}_{0}$} (P);
    \node[anchor=west] at (P) {$P(x_{p}, y_{p}, z_{p})$};

    % aperture point
    \fill (0,0.25,-0.5) coordinate (A) circle[radius=0.04];
    \begin{scope}[DarkRed,->]
      \draw (S) -- node[anchor=south]{$\vb{s}$} (A);
      \draw (A) -- node[anchor=south]{$\vb{r}$} (P);
    \end{scope}

    \node at (0,3,0) {aperture plane};
    \node at (4,3,0) {image plane};

    \node at (0,-3.5,0) {$\displaystyle E(P) = \underset {\text{aperture}}{\iint}
        \underbrace{\frac{A e^{i(ks-\omega t)}}{s}}_{\text{source
            spherical wave}} \frac{e^{ikr}}{r} \frac{e^{i\pi/2}}{\lambda}
        \underbrace{\frac{\vu{s} \vdot \vu{z} + \vu{r} \vdot \vu{z}
          }{2}}_{\text{obliquity factor}}   \dd{x}\dd{y} $};

    \node at (0,-6.5,0) {$\displaystyle s \approx \textcolor{DarkGreen}
        {\underbrace{s_{0} - \qty(x \frac{x_{s}}{s_{0}} + y \frac{y_{s}}{s_{0}}
            )}_{\text{Fraunhofer}} }
        + \textcolor{DarkRed}
        {\underbrace{\frac{x^{2} + y^{2}}{2s_{0}} - \frac{\qty(x \frac{x_{s}}{s_{0}} + y \frac{y_{s}}{s_{0}} )^{2}}{2 s_{0}}}_{\text{Fresnel}}}  $};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec/frames/lec09
filename: 07-Advantages_of_Fourier_transform_spectroscopy.tex
modified: 2020-02-02 02:03:55
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \node[ellipse,
      path picture={
          \node at (path picture bounding box.center){
            {\includegraphics[width=0.75\textwidth]{Na-fringes}}
          };
        }] {\phantom{Mary had a litt}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2012/lec
filename: lec07graphics.tex
modified: 2012-02-07 06:17:57
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      place/.style={inner sep=0mm}
    ]
    \begin{scope}
      \clip (-2,-5) rectangle (3,5);
      \node[place] (ctr) at (-20,0) {};
      \filldraw[fill=brown!30!white, draw=brown!80!black] (ctr) circle(20);
      \draw[line width=3pt,color=gray!50!white] (0,0) arc(0:-20:20);
      \draw[line width=3pt,color = gray!50!white] (0,0) arc(0:20:20);
      \draw[line width=3pt,color=black] (0,0) arc(0:10:20) node[place]
      (dq) {};
    \end{scope}
    \clip (-3,-5) rectangle (3,5);
    \draw[line width=1pt,color=blue!50!white] (dq) -- (ctr);
    \draw[line width=1pt,color=blue!50!white] (0,0) -- (ctr);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2012/tikz
filename: G2.tex
modified: 2012-01-02 00:20:31
domain: p24
source:
  \begin{tikzpicture}[x={(0.866cm,-0.5cm)}, y={(0.866cm,0.5cm)}, z={(0cm,1cm)}, scale=1.0,
      %Option for nice arrows
      >=stealth, %
      inner sep=0pt, outer sep=2pt,%
      axis/.style={thick,->},
      wave/.style={thick,color=#1,smooth},
      polaroid/.style={fill=black!60!white, opacity=0.3},
    ]
    % Colors
    \colorlet{darkgreen}{green!50!black}
    \colorlet{lightgreen}{green!80!black}
    \colorlet{darkred}{red!50!black}
    \colorlet{lightred}{red!80!black}

    % Frame
    \coordinate (O) at (0, 0, 0);
    \draw[axis] (O) -- +(14, 0,   0) node [right] {x};
    \draw[axis] (O) -- +(0,  2.5, 0) node [right] {y};
    \draw[axis] (O) -- +(0,  0,   2) node [above] {z};

    \draw[thick,dashed] (-2,0,0) -- (O);

    % monochromatic incident light with electric field
    \draw[wave=blue, opacity=0.7, variable=\x, samples at={-2,-1.75,...,0}]
    plot (\x, { cos(1.0*\x r)*sin(2.0*\x r)}, { sin(1.0*\x r)*sin(2.0*\x r)})
    plot (\x, {-cos(1.0*\x r)*sin(2.0*\x r)}, {-sin(1.0*\x r)*sin(2.0*\x r)});

    \foreach \x in{-2,-1.75,...,0}{
        \draw[color=blue, opacity=0.7,->]
        (\x,0,0) -- (\x, { cos(1.0*\x r)*sin(2.0*\x r)}, { sin(1.0*\x r)*sin(2.0*\x r)})
        (\x,0,0) -- (\x, {-cos(1.0*\x r)*sin(2.0*\x r)}, {-sin(1.0*\x r)*sin(2.0*\x r)});
      }

    \filldraw[polaroid] (0,-2,-1.5) -- (0,-2,1.5) -- (0,2,1.5) -- (0,2,-1.5) -- (0,-2,-1.5)
    node[below, sloped, near end]{Polaroid};%

    %Direction of polarization
    \draw[thick,<->] (0,-1.75,-1) -- (0,-0.75,-1);

    % Electric field vectors
    \draw[wave=blue, variable=\x,samples at={0,0.25,...,6}]
    plot (\x,{sin(2*\x r)},0)node[anchor=north]{$\vec{E}$};

    %Polarized light between polaroid and thin section
    \foreach \x in{0, 0.25,...,6}
    \draw[color=blue,->] (\x,0,0) -- (\x,{sin(2*\x r)},0);

    \draw (3,1,1) node [text width=2.5cm, text centered]{Polarized light};

    %Crystal thin section
    \begin{scope}[thick]
      \draw (6,-2,-1.5) -- (6,-2,1.5) node [above, sloped, midway]{Crystal section}
      -- (6, 2, 1.5) -- (6, 2, -1.5) -- cycle % First face
      (6,  -2, -1.5) -- (6.2, -2,-1.5)
      (6,   2, -1.5) -- (6.2,  2,-1.5)
      (6,  -2,  1.5) -- (6.2, -2, 1.5)
      (6,   2,  1.5) -- (6.2,  2, 1.5)
      (6.2,-2, -1.5) -- (6.2, -2, 1.5) -- (6.2, 2, 1.5)
      -- (6.2, 2, -1.5) -- cycle; % Second face

      %Optical indices
      \draw[darkred, ->]       (6.1, 0, 0) -- (6.1, 0.26,  0.966) node [right] {$n_{g}'$}; % index 1
      \draw[darkred, dashed]   (6.1, 0, 0) -- (6.1,-0.26, -0.966); % index 1
      \draw[darkgreen, ->]     (6.1, 0, 0) -- (6.1, 0.644,-0.173) node [right] {$n_{p}'$}; % index 2
      \draw[darkgreen, dashed] (6.1, 0, 0) -- (6.1,-0.644, 0.173); % index 2
    \end{scope}

    %Rays leaving thin section
    \draw[wave=darkred,   variable=\x, samples at={6.2,6.45,...,12}]
    plot (\x, {0.26*0.26*sin(2*(\x-0.5) r)},  {0.966*0.26*sin(2*(\x-0.5) r)});  %n'g-oriented ray
    \draw[wave=darkgreen, variable=\x, samples at={6.2,6.45,...,12}]
    plot (\x, {0.966*0.966*sin(2*(\x-0.1) r)},{-0.26*0.966*sin(2*(\x-0.1) r)}); %n'p-oriented ray
    \draw (10,1,1) node [text width=2.5cm, text centered] {Polarized and dephased light};

    \foreach \x in{6.2,6.45,...,12} {
        \draw[color=darkgreen, ->] (\x, 0, 0) --
        (\x, {0.966*0.966*sin(2*(\x-0.1) r)}, {-0.26*0.966*sin(2*(\x-0.1) r)});
        \draw[color=darkred,   ->] (\x, 0, 0) --
        (\x, {0.26*0.26*sin(2*(\x-0.5) r)}, {0.966*0.26*sin(2*(\x-0.5) r)});
      }

    %Second polarization
    \draw[polaroid]   (12, -2,  -1.5) -- (12, -2,   1.5)  %Polarizing filter
    node [above, sloped,midway] {Polaroid} -- (12, 2, 1.5) -- (12, 2, -1.5) -- cycle;
    \draw[thick, <->] (12, -1.5,-0.5) -- (12, -1.5, 0.5); %Polarization direction

    %Light leaving the second polaroid
    \draw[wave=lightgreen,variable=\x, samples at={12, 12.25,..., 14}]
    plot (\x,{0}, {0.966*0.966*0.26*sin(2*(\x-0.5) r)}); %n'g polarized ray
    \draw[wave=lightred,  variable=\x, samples at={12, 12.25,..., 14}]
    plot (\x,{0}, {-0.26*0.966*sin(2*(\x-0.1) r)});      %n'p polarized ray

    \node[align=justify, text width=14cm, anchor=north west, yshift=-2mm] at (current bounding box.south west)
    {Light behavior in a petrographic microscope with light polarizing
      device. Only one incident wavelength is shown (monochromatic light).
      The magnetic field, perpendicular to the electric one, is not drawn.};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2012/tikz
filename: graphics.tex
modified: 2012-01-02 00:10:53
domain: p24
source:
  \begin{tikzpicture}[
      force/.style={>=latex,draw=blue,fill=blue},
      axis/.style={densely dashed,gray,font=\small},
      M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
      m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
      plane/.style={draw=black,fill=blue!10},
      string/.style={draw=red, thick},
      pulley/.style={thick},
    ]

    \matrix[column sep=1cm] {
    %% Sketch
    \draw[plane] (0,-1) coordinate (base)
    -- coordinate[pos=0.5] (mid) ++(\iangle:3) coordinate (top)
    |- (base) -- cycle;
    \path (mid) node[M,rotate=\iangle,yshift=0.25cm] (M) {};
    \draw[pulley] (top) -- ++(\iangle:0.25) circle (0.25cm)
    ++ (90-\iangle:0.5) coordinate (pulley);
    \draw[string] (M.east) -- ++(\iangle:1.5cm) arc (90+\iangle:0:0.25)
    -- ++(0,-1) node[m] {};

    \draw[->] (base)++(\arcr,0) arc (0:\iangle:\arcr);
    \path (base)++(\iangle*0.5:\arcr+5pt) node {$\alpha$};
    %%

    &
    %% Free body diagram of M
    \begin{scope}[rotate=\iangle]
      \node[M,transform shape] (M) {};
      % Draw axes and help lines

      {[axis,->]
      \draw (0,-1) -- (0,2) node[right] {$+y$};
      \draw (M) -- ++(2,0) node[right] {$+x$};
      % Indicate angle. The code is a bit awkward.

      \draw[solid,shorten >=0.5pt] (\down-\iangle:\arcr)
      arc(\down-\iangle:\down:\arcr);
      \node at (\down-0.5*\iangle:1.3*\arcr) {$\alpha$};
      }

      % Forces
      {[force,->]
      % Assuming that Mg = 1. The normal force will therefore be cos(alpha)
      \draw (M.center) -- ++(0,{cos(\iangle)}) node[above right] {$N$};
      \draw (M.west) -- ++(-1,0) node[left] {$f_R$};
      \draw (M.east) -- ++(1,0) node[above] {$T$};
      }

    \end{scope}
    % Draw gravity force. The code is put outside the rotated
    % scope for simplicity. No need to do any angle calculations. 
    \draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
    %%

    &
    %%%
    % Free body diagram of m
    \node[m] (m) {};
    \draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
    {[force,->]
    \draw (m.north) -- ++(0,1) node[above] {$T'$};
    \draw (m.south) -- ++(0,-1) node[right] {$mg$};
    }

    \\
    };
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2012/tikz
filename: logo.tex
modified: 2012-01-14 02:04:15
domain: p24
source:
  \begin{tikzpicture}[
      force/.style={>=latex,draw=blue,fill=blue},
      axis/.style={densely dashed,gray,font=\small},
      M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
      m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
      plane/.style={draw=black,fill=blue!10},
      string/.style={draw=red, thick},
      pulley/.style={thick},
    ]

    %% Sketch
    \draw[plane] (0,-1) coordinate (base)
    -- coordinate[pos=0.5] (mid) ++(\iangle:3) coordinate (top)
    |- (base) -- cycle;
    \path (mid) node[M,rotate=\iangle,yshift=0.25cm] (M) {};
    \draw[pulley] (top) -- ++(\iangle:0.25) circle (0.25cm)
    ++ (90-\iangle:0.5) coordinate (pulley);
    \draw[string] (M.east) -- ++(\iangle:1.5cm) arc (90+\iangle:0:0.25)
    -- ++(0,-1) node[m] {};

    \draw[->] (base)++(\arcr,0) arc (0:\iangle:\arcr);
    \path (base)++(\iangle*0.5:\arcr+5pt) node {$\alpha$};
    %%


  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2012/exam
filename: quiz2.tex
modified: 2012-02-28 15:51:16
domain: p24
source:
  \begin{tikzpicture}[
      scale=1.2,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm}
    ]
    \draw (0,0) -- (0,3) -- ++(210:3);
    \draw[dashed, color=gray] (0,0) arc(-90:-150:3);
    \shade[ball color=blue!25!white] (0,3) ++(210:3) circle(0.25);
    \node at (-3,1.2) {$m$};
    \shade[ball color=blue] (0,0) circle(0.25);
    %  \shade[ball color=blue] (0,3) ++(210:3) circle(0.25);
    \draw (0,2.6) arc(-90:-150:0.4);
    \node at (-0.4,2.4) {$60^{\circ}$};
    \node at (-1.6,2.4) {$L$};

    % draw the floor and ramp
    \draw[brown, line width=2pt] (-1,-0.3) -- ++(0:7);
    \draw[brown, line width=2pt] (6,-0.3) -- (9, 0.2) -- ++(0:2);
    \draw[dashed] (6,-0.3) -- (11,-0.3);
    \node at (7.75,-0.15) {$\alpha$};
    \draw (7.5,-0.3) arc(0:10:1.5);
    \shade[ball color=red] (0.5,0) circle(0.25);
    \node at (0.75,0.4) {$m$};
    \filldraw[color=green!50!black] (5.5,-0.25) rectangle (6,0.25); %circle(0.25);
    \node at (5.7,0.5) {$M$};

    \draw[coord,<->] (0.75,-0.6) -- ++(0:5);
    \node at (3,-0.9) {$D$};
    \draw[coord,<->] (10.5,-0.3) -- (10.5,0.2);
    \node at (10.8,-0.05) {$\frac{L}{6}$};

    \draw[dashed,green!50!black] (9.,0.25) rectangle (9.5,0.75);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2012/exam
filename: p24_mt1_2012.tex
modified: 2012-02-13 01:18:12
domain: p24
source:
  \begin{tikzpicture}[
      scale=2,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray}
    ]
    \draw [fill=gray!50!white] (0,0) -- (1,0) arc(0:90:1) -- cycle;
    \node at (0.5,-0.2) {$R$};
    \draw [fill=blue!50!white] (-2,0.4) circle (0.1);
    \node at (-2, 0.2) {$m$};
    \draw [->,line width=1.5pt,red!50!black] (-1.8,0.4) -- ++(0:0.5)
    node[anchor=north]{$\vv_{0}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2012/exam
filename: p24_mt1_2012.tex
modified: 2012-02-13 01:18:12
domain: p24
source:
  \begin{tikzpicture}[
      scale=1.25,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      ice/.style={line width=2.5pt, color=blue!50!white},
      ground/.style={line width=1.5pt, color=brown}
    ]
    \draw[ground] (-3,-0.025) -- (8,-0.025);
    \draw[step=0.5,color=gray!25!white] (-3,0) grid (8,3);
    % draw the ice ramp
    \draw[ice] (0,2.5) arc(90:150:1) .. controls (-2,0) and (-2,0)
    ..(-3,0);
    \draw[ice] (0,2.5) arc(90:30:1) .. controls (1.5,.5) and (1.75,0.5)
    .. (2,0.5) .. controls(2.5,0.5) .. (3,1);
    % draw the radii of the circle
    \draw[line width=0.5pt] (0,1.5) -- ++(30:1) (0,1.5) -- ++(150:1);
    \draw[line width=0.5pt] (0,1.5) -- (0,2.5);
    \draw (0, 1.8) arc (90:150:0.3);
    \node at (-0.25, 2) {$60^{\circ}$};
    \draw[dashed] (0,1.5) circle (1);
    \node at (0.5,1.6) {$R$};

    \draw[coord] (-3,0) -- ++(90:2.5);
    \node at (-2.8,1.25) {$h$};

    % draw the penguin
    \filldraw (-2.8,0.05) circle [x radius=0.1, y radius = 0.05];
    \draw (-2.8,0.15) node[anchor=south,fill=white]{penguin};
    \draw[red!50!black,->,line width=1.5pt] (-2.6,0.05) -- ++(0:0.5) node[anchor=north]{$\vv_{0}$};

    \draw[coord,-] (0,0) -- (0,0.75) node[anchor=west,fill=white]{$\frac{3}{2} R$};
    \draw[coord,->] (0,0.75)--(0,1.5);
    \node at (2.8,1.2) {P};
    \draw[dashed,color=gray] (3,1) -- (2,0) (2.3,0) arc(0:45:0.3);
    \node at (2.6,0.2) {$\dg{45}$};

    \draw[coord,<->,line width=1pt] (5,0) node[anchor=north]{$x$} --( 3,0) -- (3,2.5)
    node[anchor=east]{$y$};

    \filldraw[red] (6.9,0) rectangle (7.1,0.1)
    node[anchor=north]{chocolates };
    \draw[dashed,->] (3,1) .. controls (3.5,1.5) .. (3.85,1.65);
    \draw[coord] (3.3,0) -- (3.3,1) node[anchor=west]{$R$};
    %  \draw (5.6,-0.2)--(5.8,0.2) (5.7,-0.2)--(5.9,0.2);
    % ++(240:1) (0,2.5) arc(90:30:1) -- ++(-60:1) ;
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2012/exam
filename: quiz2_v1.tex
modified: 2012-02-27 20:52:10
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm}
    ]
    \draw (0,0) -- (0,3) -- ++(210:3);
    \draw[dashed, color=gray] (0,0) arc(-90:-150:3);
    \shade[ball color=blue!25!white] (0,3) ++(210:3) circle(0.25);
    \node at (-3,1.2) {$m$};
    \shade[ball color=blue] (0,0) circle(0.25);
    %  \shade[ball color=blue] (0,3) ++(210:3) circle(0.25);
    \draw (0,2.6) arc(-90:-150:0.4);
    \node at (-0.4,2.4) {$60^{\circ}$};
    \node at (-1.6,2.4) {$L$};

    % draw the floor and ramp
    \draw[brown, line width=2pt] (-1,-0.3) -- ++(0:9);
    \draw[brown, line width=2pt] (8,-0.3) -- ++(15:4);
    \draw[dashed] (8,-0.3) -- (11,-0.3);
    \node at (9.5,-0.1) {$\alpha$};
    \draw (9,-0.3) arc(0:15:1);
    \shade[ball color=red] (0.5,0) circle(0.25);
    \node at (0.75,0.4) {$m$};
    \shade[ball color=green] (8,0) circle(0.25);
    \node at (7.7,0.4) {$M$};

    \draw[coord,<->] (0.75,-0.8) -- ++(0:7);
    \node at (4,-1.1) {$D$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2012/exam
filename: quiz2_v2.tex
modified: 2012-02-28 15:45:30
domain: p24
source:
  \begin{tikzpicture}[
      scale=1.2,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm}
    ]
    \draw (0,0) -- (0,3) -- ++(210:3);
    \draw[dashed, color=gray] (0,0) arc(-90:-150:3);
    \shade[ball color=blue!25!white] (0,3) ++(210:3) circle(0.25);
    \node at (-3,1.2) {$m$};
    \shade[ball color=blue] (0,0) circle(0.25);
    %  \shade[ball color=blue] (0,3) ++(210:3) circle(0.25);
    \draw (0,2.6) arc(-90:-150:0.4);
    \node at (-0.4,2.4) {$60^{\circ}$};
    \node at (-1.6,2.4) {$L$};

    % draw the floor and ramp
    \draw[brown, line width=2pt] (-1,-0.3) -- ++(0:7);
    \draw[brown, line width=2pt] (6,-0.3) -- (9, 0.2) -- ++(0:2);
    \draw[dashed] (6,-0.3) -- (11,-0.3);
    \node at (7.75,-0.15) {$\alpha$};
    \draw (7.5,-0.3) arc(0:10:1.5);
    \shade[ball color=red] (0.5,0) circle(0.25);
    \node at (0.75,0.4) {$m$};
    \shade[ball color=green] (6,0) circle(0.25);
    \node at (5.7,0.4) {$M$};

    \draw[coord,<->] (0.75,-0.6) -- ++(0:5);
    \node at (3,-0.9) {$D$};
    \draw[coord,<->] (10.5,-0.3) -- (10.5,0.2);
    \node at (10.8,-0.05) {$\frac{L}{6}$};

    \draw[dashed,green!50!black] (9.25,0.5) circle (0.25);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2012/exam
filename: p24_mt1_2012_v3.tex
modified: 2012-02-13 15:40:17
domain: p24
source:
  \begin{tikzpicture}[
      scale=2,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray}
    ]
    \draw [fill=gray!50!white] (0,0) -- (1,0) arc(0:90:1) -- cycle;
    \node at (0.5,-0.2) {$R$};
    \draw [fill=blue!50!white] (-2,0.4) circle (0.1);
    \node at (-2, 0.2) {$m$};
    \draw [->,line width=1.5pt,red!50!black] (-1.8,0.4) -- ++(0:0.5)
    node[anchor=north]{$\vv_{0}$};
    \node at (-1,-0.2) {top view};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2012/exam
filename: p24_mt1_2012_v3.tex
modified: 2012-02-13 15:40:17
domain: p24
source:
  \begin{tikzpicture}[
      scale=1.25,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      ice/.style={line width=2.5pt, color=blue!50!white},
      ground/.style={line width=1.5pt, color=brown}
    ]
    \draw[ground] (-5,-0.025) -- (5,-0.025);
    \draw[step=0.5,color=gray!25!white] (-5,0) grid (5,3);
    % draw the ice ramp
    \draw[ice] (0,2.5) arc(90:120:1) .. controls (-4,0)  ..(-5,0);
    \draw[ice] (0,2.5) arc(90:60:1) .. controls (2.5,.5) and (2.75,0.5)
    .. (3.5,0.5) .. controls(4,0.5) .. (4.5,1);
    % draw the radii of the circle
    \draw[line width=0.5pt] (0,1.5) -- ++(60:1) (0,1.5) -- ++(120:1);
    \draw[line width=0.5pt] (0,1.5) -- (0,2.5);
    \draw (0, 1.8) arc (90:120:0.3);
    \node at (-0.45, 1.8) {$30^{\circ}$};
    \draw[dashed] (0,1.5) circle (1);
    \node at (0.5,1.9) {$R$};

    \draw[coord] (-2,0) -- ++(90:2.5);
    \node at (-2.2,2) {$h$};

    % draw the penguin
    \filldraw (-4.8,0.05) circle [x radius=0.1, y radius = 0.05];
    \draw (-4.8,0.15) node[anchor=south,fill=white]{penguin};
    \draw[red!50!black,->,line width=1.5pt] (-4.6,0.05) -- ++(0:0.5) node[anchor=north]{$\vv_{0}$};

    \draw[coord,-] (0,0) -- (0,0.75) node[anchor=west,fill=white]{$\frac{3}{2} R$};
    \draw[coord,->] (0,0.75)--(0,1.5);
    \node at (4.7,1.2) {P};


    \draw[coord] (4.8,0) -- (4.8,1) node[anchor=west]{$R$};
    %  \draw (5.6,-0.2)--(5.8,0.2) (5.7,-0.2)--(5.9,0.2);
    % ++(240:1) (0,2.5) arc(90:30:1) -- ++(-60:1) ;
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/p24_pns/prob/ch06
filename: 6P29.tex
modified: 2013-07-21 15:51:56
domain: p24
source:
  \begin{tikzpicture}[decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm},>=stealth']
    \filldraw (0,0) circle(0.1);
    \draw[decorate] (0,0) -- (30:2);
    \shade[ball color=gray] (30:2) circle(0.25) ++(-90:0.25) node[anchor=north]{
        $m$ };
    \draw[decorate] (30:2.25) -- ++(30:2);
    \shade[ball color=gray] (30:4.5) circle(0.25) ++(-90:0.25)
    node[anchor=north]{$m$};
    \draw (30:1) ++(120:0.5) node {$k$};
    \draw (30:3) ++(120:0.5) node {$k$};
    \draw[->] (24:5) arc(24:36:5) node[anchor=south]{$\omega$};
    \node at (7:1) {$1$};
    \node at (21:3.2) {2};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/p24_pns/prob/ch05
filename: 5PiQ5.tex
modified: 2013-02-04 05:20:33
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      vel/.style={->,line width=2pt,color=DarkBlue},
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      photon/.style={line width=1.5pt,color=DarkRed,decorate,decoration={snake,post length=0.1in}},
      spring/.style={decorate,decoration={coil,aspect=0.3,segment length=3mm,amplitude=3mm}},
      traj/.style={dashed, color=gray, line width=1pt}
    ]
    \filldraw (-2,0) circle (0.1);
    \draw[vel] (-1.8,0) -- +(0:0.5) node[anchor=north]{$\vv$};
    \node at (-2,0.3){$m$};
    \filldraw (0,0) circle (0.1);
    \node at (0.3,0) {$m$};
    \filldraw (0,5) circle (0.05);
    \draw (0,0) -- node[anchor=west]{$r$}  (0,5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/p24_pns/prob/ch05
filename: 5PrQ4.tex
modified: 2013-02-03 20:00:46
domain: p24
source:
  \begin{tikzpicture}[
      scale=1.25,
      >=stealth',
      vel/.style={->,line width=2pt,color=DarkBlue},
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      photon/.style={line width=1.5pt,color=DarkRed,decorate,decoration={snake,post length=0.1in}},
      spring/.style={decorate,decoration={coil,aspect=0.3,segment length=3mm,amplitude=3mm}},
      traj/.style={dashed, color=gray, line width=1pt}
    ]
    \draw[dashed] (180:1.25) -- (0:1.25);
    \draw[dashed] (90:1.25) -- (-90:1.25);
    \draw (0,0) circle(1);
    \node at (1.4,0){$x$};
    \node at (0,1.4){$y$};
    \fill (60:1) circle(0.05) node[anchor=south]{$A$};
    \fill (0.5,0) circle(0.05) node[anchor=north]{$B$};
    \filldraw[fill=gray,draw=black] (1,0) circle(0.05);
    \node at (-10:1.1) {1};
    \draw[->] (60:1) arc(60:75:1);
    \draw[->] (0.5,0) -- +(180:0.2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/p24_pns/sol/ch06
filename: 6P22.tex
modified: 2013-07-21 15:51:56
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      vel/.style={->,line width=2pt,color=DarkBlue},
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      photon/.style={line width=1.5pt,color=DarkRed,decorate,decoration={snake,post length=0.1in}},
      spring/.style={decorate,decoration={coil,aspect=0.3,segment length=3mm,amplitude=3mm}},
      traj/.style={dashed, color=gray, line width=1pt},
      link/.style={line width=2pt}
    ]
    \draw[link] (0,0) circle[x radius=0.5, y radius=0.2]
    (0.9,0) circle[x radius=0.5, y radius=0.2]
    (1.8,0) circle[x radius=0.5, y radius=0.2];
    \node at (0,0.5) {4};
    \node at (0.9,0.5) {3};
    \node at (1.8,0.5) {2};
    \draw[force] (2.35,0) -- ++(0:0.75) node[anchor=west]{$F_{21}$};
    \draw[accel] (0.9,-0.75) -- node[anchor=north]{$a$}  ++(0:1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/p24_pns/sol/ch06
filename: 6P22.tex
modified: 2013-07-21 15:51:56
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      vel/.style={->,line width=2pt,color=DarkBlue},
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      photon/.style={line width=1.5pt,color=DarkRed,decorate,decoration={snake,post length=0.1in}},
      spring/.style={decorate,decoration={coil,aspect=0.3,segment length=3mm,amplitude=3mm}},
      traj/.style={dashed, color=gray, line width=1pt},
      link/.style={line width=2pt}
    ]
    \draw[link] (0,0) circle[x radius=0.5, y radius=0.2];
    \node at (0,0.5) {4};
    \draw[force] (0.5,0) -- ++(0:0.75) node[anchor=west]{$F_{43}$};
    \draw[accel] (-0.5,-0.75) -- node[anchor=north]{$a$}  ++(0:1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/p24_pns/sol/ch06
filename: 6P22.tex
modified: 2013-07-21 15:51:56
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      vel/.style={->,line width=2pt,color=DarkBlue},
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      photon/.style={line width=1.5pt,color=DarkRed,decorate,decoration={snake,post length=0.1in}},
      spring/.style={decorate,decoration={coil,aspect=0.3,segment length=3mm,amplitude=3mm}},
      traj/.style={dashed, color=gray, line width=1pt},
      link/.style={line width=2pt}
    ]
    \draw[link] (0,0) circle[x radius=0.5, y radius=0.2];
    \node at (0,0.5) {3};
    \draw[force] (0.5,0) -- ++(0:0.75) node[anchor=west]{$F_{32}$};
    \draw[force] (-0.5,0) -- ++(180:0.75) node[anchor=east]{$F_{34}$};
    \draw[accel] (-0.5,-0.75) -- node[anchor=north]{$a$}  ++(0:1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/p24_pns/sol/ch06
filename: 6P22.tex
modified: 2013-07-21 15:51:56
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      vel/.style={->,line width=2pt,color=DarkBlue},
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray},
      photon/.style={line width=1.5pt,color=DarkRed,decorate,decoration={snake,post length=0.1in}},
      spring/.style={decorate,decoration={coil,aspect=0.3,segment length=3mm,amplitude=3mm}},
      traj/.style={dashed, color=gray, line width=1pt},
      link/.style={line width=2pt}
    ]
    \draw[link] (0,0) circle[x radius=0.5, y radius=0.2]
    (0.9,0) circle[x radius=0.5, y radius=0.2]
    (1.8,0) circle[x radius=0.5, y radius=0.2]
    (2.7,0) circle[x radius=0.5, y radius=0.2];
    \node at (0,0.5) {4};
    \node at (0.9,0.5) {3};
    \node at (1.8,0.5) {2};
    \node at (2.7,0.5) {1};
    \draw[force] (3.25,0) -- ++(0:0.75) node[anchor=west]{$F_{0}$};
    \draw[accel] (0.9,-0.75) -- node[anchor=north]{$a$}  ++(0:1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/p24_pns/sol/sup/old
filename: SUP2.tex
modified: 2013-07-19 03:30:26
domain: p24
source:
  \begin{tikzpicture}[>=stealth',scale=.75,
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->}
    ]
    \draw (0,0) circle(0.25);
    \draw[force] (0,0.25) -- ++(90:1.5) node[anchor=east]{
      $F_{D}$ };
    \draw[coord] (0.75,0) -- ++(-90:1.) node[anchor=west]{$x$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/p24_pns/sol/ch03
filename: 3P23.tex
modified: 2013-07-21 15:51:55
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray}
    ]
    \draw (0,0) -- +(0:8);
    \filldraw (1,0.25) circle(0.25);
    \filldraw (5,0.25) circle(0.25);
    \filldraw[fill=gray,draw=black] (0,0.25) rectangle (6,0.75);
    \filldraw[fill=red] (5.5,0.75) rectangle (6,2.5);
    \draw[very thick,->] (6.2,0.5) -- +(0:0.75) node[anchor=west] {$
          \val{5.0}{m/s} $};
    \draw[very thick,->,draw=red] (5,1.5) -- +(180:0.75)
    node[anchor=east,color=red] {$ \val{10.0}{m/s} $};
    \node at (0.5,1) {$\val{100}{kg}$};
    \node[color=red] at (6.5,2) {$\val{80}{kg}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/motion/prob/ch04
filename: 04P18.tex
modified: 2014-01-11 04:59:58
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray}
    ]
    \filldraw[fill=gray] (0,0) -- (2,0) -- (1,-3) -- (0,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/motion/prob/ch04
filename: 04P17.tex
modified: 2014-01-11 05:09:32
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray}
    ]
    \filldraw[fill=gray] (0,0) -- (0:2) -- +(120:2) -- (0,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/motion/tex
filename: ch04.tex
modified: 2013-04-14 17:36:44
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray}
    ]
    \draw (0,0) -- (0:2) -- +(120:2) -- (0,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/motion/sol
filename: tikz.tex
modified: 2014-05-27 22:39:18
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed] (0,0) .. controls (1,2) .. (4,2);
    \draw[->] (-0.2,-0.4) -- (0,0) node[anchor=north west] {$v_{i}$};
    \draw[->] (4,2) -- ++(0:.5) node[anchor=west]{$v_{f}$};
    \shade[ball color=gray] (1.6,1.4) circle (0.25);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/motion/sol
filename: tikz.tex
modified: 2014-05-27 22:39:18
domain: p24
source:
  \begin{tikzpicture}[scale=1.5]
    \shade[ball color=blue!10!white] (0,0) circle[radius=2];
    \draw[vel] (0,2) --node[anchor=east]{$\omega$} +(90:1);
    \coordinate (p) at (1.13137085,1.2,1.13137085);
    \draw[line width=1,->] (0,0,0) -- (0.849,1.6,0.849);
    \draw[line width=2,->] (0.849,1.6,0.849) -- (1.2735,2.4,1.2735)
    node[anchor=west]{$\ur$};
    \draw[line width=2, ->, color=red] (0.849,1.6,0.849) --
    node[anchor=north] {$\boldsymbol{\hat{\omega}} \cross \ur$}
    ++(0.6,0,-0.6);
    \draw[line width=2, ->, color=yellow!50!white] (0.849,1.6,0.849) --
    % node[anchor=north] {$\boldsymbol{\hat{\omega}} \cross \ur$}
    ++(-0.8,0,-0.8);
    \node[color=yellow!50!white,fill=black!70!white] at (-0.9,1.5) {$\boldsymbol{\omega \cross
          (\omega \cross}\ur)$};
    \draw[->,color=DarkGreen] (0,0,0) -- (2.5,0,0) node[anchor=north]{$y$};
    \draw[->,color=DarkGreen] (0,0,0) -- (0,1.5,0) node[anchor=east]{$z$};
    \draw[->,color=DarkGreen] (0,0,0) -- (0,0,2.5) node[anchor=east]{$x$};
    \draw[dashed,color=DarkGreen] (0.849,1.6,0.849) -- (0.849,0,0.849) -- (0,0,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Makeup
filename: weighty-matter.tex
modified: 2015-07-28 22:59:15
domain: p24
source:
  \begin{tikzpicture}[scale=0.67]
    \draw[line width=6pt] (0,0) -- (0,1);
    \draw[force] (0,0) -- +(-90:1) node[anchor=east]{$mg$};
    \draw[force] (0,1) -- +(90:1) node[anchor=east]{$T$};
    \draw[accel] (1,0.5) -- +(-90:1) node[anchor=west]{$a$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Makeup
filename: hanging-banner.tex
modified: 2015-07-28 20:26:51
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    % The wall
    \draw[line width=1.5](0,-0.5) -- (0,5);
    \fill[fill=gray!50!white] (0,-0.5) rectangle(-0.25,5);
    \node[rotate=90] at (-0.5,2.5) {\textsf{side of building}};
    \draw[line width=4,color=red] (0,0) -- (3,4);
    \node at (1.5,3) {$M,L$};
    \fill (0,0) circle(0.1) node[anchor=north west]{\textsf{hinge}};
    \node at (1.75,-1) {\textsf{side view}};
    \draw[line width=2] (0,4) -- (3,4);
    \draw (3,4) -- (3,2.5);
    \filldraw[fill=gray] (3.1,2.5) rectangle (2.9,0.5);
    \node at (3.4,0.75){$m$};
    \draw[<-] (2,4.1) -- ++(135:1);
    \node at (1.3,5.1){\textsf{cable}};
    \draw (0,1.5) arc (90:54:1.5);
    \node at (71:1.8){$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Makeup
filename: hanging-banner.tex
modified: 2015-07-28 20:26:51
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    % The wall
    \draw[line width=4,color=red] (0,0) -- (3,4);
    \fill[fill=gray] (0,0) circle(0.1);
    \draw[force] (3,4) -- ++(180:1.5) node[anchor=south]{$T$};
    \draw[force] (3,4) -- ++(-90:1.25) node[anchor=west]{$mg$};
    \draw[force] (1.5,2) -- ++(-90:1.75) node[anchor=west]{$Mg$};
    \draw[force] (0,0) -- ++(0:1.5) node[anchor=north]{$F_{x}$};
    \draw[force] (0,0) -- ++(90:3) node[anchor=east]{$F_{y}$};

    \draw (0,1.5) arc (90:54:1.5);
    \node at (71:1.8){$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Makeup
filename: ballistic-pendulum.tex
modified: 2014-08-20 22:00:59
domain: p24
source:
  \begin{tikzpicture}[scale=1.25]
    \node at (90:0.25){$O$};
    \filldraw[fill=gray!25!white] (-0.15,0.05) rectangle (0.15,-3);
    \fill (0,0) circle (0.05);
    \filldraw[fill=gray!50!black] (-1.5,-2.95) --++(0,0.1) --++(0.2,0)
    --++(0.05,-0.05) --++(-0.05,-0.05) -- cycle;
    \node at (-1.5,-2.6){$m$};
    \draw[vel] (-1.1,-2.9) -- node[anchor=south]{$v$} ++(0.6,0);
    \begin{scope}[rotate=30]
      \draw[dashed] (-0.15,0.05) rectangle (0.15,-3);
      \filldraw[fill=gray!50!white] (-0.1,-2.95) --++(0,0.1) --++(0.2,0)
      --++(0.05,-0.05) --++(-0.05,-0.05) -- cycle;
    \end{scope}
    \draw[->,line width=1.5] (0,-1.5) arc(270:300:1.5);
    \node at (-75:1.7){$\theta$};
    \node at (-0.5,-1){$M,\ell$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Makeup
filename: loop-the-loop.tex
modified: 2014-08-21 05:45:38
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[color=gray, line width=3] (2,-1.03) -- (-7, -1.03); % ground
    \draw[line width=1.5] (0,0) circle(1)
    (-120:1) -- ++(150:7);
    \shade[ball color=red] (-6,2.5) circle (0.15);
    \node[text width=1.2in] at (-4, 2.8){ball of radius $r$, mass $m$};
    \draw[->,line width=1.5,dashed] (-6,-1) --node[fill=white]{$h$} (-6,2.35);
    \draw[dashed,->, line width=1.5] (0,0) -- node[anchor=north]{$R$} (165:1);
    \node at (2.5,1) {looped track};
    \node at (90:1.25){$c$};
    \node at (0:1.25){$b$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Makeup
filename: loop-the-loop.tex
modified: 2014-08-21 05:45:38
domain: p24
source:
  \begin{tikzpicture}[scale=2.25]
    \draw[line width=1.5] (0,0) circle(1) (1.5,-1) -- (-2, -1)
    (-120:1) -- ++(150:2);
    \shade[ball color=red] (0:0.925) circle (0.075);
    \draw[dashed,->, line width=1] (0,0) -- node[anchor=north]{$R$} (165:1);
    \node at (90:1.15){$c$};
    \node at (0:1.15){$b$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Makeup
filename: slip-sliding.tex
modified: 2014-09-11 03:16:10
domain: p24
source:
  \begin{tikzpicture}[scale=1.25]
    \filldraw[fill=gray!25!white] (-1,0) rectangle (4,-0.2);
    \filldraw[fill=gray!50!white] (0,0) rectangle (2,1.5);
    \filldraw[fill=gray!25!white] (2,0.5) rectangle (2.5,1);
    \node[fill=gray!10!white] at (1,0.75) {$M$};
    \node at (2.8,0.75) {$m$};
    \draw[force] (-1,0.75) -- node[anchor=south]{$F$} ++(0:1);
    \draw[<-,color=green!50!black] (2.,1) -- ++(45:0.75) node[anchor=west]{$\mu_{s}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Makeup
filename: slip-sliding.tex
modified: 2014-09-11 03:16:10
domain: p24
source:
  \begin{tikzpicture}[scale=1.5]
    \filldraw[fill=gray!25!white] (0,0) rectangle (2,1.5);
    \draw[force] (0,0.75) --node[anchor=south]{$F$} ++(0:0.75);
    \draw[force] (1,0.75) -- ++(-90:1.25) node[anchor=west]{$Mg$};
    \draw[force] (1.1,0) -- ++(90:1.25) node[anchor=west]{$N$};
    \draw[force] (2,0.75) -- node[anchor=south]{$n$} ++(180:0.75);
    \draw[force] (2,0.75) -- node[anchor=west]{$f$} ++ (-90:0.75);
    \draw[accel] (3,1.25) -- node[anchor=south]{$a$} ++(0:1);

    \begin{scope}[shift={(6,0.5)}]
      \filldraw[fill=gray!25!white] (0,0) rectangle (0.5,0.5);
      \draw[force] (0.25,0.25) -- ++(-90:1.25) node[anchor=west]{$mg$};
      \draw[force] (0,0.25) -- ++(0:1) node[anchor=south]{$n$};
      \draw[force] (0,0) -- ++(90:1) node[anchor=east]{$f$};
      \draw[accel] (1.25,1) --node[anchor=south]{$a$} ++(0:1);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Makeup
filename: spring-loop.tex
modified: 2017-09-17 02:46:58
domain: p24
source:
  \begin{tikzpicture}[scale=1,decoration={random steps, segment length=1mm}]
    % rough stuff
    \draw[decorate,line width=1.25,color=gray] (-4.5,0) -- (0,0);
    \draw[decorate,line width=1.25,color=gray] (-4.5,0) -- (0,0);
    \fill[gray!50!white] (-8,0) rectangle (-8.3,1);
    \draw[line width=1.5] (0,0) arc[start angle=-90, end angle=200, radius=1.5]
    (0,0) -- (-8,0) -- (-8,1);
    \fill (0,1.5) circle(0.05);
    \draw[->] (0,1.5) -- ++(135:1.5);
    \node at (-0.8,1.9) {$R$};
    \node at (0,0.4){$A$};
    \node at (1.8,1.5) {$B$};
    \draw[dashed] (0,1.5) -- (1.5,1.5);
    \fill (1.5,1.5) circle(0.05);
    \node at (0,3.4){$C$};
    \node at (-3,0.4){$\mu_{k}$};
    \draw[spring] (-8,0.2) -- node[anchor=south, shift={(0,0.3)}]{$k$}
    ++(0:2);
    \filldraw[fill=gray] (-6,0) rectangle(-5.6,0.4);
    \node at (-5.3,0.5){$m$};
    \draw[<->] (-4.5,-0.6) -- node[fill=white] {$L$} ++(0:4.5);
    \draw (-4.5,-0.2) -- (-4.5,-1) (0,-0.2) -- (0,-1);
    \draw[->] (-4.5,-0.6) -- ++(180:1) node[anchor=north]{$x$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Makeup
filename: spring-loop.tex
modified: 2017-09-17 02:46:58
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) rectangle (1,1);
    \draw[force] (0.5,0.5) -- ++(-90:1.5) node[anchor=west]{$mg$};
    \draw[force] (0.4,1) -- ++(-90:1.5) node[anchor=east]{$N$};
    \draw[accel] (1.5,0.5) -- ++(-90:1) node[anchor=west]{$a$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Makeup/drafts
filename: p24-makeup-exam-v4.tex
modified: 2014-08-20 00:41:53
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=1.5] (0,0) circle(1) (2,-1) -- (-7, -1)
    (-120:1) -- ++(150:7);
    \shade[ball color=red] (-6,2.5) circle (0.15);
    \node[text width=1.2in] at (-4, 2.8){ball of radius $r$, mass $m$};
    \draw[->,line width=1.5,dashed] (-6,-1) --node[fill=white]{$h$} (-6,2.35);
    \draw[dashed,->, line width=1.5] (0,0) -- node[anchor=north]{$R$} (165:1);
    \node at (2.5,1) {looped track};
    \node at (90:1.25){$c$};
    \node at (0:1.25){$b$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Makeup/drafts
filename: p24-makeup-exam-v4.tex
modified: 2014-08-20 00:41:53
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    % The wall
    \draw[line width=1.5](0,-0.5) -- (0,5);
    \fill[fill=gray!50!white] (0,-0.5) rectangle(-0.25,5);
    \node[rotate=90] at (-0.5,2.5) {\textsf{wall}};
    \draw[line width=4,color=red] (0,0) -- (3,4);
    \node at (1.5,3) {$M,L$};
    \fill (0,0) circle(0.1) node[anchor=north west]{\textsf{hinge}};
    \node at (1.75,-1) {\textsf{side view}};
    \draw[line width=2] (0,4) -- (3,4);
    \draw (3,4) -- (3,2.5);
    \filldraw[fill=gray] (3.1,2.5) rectangle (2.9,0.5);
    \node at (3.4,0.75){$m$};
    \draw[<-] (2,4.1) -- ++(135:1);
    \node at (1.3,5.1){\textsf{cable}};
    \draw (0,1.5) arc (90:54:1.5);
    \node at (71:1.8){$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Makeup/drafts
filename: p24-makeup-exam-v1.tex
modified: 2014-08-18 01:40:50
domain: p24
source:
  \begin{tikzpicture}[scale=1.25]
    \filldraw[fill=gray!25!white] (-1,0) rectangle (4,-0.2);
    \filldraw[fill=gray!50!white] (0,0) rectangle (2,1.5);
    \filldraw[fill=gray!25!white] (2,0.5) rectangle (2.5,1);
    \node[fill=white] at (1,0.75) {$M$};
    \node at (2.8,0.75) {$m$};
    \draw[force] (-1,0.75) -- node[anchor=south]{$F$} ++(0:1);
    \draw[<-,color=green!50!black] (2.,1) -- ++(45:0.75) node[anchor=west]{$\mu_{s}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Makeup/drafts
filename: p24-makeup-exam-v3.tex
modified: 2014-08-19 18:21:35
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=1.5](0,-0.5) -- (0,5);
    \fill[fill=gray!50!white] (0,-0.5) rectangle(-0.15,5);
    \draw[line width=2] (0,0) -- node[anchor=north west]{$M,L$} (3,4);
    \fill (0,0) circle(0.1) node[anchor=north west]{hinge};
    \draw (0,4) -- (3,4) -- (3,2.5);
    \filldraw[fill=gray] (3.1,2.5) rectangle (2.9,0.5);
    \node at (3.5,0.25){$m$};
    \draw[<-] (2.5,4.1) -- ++(135:1);
    \node at (1.8,5.1){cable};
    \draw (0,1.5) arc (90:54:1.5);
    \node at (71:1.8){$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Makeup/drafts
filename: p24-makeup-exam-v3.tex
modified: 2014-08-19 18:21:35
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray] (180:5) --++(270:2) --++(0:5) --++(90:1.25) arc(270:180:0.75)
    -- cycle;
    \draw[line width=1.5] (0.5,0) -- ++(-90:1.5);
    \begin{scope}[shift={(0.5,-1.5)}]
      \filldraw[fill=yellow!50!white] (0,0) -- (-0.2,0) --(-0.35,-0.5)
      --(0.35,-0.5) --(0.2,0) --cycle;
      \node at (0,-0.3){$m$};
    \end{scope}

    \begin{scope}[shift={(-3.5,0.5)}]
      % \draw[line width=1.5] (-0.5,0) sin (-0.25,-0.1) cos(0,0) sin (0.25,0.1) cos (0.5,0)
      % sin(0.75,-0.1) cos(1,0) sin(1.25,0.1) cos(1.5,0)
      % sin(1.75,-0.1) cos(2,0) sin(2.25,0.1) cos(2.5,0)
      % sin(2.75,-0.1) cos(3,0) sin(3.25,0.1) cos(3.5,0);
      \draw[line width=1.5] (-0.5,0) sin (-0.25,-0.05) cos(0,0) sin (0.25,0.05) cos (0.5,0)
      sin(0.75,-0.05) cos(1,0) sin(1.25,0.05) cos(1.5,0)
      sin(1.75,-0.05) cos(2,0) sin(2.25,0.05) cos(2.5,0)
      sin(2.75,-0.05) cos(3,0) sin(3.25,0.05) cos(3.5,0);
    \end{scope}
    \filldraw[fill=yellow!50!white] (-5,0) rectangle (-4.,1);
    \filldraw[fill=blue!25!white] (0,0) circle (0.5);
    \filldraw[fill=blue!75!white] (0,0) circle (0.1);
    \filldraw[fill=gray!50!white,opacity=0.5] (-30:0.2) arc(-30:120:0.2) -- (210:0.75) arc (210:240:0.75)
    -- cycle;
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Challenge
filename: winter.tex
modified: 2017-09-18 18:12:27
domain: p24
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[fill=gray!50!white] (0,0) circle[radius=2];
    % label for disk
    \node[anchor=south west] at (60:2.1) {$M,R$};
    % child
    \draw[fill=gray] (-3,-1.5) circle[radius=0.1] node[anchor=south]{$M$};
    \draw[<-] (-2.95, -1.6) -- ++(-60:0.75)
    node[anchor=north]{\small\textsf{Incoming child}};
    % velocity
    \draw[vel,->] (-2.8,-1.5) -- node[anchor=north]{$v$} ++(0:1.25);
    % landing site
    \filldraw (0, -1.5) circle[radius=0.035];
    \draw[coord,->] (0,0) -- node[anchor=east]{$r$} (0,-1.46);
    \draw[coord,<-] (0.1,-1.6) -- ++(-45:1)
    node[anchor=west]{\small\textsf{Landing site}};
    % top view label
    \node at (-3,2.5){\textsf{top view}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Challenge
filename: snowboard.tex
modified: 2020-07-25 18:34:13
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=2] (-4,0) -- (-3,0) coordinate (A)
    arc(180:330:3) coordinate (B)
    -- ++(0:2) ++(180:0.5) coordinate (C);
    \node[anchor=north east] at (A) {A};
    \node[anchor=north west] at (B) {B};
    \node[anchor=north] at (C) {C};
    \draw[dashed] (0,0) -- node[anchor=north east]{$R$}
    ++(-30:3) -- node[anchor=east,shift={(0,0.2)}]{\small $R/2$} ++ (90:1.5)
    -- cycle;
    \filldraw[fill=white] (0,0) circle[radius=0.05];
    \draw (0:1) arc (0:-30:1);
    \node at (-10:1.3){\small $30^{\circ}$};
    \draw[dashed,DarkSlateGray] (B) parabola[bend at end] ++(0.75,1.25)
    coordinate (D);
    \draw[dashed,DarkSlateGray,->] (D)  parabola ++(0.75, -1.25);
    \begin{scope}[shift=(A)]
      \draw[line width=1] (0,0.1) -- ++(180:0.2);
      \draw (0,0.1) arc(0:-180:0.05) (-0.1,0.1) arc(0:-180:0.05);
      \draw[line width=1.1,DarkSlateGray] (-0.15,0.1) -- ++(70:0.15)
      coordinate(E) -- ++(-60:0.15) (E) -- ++(90:0.1) -- ++(-15:0.1)
      (E) ++(0,0.2) circle[radius=0.05];
    \end{scope}
    \draw[dashed,->] (180:2.9) arc (180:225:2.9);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Challenge
filename: atom-laser.tex
modified: 2020-07-25 16:51:14
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[photon,->] (0,0) -- (2,0) ;
    \draw[photon,->] (0,0.25) -- (2,0.25) ;
    \draw[photon,->] (0,0.5) -- (2,0.5) ;
    \node at (1,1) {$\lambda$};
    \node at (1,-0.75){continuous laser beam};

    \draw[gray,line width=3pt] (9,-0.75) -- ++(90:2.);
    \node[anchor=west] at (9.25,0.25){mirror};

    \draw[coord] (9,0.25) --node[anchor=south]{$x$} ++(180:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Challenge
filename: atom-laser.tex
modified: 2020-07-25 16:51:14
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=3pt, gray!25!white] (-2,-2) rectangle (11,2);
    \node at (5,-1.7){vacuum chamber};

    \foreach \y in {-0.25,0,0.25} {
        \draw[photon,->] (0,\y) -- (2,\y);
      }

    \node at (1,1) {$\lambda$};
    \node at (1,-0.75){continuous laser beam};

    \draw[gray,line width=3pt] (9,-1) -- ++(90:2.);
    \node[anchor=west] at (9.25,0){mirror};

    \draw[coord] (9,0) --node[anchor=south]{$x$} ++(180:1);
    \draw[fill=gray!50!white] (5,0) circle[radius=0.05] node[anchor=north]{atom};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Challenge
filename: disk-drop.tex
modified: 2020-07-26 18:03:31
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed,line width=1.5,SlateBlue] (0,3) -- (0,-3);
    \cylinder{(0,2)}{1.5}{1}
    \cylinder{(0,-1)}{3}{0.5}
    \node at (-1.85,2) {$2M$};

    \begin{scope}[DarkGreen,->,line width=1.5]
      \draw (-1.25,1.25)  arc[x radius=1.5, y radius = 0.5, start
          angle=210, end angle=330];
      \node at (0,1.25) {$\omega_{0}$};
      \draw (2.5,-1.7)  arc[x radius=3, y radius = 0.75, start
          angle=330, end angle=210];
      \node at (0,-1.5) {$\omega_{0}$};
    \end{scope}
    \draw[dashed,line width=1.5,SlateBlue] (0,2) -- ++(90:0.5) (0,-1) -- ++(90:0.75);
    \begin{scope}[DarkGreen,->]
      \draw (0,2) -- node[anchor=south,shift={(0,0.35)}]{$R/2$} ++(0:1.5);
      \draw (0,-1) -- node[anchor=south]{$R$} ++(0:3);
    \end{scope}
    \node at (-3.25,-1.25) {$M$};

    \begin{scope}[shift={(5,0)},DarkSlateBlue]
      \node at (0,1.75) {\textsf{\small counterclockwise}};
      \node at (0,-1.25) {\textsf{\small clockwise}};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Challenge
filename: fbd.tex
modified: 2020-07-25 17:31:08
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \def\wid{3}
    \fill[gray!25] (-\wid,0) rectangle (\wid,-0.3);
    \draw (-\wid,0) -- (\wid,0);
    \filldraw[fill=gray!50](-1,0) rectangle (1,2);
    \node at (0,1){$M_{A}$};
    \filldraw[fill=gray!50] (1,0.5) rectangle (2,1.5);
    \node at (1.5,1) {$M_{B}$};
    \draw[vel,<-] (-1,1) -- ++(180:1.5) node[anchor=east]{$F_{0}$};
    \draw[DarkGreen,<-,line width=1.25] (1,1.5) -- ++(45:0.75) node[anchor=south west]{$\mu$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Challenge
filename: pinball.tex
modified: 2017-09-16 23:12:39
domain: p24
source:
  \begin{tikzpicture}[scale=1,
      decoration={zigzag, segment length=1mm, amplitude=0.3mm}]
    \node[anchor=west,gray] at (-8,3) {\textsf{side view}};
    % rough stuff
    \draw[decorate,line width=1.25,color=gray] (-4.5,0) -- (0,0);
    \fill[gray!50!white] (-8,0) rectangle (-8.3,1);
    \draw[line width=1.5] (0,0) arc[start angle=-90, end angle=200, radius=1.5]
    (0,0) -- (-8,0) -- (-8,1);
    \fill (0,1.5) circle(0.05);
    \draw[->] (0,1.5) -- ++(135:1.5);
    \node at (-0.8,1.9) {$R$};
    \node at (0,0.4){$A$};
    \node at (1.8,1.5) {$B$};
    \draw[dashed] (0,1.5) -- (1.5,1.5);
    \fill (1.5,1.5) circle(0.05);
    \node at (0,3.3){$C$};
    \node at (-3,0.4){$\mu_{k}$};
    \draw[spring] (-8,0.2) -- node[anchor=south, shift={(0,0.3)}]{$k$}
    ++(0:2);
    % plunger
    \draw[line width=1.5] (-6.03,0) -- ++(90:0.45);
    \filldraw[fill=gray] (-6,0) rectangle(-5.6,0.4);
    \node at (-5.3,0.5){$m$};
    \draw[<->] (-4.5,-0.6) -- node[fill=white] {$L$} ++(0:4.5);
    \draw (-4.5,-0.2) -- (-4.5,-1) (0,-0.2) -- (0,-1);
    \draw[->] (-4.5,-0.6) -- ++(180:1) node[anchor=north]{$x$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Challenge
filename: cylinder.tex
modified: 2020-07-26 18:07:13
domain: p24
source:
  \begin{tikzpicture}[scale=0.5]
    \fill[gray!60] (1.5,0) rectangle (-1.5,-4);
    \fill[gray!60] (0,-4) ellipse[x radius=1.5, y radius=0.5];
    \shadedraw[inner color=white,outer color=gray!75,gray!75] (0,0) ellipse[x
        radius=1.5,y radius=0.5];
    \draw[DarkGreen,<->] (1.75,0) -- node[anchor=west]{$h$} ++(-90:4);
    \draw[DarkGreen,<->] (0,0.75) -- node[anchor=south]{$R$} ++ (0:1.5);
    \draw[DarkGreen,dashed] (0,0) -- +(90:0.65) (1.5,0.1) -- ++(90:0.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Challenge
filename: cylinder.tex
modified: 2020-07-26 18:07:13
domain: p24
source:
  \begin{tikzpicture}[scale=0.75]
    \filldraw[fill=gray!20] (-5.5,0) rectangle +(3,3);
    \node at (-4,1.5) {$M$};
    \draw (-2.5,2) -- (1,2); % horizontal string
    \draw(2,1) -- (2,-2); % vertical string
    \filldraw[fill=gray!50] (2,-2.5) circle[radius=0.5];
    \node at (2,-2.5) {$M$};

    \draw[line width=2] (-6,0) -- (0,0) -- (0,-3); % table
    \shadedraw[inner color=white,outer color=gray!60] (1,1) circle[radius = 1];
    \draw[line width=1] (0,-0.05) -- ++(45:1.414) (-0.05,0) -- ++(45:1.414);
    \fill (1,1) circle[radius=0.1];

    \node at (45:3) {$M$};
    \draw[DarkGreen,<->] (1,1) --node[anchor=north east]{\scriptsize $R$} ++(-45:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Challenge
filename: impulsive.tex
modified: 2017-09-18 18:20:32
domain: p24
source:
  \begin{tikzpicture}[scale=0.75]
    \draw[line width=1.5] (\width,-3) -- (\width,0) arc(0:90:1) -- (1,1) (-1,1) -- (-\width+1,1) arc(90:180:1)
    -- (-\width,-3);
    \draw[spring, line width=1.5] (-1,1) -- (1,1);
    \node at (0, 1.7){$k$};
    \filldraw[fill=gray!25!white] (\width-1,0) circle(1) (-\width+1,0) circle(1);
    \filldraw[fill=black] (\width-1,0) circle(0.1) (-\width+1,0) circle(0.1);
    \filldraw[fill=blue!50!white] (\width+0.4,-3) rectangle (\width-0.4,-5)
    (-\width-0.4,-3) rectangle (-\width+0.4,-5);
    \node at (-\width+0.75,-4){$m$};
    \node at (\width-0.75,-4){$m$};
    \draw[accel] (0,-2) -- node[anchor=west]{$~~g$} ++(-90:1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/Exams/Challenge/2021
filename: cylinder.tex
modified: 2021-06-08 22:55:16
domain: p24
source:
  \begin{tikzpicture}[scale=0.75]
    \fill[gray!60] (1.5,0) rectangle (-1.5,-4);
    \fill[gray!60] (0,-4) ellipse[x radius=1.5, y radius=0.5];
    \shadedraw[inner color=white,outer color=gray!75,gray!75] (0,0) ellipse[x
        radius=1.5,y radius=0.5];
    \draw[DarkGreen,<->] (1.75,0) -- node[anchor=west]{$h$} ++(-90:4);
    \draw[DarkGreen,<->] (0,0.75) -- node[anchor=south]{$R$} ++ (0:1.5);
    \draw[DarkGreen,dashed] (0,0) -- +(90:0.65) (1.5,0.1) -- ++(90:0.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/E79
filename: LaplaceTransforms.tex
modified: 2019-12-02 00:15:37
domain: E79
source:
  \begin{tikzpicture}[scale=1,>=latex]
    \def\xrang{8}
    \begin{axis}[
        xmin=0, xmax=\xrang, ymin=0, ymax=1.5, enlargelimits=false,
        width=4in, height=2in,
        xlabel={$t$}, ylabel={$x$},
        ytick={0,.5,1,1.5},
        xtick={0,1,...,\xrang},
        % xticklabel=\empty, xticklabels{0,,$a$,,a$},
        % axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \pgfmathsetmacro{\zet}{0.25}
      \pgfmathsetmacro{\sz}{sqrt(1-\zet*\zet)}
      \pgfmathsetmacro{\wn}{2.5}
      \pgfmathsetmacro{\od}{\sz * \wn}
      \pgfmathsetmacro{\ph}{atan(\sz/\zet)}
      \pgfmathsetmacro{\trise}{(180-\ph)/deg(\od)}
      \addplot[DarkGreen, domain=0:\xrang, samples=200, line width=1pt]
      {1 - exp(-\zet * \wn * x) * sin(deg(\od * x)+\ph) / \sz};
      \draw[dashed,blue!50!white](0,1) -- (\xrang,1);
      \draw[<-] (\trise,1) -- ++(0.5,-0.25) node[anchor=north]{$t_{\rm rise}$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p54/2012/TR/jkentdobias
filename: techreport.tex
modified: 2012-05-05 21:00:48
domain: p54
source:
  \begin{tikzpicture}[scale=0.9]
    \draw (-0.5,0) -- (-0.5,10) -- (0.5,10) -- (0.5,0);
    \draw[fill=white] (-1.5,8) -- (-1.5,9) -- (1,9) -- (1,8) -- (-1.5,8);
    \draw[fill=black] (-1.6,7) -- (-0.75,7) -- (-0.75,8.25) -- (-1,8.25) -- (-1,8.9) -- (-1.35,8.9) -- (-1.35,8.25) --
    (-1.6,8.25) -- (-1.6,7);
    \draw[decorate,decoration={zigzag,segment length=4,amplitude=1}] (-1.185,8) -- node[xshift=-10] {$m_1$}(-2,0.9);
    \draw[decorate,decoration={zigzag,segment length=4,amplitude=1}] (-1.165,8) -- node[xshift=10] {$m_2$} (1.25,0);
    \draw[fill=black] (1.25,0) circle (0.05);
    \draw[fill=gray,color=gray] (-1.175,8) circle (0.75);
    \draw[fill=black] (-1.175,8) circle (0.05);
    \draw[fill=yellow,color=yellow] (-0.75,8.4) circle (0.1);
    \draw (-0.75,8.4) -- (-0,8.5);
    \draw (0.5,8.5) node {$m_{\textrm e}$};
    \draw (-0.9,7.8) node {$M$};
    \draw[thick] (-.6,8.8) arc (45:90:.9);
    \draw (-.75,9.3) node {$\theta$};
    \draw[fill=gray] (-1.625,0.25) circle (0.5);
    \draw[fill=black] (-1.625,0.25) circle (0.05);
    \draw[fill=white] (-2,1) -- (-2.125,0.875) -- (-1.625,0.125) -- (-1.5,0.25) -- (-2,1);
    \draw[decorate,decoration={brace,amplitude=5pt},yshift=-1,thick] (-1.725,0.025) --  node[xshift=-7pt,yshift=-4pt] {$l$}
    (-2.225,0.775);
    \draw[fill=black] (-2,0.875) circle (0.05);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p64/figs
filename: figtmp.tex
modified: 2022-07-23 18:06:41.283762
domain: p64
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=1, ymin=0, ymax=1, enlargelimits=false,
        width=2.5in, height=2in,
        xlabel={}, ylabel={}, ytick=\empty,xtick={0.6},%ytick={0,1}, xtick={0,1},
        xticklabel={$x_{0}$}, %xticklabels{0,,$a$,,a$},
        axis x line=bottom, axis y line=left, axis line style={gray,line width=0.5} % for no frame
      ]
      \addplot[DarkGreen, domain=0.5:0.7, samples=151, line width=0.75pt]
      {exp(-0.5*((x-0.6)/0.01)^2)};

      \draw[DarkRed] (axis cs:{0.58,0}) --
      (axis cs:{0.58,0.8}) -- (axis cs:{0.62,0.8}) --
      (axis cs:{0.62,0});
      \node at (axis cs:{0.9,-0.1}) {$x$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p64/figs
filename: figtmp.tex
modified: 2022-07-23 18:06:41.283762
domain: p64
source:
  \begin{tikzpicture}[scale=1,>=Stealth]
    \draw[dashed, SlateGray] (15:3) arc(15:60:3) (15:4) arc(15:60:4)
    (30:2) -- (30:5) (45:2) -- (45:5);
    \draw[line width=1.5, gray] (30:3) -- (30:4) arc(30:45:4) -- (45:3) arc(45:30:3);
    \begin{scope}[font=\small, DarkGreen]
      \draw[->] (37.5:3.75) -- (37.5:4.5) node[anchor=south west]{$\left. A_{r} r\dd{\theta}\right|_{r+\dd{r}}$};
      \draw[->] (37.5:2.5) node[anchor=north east]{$\left. A_r r\dd{\theta}\right|_{r}$} -- (37.5:3.25);
      \draw[->] (40:3.5) arc(40:55:3.5) node[anchor=south east]{$\left. A_{\theta} \dd{r} \right|_{\theta + \dd{\theta}}$};
      \draw[->] (20:3.5) node[anchor=north west]{$\left. A_{\theta} \dd{r} \right|_{\theta}$} arc(20:35:3.5);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p64/figs
filename: figtmp.tex
modified: 2022-07-23 18:06:41.283762
domain: p64
source:
  \begin{tikzpicture}[scale=1,>=Stealth]
    \draw[line width=1.5, gray] (0,0) rectangle (3,3);
    \draw[line width=1.5, blue] (0,3) --node[anchor=south]{$V=1$} (3,3);
    \draw[gray] (1.5,-1) coordinate (P) node[anchor=north]{$V = 0$};
    \draw[DarkGreen,->] (P) -- (1.5,0);
    \draw[DarkGreen,->] (P) .. controls (-1,-0.5) and (-1.5,1) .. (0, 1.5);
    \draw[DarkGreen,->] (P) .. controls (4,-0.5) and (4.5,1) .. (3, 1.5);
    \draw[DarkGreen] (0,0) node[anchor=north]{0} (3,0) node[anchor=north]{$L$} (0,0) node [anchor=east]{$0$} (0,3) node[anchor=east]{$L$};
    \draw[DarkGreen,<->] (-1,-1) node[anchor=north]{$x$} -- ++(-0.5,0) -- ++(0,0.5) node[anchor=east]{$y$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p64/figs
filename: figtmp.tex
modified: 2022-07-23 18:06:41.283762
domain: p64
source:
  \begin{tikzpicture}[scale=1,>=Stealth]
    \draw[gray] (0,1) -- (1,1) (0,-1) -- (1,-1);
    \filldraw[gray,fill=gray!20!white] (0,0) circle[x radius=0.1, y radius=1];
    \fill[gray!20!white] (1,0) circle[x radius=0.1, y radius=1];
    \draw[dashed, gray] (1,1) arc[x radius=0.1, y radius=1, start angle=90, end angle=270];
    \draw[gray] (1,1) arc[x radius=0.1, y radius=1, start angle=90, end angle=-90];
    \draw[DarkGreen,<-] (0,-.8) --++(-135:0.4) node[anchor=north]{$A$};
    \draw[DarkGreen] (0, 1) node[anchor=south,font=\small]{$x$} (1,1) node[anchor=south,font=\small]{$x+\delta x$};
    \draw[<-, DarkRed, line width=1.5] (0,0) -- ++(180:0.5) node[anchor=east]{$\vb{J}(x)$};
    \draw[->, DarkRed, line width=1.5] (1,0) -- ++(0:0.5) node[anchor=west]{$\vb{J}(x+\delta x)$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p64/figs
filename: figtmp.tex
modified: 2022-07-23 18:06:41.283762
domain: p64
source:
  \begin{tikzpicture}[scale=1,>=Stealth]
    \draw[->] (-3,0) -- (3,0) node[anchor=north]{$x$};
    \draw[->] (0,-1.5) -- (0,3) node[anchor=east]{$y$};
    \begin{scope}[DarkGreen, line width=1.25]
      \draw (-2.75,0) -- (-0.25, 0) arc(180:360:0.25) --
      (2.75,0) arc(0:180:2.75);
      \foreach \x in {-1,1}{\draw[->] (\x,0) -- ++(0.25,0);}
      \draw[->] (45:2.75) -- (50:2.75);
      \draw[->] (135:2.75) -- (140:2.75);
    \end{scope}
    \draw[SlateBlue,->,line width=0.75] (0,0) -- node[anchor=south]{$R$} (30:2.75);
    \fill[red] (0,0) circle[radius=0.05];
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p64/figs
filename: figtmp.tex
modified: 2022-07-23 18:06:41.283762
domain: p64
source:
  \begin{tikzpicture}
    \begin{axis}[
        ymin=0, ymax=1.02, enlargelimits=false,
        xmin=0, xmax=20,
        xlabel={$x$}, ylabel={$\ln x$},
        width=4in, height=3in,
      ]
      \def\x{0} \def\y{0}
      \pgfplotsforeachungrouped \x in {1, 2, ..., 20}
        {
          \edef\temp{\noexpand\filldraw[SlateBlue, fill=SlateBlue!33!white] (axis cs:\x,0) rectangle (axis cs:\x+1,1/\x);}
          \temp
          % \filldraw[SlateBlue, fill
          =SlateBlue!33!white] (axis cs:\x,0) rectangle (axis cs:\x+1,1/\x);
        };
      \addplot[DarkBlue, domain=1:20, samples=100,line width=1pt]
      {1/x};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022/Chapters/Ch13/prob
filename: StirlingEngine.tex
modified: 2022-08-23 23:22:02.410557
domain: Book
source:
  \begin{tikzpicture}[scale=0.75,>=Stealth]
    \def\hht{0.5}  % half height of cylinder
    \def\dy{-2.5} % shift between panels
    \begin{scope}
      \node[anchor=east] at (-0.25,0) {(1)};
      % cylinder
      \draw[gray, line width=1.5, rounded corners=10] (5,\hht) -- (0, \hht) -- (0, -\hht) -- (5,-\hht);
      % displacer
      \begin{scope}[gray, shift={(0.05,0)}]
        \draw[line width=1.25] (0.5,0) -- ++ (7,0);
        \fill[rounded corners=9] (0,0.9*\hht) rectangle (1.5,-0.9*\hht);
      \end{scope}
      % piston
      \begin{scope}[DarkBlue, shift={(3.5,0)}]
        \fill (0,\hht) rectangle (0.25,-\hht) (0,.1) rectangle (4,-0.1);
        \draw[->,line width=1.5] (0.75,-1.5*\hht) -- ++ (180:1.5);
      \end{scope}
      % heat flow
      \begin{scope}[DarkRed, shift={(2.5,\hht)}]
        \draw[->] (0,-0.2) arc(200:160:1) node[anchor=south]{$Q_{\rm out}$} ;
      \end{scope}
      % work flow
      \begin{scope}[DarkGreen, shift={(6,-1.5*\hht)}]
        \draw[<-] (0,0) -- node[anchor=north]{$W_{\rm in}$} ++(1,0);
      \end{scope}
    \end{scope}

    \begin{scope}[shift={(0,\dy)}]
      \node[anchor=east] at (-0.25,0) {(2)};
      % cylinder
      \draw[gray, line width=1.5, rounded corners=10] (5,\hht) -- (0, \hht) -- (0, -\hht) -- (5,-\hht);
      % displacer
      \begin{scope}[gray, shift={(1.,0)}]
        \draw[line width=1.25] (0.5,0) -- ++ (7,0);
        \fill[rounded corners=9] (0,0.9*\hht) rectangle (1.5,-0.9*\hht);
        \draw[line width=1.25, ->] (0,-1.5*\hht) -- ++ (1,0);
      \end{scope}
      % piston
      \begin{scope}[DarkBlue, shift={(2.6,0)}]
        \fill (0,\hht) rectangle (0.25,-\hht) (0,.1) rectangle (4,-0.1);
      \end{scope}
    \end{scope}

    \begin{scope}[shift={(0,2*\dy)}]
      \node[anchor=east] at (-0.25,0) {(3)};
      % cylinder
      \draw[gray, line width=1.5, rounded corners=10] (5,\hht) -- (0, \hht) -- (0, -\hht) -- (5,-\hht);
      % displacer
      \begin{scope}[gray, shift={(2,0)}]
        \draw[line width=1.25] (0.5,0) -- ++ (7,0);
        \fill[rounded corners=9] (0,0.9*\hht) rectangle (1.5,-0.9*\hht);
      \end{scope}
      % piston
      \begin{scope}[DarkBlue, shift={(3.6,0)}]
        \fill (0,\hht) rectangle (0.25,-\hht) (0,.1) rectangle (4,-0.1);
        \draw[<-,line width=1.5] (0.75,-1.5*\hht) -- ++ (180:1.5);
      \end{scope}
      % heat flow
      \begin{scope}[DarkRed, shift={(0.2,-\hht)}]
        \draw[->] (0.2,-0.2) node[anchor=north]{$Q_{\rm in}$} arc(200:160:1)  ;
        \begin{scope}[shift={(1,-1)},scale=0.5]
          \filldraw[yellow!75!orange]  (0,0) .. controls (-.75,.625) and (.25,1) .. (-.1,2) .. controls (.5,1.25) and (0.5,.25) .. (0,0);
          \filldraw[orange,scale=0.6,opacity=0.5]  (0,0) .. controls (-.75,.625) and (.25,1) .. (.1,2) .. controls (.5,1.25) and (0.5,.25) .. (0,0);
        \end{scope}
      \end{scope}
      % work flow
      \begin{scope}[DarkGreen, shift={(6,-1.5*\hht)}]
        \draw[->,line width=2] (0,0) -- node[anchor=north]{$W_{\rm out}$} ++(1.25,0);
      \end{scope}
    \end{scope}

    \begin{scope}[shift={(0,3*\dy)}]
      \node[anchor=east] at (-0.25,0) {(4)};
      % cylinder
      \draw[gray, line width=1.5, rounded corners=10] (5,\hht) -- (0, \hht) -- (0, -\hht) -- (5,-\hht);
      % displacer
      \begin{scope}[gray, shift={(1.,0)}]
        \draw[line width=1.25] (0.5,0) -- ++ (7,0);
        \fill[rounded corners=9] (0,0.9*\hht) rectangle (1.5,-0.9*\hht);
        \draw[line width=1.25,<-] (0,-1.5*\hht) -- ++ (1,0);
      \end{scope}
      % piston
      \begin{scope}[DarkBlue, shift={(4,0)}]
        \fill (0,\hht) rectangle (0.25,-\hht) (0,.1) rectangle (4,-0.1);
      \end{scope}
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: aproblem.tex
modified: 2022-08-26 21:47:28.843210
domain: Book
source:
  \begin{tikzpicture}[#2, scale=1+#1*0.15]
    \pgfmathsetmacro{\sides}{2+#1}
    \pgfmathsetmacro{\ang}{360/\sides}
    \def\len{0.15cm}
    \filldraw (0,0) \foreach \n in {1,2,...,\sides} {--++(\n*\ang:\len)};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch12.tex
modified: 2022-08-26 23:03:35.780566
domain: Book
source:
  \begin{tikzpicture}[scale=1.5,>=Stealth]
    \draw[->,DarkSlateGray] (0,0) --node[anchor=north]{$T$} (3,0);
    \draw[->,DarkSlateGray] (0,0) --node[anchor=east]{$p$} (0,3);
    \begin{scope}[DarkGreen,line width=1.5]
      \draw (1,1.5) coordinate (O) .. controls (0.9,1.1) and (0.7, 0.9) .. (0.4, 0.5);
      \draw (O) .. controls (2,1.85) and (2.3,2.2) .. (2.9,2.8);
      \draw (O) -- ++(110:1);
    \end{scope}
    \fill[DarkGreen] (2.02,2) coordinate (c) circle[radius=0.035];
    \fill[DarkBlue] (c) ++ (125:0.1) coordinate (a) circle[radius=0.035];
    \fill[DarkRed] (c) ++ (125:-0.1) coordinate (b) circle[radius=0.035];

    % Show the potential on the coexistence curve
    \begin{scope}[shift={(3,2)}, DarkGreen]
      \myaxes{0}{0}
      \draw[<-] (c) ++(0.05,0) to[out=0,in=210] (-0.25,0.15);
    \end{scope}

    \begin{scope}[shift={(1.6,0.75)}, DarkRed]
      \myaxes{0.05}{-0.05}
      \draw[<-] (b) ++(0,-0.05) to[out=250,in=90] (0.2,0.55);
    \end{scope}
    \begin{scope}[shift={(1.2,2.6)}, DarkBlue]
      \myaxes{-0.05}{0.05}
      \draw[<-] (a) ++(-0.05,0) to[out=180,in=270] (0.15,-0.25);
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch13.tex
modified: 2022-08-26 21:58:44.314108
domain: Book
source:
  \begin{tikzpicture}[scale=1,
      heatflow/.style={line width=2,->,DarkRed},
      workflow/.style={line width=2,->,DarkGreen}
    ]
    \def\dx{2.5}
    \begin{scope}
      \filldraw[fill=red!30!white] (-1,-0.1) rectangle (1,-1);
      \node at (0.7,-0.7){$T_{h}$};
      \cylinder{(0,0)};
      \piston{(0,0.75)};
      \draw[workflow] (0,2) -- ++(90:0.85) node[anchor=south]{$W_{a}$};
      \draw[heatflow] (0,-0.5) node[anchor=east]{$Q_{h}$} -- ++(90:.85);
      \node at (0,-1.5){(a)};
    \end{scope}

    \begin{scope}[shift={(\dx,0)}]
      \cylinder{(0,0)};
      \piston{(0,1.5)};
      \draw[workflow] (0,2.75) -- ++(90:0.85) node[anchor=south]{$W_{b}$};
      \node at (0,-1.5){(b)};
    \end{scope}

    \begin{scope}[shift={(2*\dx,0)}]
      \filldraw[fill=blue!30!white] (-1,-0.1) rectangle (1,-1);
      \node at (0.7,-0.7){$T_{c}$};
      \cylinder{(0,0)};
      \piston{(0,2.5)};
      \draw[workflow] (0,4.5) node[anchor=east]{$W_{c}$}-- ++(-90:0.85);
      \draw[heatflow] (0,0.35) -- ++(-90:.85) node[anchor=east]{$Q_{c}$};
      \node at (0,-1.5){(c)};
    \end{scope}

    \begin{scope}[shift={(3*\dx,0)}]
      \cylinder{(0,0)};
      \piston{(0,1.5)};
      \draw[workflow] (0,3.6) node[anchor=east]{$W_{d}$} -- ++(-90:0.85);
      \node at (0,-1.5){(d)};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022
filename: Ch13.tex
modified: 2022-08-26 21:58:44.314108
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \def\ratio{3}
    \def\slide{3}
    \begin{axis}[
        ymin = -0.5,
        xmin = 0.5,
        xmax = \ratio*1.1,
        ymax = \slide*1.1,
        enlargelimits = false,
        height=2.5in,
        width=2.5in,
        ylabel={$p$},
        xlabel={$V$},
        xtick=\empty,
        ytick=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1,DarkSlateGray},
        xtick align=inside,
      ]
      \addplot[
        trace01,
        domain=1:\ratio,
        samples=51,
        line width=1.5pt,
      ] {1/x^1.4};
      \addplot[
        trace01,domain=1:\ratio,samples=51,line width=1.5pt
      ]
      {\slide/x^1.4};
      \draw[trace01,line width=1.5pt] (axis cs:1,1) coordinate(B) --
      (axis cs:1,\slide) coordinate(C)
      (axis cs:\ratio,1/\ratio^1.4) coordinate(A)-- (axis
      cs:\ratio,\slide/\ratio^1.4) coordinate (D);
      \begin{scope}[font=\small,DarkGreen]
        \node[anchor=north west] at (A) {1};
        \node[anchor=north east] at (B) {2};
        \node[anchor=south east] at (C) {3};
        \node[anchor=south west] at (D) {4};
      \end{scope}
    \end{axis}
    %\draw[color=DarkGreen] (2.504,0) -- ++(90:3.88);
    %\draw[color=DarkGreen,<-] (2.51,3.9) -- ++(45:0.6) node[anchor=south west]
    %{$\overline{v}$};
    %
    %\draw[DarkBlue] (2.720,0) -- ++(90:3.55);
    %\draw[DarkBlue,<-] (2.8, 3.55) -- ++(0:0.6) node[anchor=west]{$v_{\rm rms}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022/Chapters/Ch02/sol
filename: PMT.tex
modified: 2022-06-15 23:34:17.156758
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=0.5, ymin=0.9, ymax=1.5, enlargelimits=false,
        width=2.5in, height=2in,
        xlabel={$\dot{n}\tau$}, ylabel={$\dot{N}/\dot{n}$}, ytick={1, 1.25, 1.5}, xtick={0,0.25, 0.5},
        % xticklabel=\empty, xticklabels{0,,$a$,,a$},
        % axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkGreen, domain=0.01:0.5, samples=100, line width=2pt,]
      {-ln(1-x)/x};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/hw
filename: hw05-sol.tex
modified: 2022-10-02 22:48:19.587008
domain: p117
source:
  \begin{tikzpicture}[scale=0.8]
    \begin{axis}[
        ymin = 0,
        ymax = 1.2,
        xmin = 0,
        xmax = 3.3,
        enlargelimits = false,
        height=2.5in,
        width=3.25in,
        ylabel={$f(v)$},
        ytick=\empty,
        xlabel={$v / \tilde{v}$},
        xtick={0,1,2,3},
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25},
        xtick align=inside,
      ]
      \addplot[
        trace01,
        opacity=0.5,
        domain=0:3,
        samples=201,
        line width=2pt,
      ] { x^2 * exp(1-x^2) };
      \node at (1.5, 1) [trace01,opacity=0.5] {$f_3(v)$};
      %\draw[color=DarkGreen] (1.128,0) -- ++(90:0.969);
      %\draw[color=DarkGreen,<-] (1.128,0.969) ++(30:0.02) -- ++(30:0.2)
      %node[anchor=west] {$\overline{v}$};
      %\draw[DarkBlue] (1.225,0) -- (1.225,0.91);
      %\draw[DarkBlue,<-] (1.28,0.91) --++(0:0.2) node[anchor=west]{$v_{\rm rms}$};
      \addplot[
        trace02,
        line width=2pt,
        domain=0:3,
        samples=201
      ] {sqrt(pi*e)/4 *x * exp(0.5 * (1-x^2))};
      \node at (2.5, 0.35) [trace02] {$f_2(v)$};
    \end{axis}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: Otto.tex
modified: 2022-10-26 16:09:14.322208
domain: p117
source:
  \begin{tikzpicture}[scale=1.25]
    \def\ratio{3}
    \def\slide{3}
    \begin{axis}[
        ymin = -0.5,
        xmin = 0.5,
        xmax = \ratio*1.1,
        ymax = \slide*1.1,
        enlargelimits = false,
        height=2.5in,
        width=2.5in,
        ylabel={$p$},
        xlabel={$V$},
        xtick=\empty,
        ytick=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1,DarkSlateGray},
        xtick align=inside,
      ]
      \addplot[
        trace01,
        domain=1:\ratio,
        samples=51,
        line width=1.5pt,
      ] {1/x^1.4};
      \addplot[
        trace01,domain=1:\ratio,samples=51,line width=1.5pt
      ]
      {\slide/x^1.4};
      \draw[trace01,line width=1.5pt] (axis cs:1,1) coordinate(B) --
      (axis cs:1,\slide) coordinate(C)
      (axis cs:\ratio,1/\ratio^1.4) coordinate(A)-- (axis
      cs:\ratio,\slide/\ratio^1.4) coordinate (D);
      \begin{scope}[font=\small,DarkGreen]
        \node[anchor=north west] at (A) {1};
        \node[anchor=north east] at (B) {2};
        \node[anchor=south east] at (C) {3};
        \node[anchor=south west] at (D) {4};
      \end{scope}
    \end{axis}
    %\draw[color=DarkGreen] (2.504,0) -- ++(90:3.88);
    %\draw[color=DarkGreen,<-] (2.51,3.9) -- ++(45:0.6) node[anchor=south west]
    %{$\overline{v}$};
    %
    %\draw[DarkBlue] (2.720,0) -- ++(90:3.55);
    %\draw[DarkBlue,<-] (2.8, 3.55) -- ++(0:0.6) node[anchor=west]{$v_{\rm rms}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221031-lec16.tex
modified: 2022-10-31 16:21:33.257247
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!25] (0,0) rectangle (4,0.5);
    \draw[force,DarkGreen] (2,0.25) -- ++(0,-1.2) node[anchor=north]{$\rho A g \dd{z}$};
    \begin{scope}[DarkRed,<-]
      \foreach \x in {0.5, 1.5, ..., 3.5} {
          \draw[line width=2] (\x,0) -- ++(0,-0.75);
          \draw[line width=1.5] (\x,0.5) -- ++(0,0.75);
        }
      \node[anchor=west] at (4,-0.375) {$p(z)$};
      \node[anchor=west] at (4,0.875) {$p(z+\dd{z})$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221010-lec11.tex
modified: 2022-10-10 00:10:33.749289
domain: p117
source:
  \begin{tikzpicture}[scale=0.35]
    \begin{axis}[
        ymin=0,
        ymax=1.2,
        xmin=0,
        xmax=1.2,
        enlargelimits=false,
        height=2.5in,
        width=3.5in,
        xlabel={$E$},
        ylabel={$S$},
        axis x line=bottom,
        axis y line=left,
        ytick=\empty,
        xtick=\empty,
        axis line style={line width=1.25}
      ]
      \addplot[trace01,
        domain=0:1,
        samples=101,
        line width=2pt
      ]
      {x^3};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221010-lec11.tex
modified: 2022-10-10 00:10:33.749289
domain: p117
source:
  \begin{tikzpicture}[scale=0.35]
    \begin{axis}[
        ymin=0,
        ymax=1.2,
        xmin=0,
        xmax=1.2,
        enlargelimits=false,
        height=2.5in,
        width=3.5in,
        xlabel={$E$},
        ylabel={$S$},
        axis x line=bottom,
        axis y line=left,
        ytick=\empty,
        xtick=\empty,
        axis line style={line width=1.25}
      ]
      \addplot[trace01,
        domain=0:1,
        samples=201,
        line width=2pt
      ]
      {x^(1/3)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221010-lec11.tex
modified: 2022-10-10 00:10:33.749289
domain: p117
source:
  \begin{tikzpicture}[scale=0.5]
    \begin{axis}[
        ymin=0,
        ymax=1.2,
        xmin=0,
        xmax=1.2,
        enlargelimits=false,
        height=2.5in,
        width=3.5in,
        xlabel={$S$},
        ylabel={$\E$},
        axis x line=bottom,
        axis y line=left,
        ytick=\empty,
        xtick=\empty,
        axis line style={line width=1.25}
      ]
      \addplot[trace01,
        domain=0:1,
        samples=201,
        line width=3,
        opacity=0.5
      ]
      {x^3};
      \def\dx{0.2}
      \pgfplotsforeachungrouped \x/\c in {0.2/20, 0.4/40, 0.6/60, 0.8/80, 1.0/100} {
          \pgfmathsetmacro{\y}{\x^3}
          \pgfmathsetmacro{\dy}{3*\x^2}
          \edef\temp{\noexpand\draw[green!\c!blue, line width=1.5,opacity=0.5] (axis cs:\x-\dx,
            \y-\dy*\dx) -- (axis cs:\x+\dx, \y+\dy*\dx);}
          \temp
        }
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221010-lec11.tex
modified: 2022-10-10 00:10:33.749289
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin=-2,
        ymax=1.2,
        xmin=0,
        xmax=1.2,
        enlargelimits=false,
        height=3in,
        width=5in,
        xlabel={$S$},
        ylabel={$\E$},
        axis x line=bottom,
        axis y line=left,
        ytick=\empty,
        xtick=\empty,
        axis line style={line width=1}
      ]
      \addplot[yellow,
        domain=0:1.1,
        samples=201,
        line width=2.5pt,
        opacity=0.5
      ]
      {x^3};
      \def\dx{0.2}
      \pgfplotsforeachungrouped \x/\c in {0.2/20, 0.4/40, 0.6/60, 0.8/80, 1.0/100} {
          \pgfmathsetmacro{\y}{\x^3}
          \pgfmathsetmacro{\dy}{3*\x^2}
          \edef\temp{\noexpand\draw[green!\c!blue, line width=1,opacity=0.5]
            (axis cs:0,\y-\dy*\x)  -- (axis cs:\x+\dx,\y+\dy*\dx);}
          \edef\tmp{\noexpand\filldraw[green!\c!blue] (axis cs: 0.005,\y-\dy*\x+0.005*\dy)
            circle[radius=0.05cm]
            (axis cs: \x, \y) circle[radius=0.05cm];}
          \temp\tmp
        }
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221010-lec11.tex
modified: 2022-10-10 00:10:33.749289
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{semilogyaxis}[
        enlargelimits=false,
        ylabel={Pressure (Pa)},
        xlabel={Elevation (km)},
        width=\columnwidth,
        height=\columnwidth
      ]
      \addplot [only marks,trace04] coordinates {
          (0, 101327)
          (1, 89876.7)
          (2, 79497.2)
          (5, 54021.5)
          (7.5, 38252.7)
          (10, 26437.3)
          (15, 12045.1)
          (20, 5475.21)
          (25, 2511)
          (30, 1171.95)
          (35, 558.969)
          (40, 277.546)
          (45, 143.15)
          (50, 75.9541)
          (55, 39.97)
          (60, 20.3165)
          (65, 9.92326)
          (70, 4.63487)
        };
      \addplot[
        trace01,
        domain=0:70,
      ]{ 101000*exp(-x/8.49) };
      \addplot[
        trace05,
        domain=0:70,
      ]{ 101000*exp(-x/7) };
      \draw[trace01] (25,5300) -- (30,10000) node[anchor=west,font=\small,text width = 1.8cm] {Isothermal
        atmosphere};
      \draw[trace05] (42,250) -- (37,100) node[anchor=east]{$z_{0}=\SI{7}{km}$};
    \end{semilogyaxis}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221024-lec14.tex
modified: 2022-10-24 02:59:19.937434
domain: p117
source:
  \begin{tikzpicture}[scale=1,
      heatflow/.style={line width=2,->,DarkRed},
      workflow/.style={line width=2,->,DarkGreen},
      caption/.style={text width=2.25cm, DarkSlateGray,font=\itshape}
    ]
    \def\cht{-1.75}
    \def\cx{0.5}
    \begin{scope}
      \node[caption] at (\cx,\cht) {isothermal\\expansion};
      \filldraw[fill=red!30!white] (-1,-0.1) rectangle (1,-1);
      \node at (0.7,-0.7){$T_{h}$};
      \cylinder{(0,0)};
      \piston{(0,0.75)};
      \draw[workflow] (0,2) -- ++(90:0.85) node[anchor=south]{$W_{a}$};
      \draw[heatflow] (0,-0.5) node[anchor=east]{$Q_{h}$} -- ++(90:.85);
    \end{scope}

    \begin{scope}[shift={(3,0)}]
      \node[caption] at (\cx,\cht) {adiabatic\\expansion};
      \cylinder{(0,0)};
      \piston{(0,1.5)};
      \draw[workflow] (0,2.75) -- ++(90:0.85) node[anchor=south]{$W_{b}$};
    \end{scope}

    \begin{scope}[shift={(6,0)}]
      \node[caption] at (\cx,\cht) {isothermal\\compression};
      \filldraw[fill=blue!30!white] (-1,-0.1) rectangle (1,-1);
      \node at (0.7,-0.7){$T_{c}$};
      \cylinder{(0,0)};
      \piston{(0,2.5)};
      \draw[workflow] (0,4.5) node[anchor=east]{$W_{c}$}-- ++(-90:0.85);
      \draw[heatflow] (0,0.35) -- ++(-90:.85) node[anchor=east]{$Q_{c}$};
    \end{scope}

    \begin{scope}[shift={(9,0)}]
      \node[caption] at (\cx,\cht) {adiabatic\\compression};
      \cylinder{(0,0)};
      \piston{(0,1.5)};
      \draw[workflow] (0,3.6) node[anchor=east]{$W_{d}$} -- ++(-90:0.85);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221024-lec14.tex
modified: 2022-10-24 02:59:19.937434
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \def\gam{1.4}\def\lw{1pt}
    \def\Vc{2.0} \def\Vo{1} \def\Vh{0.25}\def\Vw{0.5}
    \begin{axis}[
        xmin=0.2, xmax=2.2, ymin=0, ymax=8, enlargelimits=false,
        width=2.5in, height=2.5in,
        xlabel={$V$}, ylabel={$p$}, ytick={0,2, ..., 6}, xtick={0.5,1,1.5, 2},
        axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkGreen, domain=\Vo:\Vc, samples=30, line width=\lw,]  {1/x};
      \addplot[DarkRed, domain=\Vh:\Vo, samples=50, line width=\lw] {x^(-\gam)};
      \addplot[DarkSlateBlue, domain=\Vh:\Vw, samples=30, line width=\lw,]  {1.74/x};
      \addplot[DarkSlateGray, domain=\Vw:\Vc,
        samples=50, line width=\lw] {3.48*(x/\Vw)^(-\gam)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221024-lec14.tex
modified: 2022-10-24 02:59:19.937434
domain: p117
source:
  \begin{tikzpicture}[scale=1,line width=1.]
    \def\gam{1.4}\def\lw{2pt}
    \def\Vc{2.0} \def\Vo{1} \def\Vh{0.25}\def\Vw{0.5}

    \draw[->] (0,0) --node[anchor=north]{$S$} (4,0);
    \draw[->] (0,0) --node[anchor=east]{$T$} (0,4);
    \only<2|handout:0>{
      \begin{scope}[line width=2,shift={(1,1)}]
        \draw[DarkGreen] (2,0) -- (0,0);
        \draw[DarkRed] (0,0) -- (0,2);
        \draw[DarkSlateBlue] (0,2) -- (2,2);
        \draw[DarkSlateGray] (2,2) -- (2,0);
      \end{scope}
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221005-lec10.tex
modified: 2022-10-04 17:23:30.428914
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!25] (0,0) rectangle (4,0.25);
    \filldraw[fill=blue!25] (0,0.25) rectangle (4, 1.75) (0,0) rectangle
    (4,-1.5);
    \node[anchor=north west] at (0,1.75)
    {$\mathrm{Si}_{x}\mathrm{Ge}_{1-x}$};
    \node[anchor=south west] at (0,-1.5)
    {$\mathrm{Si}_{x}\mathrm{Ge}_{1-x}$};
    \node[font=\tiny,anchor=west] at (0,0.125){Si};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 220912-lec04.tex
modified: 2022-09-12 15:08:15.610586
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \node at (0,0) {\includegraphics[width=4cm]{\bookdir
        Chapters/Ch03/figs/GenOmega}};

    \node at (0,-4) {\includegraphics[width=4cm]{\bookdir
        Chapters/Ch03/figs/GenericS}};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 220912-lec04.tex
modified: 2022-09-12 15:08:15.610586
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \node at (0,0) {    \includegraphics[width=0.5\columnwidth]{beaker}};
    \draw[SlateGray, line width=2] (0,3) -- ++(0.25,0) -- ++(0, -4)
    -- ++(-0.1,0) -- ++(120:0.2) -- ++(240:0.4) coordinate (A) -- ++(120:0.4) -- ++(240:0.4)
    -- ++(120:0.2) -- ++(-0.1,0) -- ++(0,4) -- ++(0.25,0) (-0.25,3)
    circle[radius=0.25]
    node {$I$} (A) node[anchor=north] {$R$} ;

    \node[anchor=south,opacity = 0.5] at (1,-1.5) {\includegraphics[height=0.5\columnwidth]{thermometer}
    };
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221107-lec18.tex
modified: 2022-11-06 14:52:19.363103
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=yellow!25!white,draw=gray!25!white,line width=3pt] (0,0)
    rectangle (4,3);
    \node[anchor=west] at (0.2,0.35) {$R$};
    \node[anchor=west] at (0.2,2.5) {$T, \mu$};
    \filldraw[fill=red!25!white,draw=gray!25!white,line width=2pt] (4.5,1.5)
    circle[radius=0.5];
    \node at (4.5,0.7) {$S$};
    \draw[line width=1.25,->,color=DarkRed] (3.4,1.6)
    --node[anchor=south]{$E_{n}$} +(0:1.2);
    \draw[line width=1.25,->,color=DarkGreen] (3.4,1.4) --node[anchor=north]{$n$} +(0:1.2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221107-lec18.tex
modified: 2022-11-06 14:52:19.363103
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=1.15, ymin=0, ymax=1.15, enlargelimits=false,
        width=3.5in, height=2.5in,
        xlabel={$\epsilon$}, ylabel={$\overline{n}\FD$}, ytick={0,0.5,1}, xtick={0,
            0.5, 1},
        xticklabels={ ,$\mu$, },
        axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \draw[DarkSlateGray] (0,1) -- (0.5,1) -- (0.5,0) -- (1,0);

      \begin{scope}[domain=0:1, samples=150, line width=1.5pt]
        \addplot[trace01,samples=1000] {1 / (exp((x-0.5)/0.005) + 1)};
        \addplot[trace02] {1 / (exp((x-0.5)/0.025) + 1)};
        \addplot[trace03] {1 / (exp((x-0.5)/0.1) + 1)};
      \end{scope}
      \begin{scope}[<-,font=\small]
        \draw[trace01] (0.495, 0.85) -- ++(0.1,0)
        node[anchor=west]{$\kT=0.05$};
        \draw[trace03] (0.3, 0.86) -- ++(-0.07,-0.07) node[anchor= east]{$ \kT=1$};
        \draw[trace02] (0.47,0.7) -- ++(-0.1,-0.1) node[anchor=east] {$\kT=0.25$};
      \end{scope}
      \node[fill=gray!10!white,
        blur shadow={shadow blur steps=5}] at (0.8,0.5) {$\displaystyle \overline{n}\FD = \frac{1}{e^{\beta(\epsilon-\mu)}+1} $};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221107-lec18.tex
modified: 2022-11-06 14:52:19.363103
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=4.15, ymin=0, ymax=9, enlargelimits=false,
        width=3.5in, height=2.5in,
        xlabel={$\epsilon$}, ylabel={$\overline{n}\BE$},
        ytick={0,2, ..., 8}, xtick={0,1, 2, 3, 4},
        xticklabels={ ,$\mu$, , ,  },
        axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \draw[DarkSlateGray] (1,0) -- (1, 9);

      \begin{scope}[domain=1.01:4, samples=150, line width=1.5pt]
        \addplot[trace01] {1 / (exp((x-1)/0.25) - 1)};
        \addplot[trace02] {1 / (exp((x-1)/1) - 1)};
        \addplot[trace03] {1 / (exp((x-1)/4) - 1)};
      \end{scope}
      \begin{scope}[<-,font=\small]
        \draw[trace01] (1.1, 1) -- ++(-0.2,0) node[anchor=east]{$\kT=\epsilon_{0}$};
        \draw[trace02] (1.3, 2.5) -- ++(-0.4,0) node[anchor=east] {$\kT=4\epsilon_{0}$};
        \draw[trace03] (2.4, 2.5) -- ++(0.2,0.2) node[anchor=west]{$ \kT=16\epsilon_{0}$};
      \end{scope}
      \node[fill=gray!10!white,blur shadow={shadow blur
            steps=5},anchor=north east]
      at (3.5,8) {$\displaystyle \overline{n}\BE = \frac{1}{e^{\beta(\epsilon-\mu)}-1} $};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221102-lec17.tex
modified: 2022-11-02 15:53:28.739540
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin=-1,
        ymax=0.75,
        xmin=0.8,
        xmax=2,
        enlargelimits=false,
        height=2.5in,
        width=2in,
        ylabel={$\phi(r)$},
        xlabel={$r / r_{0}$},
        ytick={0,1},
        xtick={1,1.25,...,2},
        xticklabels={1,,1.5,,2}
      ]
      \addplot[
        trace01,
        domain=0.85:2,
        samples=201,
        line width=2pt,
      ]
      {1/(x^12)-2/(x^6)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221102-lec17.tex
modified: 2022-11-02 15:53:28.739540
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0.25,
        xmax=3,
        ymin=0,
        ymax=2.5,
        enlargelimits=false,
        height=2.5in,
        width=3.5in,
        xlabel={$V$},
        ylabel={$p$},
        xticklabel=\empty,
        yticklabel=\empty,
      ]
      \addplot[ trace01, domain=0.45:3, samples=101, line width=2pt ]
      {8/3*0.85/(x-1/3)-3/x^2};
      \addplot[ trace02, domain=0.5:3, samples=101, line width=2pt ]
      {8/3*0.925/(x-1/3)-3/x^2};
      \addplot[ trace03, domain=0.5:3, samples=101, line width=2pt ]
      {8/3*1.0/(x-1/3)-3/x^2};
      \addplot[ trace04, domain=0.5:3, samples=101, line width=2pt ]
      {8/3*1.075/(x-1/3)-3/x^2};
      \addplot[ trace05, domain=0.55:3, samples=101, line width=2pt ]
      {8/3*1.15/(x-1/3)-3/x^2};
      %      \addplot[domain=0.5:3, samples=101] { 1/(x) };
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221102-lec17.tex
modified: 2022-11-02 15:53:28.739540
domain: p117
source:
  \begin{tikzpicture}[scale=0.65]
    \def\temp{0.85}
    \begin{axis}[
        %no markers,
        xmin=0,
        xmax=1,
        ymin=-1,
        ymax=-0.5,
        enlargelimits=false,
        width=2.5in,
        height=2.5in,
        xlabel={$\tilde{p}$},
        ylabel={$g = \mu$},
        %ytick={0,1},
        %xtick={0,0.5,1,1.5,2},
        %xticklabel=\empty,
        % xticklabels{0,,$a$,,a$},
      ]
      % \addplot[
      % trace01,
      % domain=0.5:4,
      % samples=51,
      % line width=2pt,
      % ]
      % ( 2.6667 * \temp / (x-0.3333) - 3/x^2, -2.25/x - \temp * ln( x - 0.3333)
      % + \temp * x /(x - 0.3333) );
      \addplot+[mark indices={1,6,19,38,61,77,88}] table[x=p,y=g] {gibbs2.dat};
      %      \node[pin=0:0.1] at (0.5,-0.64) {2,6};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221102-lec17.tex
modified: 2022-11-02 15:53:28.739540
domain: p117
source:
  \begin{tikzpicture}[scale=0.75]
    \def\temp{0.85}
    \begin{axis}[
        %no markers,
        xmin=0,
        xmax=1,
        ymin=-1,
        ymax=-0.5,
        enlargelimits=false,
        width=3in,
        height=2.5in,
        xlabel={$\tilde{p}$},
        ylabel={$g = \mu$},
        %ytick={0,1},
        %xtick={0,0.5,1,1.5,2},
        %xticklabel=\empty,
        % xticklabels{0,,$a$,,a$},
      ]
      % \addplot[
      % trace01,
      % domain=0.5:4,
      % samples=51,
      % line width=2pt,
      % ]
      % ( 2.6667 * \temp / (x-0.3333) - 3/x^2, -2.25/x - \temp * ln( x - 0.3333)
      % + \temp * x /(x - 0.3333) );
      \addplot+[mark indices={1,6,19,38,61,77,88}] table[x=p,y=g] {gibbs2.dat};
      %      \node[pin=0:0.1] at (0.5,-0.64) {2,6};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221102-lec17.tex
modified: 2022-11-02 15:53:28.739540
domain: p117
source:
  \begin{tikzpicture}[scale=.75]
    \begin{axis}[
        xmin = 0,
        %      xmax = 6,
        ymin = 0,
        ymax = 0.9,
        enlargelimits=false,
        width=3in,
        height=2.5in,
        xlabel={$\tilde{v}$},
        ylabel={$\tilde{p}$}
      ]
      \addplot+[mark indices={1,6,19,38,61,77,88}] table[x=v,y=p] {gibbs2.dat}; %1,6,19,39,62,78,89
      %      \addplot table[x=v,y=p] {gibbs.dat};
      \draw[dashed] (0.5525,0.5046) -- (3.126,0.5046);
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221102-lec17.tex
modified: 2022-11-02 15:53:28.739540
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \def\temp{0.85}
    \begin{axis}[
        no markers,
        xmin=0,
        xmax=6,
        ymin=0,
        ymax=1.3,
        enlargelimits=false,
        width=3.75in,
        height=3in,
        xlabel={$\tilde{v}$},
        ylabel={$\tilde{p}$},
      ]
      \addplot+[dashed,color=black] table[x=vliq,y=p] {\filebase gibbs3.dat};
      \addplot+[dashed,color=black] table[x=vvap,y=p] {\filebase gibbs3.dat};
      \addplot+[color=DarkGreen!80!gray,line width=1.5] table[x=v,y=p075] {\filebase gibbs4.dat};
      \addplot+[color=DarkGreen!70!gray,line width=1.5] table[x=v,y=p080] {\filebase gibbs4.dat};
      \addplot+[solid,color=DarkGreen!60!gray,line width=1.5] table[x=v,y=p085] {\filebase gibbs4.dat};
      \addplot+[solid,color=DarkGreen!50!gray,line width=1.5] table[x=v,y=p090] {\filebase gibbs4.dat};
      \addplot+[solid,color=DarkGreen!40!gray,line width=1.5] table[x=v,y=p095] {\filebase gibbs4.dat};
      \addplot+[solid,color=DarkGreen!30!gray,line width=1.5] table[x=v,y=p100] {\filebase gibbs4.dat};
      \addplot+[solid,color=DarkGreen!20!gray,line width=1.5] table[x=v,y=p105] {\filebase gibbs4.dat};
      \addplot+[solid,color=DarkGreen!10!gray,line width=1.5] table[x=v,y=p110] {\filebase gibbs4.dat};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221019-lec13.tex
modified: 2022-10-19 16:10:21.924431
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \def\x{2.5}
    \def\y{1.5}
    \draw (0,-\y) -- (0,\y);
    \draw[line width=4pt,color=SlateGray] (-\x,-\y) rectangle (\x,\y);
    \node[anchor=west] at (0.15-\x, \y-0.5){$S_{1}(\nrg_{1}, V_{1})$};
    \node[anchor=east] at (\x-0.15, \y-0.5){$S_{2}(\nrg_{2}, V_{2})$};
    \draw[<->,color=DarkRed,line width=1.5] (-0.5,0) -- (0.5,0) node[anchor=west]{$\Delta \nrg$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221019-lec13.tex
modified: 2022-10-19 16:10:21.924431
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \def\x{2.5}
    \def\y{1.5}
    \draw[line width=4pt,color=SlateGray] (-\x,-\y) rectangle (\x,\y);
    \node[anchor=west] at (0.15-\x, \y-0.5){$T$};
    %\draw[<->,color=DarkRed,line width=1.5] (-0.5,0) -- (0.5,0)
    %node[anchor=west]{$\Delta \nrg$};
    \filldraw[line width=1.25pt,color=DarkGreen,fill=DarkGreen!10!white] (0,0) circle[radius=0.25];
    \node[anchor=west,DarkGreen] at (0.3,0) {$\E, S, V$};

    \onslide<5>{\begin{scope}[shift={(-\x+0.5,-5)},scale=0.8]
        \begin{axis}[
            xmin=0, xmax=1.1, ymin=-1, ymax=1.1, enlargelimits=false,
            width=2.5in, height=2in,
            xlabel={}, ylabel={}, ytick=\empty, xtick=\empty,
            xticklabel=\empty, yticklabel=\empty,
            axis x line=middle, axis y line=left, axis line style={line width=1} % for no frame
          ]
          \addplot[trace01, domain=0:1, samples=100, line width=2pt,]
          {-(0.001+x)^(1/3)+0.1};
          \node[trace01] at (0.8,-0.7) {$-TS$};
          \addplot[trace02, domain=0:1, samples=6, line width=2pt]
          {x};
          \node[trace02] at (0.6,0.8) {$\E$};
          \addplot[trace03, domain=0:1, samples=100, line width=2pt]
          {x+0.1-(0.001+x)^(1/3)};
          \node[trace03] at (0.6,-0.3) {$F$};
          \node at (1,-0.15) {$\E$};
        \end{axis}
      \end{scope}
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221012-lec12.tex
modified: 2022-10-11 00:41:44.343814
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \def\w{5}\def\h{3}
    % flux in q direction
    \fill[DarkGreen,opacity=0.2] (0,0) rectangle (-1,\h)
    (\w,0) rectangle (\w-0.5,\h);
    % flux in p direction
    \fill[DarkRed, opacity=0.2] (0,0) rectangle (\w,-0.5)
    (0,\h) rectangle (\w,\h-0.75);

    \draw[line width=1.25] (0,0) rectangle (\w,\h) coordinate (C);
    % flux arrows
    \draw[DarkGreen, ->,line width=1.5] (-0.5, \h/2) -- ++(0:1);
    \draw[DarkGreen, ->,line width=1.5] (\w-0.25, \h/2) -- ++(0:.75);
    \draw[DarkRed, ->, line width=1.5] (\w/2, -0.25) -- ++(0,0.75);
    \draw[DarkRed, ->, line width=1.5] (\w/2, \h-0.25) -- ++(0,1);

    \begin{scope}[dashed, gray!60!black]
      \draw (0,0) -- ++(0,-1) node[anchor=north]{$q$}
      (\w,0) -- ++(0,-1) node[anchor=north]{$q+\dd{q}$};
      \draw (0,0) -- ++(-1.5,0) node[anchor=east] {$p$}
      (0,\h) -- ++(-1.5,0) node[anchor=east] {$p+\dd{p}$};
    \end{scope}

    \begin{scope}[DarkGreen]
      \draw[<->] (-1,\h+0.2) -- node[anchor=south]{$\dot{q}\dd{t}$} ++(1,0);
      \draw[<->] (\w-0.5,\h+0.2) -- node[anchor=south]
      {$\qty(\dot{q} + \pdv{\dot{q}}{q}\dd{q})\dd{t}$} ++ (0.5,0);
    \end{scope}

    \begin{scope}[DarkRed]
      \draw[<->] (\w+0.2,-0.5) -- node[anchor=west]{$\dot{p}\dd{t}$} ++(0,0.5);
      \draw[<->] (\w+0.2,\h-0.75) -- node[anchor=west]
      {$\qty(\dot{p} + \pdv{\dot{p}}{p}\dd{p})\dd{t}$} ++ (0, 0.75);
    \end{scope}

    \node[DarkSlateGray,font=\large] at (\w/2,\h/2) {$\rho(q,p)$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221012-lec12.tex
modified: 2022-10-11 00:41:44.343814
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=1.1, ymin=-1, ymax=1.1, enlargelimits=false,
        width=2.5in, height=2in,
        xlabel={}, ylabel={}, ytick=\empty, xtick=\empty,
        xticklabel=\empty, yticklabel=\empty,
        axis x line=middle, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[trace01, domain=0:1, samples=100, line width=2pt,]
      {-(0.001+x)^(1/3)+0.1};
      \node[trace01] at (0.8,-0.7) {$-TS$};
      \addplot[trace02, domain=0:1, samples=6, line width=2pt]
      {x};
      \node[trace02] at (0.6,0.8) {$\E$};
      \addplot[trace03, domain=0:1, samples=100, line width=2pt]
      {x+0.1-(0.001+x)^(1/3)};
      \node[trace03] at (0.6,-0.3) {$F$};
      \node at (1,-0.15) {$\E$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221003-lec09.tex
modified: 2022-10-03 20:02:03.346577
domain: p117
source:
  \begin{tikzpicture}[scale=0.75]
    \def\x{4}
    \def\dy{1.0}
    \def\amp{0.4}
    \def\y{4}
    \node[anchor=north] at (\x/2,0){$L$};
    \begin{scope}[shift={(0,\dy)},color=trace01]
      \draw[dashed,color=gray] (0,0) -- (\x,0);
      \draw[line width=2] (0,0) sin (0.5*\x,\amp) cos (\x,0);
      \node[anchor=east] at (-0.2,0) {$n=1$};
      \node[anchor=west] at (\x+0.2,0) {$\lambda = 2L$};
    \end{scope}
    \begin{scope}[shift={(0,2*\dy)},color=trace02]
      \draw[dashed,color=gray] (0,0) -- (\x,0);
      \draw[line width=2] (0,0) sin (0.25*\x,0.4*\dy) cos (0.5*\x,0)
      sin(0.75*\x,-0.4*\dy) cos (\x,0);
      \node[anchor=east] at (-0.2,0) {$n=2$};
      \node[anchor=west] at (\x+0.2,0) {$\lambda = L$};
    \end{scope}
    \begin{scope}[shift={(0,3*\dy)},color=trace03]
      \draw[dashed,color=gray] (0,0) -- (\x,0);
      \draw[line width=2] (0,0) sin (\x/6,\amp) cos (\x/3,0)
      sin(\x/2,-\amp) cos (2*\x/3,0)
      sin(5*\x/6, \amp) cos(\x,0);
      \node[anchor=east] at (-0.2,0) {$n=3$};
      \node[anchor=west] at (\x+0.2,0) {$\lambda = \frac{2}{3} L$};
    \end{scope}
    \draw[color=SlateGray, line width=2] (0,0) rectangle (\x, \y);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221003-lec09.tex
modified: 2022-10-03 20:02:03.346577
domain: p117
source:
  \begin{tikzpicture}[scale=0.5]
    \def\dx{0.4}
    \foreach \x in {0,1,2,...,25} {
        \draw[line width=1.25] (\x*\dx,-0.15) -- ++(90:0.4);
      }
    \draw[color=SlateGray](0,0.05) -- (25*\dx,0.05);
    \draw[line width=2] (0,-0.2) -- ++(90:0.6)
    (25*\dx,-0.2) -- ++(90:0.6);
    \node at (0,-0.5) {$0$};
    \node at (25*\dx,-0.5){$L$};
    \draw[<-] (8*\dx,-0.4) -- ++(180:2*\dx);
    \draw[<-] (9*\dx,-0.4) -- ++(0:2*\dx);
    \node at (8.5*\dx,-0.8){$\quad\Lambda_{\rm dB}$};
    \filldraw[fill=DarkRed] (16.5*\dx,0.05) circle[radius=0.4*\dx];
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 220919-lec06.tex
modified: 2022-09-19 02:12:26.979041
domain: p117
source:
  \begin{tikzpicture}[scale=1,line width=2,DarkGreen]
    \fill[color=gray!10,drop shadow] (-0.5,-0.25) rectangle (2.25, 1.25);
    \draw (0,0) node[anchor=east]{$0$} -- ++(2,0)
    (0,1) node[anchor=east]{$\epsilon$} -- ++(2,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 220919-lec06.tex
modified: 2022-09-19 02:12:26.979041
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \draw[step=0.2,gray!50!white,thin] (-2,-2) grid (2,2);
    \draw[->] (0,-2) -- (0, 2.3) node[anchor=east]{$p$};
    \draw[->] (-2,0) -- (2.3,0) node[anchor=north]{$x$};
    \draw[DarkGreen,line width=1] (0,0) ellipse [x radius=1.75, y radius=1.25];
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 220914-lec05.tex
modified: 2022-09-14 05:18:39.490564
domain: p117
source:
  \begin{tikzpicture}[scale=.75]
    \filldraw[fill=yellow!25!white,draw=gray!25!white,line width=3pt] (0,0)
    rectangle (4,3);
    \node at (0.35,0.35) {$R$};
    \filldraw[fill=red!25!white,draw=gray!25!white,line width=2pt] (4.5,1.5)
    circle[radius=0.5];
    \node at (4.5,0.7) {$S$};
    \draw[line width=1.25,<->,color=DarkRed] (3.4,1.5) --node[anchor=south]{$\Delta E$} +(0:1.2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 220921-lec07.tex
modified: 2022-09-21 02:21:30.471446
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin = 0,
        ymax = 1.2,
        xmin = 0,
        xmax = 3.3,
        enlargelimits = false,
        height=2.5in,
        width=2.5in,
        ylabel={$f(v)$},
        ytick=\empty,
        xlabel={$v / \tilde{v}$},
        xtick={0,1,2,3},
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25},
        xtick align=inside,
      ]
      \addplot[
        trace01,
        domain=0:3,
        samples=201,
        line width=2pt,
      ] { x^2 * exp(1-x^2) };
      \draw[color=DarkRed, <-] (1,1) -- ++(165:0.2) node[anchor=east]{$\tilde{v}$};
      \draw[color=DarkGreen] (1.128,0) -- ++(90:0.969);
      \draw[color=DarkGreen,<-] (1.128,0.969) ++(30:0.02) -- ++(30:0.2)
      node[anchor=west] {$\overline{v}$};
      \draw[DarkBlue] (1.225,0) -- (1.225,0.91);
      \draw[DarkBlue,<-] (1.28,0.91) --++(0:0.2) node[anchor=west]{$v_{\rm rms}$};
    \end{axis}
    %\draw[color=DarkGreen] (2.504,0) -- ++(90:3.88);
    %\draw[color=DarkGreen,<-] (2.51,3.9) -- ++(45:0.6) node[anchor=south west]
    %{$\overline{v}$};
    %
    %\draw[DarkBlue] (2.720,0) -- ++(90:3.55);
    %\draw[DarkBlue,<-] (2.8, 3.55) -- ++(0:0.6) node[anchor=west]{$v_{\rm rms}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221026-lec15.tex
modified: 2022-10-26 04:11:41.882873
domain: p117
source:
  \begin{tikzpicture}[scale=1.25]
    \draw[->] (0,0) -- (4,0) node[anchor=north,shift={(-0.5,0)}]{$x$};
    \draw[->] (0,0) -- (0,3) node[anchor=east,shift={(0,-0.5)}]{$\E$};
    \draw (0.2,2.8) ..controls(0.5,1.25) and (0.8,1.25)..  (1,1.25) coordinate (a)
    ..controls (1.4,1.25) and (1.7,2) .. (2,2) coordinate (b)
    .. controls (2.3,2) and (2.7,0.45) .. (3,0.45) coordinate (c)
    .. controls (3.2,0.45) and (3.5,0.75) .. (3.75,1.25);
    \node[anchor=north,gray] at (a) {$a$};
    \node[anchor=north,DarkRed] at (b) {$b$};
    \node[anchor=north,DarkBlue q] at (c) {$c$};
    \fill[gray] (a) ++ (0,0.1) circle[radius=0.075];
    \filldraw[DarkRed,fill=DarkRed!25!white] (b) ++ (0,0.1) circle[radius=0.075];
    \filldraw[DarkBlue,fill=DarkBlue!50!white] (c) ++ (0,0.1) circle[radius=0.075];
    \begin{scope}[DarkGreen]
      \draw (1.2,1.25) -- ++(1.8,0) (2.2,2) -- ++(0.8,0);
      \draw[<->] (2.8,1.25) -- node[anchor=west]{$\Delta E$} ++(0,0.75);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/exams
filename: phys-117-2022-mt2-v1.tex
modified: 2022-10-27 19:01:51.609200
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin=-1.15,
        ymax=0.25,
        xmin=0.8,
        xmax=2.5,
        enlargelimits=false,
        height=2.5in,
        width=3.5in,
        ylabel={$U(r)$},
        xlabel={$r$},
        ytick=\empty,
        xtick=\empty,
        % xticklabels={$r_{0}$,,$1.5 r_{0}$,,$2 r_{0}$}
        axis x line=middle, axis y line=left, axis line style={line width=1}, % for no frame
      ]
      \addplot[
        trace01,
        domain=0.85:2.4,
        samples=201,
        line width=2pt,
      ]
      {1/(x^12)-2/(x^6)};
      \draw[<-] (0.8775,0.2) -- (1.05,0.2) node[anchor=west]{$a$};
      \draw[<-] (0.9,-.2) -- (1,-0.2) node[anchor=west]{$b$};
      \draw[<-] (1,-1) -- (1.1,-1.1) -- (1.2,-1.1) node[anchor=west]{$c$};
      \draw[<-] (1.15,-.7) -- (1.25,-0.75)-- (1.35,-0.75) node[anchor=west]{$d$};
      \draw[<-] (1.35,-.3) -- (1.45,-0.4) node[anchor=west]{$e$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/exams
filename: p117-2022-mt1-key.tex
modified: 2022-09-28 15:46:18.697338
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin=0,
        ymax=3.2,
        xmin=0,
        xmax=3.2,
        enlargelimits=false,
        height=2.5in,
        width=2.5in,
        xlabel={$\kb T/\epsilon$},
        ylabel={$E/\epsilon$},
        axis x line=bottom,
        axis y line=left,
        ytick={0,1,2,3},
        xtick={0,0.5,1,1.5,2,2.5,3},
        axis line style={line width=1.25}
      ]
      \addplot[trace01,
        domain=0.01:3,
        samples=101,
        line width=2pt
      ]
      {2/(exp(1/x)+1)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/exams
filename: p117-2022-mt1-key.tex
modified: 2022-09-28 15:46:18.697338
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin=0,
        ymax=1.2,
        xmin=0,
        xmax=3.2,
        enlargelimits=false,
        height=2.5in,
        width=2.5in,
        xlabel={$\kb T/\epsilon$},
        ylabel={$C/\kb$},
        axis x line=bottom,
        axis y line=left,
        ytick={0,1},
        xtick={0,0.5,1,1.5,2,2.5,3},
        axis line style={line width=1.25}
      ]
      \addplot[trace01,
        domain=0.01:3,
        samples=101,
        line width=2pt
      ]
      {2/x^2*exp(1/x)/(exp(1/x)+1)^2};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/exams
filename: p117-2022-mt1-key.tex
modified: 2022-09-28 15:46:18.697338
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \def\w{6}
    \draw[->] (0,0) -- (\w,0) node[anchor=north]{$T$};
    \draw[->] (0,0) -- (0,3.5) node[anchor=east]{$E$};
    \node[anchor=east] at (0,0) {$0$};
    \node[anchor=north] at (0,0) {$0$};
    \draw[gray] (0,1) node[anchor=east,black] {$\epsilon$} -- ++(\w,0);
    \draw[gray] (0,2) node[anchor=east,black] {$2\epsilon$} -- ++(\w,0);
    \draw[gray] (0,3) node[anchor=east,black] {$3\epsilon$} -- ++(\w,0);
    \begin{scope}[shift={(7,0)}]
      \draw[->] (0,0) -- (\w,0) node[anchor=north]{$T$};
      \draw[->] (0,0) -- (0,3.5) node[anchor=east]{$C$};
      \node[anchor=north] at (0,0) {$0$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221205-lec.tex
modified: 2022-12-05 02:32:33.681563
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[DarkGreen,->, line width=1]
      \draw (0,0) -- (-120:1.75) node[anchor=south east]{$n_{x}$};
      \draw (0,0) -- (-0:2) node[anchor=south east]{$n_{y}$};
      \draw (0,0) -- (90:2) node[anchor=north east]{$n_{z}$};
    \end{scope}
    \draw (-120:1) node[anchor=east] {$n$} -- (90:1.5) -- (0:1.5) -- cycle;
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221205-lec.tex
modified: 2022-12-05 02:32:33.681563
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
      xmin=0, xmax=1.2, ymin=0, ymax=1.1, enlargelimits=false,
      width=2.5in, height=2in,
      xlabel={$T/T_{\rm E}$}, ylabel={$N_{\rm o}/N$}, ytick={0,0.25, ..., 1}, xtick={0, 0.25, ..., 1},
      % xticklabel=\empty, xticklabels{0,,$a$,,a$},
      % axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkRed, domain=0:1, samples=100, line width=2pt,]
      {1 - x^3};
      \addplot[DarkRed,domain=1:1.2,samples=3,line width=2pt] {0*x};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: Bose.tex
modified: 2022-12-01 05:48:53.801057
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-1.02,
        xmax=1.5,
        ymin=-0.1,
        ymax=3,
        enlargelimits=false,
        width=3.5in,
        height=2.5in,
        xlabel={$\spe$},
        ylabel={$\overline{n}$},
        xtick={-2,-1,...,2},
        xticklabels={$\mu-2\escale$,$\mu-\escale$,$\mu\vphantom{\escale}$,
            $\mu+\escale$,$\mu+2\escale$},
      ]
      \def\temp{2}
      \addplot[trace01, domain=-1:2,samples=201, line width=2pt]
      {1 / (exp(\temp*x))};
      \addplot[trace02, domain=-1:2,samples=201, line width=2pt]
      {1 / (1+exp(\temp*x))};
      \addplot[trace03, domain=0.05:2,samples=101, line width=2pt]
      {1 / (exp(\temp*x)-1)};
      \node[trace01] at (-0.65,1.75) {Boltzmann};
      \node[trace02] at (-0.5,0.4) {Fermi-Dirac};
      \node[trace03] at (0.75,2.25) {Bose-Einstein};
    \end{axis}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: Sol.tex
modified: 2022-11-21 22:49:53.724628
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin = 0,
        ymax = 1,
        xmin = 0,
        xmax = 1300,
        enlargelimits=false,
        height=2.75in,
        width=3.5in,
        xlabel={$T$ (K)},
        ylabel={$c_{p}/3R$},
      ]
      \addplot[only marks, trace01] table {diamond.txt};
      \addplot[trace02, line width=1.5,domain=0.1:1300,samples=201,opacity=0.5]
      {((0.5*1320/x/sinh(0.5*1320/x)))^2};
      % \addplot[trace03, line width=1.5,domain=1:100] {2.2e-6*x^3};
      % \node[trace02] at (50,6e-4){$\sim T$};
      % \node[trace03] at (20,0.2){$\sim T^{3}$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: Sol.tex
modified: 2022-11-21 22:49:53.724628
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{loglogaxis}[
        ymax = 1,
        enlargelimits=false,
        height=2.75in,
        width=3.5in,
        xlabel={$T$ (K)},
        ylabel={$c_{p}/3R$},
      ]
      \addplot[only marks, trace01,opacity=0.75] table {Cu.txt};
      \addplot[only marks, trace02] table {diamond.txt};
      \node[trace01] at (20,0.1){Cu};
      \node[trace02] at (450,0.05){diamond};
      \addplot[trace02, line width=1.5, domain=150:1000,samples=201,opacity=0.5]
      {((0.5*1320/x/sinh(0.5*1320/x)))^2)))};
      \addplot[trace01, line width=1.5,domain=15:300,samples=201,opacity=0.5]
      {((0.5*228/x/sinh(0.5*228/x)))^2};
      \node[trace01,anchor=west] at (20,0.0003) {Einstein model};
    \end{loglogaxis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: Sol.tex
modified: 2022-11-21 22:49:53.724628
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin = 0,
        xmax = 1,
        ymin = 0,
        ymax = 1,
        enlargelimits=false,
        height=2.75in,
        width=3.5in,
        xlabel={$ka/\pi$},
        ylabel={$\omega/\omega_{0}$},
      ]
      \addplot+[
        only marks,
        samples=46,
        domain=0:1,
        trace02] {sin(x*90)};
      \addplot[domain=0:0.6, samples=5, trace01,line width=1.5] {pi*x/2};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: Sol.tex
modified: 2022-11-21 22:49:53.724628
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{loglogaxis}[
        ymax = 1,
        enlargelimits=false,
        height=2.75in,
        width=3.5in,
        xlabel={$T$ (K)},
        ylabel={$c_{p}/3R$},
      ]
      \addplot[only marks, trace01,opacity=0.75] table {Cu-big.txt};
      \addplot[trace02, line width=1.5,domain=0.1:100] {2.83e-5*x};
      \addplot[trace03, line width=1.5,domain=1:100] {2.2e-6*x^3};
      \node[trace02] at (50,6e-4){$\sim T$};
      \node[trace03] at (20,0.2){$\sim T^{3}$};
    \end{loglogaxis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221116-lec20.tex
modified: 2022-11-16 20:38:56.083467
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=5.5, ymin=0, ymax=5.5, enlargelimits=false,
        width=2.5in, height=2in,
        xlabel={$\kT/\hw$}, ylabel={$\overline{n}$}, ytick={0,1, ..., 5},
        xtick={0,1, ..., 5},
        axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkGreen, domain=0.01:5, samples=100, line width=2pt,]
      {1 / (exp(1/x)-1)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221121-lec21.tex
modified: 2022-11-20 20:49:27.827510
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin = 0,
        ymax = 1,
        xmin = 0,
        xmax = 1300,
        enlargelimits=false,
        height=2.in,
        width=3in,
        xlabel={$T$ (K)},
        ylabel={$c_{p}/3R$},
      ]
      \addplot[only marks, trace01,row sep=\\] table {diamond.txt};
      \addplot[trace02, line width=1.5,domain=0.1:1300,samples=201,opacity=0.5]
      {((0.5*1320/x/sinh(0.5*1320/x)))^2};
      % \addplot[trace03, line width=1.5,domain=1:100] {2.2e-6*x^3};
      % \node[trace02] at (50,6e-4){$\sim T$};
      % \node[trace03] at (20,0.2){$\sim T^{3}$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221121-lec21.tex
modified: 2022-11-20 20:49:27.827510
domain: p117
source:
  \begin{tikzpicture}[
      scale=0.8,
      >=stealth',
      decoration={coil,aspect=0.5,segment length=2mm,amplitude=2mm},
      spring/.style={line width=1.pt,color=blue,decorate},
      mass/.style={color=gray!50!white},
      coord/.style={color=DarkGreen,|->,line width=1.25},
    ]
    \foreach \x in {0,2,...,10}
      {
        \shade[ball color=gray] (\x,0) circle(0.3cm);
        \node at (\x,0.6) {$m$};
        \draw[spring] (\x,0) +(0.3,0) -- +(0:1.7) ;
        \node[color=blue] at (\x+0.9,0.45) {$\alpha$};
      }
    \draw[coord] (2,-0.75) -- node[anchor=north]{$u_{i-1}$} ++(0:1);
    \draw[coord] (4,-0.75) -- node[anchor=north]{$u_{i}$} ++(0:1);
    \draw[coord] (6,-0.75) -- node[anchor=north]{$u_{i+1}$} ++(0:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221121-lec21.tex
modified: 2022-11-20 20:49:27.827510
domain: p117
source:
  \begin{tikzpicture}[scale=0.5]
    \newcommand{\freq}{60}
    \foreach \x in {0,0.5,...,12}
    \foreach \t in {0,0.25,...,4}
      {
        \pgfmathsetmacro{\y}{0.5*sin(\freq*\x-\t*90)}
        \pgfmathsetmacro{\hue}{20 + \t*15}
        \fill[color=DarkGreen!\hue!white] ( \x+\y, -1.2*\t ) circle[radius=0.1];
      }
    \node[rotate=90,SlateGray] at (-1.5,-2.4) {longitudinal};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221121-lec21.tex
modified: 2022-11-20 20:49:27.827510
domain: p117
source:
  \begin{tikzpicture}[scale=.67]
    \begin{axis}[
        xmin=0,
        xmax=24,
        ymin=-8,
        ymax=0,
        enlargelimits=false,
        height=2.5in,
        width=3.5in,
        xlabel={$x$},
        ylabel=\empty,
        % ytick={0,1},
        xtick={0,4, 8, 12, 16, 20, 24},
        yticklabel=\empty,
        xticklabels={0,$4a$,$8a$,$12a$,$16a$,$20a$, $24a$},
      ]
      \foreach \n [count=\i] in {1,2,3,4,6,8,12} {
          \pgfmathsetmacro{\k}{360.0*\n/24}
          \addplot[trace03,domain=0:24, samples=101] {0.3*cos(x*\k)-\i};
          \addplot[trace03,mark=*,only marks, domain=0:24, samples=25] {0.3*cos(x*\k)-\i};
        }
    \end{axis}
    \foreach \n [count=\i] in {1,2,3,4,6,8,12} {
        \pgfmathsetmacro{\y}{(8.2-\i)*0.6}
        \node[anchor=west] at (2.95in,\y) {$n=\n$};
      }
    \node[rotate=90,SlateGray] at (-1.25,2) {transverse};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221121-lec21.tex
modified: 2022-11-20 20:49:27.827510
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{loglogaxis}[
        ymax = 1,
        enlargelimits=false,
        height=2.5in,
        width=3.5in,
        xlabel={$T$ (K)},
        ylabel={$c_{p}/3R$},
      ]
      \addplot[only marks, trace01,opacity=0.75] table {Cu-big.txt};
      \addplot[trace02, line width=1.5,domain=0.1:100] {2.83e-5*x};
      \addplot[trace03, line width=1.5,domain=1:100] {2.2e-6*x^3};
      \node[trace02] at (50,6e-4){$\sim T$};
      \node[trace03] at (20,0.2){$\sim T^{3}$};
    \end{loglogaxis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221121-lec21.tex
modified: 2022-11-20 20:49:27.827510
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0,
        xmax=1.5,
        ymin=0,
        ymax=1.65,
        enlargelimits=false,
        area style,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25},
        height=2.75in,
        width=3.5in,
        xlabel={$\omega$},
        ylabel={$\dos(\omega)$},
        ytick={},
        xtick={0,1,1.25},
        % xticklabel=\empty,
        xticklabels={0,$\omega_{\rm D}$,$\omega_{\rm E}$}
      ]
      \addplot[
        trace01,
        fill=DarkRed!40!white,
        domain=0:1,
        samples=51,
        line width=2pt]
      {x^2} \closedcycle;
      \addplot[trace02,domain=1.24:1.26,samples=51,fill=DarkBlue!40!white]
      {1.5*exp(-10000*(x-1.25)^2)} \closedcycle;
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221114-lec19.tex
modified: 2022-11-14 20:56:33.172174
domain: p117
source:
  \begin{tikzpicture}[scale=.75]
    \begin{axis}[
        xmin=-2,
        xmax=2.2,
        ymin=-0.05,
        ymax=1.1,
        enlargelimits=false,
        width=3.5in,
        height=2.5in,
        xlabel={$\varepsilon$},
        ylabel={$\nfd$},
        ytick={0,0.5,1},
        xtick={-2,-1,...,2},
        xticklabels={$\mu-2\escale$,$\mu-\escale$,$\mu\vphantom{\escale}$,$\mu+\escale$,$\mu+2\escale$},
        axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      % T = 0 line
      \draw[DarkSlateGray] (-2,1) -- (0,1) -- (0,0) -- (2,0);

      \addplot[trace01, domain=-2:2,samples=201, line width=2pt]  {1 / (1+exp(2*x))};
      \addplot[trace02, domain=-2:2,samples=201, line width=2pt]  {1 / (1+exp(4*x))};
      \addplot[trace03, domain=-2:2,samples=201, line width=2pt]  {1 / (1+exp(8*x))};
      \addplot[trace04, domain=-2:2,samples=201, line width=2pt]  {1 / (1+exp(16*x))};

      \begin{scope}[<-,font=\small]
        \draw[trace01] (-1.5,0.92) -- (-1.5,0.85)
        node[anchor=north] {$\kT = \frac{1}{2}\escale$};
        \draw[trace02] (-0.5,0.85) -- (-0.8,0.65) node[anchor=east]{$\kT=\frac{1}{4}\escale$};
        \draw[trace03] (-0.18,0.78) -- (-0.8,0.5) node[anchor=east]{$\kT=\frac{1}{8}\escale$};
        \draw[trace04] (0.025,0.35) -- (-0.2,0.35) node[anchor=east]{$\kT=\frac{1}{16}\escale$};
      \end{scope}

      \node[fill=gray!10!white,
        blur shadow={shadow blur steps=5}, anchor=north east] at (2,1)
      {$\displaystyle \overline{n}\FD = \frac{1}{e^{\beta(\varepsilon-\mu)}+1} $};

    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221114-lec19.tex
modified: 2022-11-14 20:56:33.172174
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \def\ef{0.75} % fermi energy
    \def\fd{0.25}  % amplitude of Fermi-Dirac
    \begin{axis}[
        xmin=0,
        xmax=1.2,
        ymin=0,
        ymax=1,
        enlargelimits=false,
        width=\fermiwid,
        height=\fermihgt,
        xlabel={$\varepsilon$},
        ylabel=\empty,
        ytick=\empty,
        xtick=\empty,
        xticklabel=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1},
        axis on top=true,
        x label style={xshift=0.75in},
      ]
      \addplot[color=white,domain=0:\ef,samples=101,line width=0pt,fill=blue!20!white ]
      {sqrt(x)} \closedcycle;
      \addplot[domain=0:1,samples=101,line width=1pt, DarkBlue]
      {sqrt(x)};
      %    \addplot[domain=0:1,samples=151,line width=1.5pt,trace02]
      %   {sqrt(x)/(1+exp(32*(x-0.75)))};
      % show the FD distribution at T = 0
      \draw[DarkRed,line width=1.5] (0,\fd) -- (\ef,\fd) -- (\ef,0) -- (1,0);
      \node[DarkBlue] at (0.75,0.95) {$\dos{\spe}$};
      \node[DarkRed, anchor=west] at (\ef,\fd) {$n_{\rm FD}(T=0)$};
    \end{axis}
    \node at (4.65,-0.25){$\efermi$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221114-lec19.tex
modified: 2022-11-14 20:56:33.172174
domain: p117
source:
  \begin{tikzpicture}[scale=1,
      fat/.style={line width=1.5},
      z={(-0.4cm,-0.7cm)}]
    \draw[->] (0,0,0) -- (2.5,0,0) node[anchor=north]{$k_{y}$};
    \draw[->] (0,0,0) -- (0,2.5,0) node[anchor=east]{$k_{z}$};
    \draw[->] (0,0,0) -- (0,0,3) node[anchor=east]{$k_{x}$};

    \shadedraw[ball color=gray,opacity=0.5] (0,0) circle[radius=2];
    \draw[fat, ->] (0,0) -- (1.4,1.4) node[anchor=south west]{$k\fermi$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/lec
filename: 221114-lec19.tex
modified: 2022-11-14 20:56:33.172174
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \def\ef{0.75} % fermi energy
    \def\fd{0.25}  % amplitude of Fermi-Dirac
    \begin{axis}[
        xmin=0,
        xmax=1.2,
        ymin=0,
        ymax=1,
        enlargelimits=false,
        width=\fermiwid,
        height=\fermihgt,
        xlabel={$\spe$},
        ylabel=\empty,
        ytick=\empty,
        xtick=\empty,
        xticklabel=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1},
        axis on top=true,
        x label style={xshift=0.75in},
      ]
      \addplot[color=white,domain=0:\ef,samples=101,line width=0pt,fill=blue!20!white ]
      {sqrt(x)} \closedcycle;
      \addplot[color=white,domain=0:1,samples=151,line
        width=0pt,fill=red,opacity=0.2]
      {sqrt(x)/(1+exp(32*(x-\ef)))} \closedcycle;
      \addplot[domain=0:1,samples=151,line width=1pt,trace02,opacity=0.25]
      {sqrt(x)/(1+exp(32*(x-0.75)))};

      \addplot[domain=0:1,samples=101,line width=1pt, DarkBlue]
      {sqrt(x)};
      % show the FD
      \addplot[domain=0:1,samples=101,line width=1pt,DarkRed]
      {\fd /(1 + exp(32*(x-\ef)))};

      \node[DarkBlue] at (0.75,0.95) {$\dos{\spe}$};
      \node[DarkRed, anchor=south,font=\scriptsize] at (\ef/2,\fd) {$n_{\rm
              FD}(T>0)$};
      \draw[DarkBlue!50!white,<-] (\ef,0.7) -- (\ef+0.1,0.7)
      node[anchor=west,font=\scriptsize] {removed};
      \draw[DarkRed!50!white,<-] (\ef+0.05,0.15) -- (\ef+0.15,0.15)
      node[anchor=west,font=\scriptsize] {added};
      \only<2|handout:0>{
        \draw[dashed] (\ef-0.02,0) -- (\ef-0.02,0.85);
      }
    \end{axis}
    \node at (4.65,-0.25) {$\efermi$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/exams
filename: _region_.tex
modified: 2022-12-09 22:47:10.214089
domain: p117
source:
  \begin{tikzpicture}[scale=1.25]
    \def\Si{0.2}
    \def\clad{1}
    \def\metal{0.4}
    \def\wid{10}
    \filldraw[fill=yellow!50] (0,\Si/2) rectangle ++(\wid,\clad)
    (0,-\Si/2) rectangle ++ (\wid,-\clad);
    \filldraw[fill=gray!50] (0,-\Si/2) rectangle (\wid,\Si/2);
    \filldraw[fill=gray!75] (0, \clad+\Si/2) rectangle
    ++(\wid/2-0.1,\metal)
    (0,-\clad-\Si/2) rectangle ++(\wid,-\metal) % bottom grounded electrode
    (\wid, \clad+\Si/2) rectangle ++(-\wid/2+0.1,\metal);

    % Ground wire
    \draw[line width=1.5] (\wid, -\clad-0.5*\metal-0.5*\Si) -- ++(0.5,0)
    coordinate (g) -- ++ (0,\Si+2*\clad+\metal) -- ++(-0.5,0)
    (g) -- ++(0,-0.5) coordinate (G);
    \begin{scope}[shift={(G)},line width=1]
      \foreach \x/\y in {0.2/0, 0.15/0.1, 0.1/0.2} {
          \draw (-\x,-\y) -- (\x,-\y);
        }
    \end{scope}
    % applied potential
    \draw[line width=1.5] (0, 0.5*\Si+0.5*\metal+\clad) -- ++(-0.5,0)
    -- ++(0, -2*\clad-\metal-\Si) -- ++(0.5,0);
    \filldraw[fill=white] (-0.5,0) circle[radius=0.4];
    \node at (-0.5,0) {$V$};
    \node[font=\scriptsize] at (-0.7,0.55) {$+$};
    \node[font=\scriptsize] at (-0.7,-0.55) {$-$};
    % label the silicon
    \draw[<-] (\wid-0.25,0) -- ++(1.25,0) node[anchor=west]{Si};
    % label the SiGe layers
    \foreach \y in {-0.6*\clad, 0.6*\clad} {
        \node[anchor=east] at (\wid-0.2,\y) {\SiGe};
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/exams
filename: _region_.tex
modified: 2022-12-09 22:47:10.214089
domain: p117
source:
  \begin{tikzpicture}[scale=1.33]
    \draw[DarkGreen, ->] (0,0) -- (5,0) node[anchor=north]{$S$};
    \draw[DarkGreen, ->] (0,0) -- (0,4) node[anchor=east]{$p$};
    \draw[line width=1.5] (1,1) coordinate (A) -- ++ (3,0) coordinate (B)
    -- ++(0, 2.5) coordinate (C) -- ++(-3,0) coordinate (D) -- cycle;
    \draw (1,0) node[anchor=north] {$S_{1}$} -- ++(0,0.2);
    \draw (4,0) node[anchor=north] {$S_{3}$} -- ++(0,0.2);
    \draw (0, 1) node[anchor=east] {$p_{1}$} -- ++(0.2,0);
    \draw (0, 3.5) node[anchor=east] {$p_{3}$} -- ++(0.2,0);
    \begin{scope}[font=\scriptsize]
      \node[anchor=north east,draw,circle,shift={(-.1,-.1)}] at (A) {1};
      \node[anchor=south west,draw,circle,shift={(.1,.1)}] at (C) {3};
      \node[anchor=north west,draw,circle,shift={(.1,-.1)}] at (B) {\vphantom{3}};
      \node[anchor=south east,draw,circle,shift={(-.1,0.1)}] at (D) {\vphantom{3}};
    \end{scope}

    \begin{scope}[shift={(6,0)}]
      \draw[DarkGreen, ->] (0,0) -- (5,0) node[anchor=north]{$V$};
      \draw[DarkGreen, ->] (0,0) -- (0,4) node[anchor=east]{$p$};
      \draw (0, 1) node[anchor=east] {$p_{1}$} -- ++(0.2,0);
      \draw (0, 3.5) node[anchor=east] {$p_{3}$} -- ++(0.2,0);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/exams
filename: _region_.tex
modified: 2022-12-09 22:47:10.214089
domain: p117
source:
  \begin{tikzpicture}[scale=0.85]
    \draw[DarkGreen,->] (0,0) --node[anchor=north,shift={(0,-0.2)}]{$x$} (10,0) ;
    \draw[DarkGreen,->] (0,0) -- (0, 7) node[anchor=east]{$G$};
    \draw[DarkGreen,dashed] (9,0) node[anchor=north] {1} -- ++(0,7); \draw[line
      width=1.5] (0,3) coordinate (A) --node[anchor=south,rotate=12]{no mixing}
    (9,5) coordinate (B); \node[anchor=north,DarkGreen] at (0,0) {0};
    \node[anchor=east] at (A) {$g_{A}^{\circ}$}; \node[anchor=west] at (B)
    {$g_{B}^{\circ}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/exams
filename: _region_.tex
modified: 2022-12-09 22:47:10.214089
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=1.2, ymin=0, ymax=3.5, enlargelimits=false,
        width=5in, height=3.5in,
        xlabel={$x$}, ylabel={$G$}, ytick={2,3}, xtick={0,1},
        yticklabels={$g_{A}^{\circ}$,$g_{B}^{\circ}$},
        axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[black, domain=0:1,samples=3, line width=1pt] {2+x};
      \addplot[DarkGreen, domain=0.0001:0.9999, samples=100, line width=2pt,]
      {2 + x + 3 * (x * ln(x) + (1-x) * ln(1-x))};
      \addplot[DarkRed, dashed, domain=0.0001:0.9999, samples=100, line width=2pt,]
      {2 + x + 1 * (x * ln(x) + (1-x) * ln(1-x))};
      \draw[dashed] (1,0) -- (1,3.5) (0,3) -- (1.1,3);
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/exams
filename: _region_.tex
modified: 2022-12-09 22:47:10.214089
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=1.2, ymin=0, ymax=3.5, enlargelimits=false,
        width=5in, height=3.5in,
        xlabel={$x$}, ylabel={$G$}, ytick={2,3}, xtick={0,0.06,0.91,1},
        xticklabels={0,$x_{1}$,$x_{2}$,1},
        yticklabels={$g_{A}^{\circ}$,$g_{B}^{\circ}$},
        axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[black, domain=0:1,samples=3, line width=0.5pt] {2+x};
      \addplot[DarkGreen, domain=0.0001:0.9999, samples=100, line width=2pt,]
      {2 + x + 5 * (x * ln(x) + (1-x) * ln(1-x)) + 15*x*(1-x)};
      \draw[dashed] (0.06,0)-- ++ (0,1.8) (0.91,0) -- ++(0, 2.6);
      \draw[dashed] (0,3) -- (1,3) -- (1,0);
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/exams
filename: phys-117-2022-final-v2.tex
modified: 2022-12-12 18:00:23.321610
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \fill[gray!50,rounded corners] (-1,0) rectangle (1,-5);
    \fill[white, rounded corners] (-0.1,-0.1) rectangle (0.1,-4.6);
    \draw[white,line width=2] (0,0.05) -- (0,-0.2);
    \draw[DarkGreen,<-] (0.1,-0.5) -- ++ (0.4,0);
    \draw[DarkGreen,<-] (-0.1,-0.5) -- ++(-0.4,0) node[anchor=south,font=\tiny]{0.1 mm} ;
    \node[font=\small\sffamily] at (0,-5.5) {side view};
    \draw[dotted,line width=1] (0.1,-0.2) -- (0.1,-4.4);
    \draw[<-] (0.1,-2.5) -- ++(0.3,0) node[anchor=west,font=\tiny]{face of area
      $\SI{0.01}{m^{2}}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/exams
filename: phys-117-2022-final-v2.tex
modified: 2022-12-12 18:00:23.321610
domain: p117
source:
  \begin{tikzpicture}[scale=1.33]
    \draw[dashed, gray] (0,1) -- (4.5,1)
    (0,3.5) -- (4.5,3.5)
    (1,0) -- (1,4.)
    (4,0) -- (4,4.);
    \draw[DarkGreen, ->] (0,0) -- (5,0) node[anchor=north]{$S$};
    \draw[DarkGreen, ->] (0,0) -- (0,4) node[anchor=east]{$p$};
    \draw[line width=1.5] (1,1) coordinate (A) -- ++ (3,0) coordinate (B)
    -- ++(0, 2.5) coordinate (C) -- ++(-3,0) coordinate (D) -- cycle;
    \draw (1,0) node[anchor=north] {$S_{1}$} -- ++(0,0.2);
    \draw (4,0) node[anchor=north] {$S_{3}$} -- ++(0,0.2);
    \draw (0, 1) node[anchor=east] {$p_{1}$} -- ++(0.2,0);
    \draw (0, 3.5) node[anchor=east] {$p_{3}$} -- ++(0.2,0);
    \begin{scope}[font=\scriptsize]
      \node[anchor=north east,draw,circle,shift={(-.1,-.1)}] at (A) {1};
      \node[anchor=south west,draw,circle,shift={(.1,.1)}] at (C) {3};
      \node[anchor=north west,draw,circle,shift={(.1,-.1)}] at (B) {\vphantom{3}};
      \node[anchor=south east,draw,circle,shift={(-.1,0.1)}] at (D) {\vphantom{3}};
    \end{scope}

    \begin{scope}[shift={(6,0)}]
      \draw[dashed, gray] (0,1) -- (4.5,1)
      (0,3.5) -- (4.5,3.5);
      \draw[DarkGreen, ->] (0,0) -- (5,0) node[anchor=north]{$V$};
      \draw[DarkGreen, ->] (0,0) -- (0,4) node[anchor=east]{$p$};
      \draw (0, 1) node[anchor=east] {$p_{1}$} -- ++(0.2,0);
      \draw (0, 3.5) node[anchor=east] {$p_{3}$} -- ++(0.2,0);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/exams
filename: final-scrap.tex
modified: 2022-12-09 06:59:35.684425
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \draw[->] (0,0) -- (9,0) node[anchor=north]{$T$};
    \draw[->] (0,0) -- (0,6) node[anchor=east]{$E$};
    \node[anchor=east] at (0,0) {$0$};
    \node[anchor=east] at (0,1.25) {$\frac{1}{4}\spe$};
    \node[anchor=east] at (0,2.5) {$\frac{1}{2}\spe$};
    \node[anchor=east] at (0,3.75) {$\frac{3}{4} \spe$};
    \node[anchor=east] at (0,5) {$\spe$};
    \foreach \y in {1.25,2.5,3.75,5}{
        \draw[color=SlateGray,dashed] (0,\y) -- ++(9,0);
      }
    \foreach \x in {1,2,3,4} {
        \draw[color=SlateGray,dashed] (\x*2,0) -- ++(0,6);
      }
    \node[anchor=north] at (2,0) {$\displaystyle\frac{\spe}{\kb}$};
    \node[anchor=north] at (4,0) {$\displaystyle 2 \frac{\spe}{\kb}$};
    \node[anchor=north] at (6,0) {$\displaystyle 3 \frac{\spe}{\kb}$};
    \node[anchor=north] at (8,0) {$\displaystyle 4 \frac{\spe}{\kb}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022/Chapters/Ch15
filename: text.tex
modified: 2022-10-30 03:29:14.514944
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!25] (0,0) rectangle (4,0.5);
    \draw[force] (2,0.25) -- ++(0,-1.2) node[anchor=north]{$\rho A g \dd{z}$};
    \begin{scope}[DarkRed,<-]
      \foreach \x in {0.5, 1.5, ..., 3.5} {
          \draw[line width=2] (\x,0) -- ++(0,-0.75);
          \draw[line width=1.5] (\x,0.5) -- ++(0,0.75);
        }
      \node[anchor=west] at (4,-0.375) {$p(z)$};
      \node[anchor=west] at (4,0.875) {$p(z+\dd{z})$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022/Chapters/Ch14
filename: text.tex
modified: 2022-10-25 22:40:52.070145
domain: Book
source:
  \begin{tikzpicture}[scale=1.25]
    \draw[->] (0,0) -- (4,0) node[anchor=north,shift={(-0.5,0)}]{$x$};
    \draw[->] (0,0) -- (0,3) node[anchor=east,shift={(0,-0.5)}]{$\E$};
    \draw (0.2,2.8) ..controls(0.5,1.25) and (0.8,1.25)..  (1,1.25) coordinate (a)
    ..controls (1.4,1.25) and (1.7,2) .. (2,2) coordinate (b)
    .. controls (2.3,2) and (2.7,0.45) .. (3,0.45) coordinate (c)
    .. controls (3.2,0.45) and (3.5,0.75) .. (3.75,1.25);
    \node[anchor=north] at (a) {$a$};
    \node[anchor=north] at (b) {$b$};
    \node[anchor=north] at (c) {$c$};
    \fill[gray] (a) ++ (0,0.1) circle[radius=0.075];
    \filldraw[DarkRed,fill=DarkRed!25!white] (b) ++ (0,0.1) circle[radius=0.075];
    \filldraw[DarkBlue,fill=DarkBlue!50!white] (c) ++ (0,0.1) circle[radius=0.075];
    \begin{scope}[DarkGreen]
      \draw (1.2,1.25) -- ++(1.8,0) (2.2,2) -- ++(0.8,0);
      \draw[<->] (2.8,1.25) -- node[anchor=west]{$\Delta E$} ++(0,0.75);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022/Chapters/Ch03
filename: text.tex
modified: 2022-10-11 23:19:18.814637
domain: Book
source:
  \begin{tikzpicture}[scale=1.5]
    \begin{axis}[
        xmin=0, xmax=100, ymin=0, ymax=5, enlargelimits=false,
        width=2.5in, height=2in,
        every axis y label/.style={at={(ticklabel cs:0.5)},rotate=90,anchor=near ticklabel},
        xlabel={$\nrg$}, ylabel={$S$}, ytick=\empty, xtick=\empty,
        xticklabel=\empty, yticklabel=\empty,
        axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkGreen, domain=0:100, samples=300, line width=1.5pt,]
      {ln(1+x)};
      \begin{scope}[font=\small,line width=1]
        \begin{scope}[DarkBlue]
          \draw (10,2.4) coordinate (A) -- ++(8,8/11) (A) -- ++(-8,-8/11);
          \draw[<-] (A) -- ++(5, -0.5) -- ++(5,0) node[anchor=west]{low $T$};
        \end{scope}
        \begin{scope}[DarkRed]
          \draw (70,4.26) coordinate (B) -- ++(30,30/71) (B) -- ++(-30,-30/71);
          \draw[<-] (B) -- ++(-5, 0.5) -- ++(-5,0) node[anchor=east]{high $T$};
        \end{scope}
      \end{scope}
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022/Chapters/Ch03
filename: text.tex
modified: 2022-10-11 23:19:18.814637
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=1.1, ymin=0, ymax=1, enlargelimits=false,
        width=2.5in, height=2in,
        every axis y label/.style={at={(ticklabel cs:0.5)},rotate=90,anchor=near ticklabel},
        xlabel={$\nrg$}, ylabel={$\nos(\nrg)$}, ytick=\empty, xtick=\empty,
        xticklabel=\empty, yticklabel=\empty,
        axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkGreen, domain=0:1, samples=300, line width=1.5pt,]
      {x^100};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022/Chapters/Ch03
filename: text.tex
modified: 2022-10-11 23:19:18.814637
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=100, ymin=0, ymax=5, enlargelimits=false,
        width=2.5in, height=2in,
        every axis y label/.style={at={(ticklabel cs:0.5)},rotate=90,anchor=near ticklabel},
        xlabel={$\nrg$}, ylabel={$S$}, ytick=\empty, xtick=\empty,
        xticklabel=\empty, yticklabel=\empty,
        axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkGreen, domain=0:100, samples=300, line width=1.5pt,]
      {ln(1+x)};
      \begin{scope}[font=\small,line width=1]
        \begin{scope}[DarkBlue]
          \draw (10,2.4) coordinate (A) -- ++(8,8/11) (A) -- ++(-8,-8/11);
          \draw[<-] (A) -- ++(5, -0.5) -- ++(5,0) node[anchor=west]{low $T$};
        \end{scope}
        \begin{scope}[DarkRed]
          \draw (70,4.26) coordinate (B) -- ++(30,30/71) (B) -- ++(-30,-30/71);
          \draw[<-] (B) -- ++(-5, 0.5) -- ++(-5,0) node[anchor=east]{high $T$};
        \end{scope}
      \end{scope}
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022/Chapters/Ch03
filename: text.tex
modified: 2022-10-11 23:19:18.814637
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=3, ymin=0, ymax=20, enlargelimits=false,
        width=2.5in, height=2in,
        every axis y label/.style={at={(ticklabel cs:0.5)},rotate=90,anchor=near ticklabel},
        xlabel={$\nrg$}, ylabel={$S$}, ytick=\empty, xtick=\empty,
        xticklabel=\empty, yticklabel=\empty,
        axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkGreen, domain=0:3, samples=30, line width=1.5pt,]
      {exp(x)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022/Chapters/Ch03
filename: text.tex
modified: 2022-10-11 23:19:18.814637
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=1.1, ymin=0, ymax=4.5, enlargelimits=false,
        width=2.5in, height=2in,
        every axis y label/.style={at={(ticklabel
                cs:0.5)},rotate=90,anchor=near ticklabel},
        every axis x label/.style={at={(ticklabel cs:0.475)}, anchor=center,
            shift={(0,0.07)}},
        xlabel={$\nrg_{1}$}, ylabel={$S$}, ytick=\empty, xtick={1},
        xticklabel={\textcolor{DarkRed}{$\nrg\total$}}, yticklabel=\empty,
        axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkGreen, domain=0:1, samples=50, line width=1.5pt,]
      {ln(1+10*x)};
      \node[DarkGreen] at (0.875,1.9) {$S_{1}(\nrg_{1})$};
      \addplot[DarkRed,domain=0:1, samples=50, line width=1.5pt]
      {ln(1+10*(1-x))};
      \node[DarkRed,anchor=east] at (0.3,1.85){$S_{2}(\nrg_{2})$};
      \addplot[DarkBlue, domain=0:1,samples=50, line width=1.5pt]
      {ln(1+10*(1-x))+ln(1+10*x)};
      \node[DarkBlue,anchor=south] at (0.5, 3.7)
      {$S\total = S_{1}(\nrg_{1})+S_{2}(\nrg\total-\nrg_{1})$};
      \draw[dashed,gray] (0.5,0) -- (0.5,4);
      \node[anchor=north, DarkRed] at (1,0) {$\nrg\total$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022/Chapters/Ch03
filename: text.tex
modified: 2022-10-11 23:19:18.814637
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \def\xtent{3}
    \draw[->] (-\xtent,0) -- (\xtent,0) node[anchor=north east] {$\nrg$} ;
    \draw[->] (0,0) -- (0,\xtent) node[anchor=north east] {$S$};
    \draw[DarkGreen, line width=1.5] (0,2.5) parabola (-2.5,0.5);
    \draw[DarkGreen, line width=1.5, dashed] (0,2.5) parabola (2.5,0.5);
    \node[anchor=north] at (0,0) {$0$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022/Chapters/Ch05
filename: text.tex
modified: 2022-10-11 23:19:18.834969
domain: Book
source:
  \begin{tikzpicture}
    \begin{axis}[
        ymin=0,
        ymax=1,
        enlargelimits=false,
        height=1.5in,
        ylabel={$\probab$},
        ytick={0,1},
        xtick={0,0.5,1,1.5,2},
        xticklabel=\empty,
      ]
      \addplot[
        trace01,
        domain=0.001:2,
        samples=201,
        line width=2pt,
      ]
      {1 / (1 + exp(-1/x))};
      \addplot[
        trace02,
        domain=0.001:2,
        samples=201,
        line width=2pt,
      ]
      {1 / (1 + exp(1/x))};
    \end{axis}

    \node[color=trace01] at (4.5,1.75) {$\probab(0)$};
    \node[color=trace02] at (4.5,0.45) {$\probab(\epsilon)$};
    \node at (5.5,0.3){(a)};

    \begin{scope}[shift={(0,-2.75)}]
      \begin{axis}[
          ymin=0,
          ymax=0.5,
          enlargelimits=false,
          height=1.5in,
          ylabel={$\avg{E}$},
          minor tick num=0,
          ytick={0},
          xtick={0,0.5,1,1.5,2},
          xticklabel=\empty,
          extra y ticks={0.5},
          extra y tick labels={$\frac{\epsilon}{2}$},
        ]
        \addplot[
          trace03,
          domain=0.001:2,
          samples=201,
          line width=2pt,
        ]
        {1 / (1 + exp(1/x))};
      \end{axis}

      \node at (5.5,0.3) {(b)};
    \end{scope}

    \begin{scope}[shift={(0,-5.5)}]
      \begin{axis}[
          ymin=0,
          ymax=0.5,
          enlargelimits=false,
          height=1.5in,
          ylabel={$C$},
          xlabel={$\kT/\epsilon$},
          minor tick num=0,
          ytick={0},
          xtick={0,0.5,1,1.5,2},
          extra y ticks={0.5},
          extra y tick labels={$\frac{\kb}{2}$},
        ]
        \addplot[
          trace04,
          domain=0.001:2,
          samples=201,
          line width=2pt,
        ]
        {1 / (2*x * cosh(0.5/x))^2};
      \end{axis}

      \node at (5.5,1.85) {(c)};
    \end{scope}


  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022/Chapters/Ch18
filename: text.tex
modified: 2022-11-15 23:23:29.593133
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=1, ymin=0, ymax=1, enlargelimits=false,
        width=2.5in, height=2in,
        xlabel={$p = \hb k$},
        ylabel={$\spe = \hb \omega$},
        ytick=\empty,
        xtick=\empty,
        % xticklabel=\empty, xticklabels{0,,$a$,,a$},
        axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkGreen, domain=0:1, samples=100, line width=2pt,]
      {x^2};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022/Chapters/Ch17
filename: text.tex
modified: 2022-11-05 15:59:16.543128
domain: Book
source:
  \begin{tikzpicture}[scale=0.75]
    \filldraw[fill=yellow!25!white,draw=gray!25!white,line width=3pt] (0,0)
    rectangle (4,3);
    \node[anchor=west] at (0.2,0.35) {$R$};
    \node[anchor=west] at (0.2,2.5) {$T, \mu$};
    \filldraw[fill=red!25!white,draw=gray!25!white,line width=2pt] (4.5,1.5)
    circle[radius=0.5];
    \node at (4.5,0.7) {$S$};
    \draw[line width=1.25,->,color=DarkRed] (3.4,1.6)
    --node[anchor=south]{$E_{n}$} +(0:1.2);
    \draw[line width=1.25,->,color=DarkGreen] (3.4,1.4) --node[anchor=north]{$n$} +(0:1.2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022/Chapters/Ch19/sol
filename: BECinHarmonicTrap.tex
modified: 2022-12-05 16:39:05.574914
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
      xmin=0, xmax=1.2, ymin=0, ymax=1.1, enlargelimits=false,
      width=2.25in, height=1.75in,
      xlabel={$T/T_{\rm E}$}, ylabel={$N_{\rm o}/N$}, ytick={0,0.25, ..., 1}, xtick={0, 0.25, ..., 1},
      % xticklabel=\empty, xticklabels{0,,$a$,,a$},
      % axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \addplot[DarkRed, domain=0:1, samples=100, line width=2pt,]
      {1 - x^3};
      \addplot[DarkRed,domain=1:1.2,samples=3,line width=2pt] {0*x};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/smbook/2022/Chapters/Ch19/sol
filename: PowerFlux.tex
modified: 2022-11-18 03:08:28.520393
domain: Book
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[rotate=90]
      \draw[line width=2pt] (0,0.5) -- (0,2) (0,-0.5) -- (0,-2) ;
      % draw the slant cylinder
      \filldraw[color=gray,fill=yellow!60!white,dashed] (0,0.5) -- ++(150:2.5) -- ++(-90:1)
      -- ++(-30:2.5) -- cycle;
      \draw[dashed] (-2,0) -- (2,0);
      \draw[gray] (150:2.5) -- ++(-30:5);
      \draw (0:1) arc (0:-30:1);
      \node at (-15:1.25){$\theta$};
      \draw[<->,DarkGreen] (0,0.75) -- node[anchor=south,rotate=60]{$c \delta t$}
      ++(150:2.5);
      \draw[<-,DarkGreen] (0,0.2) -- ++(30:0.75) node[anchor=south]{$\delta A$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Core79/logo
filename: logo23.tex
modified: 2022-12-15 18:03:57.775282
domain: Core79
source:
  \begin{tikzpicture}[mindmap]
    \fill[gray!15] (-10,-10) rectangle (10,6);
    %  \fill[black!55!white] (0,0) circle[radius=3];
    %  \fill[black,path fading=fade out,even odd rule] (0,0) circle[radius=6] (0,0)
    %  circle[radius=3];
    \fill[black,path fading=fade out] (0,0) circle[radius=6];
    \begin{scope}[
        every node/.style={concept, circular drop shadow,execute at begin
            node=\hskip0pt},
        root concept/.append style={
            concept color=black, fill=gray!20!white, line width=1ex, text=black, font=\large\scshape},
        text=white,
        core/.style={concept color=\cola,faded/.style={concept color=red!50}},
        creativity/.style={concept color=\colb,faded/.style={concept color=red!50}},
        communication/.style={concept color=\colc,faded/.style={concept color=blue!50}},
        collaboration/.style={concept color=\cold,faded/.style={concept color=orange!50}},
        context/.style={concept color=\colb,faded/.style={concept
                color=green!50!black!50}},
        grow cyclic,
        level 1/.append style={level distance=4.5cm,sibling angle=90,font=\scshape},
        level 2/.append style={level distance=3cm,sibling angle=45,font=\scriptsize}]

      \node [root concept] {\huge Climate\\[.1in]Change} % root
      child[grow=45,core] {node {Core}}
      child[grow=135,collaboration] {node {Collaboration}}
      child[grow=225,communication] {node {Communication}}
      child[grow=-45,context] {node {Context}};
      %  child[core] {node {Core}};
    \end{scope}

    \draw[decoration={
    text along path,
    text format delimiters={[}{]},
    text = {[\huge\color{white}\sc]Critical},
    text align={center},
    raise=0.2cm},decorate]
    (120:3) arc(120:60:3);

    \draw[decoration={
    text along path,
    text format delimiters={[}{]},
    text = {[\huge\color{white}\sc]Analysis},
    text align={center},
    raise=0.2cm},decorate]
    (210:3) arc(210:150:3);

    \draw[decoration={
    text along path,
    text format delimiters={[}{]},
    text = {[\huge\color{white}\sc]Critical},
    text align={center},
    raise=0.2cm},decorate]
    (300:3) arc(300:240:3);

    \draw[decoration={
    text along path,
    text format delimiters={[}{]},
    text = {[\huge\color{white}\sc]Analysis},
    text align={center},
    raise=0.2cm},decorate]
    (30:3) arc(30:-30:3);

    % Other cs
    % creativity, complexity, crisis, caring, cancer, consensus,
    % 
    \begin{scope}[shift={(-1.25,0)},every extra concept/.append style={minimum
            size=2.5cm,
            circular drop shadow}]
      \def\rad{8}
      \def\angs{25}
      \def\rot{45}
      \node [extra concept,anchor=west,white,fill=\colc] at (150:\rad) {\sc Nuclear Power?};
      \node [extra concept,anchor=west,white,fill=\colb] at (190:\rad) {\sc Biodiversity Policy};
      \node [extra concept,anchor=west,white,fill=\cola] at (230:\rad) {\sc Geo\-engineering};
      \node [extra concept,anchor=west,white,fill=\cold] at (270:\rad) {\sc Eco-feminism};
      \node [extra concept,anchor=west,white,fill=\colc] at (310:\rad) {\sc Art};
      \node [extra concept,anchor=west,white,fill=\colb] at (350:\rad) {\sc Temporo\-spatial Data};
      \node [extra concept,anchor=west,white,fill=\cola] at (30:\rad) {\sc Community Organizing};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Core79/Heaberlin
filename: Heaberlin-6.tex
modified: 2022-12-23 19:12:31.871878
domain: Core79
source:
  \begin{tikzpicture}
    \node[draw,rounded corners,fill=DarkGreen!10!white,font=\tiny] at (0,0) {$#1 \rightarrow$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2022/projects
filename: Ranlett.tex
modified: 2022-12-21 01:38:09.909503
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=0.025] (0,0) -- (1,0);
    \filldraw[fill=gray!50] (0,0) circle[radius=0.2] (1,0) circle[radius=0.2];
    \node at (1.5,0) {or};
    \draw[line width=3] (2,0) -- (3,0);
    \filldraw[fill=gray!50] (2,0) circle[radius=0.1] (3,0) circle[radius=0.1];
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Core79/2023
filename: tent-template.tex
modified: 2023-01-18 22:04:00.787736
domain: Core79
source:
  \begin{tikzpicture}[scale=1]
    \draw[gray!25] (-\wid,-\heit) rectangle (\wid,\heit);
    \begin{scope}[shift={(0, 2.2in)}]
      \node at (0,-1in) {#1 #2};
      \node[rotate=180] at (0, 1in) {#1 #2};
    \end{scope}
    \begin{scope}[shift={(0,-2.7in)}]
      \node at (0,-1in) {#3 #4};
      \node[rotate=180] at (0, 1in) {#3 #4};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p64/2023/lec
filename: 230124-lec03.tex
modified: 2023-01-24 19:23:50.042620
domain: p64
source:
  \begin{tikzpicture}[scale=1]
    \draw[coord] (0,0) -- (3,0) node[anchor=north]{$x$};
    \draw[coord] (0,0) -- (0,3) node[anchor=east] {$y$};
    \def\ang{25}
    \begin{scope}[rotate=\ang,dashed]
      \draw[coord, DarkRed] (0,0) -- (3,0) node[anchor=north]{$x'$};
      \draw[coord, DarkRed] (0,0) -- (0,3) node[anchor=east] {$y'$};
    \end{scope}

    \draw (0.5,0) arc (0:\ang:0.5);
    \node[anchor=west] at (\ang/1.5:0.7) {$\theta$};
  \end{tikzpicture}


