# django_admin_log

action_time: 2022-06-13 03:19:14.305182
object_id: 1
change_message: [{"changed": {"fields": ["Description"]}}]
object_repr:
  To change the amount of space allocated to axis labels, use e.g.
  ```
  plt.subplots_adjust(left=0.2, bottom=0.15)
  ```
  which uses 20% of the plot width for the region to the left of the *y* axis.


action_time: 2022-12-30 01:53:30.974078
object_id: 1
change_message: [{"added": {}}]
object_repr:
  To include a python code example, use the following:
  ```
  \begin{minted}{python}
  import numpy as np
  import matplotlib.pyplot as plt

  fig, ax = plt.subplots()
  x = np.linspace(0,10,11)
  ax.plot(x,


action_time: 2022-12-30 04:31:28.524753
object_id: 3
change_message: [{"added": {}}]
object_repr:
  [cleveref] (37141) Suppose that you have a figure labeled with the command `\label{fig:gamma}`
  In "normal" LaTeX, you 


action_time: 2022-12-30 04:41:44.961009
object_id: 4
change_message: [{"added": {}}]
object_repr:
  [fancyhdr] (8377) ```
  \renewcommand{\footrulewidth}{0.4pt}
  \newcommand*{\ffcolor}{DarkOliveGreen}
  \newcommand*{\ffs


action_time: 2022-12-30 04:42:24.910007
object_id: 5
change_message: [{"added": {}}]
object_repr:
  [hyperref] (8270) To link to an external source, you can use the command
  ```
  \hyperref{url}{x}{y}{tag text}
  ```
  wh


action_time: 2022-12-30 04:42:59.838725
object_id: 6
change_message: [{"added": {}}]
object_repr:
  [minted] (10209) To include a python code example, use the following:
  ```
  \begin{minted}{python}
  import numpy as n


action_time: 2022-12-30 04:48:07.520939
object_id: 7
change_message: [{"added": {}}]
object_repr:
  [pageslts] (4746) Near the top of the document, include

  ```
  \pagenumbering{arabic} % or other style
  ```

  In a f


action_time: 2022-12-30 13:05:34.882893
object_id: 8
change_message: [{"added": {}}]
object_repr:
  [physics] (11184) The following surrounds the fraction a/b with parentheses that are sized appropriately. You can also


action_time: 2022-12-30 13:06:06.463781
object_id: 9
change_message: [{"added": {}}]
object_repr:
  [sidecap] (9944) ```
  \begin{SCfigure}[5][tb]
    \centering
    \includegraphics[width=3in]{2D-0015-stop}
    \caption{


action_time: 2022-12-30 13:06:34.859163
object_id: 10
change_message: [{"added": {}}]
object_repr:
  [siunitx] (5803) ```
  The counterweight's mass was $m = \SI{2.34(2)e3}{kg}$
  ```
  Note: recent versions of **siunitx*


action_time: 2022-12-30 13:08:21.235257
object_id: 11
change_message: [{"added": {}}]
object_repr:
  [subcaption] (12723) The example below shows how to create a figure with two subfigures. Each subfigure is drawn by **tik


action_time: 2022-12-30 13:09:26.691930
object_id: 12
change_message: [{"added": {}}]
object_repr:
  [wrapfig] (5357) ```
  % \begin{wrapfigure}[nlines]{<rl>}[overhang into margin]{width or 0pt}
  \begin{wrapfigure}{r}{0


action_time: 2022-12-30 13:11:38.832017
object_id: 14
change_message: [{"added": {}}]
object_repr:
  [xifthen] ``` latex
  \ifthenelse{\isempty{#1}}
      {Do something when the first argument is empty}
      {Do s


action_time: 2022-12-30 17:36:02.720780
object_id: 21
object_repr: [layout] fancyhdr
change_message:
  [{"changed": {"name": "example", "object": "[fancyhdr] (33327) ```\r\n\\renewcommand{\\footrulewidth}{0.4pt}\r\n\\newcommand*{\\ffcolor}{DarkOliveGreen}\r\n\\newcommand*{\\ffs", "fields": ["Text", "Preamble"]}}]


action_time: 2022-12-30 17:37:35.127641
object_id: 21
object_repr: [layout] fancyhdr
change_message:
  [{"changed": {"name": "example", "object": "[fancyhdr] (3236) ```\r\n\\renewcommand{\\footrulewidth}{0.4pt}\r\n\\newcommand*{\\ffcolor}{DarkOliveGreen}\r\n\\newcommand*{\\ffs", "fields": ["Preamble"]}}]


action_time: 2022-12-30 17:38:29.227302
object_id: 21
object_repr: [layout] fancyhdr
change_message:
  [{"changed": {"name": "example", "object": "[fancyhdr] (33327) ```\r\n\\renewcommand{\\footrulewidth}{0.4pt}\r\n\\newcommand*{\\ffcolor}{DarkOliveGreen}\r\n\\newcommand*{\\ffs", "fields": ["Preamble"]}}]


action_time: 2022-12-30 17:42:07.023239
object_id: 21
object_repr: [layout] fancyhdr
change_message:
  [{"changed": {"name": "example", "object": "[fancyhdr] (33327) ```\r\n\\renewcommand{\\footrulewidth}{0.4pt}\r\n\\newcommand*{\\ffcolor}{DarkOliveGreen}\r\n\\newcommand*{\\ffs", "fields": ["Preamble", "Error"]}}]


action_time: 2022-12-30 17:43:26.262004
object_id: 21
object_repr: [layout] fancyhdr
change_message:
  [{"changed": {"name": "example", "object": "[fancyhdr] (33327) ```\r\n\\renewcommand{\\footrulewidth}{0.4pt}\r\n\\renewcommand*{\\ffcolor}{DarkOliveGreen}\r\n\\renewcommand*{", "fields": ["Text", "Error"]}}]


action_time: 2022-12-30 17:44:43.163036
object_id: 21
object_repr: [layout] fancyhdr
change_message:
  [{"changed": {"name": "example", "object": "[fancyhdr] (25982) ```\r\n\\renewcommand{\\footrulewidth}{0.4pt}\r\n\\renewcommand*{\\ffcolor}{DarkOliveGreen}\r\n\\renewcommand*{", "fields": ["Text", "Error"]}}]


action_time: 2022-12-30 17:51:48.934683
object_id: 21
object_repr: [layout] fancyhdr
change_message:
  [{"changed": {"name": "example", "object": "[fancyhdr] (25982) ```\r\n\\renewcommand{\\footrulewidth}{0.4pt}\r\n\\renewcommand*{\\ffcolor}{DarkOliveGreen}\r\n\\renewcommand*{", "fields": ["Text"]}}]


action_time: 2022-12-30 18:06:35.128341
object_id: 27
object_repr: [layout] pageslts
change_message:
  [{"changed": {"name": "example", "object": "[pageslts] (9921) Near the top of the document, include\r\n\r\n```\r\n\\pagenumbering{arabic} % or other style\r\n```\r\n\r\nIn a f", "fields": ["Text", "Preamble"]}}]


action_time: 2022-12-30 18:07:55.370122
object_id: 27
object_repr: [layout] pageslts
change_message:
  [{"changed": {"name": "example", "object": "[pageslts] (7149) Near the top of the document, include\r\n\r\n```\r\n\\pagenumbering{arabic} % or other style\r\n```\r\n\r\nIn a f", "fields": ["Preamble"]}}]


action_time: 2022-12-30 18:09:11.143060
object_id: 27
object_repr: [layout] pageslts
change_message:
  [{"changed": {"name": "example", "object": "[pageslts] (7149) Near the top of the document, include\r\n\r\n```\r\n\\pagenumbering{arabic} % or other style\r\n```\r\n\r\nIn a f", "fields": ["Text", "Preamble"]}}]


action_time: 2022-12-30 18:09:51.846272
object_id: 27
object_repr: [layout] pageslts
change_message:
  [{"changed": {"name": "example", "object": "[pageslts] (7149) Near the top of the document, include\r\n\r\n```\r\n\\pagenumbering{arabic} % or other style\r\n```\r\n\r\nIn a f", "fields": ["Text"]}}]


action_time: 2022-12-30 18:11:02.491522
object_id: 27
object_repr: [layout] pageslts
change_message:
  [{"changed": {"name": "example", "object": "[pageslts] (36950) Near the top of the document, include\r\n\r\n```\r\n\\pagenumbering{arabic} % or other style\r\n```\r\n\r\nIn a f", "fields": ["Preamble"]}}]


action_time: 2022-12-30 18:19:50.899191
object_id: 30
object_repr: [layout] titletoc
change_message:
  [{"added": {"name": "example", "object": "[titletoc] (9268) ```\r\n\\definecolor{mygray}{gray}{0.4}\r\n\\definecolor{darkgray}{gray}{0.25}\r\n\\definecolor{gold}{RGB}{17"}}]


action_time: 2022-12-30 18:23:07.254206
object_id: 25
object_repr: [layout] titlesec
change_message:
  [{"added": {"name": "example", "object": "[titlesec] (6782) ```\r\n\\titleformat{\\chapter}[display]\r\n  {\\normalfont\\bfseries\\color{gold}}\r\n  {\\filleft\\hspace*{-60p"}}]


action_time: 2022-12-30 18:25:36.328354
object_id: 30
object_repr: [layout] titletoc
change_message:
  [{"changed": {"name": "example", "object": "[titletoc] (9268) ```\r\n\\definecolor{mygray}{gray}{0.4}\r\n\\definecolor{darkgray}{gray}{0.25}\r\n\\definecolor{gold}{RGB}{17", "fields": ["Preamble"]}}]


action_time: 2022-12-30 18:29:51.852387
object_id: 16
change_message: []
object_repr:
  [titletoc] ```
  \definecolor{mygray}{gray}{0.4}
  \definecolor{darkgray}{gray}{0.25}
  \definecolor{gold}{RGB}{17


action_time: 2022-12-30 18:46:09.735015
object_id: 17
change_message: []
object_repr:
  [titlesec] ```
  \titleformat{\chapter}[display]
    {\normalfont\bfseries\color{gold}}
    {\filleft\hspace*{-60p


action_time: 2022-12-30 18:52:16.115303
object_id: 26
object_repr: [layout] multicol
change_message:
  [{"changed": {"fields": ["Description"]}}, {"added": {"name": "example", "object": "[multicol] (6782) ```\r\nThis part is set before we start using multicols. The text spans the width of the page.\r\n\r\n\\beg"}}]


action_time: 2022-12-30 18:54:51.420675
object_id: 18
change_message: [{"changed": {"fields": ["Preamble"]}}]
object_repr:
  [multicol] (6782) ```
  This part is set before we start using multicols. The text spans the width of the page.

  \beg


action_time: 2022-12-30 18:56:59.054744
object_id: 18
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [multicol] (6782) ```
  This part is set before we start using multicols. The text spans the width of the page.
  \small


action_time: 2022-12-30 18:57:51.436074
object_id: 18
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [multicol] (47117) ```
  This part is set before we start using multicols. The text spans the width of the page.
  \small


action_time: 2022-12-30 19:10:11.026033
object_id: 23
object_repr: [figures] caption
change_message:
  [{"added": {"name": "example", "object": "[caption] (170666) In the preamble:\r\n``` x\r\n\\usepackage{caption}\r\n\\DeclareCaptionFont{quack}{\\sansserif}\r\n\\captionsetup"}}]


action_time: 2022-12-30 19:11:13.720387
object_id: 19
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [caption] (94565) In the preamble:
  ``` x
  \usepackage{caption}
  \DeclareCaptionFont{quack}{\sansserif}
  \captionsetup


action_time: 2023-01-03 17:42:55.546826
object_id: 13
object_repr: [figures] wrapfig
change_message:
  [{"changed": {"name": "example", "object": "[wrapfig] (361630) ```\r\n% \\begin{wrapfigure}[nlines]{<rl>}[overhang into margin]{width or 0pt}\r\n\\begin{wrapfigure}{r}{0", "fields": ["Text"]}}]


action_time: 2023-01-03 17:43:11.431149
object_id: 12
change_message: []
object_repr:
  [wrapfig] (361630) ```
  % \begin{wrapfigure}[nlines]{<rl>}[overhang into margin]{width or 0pt}
  \begin{wrapfigure}{r}{0


action_time: 2023-01-03 17:44:01.894938
object_id: 12
change_message: [{"changed": {"fields": ["Text", "Preamble"]}}]
object_repr:
  [wrapfig] (426561) ```
  % \begin{wrapfigure}[nlines]{<rl>}[overhang into margin]{width or 0pt}
  \begin{wrapfigure}{r}{0


action_time: 2023-01-03 17:44:35.360938
object_id: 12
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [wrapfig] (219657) ```
  % \begin{wrapfigure}[nlines]{<rl>}[overhang into margin]{width or 0pt}
  \begin{wrapfigure}{r}{0


action_time: 2023-01-03 17:45:02.775229
object_id: 12
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [wrapfig] (240909) ```
  % \begin{wrapfigure}[nlines]{<rl>}[overhang into margin]{width or 0pt}
  \begin{wrapfigure}{r}{0


action_time: 2023-01-03 17:50:35.409324
object_id: 19
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [caption] (240909) In the preamble:
  ``` x
  \usepackage{caption}
  \DeclareCaptionFont{quack}{\sansserif}
  \captionsetup


action_time: 2023-01-03 17:53:12.857280
object_id: 19
change_message: [{"changed": {"fields": ["Text", "Preamble"]}}]
object_repr:
  [caption] (136910) In the preamble:
  ``` x
  \usepackage{caption}
  \DeclareCaptionFont{quack}{\sansserif}
  \captionsetup


action_time: 2023-01-03 18:06:37.255233
object_id: 19
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [caption] (211901) In the preamble:
  ``` x
  \usepackage{caption}
  \DeclareCaptionFont{quack}{\sffamily}
  \captionsetup{


action_time: 2023-01-03 18:08:57.486426
object_id: 11
change_message: [{"changed": {"fields": ["Text", "Preamble"]}}]
object_repr:
  [subcaption] (12229) The example below shows how to create a figure with two subfigures. Each subfigure is drawn by **tik


action_time: 2023-01-03 18:10:24.188980
object_id: 11
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [subcaption] (30975) The example below shows how to create a figure with two subfigures. Each subfigure is drawn by **tik


action_time: 2023-01-03 20:20:36.947015
object_id: 13
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [xcolor] (8722) ```
  There are two ways to change the color of text. To alter the color in a small block, you can us


action_time: 2023-01-03 20:23:24.026553
object_id: 13
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [xcolor] (11590) ```
  ```
  There are two ways to change the color of text. To alter the color in a small block, you c


action_time: 2023-01-03 20:24:01.278690
object_id: 13
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [xcolor] (11550) ```
  There are two ways to change the color of text. To alter the color in a small block, you can us


action_time: 2023-01-03 20:24:45.579888
object_id: 13
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [xcolor] (11550) ```
  There are two ways to change the color of text. To alter the color 
  in a small block, you can 


action_time: 2023-01-03 20:53:41.951342
object_id: 6
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [minted] (10209) To include a python code example, use the following:

  ```
  \begin{minted}{python}
  import numpy as


action_time: 2023-01-05 00:40:00.243094
object_id: 7
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [pageslts] (37548) Near the top of the document, include

  ```
  \pagenumbering{arabic} % or other style
  ```

  In the


action_time: 2023-01-05 00:41:42.156963
object_id: 7
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [pageslts] (37306) Near the top of the document, include

  ```
  \pagenumbering{arabic} % or other style
  ```

  In the


action_time: 2023-01-05 01:03:15.670703
object_id: 7
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [pageslts] (35339) Near the top of the document, include

  ```
  \pagenumbering{arabic} % or other style 
  ```

  In th


action_time: 2023-01-05 18:12:07.266282
object_id: 19
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [caption] (5255) In the preamble:
  ``` x
  \usepackage{caption}
  \DeclareCaptionFont{quack}{\sffamily}
  \captionsetup{


action_time: 2023-01-05 18:57:12.538911
object_id: 19
change_message: []
object_repr:
  [caption] (3906) In the preamble:
  ``` x
  \usepackage{caption}
  \DeclareCaptionFont{quack}{\sffamily}
  \captionsetup{


action_time: 2023-01-05 18:58:21.589687
object_id: 19
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [caption] (3906) In the preamble:
  ``` xx
  \usepackage{caption}
  \DeclareCaptionFont{quack}{\sffamily}
  \captionsetup


action_time: 2023-01-05 19:00:36.732768
object_id: 19
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [caption] (211425) In the preamble:
  ``` x
  \usepackage{caption}
  \DeclareCaptionFont{quack}{\sffamily}
  \captionsetup{


action_time: 2023-01-06 00:24:47.503710
object_id: 9
change_message: [{"changed": {"fields": ["Text", "Preamble"]}}]
object_repr:
  [sidecap] (48844) ```
  \begin{SCfigure}[5][tb]
    \centering
    \includegraphics[width=3in]{2D-0015-stop}
    \caption{


action_time: 2023-01-06 00:26:08.410654
object_id: 9
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [sidecap] (239312) ```
  \begin{SCfigure}[5][tb]
    \centering
    \includegraphics[width=2in]{sample}
    \caption{The de


action_time: 2023-01-06 00:31:24.526907
object_id: 3
change_message: [{"changed": {"fields": ["Text", "Preamble"]}}]
object_repr:
  [cleveref] (37141) Suppose that you have a figure labeled with the command `\label{fig:sample}`, such as by using

  ``


action_time: 2023-01-06 00:31:46.222042
object_id: 3
change_message: [{"changed": {"fields": ["Preamble", "Error"]}}]
object_repr:
  [cleveref] (164297) Suppose that you have a figure labeled with the command `\label{fig:sample}`, such as by using

  ``


action_time: 2023-01-06 00:34:56.862356
object_id: 3
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [cleveref] (186936) Suppose that you have a figure labeled with the command `\label{fig:sample}`, such as by using

  ``


action_time: 2023-01-06 00:36:04.261720
object_id: 3
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [cleveref] (199796) Suppose that you have a figure labeled with the command `\label{fig:sample}`, such as by using

  ``


action_time: 2023-01-06 00:39:20.066024
object_id: 11
change_message: [{"changed": {"fields": ["Text"]}}]
object_repr:
  [subcaption] (24121) The example below shows how to create a figure with two subfigures. Each subfigure is drawn by **tik


# django_session

session_key: lt5lcw8d25xsv8ab0zxpx5y87qvdmxv9
expire_date: 2022-06-19 19:24:55.780782
session_data:
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session_key: i97s06k8dywj29ki3p8zxrg5tzy3tuov
expire_date: 2022-06-27 02:26:19.426956
session_data:
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session_key: 7t0h4pvsd0q6mfpe42yialq75ls7srek
expire_date: 2022-06-29 14:04:49.101033
session_data:
  .eJxVjEEOwiAQRe_C2hAGBgWX7nsGMsAgVUOT0q6Md7dNutDtf-_9twi0LjWsnecwZnEVIE6_W6T05LaD_KB2n2Sa2jKPUe6KPGiXw5T5dTvcv4NKvW51TJ60QgbrPZ5TzmxNUhdXisbMwFo5uzlAEBkMgnMKiylctE2I1ojPF-qWN8w:1o1TdZ:LlNzhVzw9gvqyRI73DV-BRkNBrNZN3EgXth5b526jJo


session_key: 6rmtaeank2f7x5su9051m18bcxrzo0eu
expire_date: 2022-07-03 15:22:34.282478
session_data:
  .eJxVjEEOwiAQRe_C2hAGBgWX7nsGMsAgVUOT0q6Md7dNutDtf-_9twi0LjWsnecwZnEVIE6_W6T05LaD_KB2n2Sa2jKPUe6KPGiXw5T5dTvcv4NKvW51TJ60QgbrPZ5TzmxNUhdXisbMwFo5uzlAEBkMgnMKiylctE2I1ojPF-qWN8w:1o2wl0:urMqtfeO32ZMCWtFf7QljGRi1QfX79lr6xB7BSSMlPc


session_key: bhe9hwmr5p32df5t9dze68g662xzvt4s
expire_date: 2022-07-28 20:57:45.246418
session_data:
  .eJxVjEEOwiAQRe_C2hAGBgWX7nsGMsAgVUOT0q6Md7dNutDtf-_9twi0LjWsnecwZnEVIE6_W6T05LaD_KB2n2Sa2jKPUe6KPGiXw5T5dTvcv4NKvW51TJ60QgbrPZ5TzmxNUhdXisbMwFo5uzlAEBkMgnMKiylctE2I1ojPF-qWN8w:1oC5u5:LgYoJaPK4RcQt7BcisZbCcxZsATiBxDP7iTv7Dhq-0w


session_key: 8ibd0z94qbv1cvg9q7qvnh9gk4l66fze
expire_date: 2022-08-29 03:18:17.407796
session_data:
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session_key: mp22z8uhp8br8jjgp1u3arp70gp2dx7f
expire_date: 2022-09-17 05:09:59.467533
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session_key: gw9v69lbshe43y75o7ipv2hiraao3voi
expire_date: 2022-10-02 20:13:09.992562
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expire_date: 2022-10-14 16:36:46.669760
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expire_date: 2022-11-11 22:46:24.735922
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session_key: 546tbtc6d4gmql0nwmny9b1jldhojn9p
expire_date: 2022-12-27 05:09:09.257270
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session_key: uyli9e1ohl5izu6dcrnsl9quim43nno0
expire_date: 2022-12-27 18:12:04.101796
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session_key: 0ndxu81tcq8h9ioolalvq0gwv2ccfutn
expire_date: 2023-01-07 01:57:00.087675
session_data:
  .eJxVjMsOwiAQRf-FtSG8BZfu-w1kZgCpGkhKuzL-uzbpQrf3nHNfLMK21riNvMQ5sQuT7PS7IdAjtx2kO7Rb59TbuszId4UfdPCpp_y8Hu7fQYVRvzVqV0rRCrNKIYiQMABi8EJIUsY4JzVZXYwD68FZk5z20tIZirfkSbL3B-jWN6s:1p8tmW:uvTdK1I-VTO5etQfrcRBkfxP7SyZfVDW9CaNzPFoi3A


session_key: v77prq0fbg5knwpmkmoqowqb8c9ftzlc
expire_date: 2023-01-12 23:58:06.354908
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session_key: 0ot4a7i7yd7rtfrpa0mj74xw2un927k3
expire_date: 2023-02-01 18:23:27.546726
session_data:
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session_key: xgb0ulaxeqa50ansujyhuhrfczv4xfuu
expire_date: 2023-02-19 21:29:47.934695
session_data:
  .eJxVjMsOwiAQRf-FtSG8BZfu-w1kZgCpGkhKuzL-uzbpQrf3nHNfLMK21riNvMQ5sQuT7PS7IdAjtx2kO7Rb59TbuszId4UfdPCpp_y8Hu7fQYVRvzVqV0rRCrNKIYiQMABi8EJIUsY4JzVZXYwD68FZk5z20tIZirfkSbL3B-jWN6s:1pOma3:xO9yRECtpeMXb8xE5L8iKe9zgBmjIBe_P990DHivTdI


session_key: 4rn5ry03rlrexu4yfhxp11wbvd196sv6
expire_date: 2023-02-19 21:33:26.088007
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  .eJxVjMsOwiAQRf-FtSG8BZfu-w1kZgCpGkhKuzL-uzbpQrf3nHNfLMK21riNvMQ5sQuT7PS7IdAjtx2kO7Rb59TbuszId4UfdPCpp_y8Hu7fQYVRvzVqV0rRCrNKIYiQMABi8EJIUsY4JzVZXYwD68FZk5z20tIZirfkSbL3B-jWN6s:1pOmda:vCymb9lLoZy3G_0zZhVXSnMyUL1wE-dkcZUrw226dRk


session_key: wcs4hw4sjcu8k99sp0wvp8qrvltma6un
expire_date: 2023-03-20 17:16:00.696249
session_data:
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session_key: cpwm1wpqg16tia8ntjpb49j275xrjvq2
expire_date: 2023-04-01 22:06:20.560070
session_data:
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# latex_option

code: svgnames
description:
  Adds a number of useful color names, such as `DarkRed`, `DarkSlateBlue`, etc., as described on page 42 of the documentation.


code: dvipsnames
description:
  Adds a number of handy color names, including `ForestGreen`, `RawSienna`, etc., as described on page 42 of the documentation.


# latex_package

name: xspace
comment: handle spacing at the end of macros you define
description:
  The **xspace** package defines a single macro that handles spacing following a macro you define, making sure to insert a space before the next token unless that token is punctuation.


name: xifthen
description:
  Provides if-then-else control structures in macros, with some extra bells and whistles compared to **ifthen**.


name: physics
description:
  The physics package supplies a great many conveniences for typesetting physics equations. Among these is an improved version of the `\left( stuff \right)` structure `\qty( stuff )`. Works well in combination with the `siunitx` package.


name: subcaption
comment: Use subcaption to add separate captions to parts of a multipart fig/table
initialization: [labelformat=simple]
description:
  The **subcaption** package allows you to add separate captions to parts of a multipart figure or table. It supersedes older packages such as **subfig** and **subfigure**.


name: hvfloat
description:
  A powerful package to insert figures, with options to rotate captions, position them on any side of the graphic(s).


name: sidecap
description:
  The **sidecap** package allows you place the caption for a figure or table on either the left side or the right side. See also **hvfloat**.


name: cleveref
description: A package for making cross-referencing much easier. Very useful with **hyperref**.
comment: make cross-referencing much easier
initialization:
  \crefname{equation}{Eq.}{Eqs.} % Use Eq. and Eqs. in references to equations
  \Crefname{equation}{Equation}{Equations} % At the start of a sentence, use this instead
  \crefname{figure}{Fig.}{Figs.}
  \Crefname{figure}{Figure}{Figures}


name: hyperref
comment: generates clickable links in PDF documents
description:
  Creates clickable links in pdf documents.You can either set options when you load the package or call `\hypersetup{option list}` later in the document. If you use **hyperref**, don't also include the **url** package, since **hyperref** sets up its own version of the `\url{}` command.


name: tikz
initialization: \tikzset{every picture/.style={>=Stealth}}
description:
  An incredible package for generating graphics with LaTeX. If you also want to generate plots using **TikZ**, load the **pgfplots** package.


name: fancyhdr
description: Manage running headers and footers.
comment: running headers and footers
initialization:
  \renewcommand{\footrulewidth}{0.4pt}
          \newcommand{\ffcolor}{DarkOliveGreen}
          \renewcommand{\headrule}{{\color{\ffcolor}%
              \hrule width\headwidth height\headrulewidth \vskip-\headrulewidth}}
          \renewcommand{\footrule}{{\color{\ffcolor}%
              \hrule width\headwidth height\footrulewidth \vskip-\footrulewidth}}
  		\newcommand{\ffstyle}[1]{{\scriptsize\textcolor{\ffcolor}{\nouppercase#1}}}
  		\fancyfoot[LE,RO]{\ffstyle{\theTitle}}
  		\fancyfoot[RE,LO]{\ffstyle{\theDate}}
  %		\pagestyle{fancy} if this is in, then you can't fix the 
  		% header width; you have to set fancy within the document
  		\thispagestyle{plain}
  		\newcommand{\theCourse}{}
  		\newcommand{\theTerm}{}
  		\newcommand{\theNumber}{1}
  		\newcommand{\SetHeaders}{%
  			\fancyhead{} % clear all fields
  			\fancyhead[LO,RE]{\ffstyle{\theTitle}}%
  			\fancyhead[RO,LE]{\ffstyle{\theDate}}%
  			\fancyfoot[LO,RE]{\ffstyle{\theCourse}}%
  			\fancyfoot[RO,LE]{\ffstyle{\theTerm}}%
  			}
  		\fancypagestyle{first}{\fancyhf{}%
  			\fancyfoot[LO,RE]{\ffstyle{\theTitle}}%
  			\fancyfoot[RO,LE]{\ffstyle{\theDate}}%
  			\renewcommand\headrulewidth{0pt}
  		}


name: caption
description:
  Customize the format of figure and table captions. You can either pass options to the class in a `\usepackage[options]{caption}`
  or you can set them anywhere in the document with
  `\captionsetup{options}`.


name: multicol
description:
  You can set up a portion of a document to be set in two or more columns. There are two different forms of the `\begin{multicols}{n}` command. Without a star, LaTeX will attempt to balance the column length on the final page that is set in multiple columns. With the star, it will not attempt this balance.


name: newverbs
description:
  Allows easy definition of new verbatim environments and automatic insertion of code before and after a verbatim entry.


name: minted
description:
  The minted package creates nicely formatted and colorized code listings. It requires that you run `pdflatex` with the flag `-shell-escape`.


name: titletoc
description: Adjust the formatting of the table of contents
initialization:
  \definecolor{mygray}{gray}{0.4}
  \definecolor{darkgray}{gray}{0.25}
  \definecolor{gold}{RGB}{178, 139, 51} %hmc-official gold

  \usepackage{titletoc}
  \titlecontents{chapter}[3em]{\addvspace{1.5pc}\bfseries}%
  {\contentslabel{3.em}}{\sf}%
  {\hspace{0.5em}{\color{gold}\footnotesize$\bullet$}\hspace{0.5em}{\thecontentspage}}
  \titlecontents{section}[3em]{}%
  {\contentslabel{3.em}}{}%
  {\hspace{0.5em}{\color{mygray}\footnotesize$\bullet$}\hspace{0.5em}{\thecontentspage}}
  \titlecontents{subsection}[3em + 3.5em]{\small}%
  {\contentslabel{3em}}{ }%
  {\hspace{0.5em}{\color{darkgray}\scriptsize$\bullet$}\hspace{0.5em}{\thecontentspage}}
  \titlecontents{figure}[3em]{}%
  {\contentslabel{3.em}}{\sf}%
  {\hspace{0.5em}{\color{mygray}\footnotesize$\bullet$}\hspace{0.5em}{\thecontentspage}}
  \titlecontents{table}[3em]{}%
  {\contentslabel{3.em}}{\sf}%
  {\hspace{0.5em}{\color{mygray}\footnotesize$\bullet$}\hspace{0.5em}{\thecontentspage}}


# mpl_tip

created: 2022-06-11 02:15:25.746746
modified: 2022-06-13 15:16:28.456563
name: Plot size and margins
description:
  To set the size of a plot during creation, pass `figsize=(width, height)` to the call, such as 
  ```
  fig, ax = plt.subplots(nrows, ncols, figsize=(10,5))
  ```
  To readjust the size after the plot has been created, use 
  ```
  plt.gcf().set_size_inches(width, height)
  ```
  To change the amount of space allocated to axis labels, use e.g.
  ```
  plt.subplots_adjust(left=0.2, bottom=0.15)
  ```
  which uses 20% of the plot width for the region to the left of the *y* axis.


created: 2022-06-13 15:24:31.155453
modified: 2022-06-13 15:24:31.155474
name: Shapes
description:
  Shapes, such as Rectangles, Circles, etc., are defined in [matplotlib.patches](https://matplotlib.org/stable/api/patches_api.html).

  ```
  from matplotlib.patches import Circle, Rectangle
  # other options include Ellipse, Polygon, Shadow

  sun = Circle((0,0), radius=0.05, color='y')
  ax.add_patch(sun)
  ```


created: 2022-07-14 20:58:19.333714
modified: 2023-01-18 18:31:25.603257
name: Put legend outside frame
description:
  To move the legend outside the plot frame

  ```python
  ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
  plt.subplots_adjust(right=0.7)
  ```


created: 2022-09-16 16:38:01.938044
modified: 2022-09-16 16:38:01.938079
name: Adjust position of tick labels
description:
  With logarithmic axes, MPL seems to put the label too close to the axis. To move it down (left) a bit, try

  `ax.tick_params(axis='x', which='both', pad=8);`


# tikz_tikz

folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}[scale=1]
    \draw[vel] (0,0) -- ++(0:3) node[anchor=west]{vel};
    \draw[accel] (0,0) -- ++(30:3) node[anchor=west]{accel};
    \draw[spring] (0,0) -- ++(60:3) node[anchor=south west]{spring};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}[scale=2.5,>=stealth']
    \draw[->] (-1, 0) -- (1.5, 0) node[anchor=north] {$ x $};
    \draw[->]  (0,-0.5) -- (0,1.5) node[anchor=east] {$ y $};
    \draw[very thick,blue] (-0.75,1.25) -- (1.25,0.25);
    \draw[thin,gray] (0,0) node[anchor=north east] {$ O $} -- (0.35,  0.69) node[anchor=south west] {$ C $};
    \path (0.15,0.50) node {$h$};
    \draw[->]  (1,1) arc (45:60:60pt) node[anchor=south] {$\omega$};
    \node at (0.78,0.48) [circle,draw=red,fill=red,inner sep=0pt,minimum size=2mm] {};
    \node at (0.92,0.6) {$m$};
    \draw[->] (0.3,0) arc (0:60:9pt);
    \node at (0.35, 0.2)  {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}
    \filldraw[color=gray] (-0.1,3,0) -- (-0.01,2.95,0) -- (0.08,3.03,0)-- (0.1,3,0)  -- (0.1,-3,0) -- (0.01,-2.95,0) --
    (-0.08,-3.03,0)
    -- (-0.1,-3,0) -- (-0.1,3,0);
    \shadedraw[ball color=gray] (4,2,2) circle (0.4);
    \shadedraw[ball color=gray] (-1,-2,1) circle (0.2);
    \draw[->,very thick] (0,0,0) -- node[fill=white] {$\mathbf r_1$} (-1,-2,1);
    \draw[->,very thick] (0,0,0) -- node[fill=white] {$\mathbf r_2$} (4,2,2);
    \draw[decorate,decoration={brace,amplitude=5pt}] (-1,.25,1) -- node[above=6pt] {$\rho_1$} (-0.1,.25,0);
    \draw[decorate,decoration={brace,amplitude=5pt}] (4,-.25,2) -- node[below=6pt] {$\rho_2$} (0.1,-.25,0);
    \draw[decorate,decoration={brace,amplitude=5pt}] (-1.25,-2,1) -- node[left=6pt] {$z_1$} (-1.25,0,1);
    \draw[decorate,decoration={brace,amplitude=5pt}] (4.45,2,2) -- node[right=6pt] {$z_2$} (4.45,0,2);
    \draw[thick] (0,0,0) -- (4,0,0);
    \draw (0,0,0) -- (4,0,2);
    \draw (0,0,0) -- (3,0,0) arc (-25:-70:1);
    \draw (3.1,-.4) node {$\theta_1$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}
    \filldraw[color=gray] (-0.1,3) -- (-0.01,2.95) -- (0.08,3.03)-- (0.1,3)  -- (0.1,-3) -- (0.01,-2.95) -- (-0.08,-3.03)
    -- (-0.1,-3) -- (-0.1,3);
    \shadedraw[ball color=gray] (2,1) circle (0.4);
    \shadedraw[ball color=gray] (-1,-2) circle (0.2);
    \draw[->,very thick] (0,0) -- node[fill=white] {$\mathbf r_1$} (-1,-2);
    \draw[->,very thick] (0,0) -- node[fill=white] {$\mathbf r_2$} (2,1);
    \draw[decorate,decoration={brace,amplitude=5pt}] (-0.1,-2.25) -- node[below=6pt] {$\rho_1$} (-1,-2.25);
    \draw[decorate,decoration={brace,amplitude=5pt}] (0.1,1.45) -- node[above=6pt] {$\rho_2$} (2,1.45);
    \draw[decorate,decoration={brace,amplitude=5pt}] (-1.25,-2) -- node[left=6pt] {$z_1$} (-1.25,0);
    \draw[decorate,decoration={brace,amplitude=5pt}] (2.45,1) -- node[right=6pt] {$z_2$} (2.45,0);
    \draw[very thin] (0,0) -- (2,-1) -- (2,1);
    \draw[very thin] (0,0) -- (1,0) arc (0:-27:1);
    \draw[very thin] (0,0) -- (1.3,0);
    \draw (1.2,-0.3) node {$\theta_2$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}[scale=2.5,>=stealth']
    \draw[->] (-1, 0) -- (1.5, 0) node[anchor=north] {$ x $};
    \draw[->]  (0,-0.5) -- (0,1.5) node[anchor=east] {$ y $};
    \draw[very thick,blue] (-0.75,1.25) -- (1.25,0.25);
    \draw[thin,gray] (0,0) node[anchor=north east] {$ O $} -- (0.35,
    0.69) node[anchor=south west] {$ C $};
    \draw[->,gray] (0.3,0.6) -- +(-25:0.48) node[anchor=north]{$ q $};
    \path (0.15,0.50) node {$h$};
    \draw[->]  (1,1) arc (45:60:60pt) node[anchor=south] {$\omega$};
    \node at (0.78,0.48) [circle,draw=red,fill=red,inner sep=0pt,minimum size=2mm] {};
    \node at (0.92,0.6) {$m$};
    \draw[->] (0.3,0) arc (0:60:9pt);
    \node at (0.35, 0.2)  {$\theta$};
    \draw[->,very thick, gray] (-1,0.25) -- +(90:0.5) node[anchor=west]{\textbf{up}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}[
      scale=1,
      >=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}
    ]
    \draw[fill=black] (0,.25) circle(0.1);
    \draw[thick] (-1,-0.5) -- +(0:14);
    \draw[spring] (0.1,0.25) -- +(0:2.87);
    \draw[spring] (5.0,0.25) -- +(0:3);
    \draw[spring] (10.0,0.25) -- +(0:3);

    % draw the carts
    \foreach \x in {3,8}
      {
        \draw[fill=gray] (\x+0.35,-0.25) circle (0.25);
        \draw[fill=gray] (\x+1.65,-0.25) circle (0.25);
        \draw[fill=gray!50!white] (\x,-0.25) rectangle (\x+2,0.75);
        \node at (\x+1,0.25) {$m$};
      }
    \draw[fill=gray!50!white] (2.5,-.10) rectangle (3,-0.25);
    \draw[fill=black] (2.6,-0.4) rectangle (2.9,-0.3);

    \foreach \x in {1.5, 6.5, 11.5}
      { \node[color=blue] at (\x, 0.8) {$k$}; }
    \draw[fill=black] (13,-0.5) rectangle (13.2,1);
    \draw[<->, line width=1.5] (-0.5,0.75) -- +(0:1);
    \node at (0,1.25){$D \cos(\omega t)$};
    \draw[|->] (4,-1) -- +(0:1) node[anchor=west]{$x_{1}$};
    \draw[|->] (9,-1) -- +(0:1) node[anchor=west]{$x_{2}$};
    % \foreach \x in {0,2,...,10}
    % {
    %   \shade[ball color=gray] (\x,0) circle(0.35cm);
    %   \node at (\x,0.6) {$m$};
    %   \draw[spring] (\x,0) +(0.35,0) -- +(0:1.65) ;
    %   \node[color=blue] at (\x+0.9,0.45) {$\alpha$};
    % }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}[
      scale=1.5,
      >=stealth',
      pathstyle/.style={line width=0.75pt,color=gray},
      dim/.style={color=green!40!black,<->},
      accel/.style={->,line width=3pt,color=gray},
      vel/.style={->,line width=2pt,color=red!50!black},
      dotted/.style={line width=0.75pt, color=gray, dashed}
    ]


    \draw[dim] (-3,0) -- node[anchor=west]{$b$}  (-3,0.5);
    \shade[ball color=blue!30!white] (0,0) circle(0.75);
    \shade[ball color=red!30!white] (-5,0.5) circle(0.25);
    \shade[ball color=red!15!white] (150:1) circle(0.25);
    \draw[pathstyle] (-5,0) -- (2,0);
    \draw[line width=1.5] (0,0) -- (150:1);
    \node at (-0.2,0.42) {$R + a$};
    \draw[pathstyle] (180:0.3) arc(180:150:0.3);
    \node at (165:0.5) {$\psi$};
    \draw[dotted] (-5,0.5) -- +(0:4.15);
    \draw[dotted] (150:1) -- +(120:1.5);
    \draw[vel] (-4.75,0.5) -- +(0:0.6);
    \draw[vel] (150:1)  +(120:1) -- +(120:1.5);
    \draw[color=blue!70!black] (0:1.25) arc (0:120:1.825);
    \node at (0.5,1.8) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}[
      scale=2.,
      >=stealth'
    ]
    \draw [fill=gray!25!white] (1.73205,0) -- (0,0) -- (30:2) -- cycle;
    \draw[->] (0,0) -- (2,0) node[anchor=north] {$x$};
    \draw[->] (0,0) -- (0,1) node[anchor=east] {$y$};
    \draw[fill=blue!50!white] (32:1.6) circle (0.05);
    \node at (36:1.48) {$m$};
    \node at (0.3,0.08) {$\alpha$};
    \draw (0:0.2) arc(0:30:0.2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}[
      scale=1,
      >=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}
    ]
    \foreach \x in {0,2,...,10}
      {
        \shade[ball color=gray] (\x,0) circle(0.35cm);
        \node at (\x,0.6) {$m$};
        \draw[spring] (\x,0) +(0.35,0) -- +(0:1.65) ;
        \node[color=blue] at (\x+0.9,0.45) {$\alpha$};
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}[scale=4,>=stealth']
    \draw[->] (-0.8, 0) -- (1.2, 0) node[anchor=north] {$ x $};
    \draw[->]  (0,-1) -- (0,0.2) node[anchor=east] {$ y $};
    \draw[->] (0,-0.4) arc(90:40:0.2);
    \node at (0.1,-0.3){$\theta$};
    \draw[very thick,blue] (0, -0.6) --node[anchor=north]{$\ell$} (0.8, 0);
    \node at (0,-0.6) [circle,draw=red,fill=red,inner sep=0pt,minimum size=2mm]{};
    \node at (0.8,0) [circle,draw=red,fill=red,inner sep=0pt,minimum size=2mm]{};
    \node at (-0.125,-0.6){$m_{2}$};
    \node at (0.8, 0.125){$m_{1}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}[scale=0.8]
    \draw[line width=1.5pt,color=DarkBlue] (-2,4) parabola bend (0,0) (2,4);
    \shade[ball color=gray] (1,1) circle(0.25);
    \draw[->] (0,-0.25) -- (0,4) node[anchor=east]{$z$};
    \draw[->] (-0.5,3) arc(120:420:1 and 0.3) node[anchor=south west]{$\omega$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!50!white] (4.1,0) ellipse (20pt and 2.85cm)
    (-5.7,0) ellipse (.2 and 0.75);
    \filldraw[fill=white] (4.1,0) ellipse (13pt and 2.35cm)
    (-5.7,0) ellipse (0.15 and 0.5);
    \draw[dashed] (-6,0) -- (5.5,0);
    \draw[dashed] (0,0) -- (30:5);
    \filldraw[fill=blue!50!white,draw=blue] (0,0) circle(0.2) (-6,0.5)
    circle(0.1);
    %\draw plot [smooth] coordinates {(-5.8,0.5)  (-2.97,0.5)  (40:3)  (35:4.5)};
    \draw (-5.8,0.5) to[out=0,in=180] (-3,0.5) to[out=0,in=210] (2,1.6)
    to[out=30,in=210] (35:5);
    \draw[dashed,color=red!50!black] (-5.8,0.75) to[out=0,in=190] (100:1.)
    to[out=10,in=200] (28.6:5);
    \draw[color=green!50!black,<->] (0:1.5) arc(0:30:1.5);
    \draw[color=green!50!black] (15:1.8) node {$\Theta$};
    \draw[<->] (-4,0) -- (-4,0.5);
    \node at (-3.75,0.25) {$b$};
    \draw[vel] (-5.8,0.5) -- +(0:1) node[anchor=north]{$\vv$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}[scale=0.75]
    \draw [red] (0,0) circle [radius=2];;
    \draw [fill=red] (1.732,1) circle [radius=0.3];;
    \draw [red] (0,0)-- (1.732,1);
    \draw [red, dashed] (0,-0.67) arc [radius=0.67, start angle = -90, end angle=30];;
    \draw [green] (0,0) circle [radius=3];;
    \draw [fill=green] (-1.5,-2.598) circle [radius=0.3];;
    \draw [green] (0,0)-- (-1.5,-2.598);
    \draw [green, dashed] (0,-1.33) arc [radius=1.33, start angle = -90, end angle=-120];;
    \draw [black, dashed] (0,0) -- (0,-3);
    \draw [thick,->] (4,3) -- (4,-3);
    \node at (0.9,-0.5) {$\theta_1$};
    \node at (-0.5,-1.6) {$-\theta_2$};
    \node at (0.5,0.7) {$\ell_1$};
    \node at (-0.9,-0.9) {$\ell_2$};
    \node at (2.28,1) {$q_1$};
    \node at (-2.1,-2.598) {$q_2$};
    \node at (3.7,-2.9) {$g$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}
    \draw[thick] (6,0) arc [radius=6, start angle=0, end angle=45];
    \draw[thick] (4,0) arc [radius=4, start angle=0, end angle=30];
    \draw[dashed] (0,0) -- (7,0);
    \draw[ultra thick] (0,0) -- (3.464,2);
    \draw[ultra thick] (0,0) -- (4.242,4.242);
    \draw[fill,green] (0,0) circle [radius=0.25];
    \draw[fill,red] (3.464,2) circle[radius=0.1];
    \draw[fill,blue] (4.242,4.242) circle[radius=0.1];
    \node [above left] at (2.121,2.121) {$r_{1}$};
    \node [above left] at (4.242,4.242) {$m_{1}$};
    \node [right] at (5.544,2.296) {$\theta_{1}$};
    \node [below right] at (1.732,1) {$r_{2}$};
    \node [above right] at (3.464,2) {$m_{2}$};
    \node [right] at (3.864,1.036) {$\theta_{2}$};
    \node [above left] at (0,0.25) {$M$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}


    %draws the disk
    \draw (2,2) circle (4cm);

    %draws the erratic mass
    \filldraw[color=gray] (2, 6) circle (0.4cm);

    %draws the damping magnet
    \draw[dashed] (-0.5,2) circle (0.8cm);

    %draws radii to mass, damping magnet
    \draw (2,2)--(2,6) node [midway,fill=white] {l};
    \draw (2,2)--(-0.5,2) node [midway, fill=white] {h};
    \draw (2,2)--(3.5,-1.708) node [midway, fill=white] {R};

    %draws the square body behind the disk
    \draw (-2.2, 7) -- (6.2,7) -- (6.2,-4.3) -- (-2.2,-4.3) -- (-2.2,7);

    %draws the axis from which we measure theta
    \draw[dotted,  thick] (2,6) -- (2,8);
    \draw[ultra thick] (2,7.5)--(2,7.8);
    \draw[ultra thick, ->] (2,7.65) arc [radius = 0.5, start angle = 90, end angle = 0] node [above,shift={(-0.2cm, 0.4cm)}] {\large $\theta$};

    %draws the stepper motor
    \filldraw[color=gray] (-5.7, -7.8) -- (-4.6,-7.8) -- (-4.6,-9.2) -- (-5.7,-9.2);
    \filldraw[color=white] (-5.5, -8) -- (-2,-8) -- (-2,-9) -- (-5.5,-9) -- (-5.5,-8);
    \draw (-5.5,-8.5) -- (-2,-8.5) node [midway, fill=white] {A};
    \draw (-5.5, -8) -- (-2,-8) -- (-2,-9) -- (-5.5,-9) -- (-5.5,-8);
    \draw (-2,-8) -- (-2,-7.5) -- (-2.7,-7.5) -- (-2.7,-8);
    \draw (-2.35,-7.7) circle (0.1cm);

    %draws the springs
    %new left spring
    \draw (-2.35,-7.6) -- (-2.25,-6.69);
    \draw (-1.7,-1.7) -- (-1.5,0.1);
    \draw [decoration = {zigzag,segment length=2mm,amplitude=2mm},decorate] (-2.25,-6.69) -- (-1.7,-1.7);
    %new right spring
    \draw (6.35,-7.6)--  (6.249,-6.69);
    \draw (5.6987,-1.7) -- (5.5,0.1);
    \draw [decoration = {zigzag,segment length=2mm,amplitude=2mm},decorate] (6.249,-6.69) -- (5.6987,-1.7);

    %draws the attachment for the second spring
    \draw (6.35,-7.7) circle (0.1cm);

    %draws the angle measurement for the stepper motor
    \draw[dotted,thick] (-5.15,-9.2) -- (-5.15,-10);
    \draw [ultra thick] (-5.15,-9.5) -- (-5.15,-9.8);
    \draw [ultra thick, ->] (-5.15,-9.65) arc [radius=0.5, start angle = -90, end angle=-45] node [below,shift={(-0.1cm,-0.1cm)}] {\large $\phi$};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}[scale=1.25]
    \draw[line width=1.5] (-0.5,0) -- (7.5,0);
    \draw[dashed] (0,0) -- (0, -3) (7,0) --(7,-3);
    \draw (0,0) -- (0.2,-0.4);
    \draw[spring] (0.2,-0.4) -- (1,-2);
    \draw (1,-2) -- (1.2,-2.4);
    \draw[line width=3] (1.2,-2.4) --node[anchor=south]{$m$} (5.8,-2.4);
    \draw (7,0) -- (6.8,-0.4) (5.8,-2.4) -- (6,-2);
    \draw[spring] (6.8,-0.4) -- (6,-2);
    \node at (1,-1) {$k$};
    \node at (6,-1){$k$};
    \node at (3.5,-2.75) {$\ell$};
    \draw[<->] (0,-2.35) arc(-90:-64:2.35);
    \draw[<->] (7,-2.35) arc(-90:-116:2.35);
    \node at (0.65,-2.5) {$\theta_{0}$};
    \node at (6.45,-2.5) {$\theta_{0}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}[scale=0.75,
      decoration={coil,aspect=0.3,segment
          length=3mm,amplitude=3mm},
      >=stealth',
      beef/.style={line width=1.5}]
    \draw[line width=2] (-1,0) -- (3.5,0);
    \draw[line width=2] (-1,6) -- +(0:4.5);
    \draw[line width=2] (4.5,0) -- +(0:3) (4.5,6) -- +(0:3);
    % Draw the applied force
    \draw[->, beef] (0,3) -- (0,1.5)
    node[anchor=north]{$\VEC{F}$};
    % Draw the second spring
    \draw[decorate,beef] (2,0) -- ++(90:2);
    \draw[beef] (2,2) -- (2,3);
    \node at (2.9,.8) {$k_{2}$};
    % Draw the pulley
    \filldraw[fill=blue!10!white,draw=blue] (1,3) circle(1);
    \filldraw[fill=blue!50!black] (1,3) circle(0.05);
    % Draw the first spring
    %\usetikzlibrary{decorations.pathmorphing}
    \draw[decorate,beef] (1,6) -- ++(270:2) ;
    \node at (1.9,5.2) {$k_{1}$};
    \draw[beef] (1,3) -- (1,4);
    % Draw the effective spring
    \draw[decorate,beef] (6,6) -- (6,3.5);
    \node at (6.9,4.8){$k_{\rm eff}$};
    \draw[beef,->] (6,3.5) -- (6,3) node[anchor=north]{$\VEC{F}$};
    \draw[dashed] (4,-0.5) -- (4,6.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=2] (-6,-2.04) -- +(0:12);
    \filldraw[fill=blue!40!white] (0,0) circle(2);
    \filldraw[fill=yellow!50!white] (-20:2) arc(-20:160:2) -- cycle;
    \node at (145:1.5) {$\rho$};
    \node at (175:1.5) {$2\rho$};
    \draw[->] (0,0) -- node[anchor=south east]{$R$} (45:2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=yellow!50!white] (0,0) circle(2) (-45:1.4) node {$M$};
    \filldraw[fill=white] (0,2) circle(0.2) (0,-2) circle(0.2);
    \filldraw[fill=gray] (2,0) circle(0.2) (-2,0) circle(0.2);
    \node at (4:2.4) {$q$};
    \node at (180:2.45) {$q$};
    \node at (90:2.4) {$-q$};
    \node at (270:2.4) {$-q$};
    \draw[line width=2,->] (0,0) -- node[anchor=south east]{$R$} (45:2);
    \draw[dashed] (0,0) --node[anchor=north]{$r$} (0:10);
    \filldraw[fill=black] (10,0) circle (0.3);
    \node at (10,-0.5) {planet};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111
filename: tikz.tex
modified: 2014-03-10 23:46:51
domain: p111
source:
  \begin{tikzpicture}[scale=0.75,
      decoration={coil,aspect=0.3,segment
          length=3mm,amplitude=3mm},
      >=stealth',
      coord/.style={line width=1,color=green!50!black,|->},
      beef/.style={line width=1.5}]
    \draw[line width=2] (-1,0) -- (3.5,0);
    \draw[line width=2] (-1,6) -- +(0:4.5);

    % Draw the applied force
    \draw[->, beef] (0,3) -- (0,1.5)
    node[anchor=north]{$\VEC{F}$};
    \draw[coord] (-0.5,2) -- +(270:1) node[anchor=north]{$x$};
    % Draw the second spring
    \draw[decorate,beef] (2,0) -- ++(90:2);
    \draw[beef] (2,2) -- (2,3);
    \node at (2.9,.8) {$k_{2}$};
    % Draw the pulley
    \filldraw[fill=blue!10!white,draw=blue] (1,3) circle(1);
    \filldraw[fill=blue!50!black] (1,3) circle(0.05);
    \draw[coord] (-0.5,4.5) -- +(270:1) node[anchor=north]{$x_{1}$};
    \draw[coord] (3,1.75) -- +(90:1) node[anchor=south]{$x_{2}$};
    % Draw the first spring
    %\usetikzlibrary{decorations.pathmorphing}
    \draw[decorate,beef] (1,6) -- ++(270:2) ;
    \node at (1.9,5.2) {$k_{1}$};
    \draw[beef] (1,3) -- (1,4);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111/2013/lec
filename: lec131016_Rutherford.tex
modified: 2021-03-28 03:30:02
domain: p111
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) circle(2);
    \draw[dashed] (-1,2) -- (-1,-2);
    \draw[color=gray,dashed] (0,0) -- (60:2.5);
    \draw[line width=2] (120:2)  -- (0,0) --(240:2);
    %    \draw[<->, color=blue] (120:0.5) arc (120:240:0.5);
    %    \draw[color=blue] (180:0.7) node[]{$\theta$};
    \draw[dashed] (0,0) -- (0:2.25);
    \draw[color=green!50!black, ->] (0:0.75) arc (0:120:0.75);
    \draw[color=green!50!black] (60:0.8) node[anchor=south]{$\theta$};
    \draw[decoration={text along path, text={allowed region},text
    align={center},text color=red!50!black},decorate] (240:2.3)
    arc(240:120:2.3);
    \draw[color=red!50!black,line width=2] (120:2) arc (120:240:2);
    \draw[color=blue!50!black,line width=1.5,->] (60:2.5) arc(60:120:2.5);
    \draw[color=blue!50!black] (90:2.75) node {$\Theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111/2013/lec
filename: lec131016_Rutherford.tex
modified: 2021-03-28 03:30:02
domain: p111
source:
  \begin{tikzpicture}[scale=1]
    \draw[vel] (-2.5,0) -- node[anchor=north]{$\VEC{v}'_{1}$} +(0:2);
    \draw[dashed] (0,0) -- (2,0);
    \draw[<->] (1,0) arc (0:60:1);
    \node at (30:1.25) {$\Theta$};
    \draw[vel] (0,0) -- node[anchor=south east]{$\vv'_{1}$} +(60:2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p111/2013/lec
filename: lec131016_Rutherford.tex
modified: 2021-03-28 03:30:02
domain: p111
source:
  \begin{tikzpicture}[scale=1]
    \draw[vel] (-3.5,0) -- node[anchor=north]{$\VEC{v}_{0}$} +(0:3);
    \draw[dashed] (0,0) -- (2,0);
    \draw[<->] (.75,0) arc (0:60:.75);
    %      \node at (30:1.25) {$\Theta$};
    \draw[vel] (0,0) -- node[anchor=south east]{$\vv'_{1}$} +(60:2);
    \draw[vel] (60:2) -- node[anchor=south]{$\VEC{V}$} ++(0:2) coordinate(ending);
    \draw[vel] (0,0) --node[anchor=south]{$\VEC{v}_{1}$\,} (ending);
    \draw[<->, color=red!50!black] (1.25,0) arc (0:30:1.25);
    \draw[color=red!50!black] (15:1.5) node {$\vartheta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/archive/2016 Manual
filename: Fresnel-Diffraction.tex
modified: 2016-02-12 22:09:24
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed] (0,0) -- (10,0);
    \fill (10,0) circle[radius=0.05] node[anchor=west]{P};
    \fill[fill=DarkRed] (0,0) circle[radius=0.05];
    \draw[line width=2] (1,-1) -- (1,0.25);
    \draw[color=DarkRed] (0,0) --node[anchor=south]{$\rho$} (1,0.5)
    --node[anchor=south]{$r$} (10,0);
    \draw[color=DarkGreen,->] (1,0) -- (1,1) node[anchor=south]{$x$};
    \node at (0.5,-0.3) {$\rho_{0}$};
    \node at (5.5, -0.3) {$r_{0}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/archive/2016 Manual
filename: Ex3.tex
modified: 2015-12-31 06:25:13
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \draw (-4,0) -- (5,0);
    \node at (-2,0.35) {$2p^{5}\; 3p$ (Paschen $2p_{4}$)};
    \node at (-2, -0.35){$J=2$, $g = 1.301$};
    \foreach \y in {-2, -1, ..., 2} {
        \draw (0,0) -- (1.5,\y) -- (5,\y);
        \node[anchor=west] at (2,\y+0.25) {$m_{j} = \y$};
      }
    \draw (-4,5) -- (5,5);
    \node at (-2,5.35) {$2p^{5}\; 5s$ (Paschen $3 s_{2}$)};
    \node at (-2, 4.65){$J=1$, $g = 1.295$};
    \foreach \y in {-1, 0, 1} {
        \draw (0,5) -- (1.5, 5+\y) -- (5,5+\y);
        \node[anchor=west] at (2,\y+5.25) {$m_{j} = \y$};
      }
    \draw[<->] (4,5) --node[anchor=west]{$\Delta E = g \muB B$} (4,6);
    \draw[transition] (4,4) -- (4,0);
    \draw[transition] (4.5,4) --
    node[anchor=south west]{$\Delta m_{j} = \pm 1$}
    (4.5,-2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/figs/tikz
filename: michelson.tex
modified: 2018-01-25 03:19:35
domain: p134
source:
  \begin{tikzpicture}[scale=1,
      blabel/.style= {DarkRed,font=\sffamily},
      olabel/.style={DarkGreen,font=\sffamily}
    ]

    \def\beam{2cm}
    \def\bsthick{0.25cm}

    % beamsplitter
    \begin{scope}[rotate=45]
      \filldraw[fill=gray!20] (-1*\beam,0) rectangle (1.*\beam,-\bsthick);
      \draw[line width=1.5pt] (-\beam,-\bsthick) -- (\beam,-\bsthick);
      \node[olabel,anchor=north east] at (-\beam,0) {beam splitter};
    \end{scope}

    % compensator
    \begin{scope}[shift={(1.5,0)},rotate=45]
      \filldraw[fill=gray!20] (-1.*\beam,0) rectangle (1.*\beam,-\bsthick);
      \node[olabel,anchor=south] at (\beam,0) {compensator};
    \end{scope}
    % top mirror
    \filldraw[fill=gray!30] (-\beam,2*\beam) rectangle (\beam,2*\beam+\bsthick);
    \draw[line width=2] (-\beam,2*\beam) -- +(0:2*\beam);
    % right mirror
    \begin{scope}[shift={(2*\beam,0)},opacity=0.25]
      \filldraw[fill=gray!30] (0,-\beam) rectangle (\bsthick,\beam);
      \draw[line width=2] (0,-\beam) -- ++(90:2*\beam);
    \end{scope}

    \begin{scope}[shift={(2.5*\beam,0)}]
      \filldraw[fill=gray!30] (0,-\beam) rectangle (\bsthick,\beam);
      \draw[line width=2] (0,-\beam) -- ++(90:2*\beam);
    \end{scope}

    \draw[beam] (-2.5*\beam,0.5) -- (2.5*\beam,0.5) ; % incident beam
    \draw[beam,->] (-1.5*\beam,0.5) -- +(0:.25); % arrows for incident beam
    \draw[beam,->] (1.5*\beam,0.5) --+(0:.25);

    \draw[beam] (0.5,0.5) -- (0.5,2*\beam);  % towards top mirror
    \draw[beam,->] (0.5,\beam) -- +(90:0.5);

    \draw[beam,->] (-0.5,2*\beam) -- ++(-90:4*\beam) node[blabel,anchor=north]
    {$E_{\rm out}$}; % from top mirror
    \draw[beam,->] (-0.5,\beam) -- ++(-90:0.25);

    \draw[beam,->] (2.5*\beam,-0.2) -- (-2*\beam,-0.2);
    \draw[beam,->] (1.5*\beam,-0.2) -- +(180:0.25);

    \draw[beam,->] (-0.2,-0.2) -- (-0.2,-2*\beam);
    \draw[beam,->] (-0.5,-0.5) -- (-2*\beam,-0.5);

    \draw[DarkGreen,|->] (2*\beam,-1.25*\beam) -- node[anchor=north]{$d$}
    (2.5*\beam,-1.25*\beam);

    % labels
    \node[blabel,anchor=south west] at (-2.5*\beam,0.5) {$E_{\rm in}(t)$};
    \begin{scope}[shift={(2.7*\beam,0)},rotate=90]
      \node[olabel,anchor=north,rotate=90] at (0,0) {translatable mirror};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/figs/tikz
filename: gaussian-beam.tex
modified: 2018-02-19 17:34:33
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \def\wzero{1}
    \def\zr{3}

    \begin{axis}[width=6cm,height=4cm,enlargelimits=false,
        xmin=-0.5, xmax=9, ymin=-3, ymax=3,
        xlabel={$z$},ylabel={},xtick=\empty,ytick=\empty,
        axis x line=middle, axis y line=middle]
      \addplot[gray,domain=-0.5:8, samples=51] { \wzero * sqrt(1 + (x/\zr)^2)
      };
      \addplot[gray,domain=-0.5:8, samples=51] { -\wzero * sqrt(1 + (x/\zr)^2) };
      \draw[dashed,SlateBlue] (0,0) -- (8,2.85);
      \draw[dashed,SlateBlue] (0,0) -- (8,-2.85);
      \draw[DarkGreen,line width=1.5,->] (0,0) --
      (axis cs:\zr,0) node[anchor=south west]{$z_{R}$};


      \phasefront[blue](1:6.04:10)
      \phasefront[blue](2:10.6:6.5)
      \phasefront[blue](3:13.5:6)
      \phasefront[blue](4:15.3:6.25)
      \phasefront[blue](5:16.4:6.8)
      \phasefront[blue](6:17:7.5)
      \phasefront[blue](7:17.4:8.29)
      \phasefront[blue](8:17.6:9.125)

    \end{axis}

    \begin{scope}[shift={(-0.6,2.15)},rotate={-90}]
      \begin{axis}[
          xmin=-2.5,
          xmax=2.5,
          ymin=0,
          ymax=1.5,
          enlargelimits=false,
          width=3.5cm,
          height=2cm,
          xlabel={},
          ylabel={},
          ytick=\empty,
          xtick=\empty,
          xticklabel=\empty,
          yticklabel=\empty,
          axis x line=bottom,
          axis y line=middle
        ]
        \addplot[
          DarkRed,
          domain=-1.8:1.8,
          samples=51,
          line width=1pt,
        ]
        {exp(-x*x)};
      \end{axis}
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/figs/tikz
filename: qo-setup.tex
modified: 2018-02-08 18:17:44
domain: p134
source:
  \begin{tikzpicture}[scale=1]

    \def\thick{0.25}
    \def\height{1}
    \def\diverge{8} % degrees
    \def\PBS{\filldraw[fill=gray!5,opacity=0.5] (-0.2,-0.2) rectangle (0.2,0.2); \draw
      (-0.2,-0.2) -- (0.2,0.2); }
    \draw[uvbeam] (10,0) -- (-2,0);
    \filldraw[fill=DarkOrchid!25] (10,-0.5) rectangle (13,0.5);
    \node[color=DarkOrchid] at (11.5,0){\Large\textbf{Laser 405 nm}};

    % beam dump
    \fill (-2,0.5\height) rectangle (-2.5,-0.5\height);
    \node[anchor=east,text width=1cm] at (-2.75,0) {Beam dump};
    % HWP
    \filldraw[hwp] (9,-\height) rectangle(9+\thick,\height);
    \node[anchor=south] at (9+\thick/2,\height){$\lambda/2$};

    % quartz plate
    \begin{scope}[shift={(8,0)},rotate=15]
      \filldraw[fill=gray!30,opacity=0.5] (0,-\height) rectangle(\thick,\height);
      \node[anchor=south,text width=1cm,align=center] at
      (\thick/2,\height){quartz\par plate};
      \begin{scope}[shift={(\thick/2-0.125,0.2)}]
        \draw[->,line width=1pt] (120:0.2) arc(120:420:0.4);
      \end{scope}
    \end{scope}

    % SPD crystals
    \begin{scope}[shift={(7,0)}]
      \filldraw[fill=gray!40,opacity=0.5] (0,-0.5*\height) rectangle
      (0.15,0.5*\height);
      \filldraw[fill=gray!40,opacity=0.5] (0.15,-0.5*\height) rectangle
      (0.3,0.5*\height);
      \node[anchor=south] at (0.15, 0.6\height) {SPD};
      \node[anchor=north] at (0.15, -0.6\height) {crystals};
    \end{scope}

    % IR photons
    \draw[beam] (7.15,0) -- ++(180-\diverge:8);
    \draw[beam] (7.15,0) -- ++(180+\diverge:8);
    \begin{scope}[shift={(0,1)},rotate=90-\diverge]
      \draw[beam] (0,0) -- ++(0:0.8);
      \detector{(90:0.8)}{90}
      \node[anchor=east] at (90:1.25){$T$};
      \detector{(0:0.8)}{0}
      \node[anchor=south] at (0:1.25){$R$};
      \PBS
      \filldraw[hwp] (-0.3,-0.8) rectangle (0.3,-0.9);
      \node[anchor=south] at (0.3,-0.85){$\lambda/2$};
    \end{scope}

    \begin{scope}[shift={(0,-1)},rotate=90+\diverge]
      \draw[beam] (0,0) -- ++(180:0.8);
      \detector{(90:0.8)}{90}
      \node[anchor=east] at (90:1.25){$G$};
      \detector{(180:0.8)}{180}
      \node[anchor=north] at (180:1.25){$G'$};
      \begin{scope}[rotate=90]
        \PBS
        \filldraw[hwp] (-0.8,-0.3) rectangle (-0.9,0.3);
        \node[anchor=north] at (-0.85,0.35){$\lambda/2$};
      \end{scope}
    \end{scope}


  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/figs/tikz
filename: diffraction.tex
modified: 2018-02-21 15:28:24
domain: p134
source:
  \begin{tikzpicture}[decoration={snake,amplitude=1,segment length=10}]
    \def\image{5}

    \fill (-4,1,0) coordinate (S) circle[radius=0.04] node[anchor=south east]{$S(x_{s}, y_{s}, z_{s})$};

    % aperture plane
    \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,decorate] (0,0,0) circle[x radius=0.3, y radius = 1];
    \draw[DarkGreen,->] (0,0,0) -- (\image+2,0,0) node[anchor=north] {$z$ };
    \begin{scope}[shift={(\image,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,->] (\image,0,0) -- (\image+2,0,0) node[anchor=north] {$z$ };

    \draw[DarkBlue,->] (S) -- node[anchor=north] {$\vb{s}_{0}$} (0,0);
    \fill (\image,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 (0,2.5,0) {aperture plane};
    \node at (\image,2.5,0) {image plane};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec02.tex
modified: 2019-01-28 23:34:59
domain: p134
source:
  \begin{tikzpicture}[scale=.67]
    \begin{axis}[
        ymin=0,
        ymax=0.5,
        enlargelimits=false,
        height=2in,
        width=3in,
        xlabel={$x$},
        ylabel={$P(x)$},
        xticklabels={,,}
        %        ytick={0,1,2},
        %        xtick={0,100,200,300,400,500}
      ]
      \addplot[domain=1:7, samples=80, line width=0pt, fill=red!60!white]
      {1/sqrt(2*pi) / exp((x-4)^2 / 2)} \closedcycle;

      \addplot[domain=2:6, samples=60, line width=0pt, fill=red!40!white]
      {1/sqrt(2*pi) / exp((x-4)^2 / 2)} \closedcycle;

      \addplot[domain=3:5, samples=40, line width=0pt, fill=red!20!white]
      {1/sqrt(2*pi) / exp((x-4)^2 / 2)} \closedcycle;

      \draw[dashed,color=gray] (5,0) -- (5,0.4)
      node[anchor=south]{\color{black}$\scriptsize{\mu+\sigma}$} ;
      \draw[dashed,color=gray] (3,0) -- (3,0.4)
      node[anchor=south]{\color{black} $\scriptsize{\mu-\sigma}$};
      \draw[dashed,color=gray] (6,0) -- (6,0.325)
      node[anchor=south]{\color{black}$\scriptsize{\mu+2\sigma}$} ;
      \draw[dashed,color=gray] (2,0) -- (2,0.325)
      node[anchor=south]{\color{black} $\scriptsize{\mu-2\sigma}$};
      \draw[dashed,color=gray] (4,0) -- (4,0.4)
      node[anchor=south]{\color{black}$\mu$};

      \addplot[
        domain=0:8,
        samples=100,
        line width=1pt,
        color=red!65!black
      ]
      {1/sqrt(2*pi) / exp((x-4)^2 / 2)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec03.tex
modified: 2019-01-29 17:26:10
domain: p134
source:
  \begin{tikzpicture}[scale=0.75]

    \def\thick{0.5}
    \def\height{1}
    \def\diverge{8} % degrees
    \def\PBS{\filldraw[fill=gray!5,opacity=0.5] (-0.2,-0.2) rectangle (0.2,0.2); \draw
      (-0.2,-0.2) -- (0.2,0.2); }
    \draw[uvbeam] (10,0) -- (-2,0);
    \filldraw[fill=DarkOrchid!25] (10,-0.5) rectangle (13,0.5);
    \node[color=DarkOrchid] at (11.5,0){\textbf{Laser 405 nm}};

    % beam dump
    \fill (-2,0.5\height) rectangle (-2.5,-0.5\height);
    \node[anchor=east,text width=1cm] at (-2.75,0) {Beam dump};
    % HWP
    \filldraw[fill=gray!50,opacity=0.5] (9,-\height) rectangle(9+\thick,\height);
    \node[anchor=south] at (9+\thick/2,\height){$\lambda/2$};

    % quartz plate
    \filldraw[fill=gray!30,opacity=0.5] (8,-\height) rectangle(8+\thick,\height);
    \node[anchor=south,text width=1cm,align=center] at
    (8+\thick/2,\height){quartz\par plate};
    \begin{scope}[shift={(8+\thick/2-0.125,0.2)}]
      \draw[->,line width=1pt] (120:0.2) arc(120:420:0.4);
    \end{scope}

    % SPD crystals
    \begin{scope}[shift={(7,0)}]
      \filldraw[fill=gray!40,opacity=0.5] (0,-0.5*\height) rectangle
      (0.15,0.5*\height);
      \filldraw[fill=gray!40,opacity=0.5] (0.15,-0.5*\height) rectangle
      (0.3,0.5*\height);
      \node[anchor=south] at (0.15, 0.6\height) {SPD};
      \node[anchor=north] at (0.15, -0.6\height) {crystals};
    \end{scope}

    % IR photons
    \draw[beam] (7.15,0) -- node[rotate=-\diverge,anchor=south]{signal} ++(180-\diverge:8);
    \draw[beam] (7.15,0) -- node[rotate=\diverge,anchor=north]{idler} ++(180+\diverge:8);
    \begin{scope}[shift={(0,1)},rotate=90-\diverge]
      \draw[beam] (0,0) -- ++(0:0.8);
      \detector{(90:0.8)}{90}
      \node[anchor=east] at (90:1.25){$T$};
      \detector{(0:0.8)}{0}
      \node[anchor=south] at (0:1.25){$R$};
      \PBS
    \end{scope}

    \begin{scope}[shift={(0,-1)},rotate=90+\diverge]
      \draw[beam] (0,0) -- ++(180:0.8);
      \detector{(90:0.8)}{90}
      \node[anchor=east] at (90:1.25){$G$};
      \detector{(180:0.8)}{180}
      \node[anchor=north] at (180:1.25){$G'$};
      \begin{scope}[rotate=90]\PBS\end{scope}
    \end{scope}


  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec03.tex
modified: 2019-01-29 17:26:10
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \node[anchor=south west,inner sep=0] at (0,0) {
      \includegraphics[width=0.675\textwidth]{lec04fit01}
    };

    \onslide<2>{
      \coordinate (A) at (1.15,6.45);
      \draw[DarkRed,ultra thick,rounded corners] (A) rectangle +(2.9,0.4);
      \node[anchor=north east,text width=4cm,DarkRed] at (0.5,6)
      {\small Either select a function from the menu, or click to define a
        \textbf{New Fit Function\ldots}};
      \draw[DarkGreen,ultra thick,rounded corners] (1.6,4.85) rectangle +(2.,0.4);
      \draw[DarkGreen,ultra thick,rounded corners] (2.3,2.75) rectangle +(3.2,1);
    }

    \onslide<3>{
      \draw[DarkRed,ultra thick,rounded corners] (4.2,6.45) rectangle +(2.1,0.4);
      \node[DarkRed,anchor=west,text width=4cm] at (6.5,5.5) {\small Select the
        dependent variable and the independent variable (or \_calculated\_)};
    }

    \onslide<4>{
      \coordinate (A) at (6.6,6.8);
      \draw[DarkBlue,ultra thick,rounded corners] (A) rectangle +(1.5,0.4);
      \node[DarkBlue,anchor=west,text width=4cm] at (7.,5.9) {\small
        Checking \textbf{From Target} limits the waves you can pick to those on
        the top graph};
    }


  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec03.tex
modified: 2019-01-29 17:26:10
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \node[anchor=south west, inner sep=0] at (0,0) {
      \includegraphics[width=0.675\textwidth]{lec04fit02} };
    \draw[DarkRed,ultra thick,rounded corners] (3.6,5.95) rectangle
    +(3.6,0.8);
    \node[DarkRed,anchor=north west,text width=4cm] at (7.5,6.75) {Select
      the wave containing the uncertainties};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec03.tex
modified: 2019-01-29 17:26:10
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \node[anchor=south west, inner sep=0] at (0,0) {
      \includegraphics[width=0.675\textwidth]{lec04fit04}};
    \draw[DarkRed,ultra thick,rounded corners] (0.8,5.65) rectangle +(3,0.35);
    \draw[DarkRed,ultra thick,rounded corners] (1.3,5.1) rectangle
    +(2.5,0.35);
    \node[DarkRed,text width=4cm] at (10.2,5.5) {
      Be sure to add a textbox and set the Textbox Preferences to include the
      function name.
    };
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec03.tex
modified: 2019-01-29 17:26:10
domain: p134
source:
  \begin{tikzpicture}[scale=1]

    \node[anchor=south west,inner sep=0] at (0,0) {
      \includegraphics[width=0.8\textwidth]{lec04fig01}};
    \node<1-> at (-1.5,6) {\small \textbf{lec03.pxp}};
    \node<2->[anchor=south west,inner sep=0,fill=gray!15!white] at (-1.25,1){
      \includegraphics[width=5.5cm]{Fraunhofer}};
    \node<3->[anchor=south west,fill=DarkGreen!15,text width=4cm] at (6,1)
    {\small Plot the data, fit to the AiryDisk function, and see what
      conclusions you can draw. };
    \node<3->[anchor=south west,fill=DarkGreen,text=yellow,font=\bfseries] at (-1.25,0) {%
      Hint: $J_{1}(x) =$\ \texttt{besselJ(1,x)} };
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec01.tex
modified: 2019-01-23 21:40:53
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin=0,
        ymax=0.5,
        enlargelimits=false,
        height=2in,
        width=3in,
        xlabel={$x$},
        ylabel={$P(x)$},
        xticklabels={,,}
        %        ytick={0,1,2},
        %        xtick={0,100,200,300,400,500}
      ]
      \addplot[domain=1:7, samples=80, line width=0pt, fill=red!60!white]
      {1/sqrt(2*pi) / exp((x-4)^2 / 2)} \closedcycle;

      \addplot[domain=2:6, samples=60, line width=0pt, fill=red!40!white]
      {1/sqrt(2*pi) / exp((x-4)^2 / 2)} \closedcycle;

      \addplot[domain=3:5, samples=40, line width=0pt, fill=red!20!white]
      {1/sqrt(2*pi) / exp((x-4)^2 / 2)} \closedcycle;

      \draw[dashed,color=gray] (5,0) -- (5,0.4)
      node[anchor=south]{\color{black}$\scriptsize{\mu+\sigma}$} ;
      \draw[dashed,color=gray] (3,0) -- (3,0.4)
      node[anchor=south]{\color{black} $\scriptsize{\mu-\sigma}$};
      \draw[dashed,color=gray] (6,0) -- (6,0.325)
      node[anchor=south]{\color{black}$\scriptsize{\mu+2\sigma}$} ;
      \draw[dashed,color=gray] (2,0) -- (2,0.325)
      node[anchor=south]{\color{black} $\scriptsize{\mu-2\sigma}$};
      \draw[dashed,color=gray] (4,0) -- (4,0.4)
      node[anchor=south]{\color{black}$\mu$};

      \addplot[
        domain=0:8,
        samples=100,
        line width=1pt,
        color=red!65!black
      ]
      {1/sqrt(2*pi) / exp((x-4)^2 / 2)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec14.tex
modified: 2019-03-11 21:06:28
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed,DarkSlateGray] (-5.5,0) -- (4,0);
    \foreach \y in {-3,-2,...,3}{
        \draw[DarkRed,->] (-5,\y*0.2) -- ++(0:2);
        \only<1>{
          \draw[DarkRed,->] (-1.5,\y*0.2) -- ++(15:5);
        }
      }
    \only<1>{
      \draw (3.25,0) arc(0:15:2.4);
      \node[anchor=west] at (3.25,0.35) {$\theta$};
    }
    \draw[line width=2] (-2,0.5) -- ++(90:2);
    \draw[line width=2] (-2,-0.5) -- ++(-90:2);

    \node[anchor=west,text width=1.5in] at (4,2) {%
      Far-field behavior assumes rays emerge parallel from the aperture.};

    \only<2>{
      \draw[] (-1,0) arc(180:150:6) coordinate (A);
      \draw (-1,0) arc(180:210:6) coordinate (B);
      \fill[fill=gray,opacity=0.25,black] (B) arc(210:150:6) -- cycle;
      \draw (A) -- (B);
      \draw[gray,line width=2] (3.5,2) -- (3.5,-2); % screen
      \coordinate (C) at (3.5,1);
      \foreach \y in {-3,-2,...,3}{
          \draw[DarkRed] (-1.5,\y*0.2) -- ++(15:0.5) -- (C);
        };
      \draw[->,line width=1.5,DarkGreen] (-.5,-1) --
      node[anchor=south]{$f$} (3.5,-1);
      \node[DarkGreen,text width=1.5in,anchor=west] at (4,-1) {%
        A lens focuses parallel rays at its focal plane, \textbf{producing the
          Fraunhofer diffraction pattern} there.};
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec14.tex
modified: 2019-03-11 21:06:28
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \coordinate (R) at (10,0);
    \draw (-1.5,0) coordinate(S) -- (R);
    \node[anchor=north] at (-.75,0) {$s_{0}$};
    \fill[DarkRed] (S) circle[radius = 0.05];
    \draw[line width=2] (0,-2) -- (0,0.5);
    \draw[<-] (-.1,-2.1) -- ++(225:1.25) node[anchor=north]{razor};
    \draw[line width=1.5,DarkRed] (S) -- (0,1) -- (R);
    \node[anchor=west] at (R) {$P$};
    \node[anchor=north] at (5,0) {$r_{0}$};
    \draw[DarkGreen,->] (0.2,0) -- node[anchor=west]{$\xi$} (0.2,1);
    \draw[DarkGreen,->] (-0.2,0) -- node[anchor=east]{$x$} (-0.2,0.5);

    \node[anchor=north,text width=3in] at (4,-1) {%
    $$ E_{P} \sim \int_{-\infty}^{\infty} \dd{\eta} \int_{x}^{\infty} \dd{\xi} e^{i k
          f(\xi,\eta)} $$

    $$ f(\xi,\eta) = \frac{\xi^{2} + \eta^{2}}{2} \qty(\frac{1}{s_{0}} +
      \frac{1}{r_{0}})  $$

    $$ u^{2} \equiv \frac{2(s_{0}+r_{0})}{\lambda s_{0} r_{0}} \xi^{2}
      \qquad
      v^{2} \equiv \frac{2(s_{0}+r_{0})}{\lambda s_{0} r_{0}} \eta^{2}
    $$
    };
    \node[draw,fill=yellow!25!white,
      anchor=east,
      text width=1.25in,
      text=DarkRed,
      font=\small] at (11,-2) {
      For simplicity, put both $S$ and $P$ on the $z$ axis:
      $x_{s} = y_{s} = 0$ and $x_{p} = y_{p} = 0$.
    };
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec14.tex
modified: 2019-03-11 21:06:28
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \coordinate (R) at (10,0);
    \draw (-1.5,0) coordinate(S) -- (R);
    \node[anchor=north] at (-.75,0) {$s_{0}$};
    \fill[DarkRed] (S) circle[radius = 0.05];
    \draw[line width=2] (0,-1) -- (0,0);
    \draw[line width=1.5,DarkRed] (S) -- (0,1) -- (R);
    \node[anchor=west] at (R) {$P$};
    \node[anchor=north] at (5,0) {$r_{0}$};
    \draw[DarkGreen,->] (0.2,0) -- node[anchor=west]{$\xi$} (0.2,1);
    \node[DarkGreen,anchor=west] at (0.2,-0.4){$x = 0$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec04.tex
modified: 2019-02-04 23:42:31
domain: p134
source:
  \begin{tikzpicture}[scale=0.6]
    \shade<1>[shading=radial,inner color=blue!50!white] (0,0)
    circle[radius=2];
    \fill<1>[color=red] (0,0) circle[radius=0.1];
    \shade<2->[shading=radial,inner color=blue!50!white] (-0.1,0)
    circle[radius=2];
    \fill<2->[color=red] (0.1,0) circle[radius=0.1];
    \draw<2->[->,line width=3,gray] (-1,2) -- +(0:2) node[anchor=south]{$E$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec04.tex
modified: 2019-02-04 23:42:31
domain: p134
source:
  \begin{tikzpicture}[scale=1.25]
    \node at (-3,0) {$\rho_{\rm b} = -\div\vb{P}$};
    \fill[red] (0,0) circle[radius=0.1];
    \foreach \a in {0,30,...,330} {
        \node[blue,font=\tiny] at (\a:0.2){$-$};
        \node[red,font=\tiny] at (\a:0.8){$+$};
        \draw[DarkGreen, ->] (\a:0.3) -- ++(\a:0.4);
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec04.tex
modified: 2019-02-04 23:42:31
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    % metal plates
    \draw[gray!50!white,line width=4pt] (0,0) -- (10,0) (0,2) -- (10,2) coordinate (A);
    \fill [yellow!20!white] (0,0.3) rectangle (10,1.7);
    \foreach \x in {0.5,1,...,9.5}{
        \node[color=red,font=\small] at (\x,2) {$+$};
        \node[color=blue,font=\small] at (\x,0) {$-$};
        \node[color=blue,font=\tiny] at (\x,1.6){$-$};
        \node[color=red,font=\tiny] at (\x,0.4){$+$};
        \draw[->,DarkGreen!50,line width=1.5pt] (\x,1.4) -- (\x,0.6);
      }
    \node[DarkGreen,anchor=west] at (10,1){$\displaystyle
      \vb{E}_{\text{in medium}} =
      \frac{\vb{E}_{\rm applied}}{\varepsilon}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec04.tex
modified: 2019-02-04 23:42:31
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \shade[shading=radial,inner color=blue!50!white] (-0.1,0)
    circle[radius=2];
    \fill[color=red] (0.1,0) circle[radius=0.1];
    \draw[->,line width=3,gray] (-1,2) -- +(0:2);
    \node[anchor=south,scale=2,gray] at (0,2.2) {$E_{0} e^{-i\omega t}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec04.tex
modified: 2019-02-04 23:42:31
domain: p134
source:
  \begin{tikzpicture}[scale=0.75]
    \fill[yellow!20!white] (0,0) rectangle (8,3);
    \fill[green!20!white] (0,0) rectangle (8,-3);
    \draw (0,0) -- (8,0);
    \draw[dashed](4,-3) -- (4,3);
    \draw[DarkRed,<-,line width=1.5pt] (4,0) -- ++(135:3);
    \draw[DarkRed,->,line width=1.5pt] (4,0) -- ++(-60:3);
    \draw (4,1) arc (90:135:1);
    \node at (3.6,1.25) {$\theta_{\rm i}$};
    \draw (4,-1) arc(-90:-60:1);
    \node at (4.35,-1.25) {$\theta_{\rm t}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec04.tex
modified: 2019-02-04 23:42:31
domain: p134
source:
  \begin{tikzpicture}[scale=1.,
      kvec/.style={->,line width=1.25pt,color=DarkBlue},
    ]
    \def\len{3}
    \def\wid{4}
    \def\ang{40}
    \def\refr{59}
    \def\tlen{2.25}
    \def\bgnd{yellow!20!white} % background color of upper medium
    \def\Bgnd{green!20}            % background color of lower medium

    % arcs for the k vectors
    \fill[fill=\bgnd] (-\wid,0) rectangle (\wid,\len);
    \fill[fill=\Bgnd] (-\wid,0) rectangle (\wid,-\len);

    \onslide<2->{
      \draw[color=DarkRed,dashed] (\len,0) arc[radius=\len,start angle=0,end
          angle=180];

      \draw[color=DarkRed,dashed] (\len*0.75,0) arc[radius=\len*0.75,start angle=0,end angle=-180];
    }
    % axes and materials

    \draw[color=black!50!white,->] (-\wid,0) -- (\wid+0.25,0)
    node[anchor=west]{$x$};
    \draw[color=SlateBlue!70,dashed,->] (0,-\len) -- (0,\len+0.25)
    node[anchor=south]{$z$};

    \node at (-0.85*\wid,0.9*\len) {$\mu_{1}, \epsilon_{1}$};
    \node at (-0.85*\wid,-0.9*\len) {$\mu_{2}, \epsilon_{2}$};

    \onslide<3->{
      \draw[dashed] (-1.93, 0.85*\len) -- (-1.93, -0.4);
      \draw[DarkRed,->,line width=1] (-1.93,-0.02) --node[anchor=north]{$k_{x}$}
      (0,-0.02);
    }


    % incident beam


    \coordinate (A) at (90+\ang:0.75*\len); % field anchor

    \draw[kvec,<-] (0,0) --node[anchor=east]{$k_{\rm i}$} ++(90+\ang:\len);

    \onslide<3->{
      % reflected beam
      \draw[kvec] (0,0) --node[anchor=north west]{$k_{\rm r}$} ++(90-\ang:\len)
      coordinate (kr);
      \coordinate (B) at (90-\ang:0.75*\len);





      % refracted beam

      \draw[kvec] (0,0) -- node[anchor=north]{$k_{\rm t}$} ++(-90+\refr:\tlen)
      coordinate (kt);
      \coordinate (C) at (-90+\refr:0.35*\len);
    }

    \onslide<3,4>{
      \draw[kvec,DarkRed] (0,0) -- node[anchor=south]{$k_{x}$} (1.93,0);
      \draw[dashed] (kr) -- ++(-90:4);  % marking k_x
    }

    % label angles
    \def\arcrad{0.4}
    \draw (90:\arcrad) arc(90:130:\arcrad);
    \node at (110:\arcrad+0.3) {$\theta_{\rm i}$};
    \onslide<4->{
      \draw (-90:\arcrad) arc(-90:-35:\arcrad);
      \node at (-60:\arcrad+0.2) {$\theta_{\rm t}$};
    }

    \onslide<5->{
      \draw[DarkRed,<-,line width=1] (kr) -- node[fill=\bgnd,anchor=west]{$w_{1}$}
      ++(-90:2.3);

      \draw[DarkRed,<-|,line width=1] (kt) --
      node[fill=\Bgnd,anchor=west]{$w_{2}$} ++(90:1.165);
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec04.tex
modified: 2019-02-04 23:42:31
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \fill[DarkSlateBlue!25!white] (0.1,2) arc(12:-12:9.62) --
    (-0.1,-2) arc(192:168:9.62) -- cycle;

    \draw (-5,0) -- (5,0); % symmetry line

    \draw[gray,line width=3,<->] (0,-2.5) -- (0,2.5);
    \coordinate (A) at (0,1.5);
    \draw[DarkRed,line width=1.5] (-4,0) --  (A) -- (2.5,0);
    \draw (-3,0) arc(0:20:1);
    \node at (-2.7,0.2){$\alpha_{1}$};
    \draw (1.8,0) arc(180:148:0.7);
    \node at (1.5,0.2){$\alpha_{2}$};
    \node[anchor=east] at (0,0.8){$y$};
    \draw[<->,DarkGreen] (-4,-0.3) -- node[anchor=north]{$x_{1}$} (0,-0.3);
    \draw[<->,DarkGreen] (0,-0.3) -- node[anchor=north]{$x_{2}$} (2.5,-0.3);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec04.tex
modified: 2019-02-04 23:42:31
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \draw (-5,0) -- (5,0); % symmetry line
    \draw[gray,line width=3,<->] (0,-2) -- (0,2);
    \newcommand*{\f}{1.5}

    \node[scale=2] at (-1,-3) {$\frac{1}{o} + \frac{1}{i} = \frac{1}{f} $};

    \onslide<beamer:1|handout:0>{

      \foreach \y in {0.25,0.5,...,1.25}{
          \draw[DarkRed,->] (-4,\y) -- (0,\y) -- ($(0,\y)!1.5!(\f,0)$);
        }
      \draw[<->,DarkGreen] (0,-0.3) -- node[anchor=north]{$f$} (\f,-0.3);
    }
    \fill[DarkGreen] (\f,0) circle[radius=0.05];

    \onslide<beamer:2-|handout:0>{
      \fill[DarkGreen] (-\f,0) circle[radius=0.05];
    }
    \onslide<beamer:2|handout:0>{
      \foreach \y in {0.25,0.5,...,1.25}{
          \draw[DarkBlue,->] (-\f,0) -- (0,\y) -- (4,\y);
        }
      \draw[<->,DarkGreen] (-\f,-0.3) -- node[anchor=north]{$f$} (0,-0.3);
    }
    \onslide<3->{
      \foreach \y in {-1, -0.5, ..., 1.}{
          \draw[DarkGreen,->] (-3*\f,1) -- (0,\y) -- ($(0,\y)!1.5!(1.5*\f,-0.5)$);
          \draw[DarkGreen,line width=3,<-] (-3*\f,1) -- ++(-90:1);
          \draw[DarkGreen,line width=1.5,<-] (1.5*\f,-.5) --++(90:0.5);
        }
      \draw[dashed] (-3*\f,0) -- (-3*\f,-1.5);
      \draw[|->] (0,-1.25) -- node[anchor=north]{$o$} (-3*\f,-1.25);
      \draw[dashed] (1.5*\f,-0.7) -- ++(-90:0.8);
      \draw[|->] (0,-1.25) -- node[anchor=north]{$i$} (1.5*\f,-1.25);
    }

    \onslide<4>{
      \draw[DarkRed,<-,line width=1.5] (1.6*\f,-0.7) --
      ++(-60:1.2) node[anchor=north,
        font=\small,
        text width=1.2in]{Rays emerge from image just like an object and
        could be imaged by a downstream lens};
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec04.tex
modified: 2019-02-04 23:42:31
domain: p134
source:
  \begin{tikzpicture}[
      scale=1,
      ray/.style={DarkRed, line width=1.5pt,->}
    ]
    \draw (-5,0) -- (4,0); % symmetry line
    \draw[gray,line width=3,<->] (0,-2) -- (0,2);
    \newcommand*{\f}{1.5}

    \node[scale=2] at (0,-3.5) {$\frac{1}{o} + \frac{1}{i} = \frac{1}{f} $};

    \fill[DarkGreen] (-\f,0) circle[radius=0.05] (\f,0) circle[radius=0.05];

    \onslide<beamer:1|handout:0>{
      \foreach \y in {-1, -0.5, ..., 1.}{
          \draw[DarkGreen,->] (-3*\f,1) -- (0,\y) -- ($(0,\y)!1.5!(1.5*\f,-0.5)$);
          \draw[DarkGreen,line width=3,<-] (-3*\f,1) -- ++(-90:1);
          \draw[DarkGreen,line width=1.5,<-] (1.5*\f,-.5) --++(90:0.5);
        }
      \draw[dashed] (-3*\f,0) -- (-3*\f,-1.5);
      \draw[|->] (0,-1.25) -- node[anchor=north]{$o$} (-3*\f,-1.25);
      \draw[dashed] (1.5*\f,-0.7) -- ++(-90:0.8);
      \draw[|->] (0,-1.25) -- node[anchor=north]{$i$} (1.5*\f,-1.25);

    }

    \draw[|->,DarkSlateGray] (0,-2.2) -- node[anchor=north]{positive $o$}
    ++(180:2.5);
    \draw[|->,DarkSlateGray] (0,-2.2) -- node[anchor=north]{positive $i$}
    ++(0:2.5);
    % Object
    \onslide<beamer:2- |handout:0>{
      \draw[ray,line width=2pt] (-\f/2,0) -- ++(90:0.75) coordinate (a);
    };

    % ray through the center of the lens
    \onslide<3->{
      \draw[ray] (a) -- ($(a)!3!(0,0)$);
    };
    % ray parallel to the optic axis
    \onslide<4->{
      \draw[ray] (a) -- (0,0.75) -- ($(0,0.75)!2!(\f,0)$);
    }

    % ray passing through object focus
    \onslide<5->{
      \draw[ray] (a) -- (0,1.5) -- ++(0:3);
      \draw[DarkRed,dashed] (a) -- (-\f,0);
    }
    % extending the lines
    \onslide<6->  {
      \draw[DarkRed!50!white,line width=3,->]  (-\f,0) -- ++(90:1.5);
      \draw[DarkRed,->,line width=1.5] (a) -- (0,1.5) -- ++(0:3);
      \draw[DarkRed,->,line width=1.5] (a) -- (0,0.75) --($(0,0.75)!2!(\f,0)$);
      \draw[DarkRed,->,line width=1.5] (a) -- ($(a)!3!(0,0)$);
      \draw[DarkRed,dashed] (0,1.5) -- (-\f,1.5) -- (-\f/2,0.75)
      (-\f,1.5) -- (0,0.75);
    };
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec04.tex
modified: 2019-02-04 23:42:31
domain: p134
source:
  \begin{tikzpicture}[scale=1,
      ray/.style={->,DarkRed,line width=1.5pt}]
    \newcommand*{\f}{3}

    \draw (-5,0) -- (3.5,0);
    % lens
    \draw[gray,line width=3] (0,-2) -- (0,2) -- ++(70:0.4)
    (0,2) -- ++(110:0.4)
    (0,-2) -- ++(290:0.4)
    (0,-2) -- ++(250:0.4);

    \draw[|->,DarkSlateGray] (0,-2.5) -- node[anchor=north]{positive $o$}
    ++(180:2.5);
    \draw[|->,DarkSlateGray] (0,-2.5) -- node[anchor=north]{positive $i$}
    ++(0:2.5);

    % focal points
    \fill[DarkGreen] (\f,0) circle[radius=0.05] (-\f,0) circle[radius=0.05];
    \draw[DarkGreen,<-] (\f,-0.1) -- ++(-90:1) node[anchor=north]{object focal
      point};
    \draw[DarkGreen,<-] (-\f,-0.1) -- ++(-90:1) node[anchor=north]{image focal
      point};

    % object

    \draw[DarkRed,line width=3pt,->] (-1.5*\f,0) -- ++(90:1.5)
    coordinate (c);

    % principal rays
    \draw[ray] (c) -- ($(c)!1.5!(0,0)$);
    \draw[ray] (c) -- ++(0:1.5*\f) coordinate (d) -- ++(1.5,0.75);
    \draw[ray] (c) -- (0,0.6) -- ++(0:2);
    \draw[DarkRed,dashed] (d) -- (-\f,0)
    (0,0.6) -- (\f,0)
    (0,0.6) -- (-0.6*\f,0.6);

    \onslide<2->{
      % image
      \draw[DarkRed!50!white,line width=2,->] (-0.6*\f,0) -- ++(90:0.6);
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec04.tex
modified: 2019-02-04 23:42:31
domain: p134
source:
  \begin{tikzpicture}[scale=0.8,
      ray/.style={->,DarkRed,line width=1.pt}]

    \draw (-10,0) -- (3,0);
    \fill[DarkGreen] (0,0) circle[radius=0.05];

    % lens
    \draw[gray,line width=3,<->] (-8,-2) -- (-8,2);
    \draw[gray,line width=2,<->] (2,-1) -- (2,1);

    \foreach \y in {-1.5,-1,...,1.5}{
        \draw[ray] (-10,\y) -- (-8,\y) -- ($(-8,\y)!1.25!(0,0)$) -- ++(0:1);
      }
    \draw[coord] (0,-2.5) --node[anchor=north]{$f_{1}$} ++(180:8);
    \draw[coord] (0,-2.5) --node[anchor=north]{$f_{2}$} ++(0:2);
    \draw[DarkGreen,dashed] (0,-0.1) -- (-90:2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec04.tex
modified: 2019-02-04 23:42:31
domain: p134
source:
  \begin{tikzpicture}[scale=1.125,
      kvec/.style={->,line width=1.25pt,color=DarkBlue},
    ]
    \def\len{3}
    \def\wid{4}
    \def\ang{40}
    \def\refr{59}
    \def\tlen{2.25}
    \def\bgnd{yellow!20!white} % background color of upper medium
    \def\Bgnd{green!20}            % background color of lower medium

    % arcs for the k vectors
    \fill[fill=\bgnd] (-\wid,0) rectangle (\wid,\len);
    \fill[fill=\Bgnd] (-\wid,0) rectangle (\wid,-\len);
    \draw[color=DarkRed,dashed] (\len,0) arc[radius=\len,start angle=0,end
        angle=180];
    \draw[color=DarkRed,dashed] (\len*0.75,0) arc[radius=\len*0.75,start angle=0,end angle=-180];

    % axes and materials

    \draw[color=black!50!white,->] (-\wid,0) -- (\wid+0.25,0)
    node[anchor=west]{$x$};
    \draw[color=SlateBlue!70,dashed,->] (0,-\len) -- (0,\len+0.25)
    node[anchor=south]{$z$};

    \node at (-0.85*\wid,0.9*\len) {$\mu_{1}, \epsilon_{1}$};
    \node at (-0.85*\wid,-0.9*\len) {$\mu_{2}, \epsilon_{2}$};
    \node at (0.9*\wid,-0.9*\len) {TE};

    \draw[dashed] (-1.93, 0.85*\len) -- (-1.93, -0.4);
    \draw[DarkRed,->,line width=1] (-1.93,-0.02) --node[anchor=north]{$k_{x}$}
    (0,-0.02);



    % incident beam


    \coordinate (A) at (90+\ang:0.75*\len); % field anchor
    \node[anchor=west,fill=\bgnd] at (A) {\;\;$E_{\rm i}$};
    \draw[kvec,<-] (0,0) --node[anchor=east]{$k_{\rm i}$} ++(90+\ang:\len);
    \draw[force] (A) -- ++(\ang:1) node[anchor=south,fill=\bgnd] {$H_{\rm  i}$};
    \filldraw[fill=\bgnd] (A) circle[radius=0.15];
    \draw[line width=1.5] (A) +(45:0.15) -- ++(225:0.15) (A) +(135:0.15) -- ++(-45:0.15);


    % reflected beam
    \draw[kvec] (0,0) --node[anchor=north west]{$k_{\rm r}$} ++(90-\ang:\len)
    coordinate (kr);
    \coordinate (B) at (90-\ang:0.75*\len);
    \draw[force] (B) -- ++(180-\ang:1) node[anchor=south,fill=\bgnd] {$H_{\rm  r}$};
    \filldraw[fill=\bgnd] (B) circle[radius=0.15];
    \draw[line width=1.5] (B) +(45:0.15) -- ++(225:0.15) (B) +(135:0.15) --
    ++(-45:0.15);

    \node[anchor=east] at (B) {$E_{\rm r}$\;\;};
    \draw[DarkRed,<-,line width=1] (kr) -- node[fill=\bgnd,anchor=west]{$w_{1}$}
    ++(-90:2.3);

    % refracted beam
    \draw[kvec] (0,0) -- ++(-90+\refr:\tlen) node[anchor=north]{$k_{\rm t}$}
    coordinate (kt);
    \coordinate (C) at (-90+\refr:0.35*\len);
    \draw[force] (C) -- ++(\refr:1) node[anchor=west] {$H_{\rm  t}$};
    \filldraw[fill=\Bgnd] (C) circle[radius=0.15];
    \draw[line width=1.5] (C) +(45:0.15) -- ++(225:0.15) (C) +(135:0.15) -- ++(-45:0.15);
    \node[anchor=north east] at (C) {$E_{\rm t}$};

    \draw[DarkRed,<-|,line width=1] (kt) --
    node[fill=\Bgnd,anchor=west]{$w_{2}$} ++(90:1.165);

    % label angles
    \def\arcrad{0.4}
    \draw (90:\arcrad) arc(90:130:\arcrad);
    \node at (110:\arcrad+0.3) {$\theta_{\rm i}$};
    \draw (-90:\arcrad) arc(-90:-35:\arcrad);
    \node at (-60:\arcrad+0.2) {$\theta_{\rm t}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec04.tex
modified: 2019-02-04 23:42:31
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[shift={(-2,.4)}]
      \fill[gray!5!white] (0,0) rectangle(3,1);
      \fill[gray!25!white] (0,0) rectangle(3,-1);
      \node[anchor=south west] at (0,-1) {$n=1.5$};
      \node[anchor=north east] at (3,1) {$n = 1$};
      \draw (0,0) -- (3,0);
      \draw[dashed] (1.5,-1) -- (1.5,1);
      \draw[DarkRed,<-,line width=1.5] (1.5,0) -- ++(135:1.25);
      \draw[DarkRed,->,line width=1.5] (1.5,0) -- ++(-60:1);
      \draw(1.5,0.5) arc(90:135:0.5) (1.5,-0.5) arc(-90:-60:0.5);
      \node at (1.2,0.7){$\theta_{\rm i}$};
      \node at (1.7,-0.8){$\theta_{\rm t}$};
    \end{scope}

    \onslide<2>{\node at (0,0)
      {\includegraphics[width=\textwidth]{Reflectivity}};}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec04.tex
modified: 2019-02-04 23:42:31
domain: p134
source:
  \begin{tikzpicture}[scale=0.8]
    \begin{scope}[shift={(0.5,.4)}]
      \fill[gray!5!white] (0,0) rectangle(3,-1);
      \fill[gray!25!white] (0,0) rectangle(3,1);
      \node[anchor=south west] at (0,-1) {$n=1$};
      \node[anchor=north east] at (3,1) {$n = 1.5$};
      \draw (0,0) -- (3,0);
      \draw[dashed] (1.5,-1) -- (1.5,1);
      \draw[DarkRed,<-,line width=1.5] (1.5,0) -- ++(135:1.25);
      \draw[DarkRed,->,line width=1.5] (1.5,0) -- ++(-15:1.5);
      \draw(1.5,0.5) arc(90:135:0.5) (1.5,-0.5) arc(-90:-15:0.5);
      \node at (1.2,0.7){$\theta_{\rm i}$};
      \node at (2,-0.7){$\theta_{\rm t}$};
    \end{scope}

    \onslide<2>{
      \node at (0,0)
      {\includegraphics[width=\textwidth]{ReflectivityInternal}};
    }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec10.tex
modified: 2019-02-25 04:03:57
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) node[anchor=east]{$\ket{g}$} --(1,0);
    \draw[line width=3,gray] (0,2) node[anchor=east,black]{$\ket{e}$} --
    (1,2);
    \draw[DarkGreen,line width=3,->] (0.5,0) -- (0.5,2);
    \node at (0.5,-0.6) {$t = 0$};

    \begin{scope}[shift={(2.5,0)}]
      \draw (0,0) node[anchor=east]{$\ket{g}$} --(1,0);
      \draw[line width=3,gray] (0,2) node[anchor=east,black]{$\ket{e}$} --
      (1,2);
      \draw[DarkGreen,photon,->] (0.5,2) --node[anchor=west]{$\omega$} (0.5,0);
      \node at (0.5,-0.6) {$t$};

    \end{scope}

    \node[text width=2in,anchor=north,align=center,SlateGray] at (1.25,-1){initial excited population $N_{0}$\\
      excited state mean lifetime $\tau_{L}$};

    % Eyeball %%%%%%%%%%%%%%%%%%%%%%%%%

    \begin{scope}[shift={(0,3)}]
      \foreach \i in {0,1,...,60}
        {
          \fill[NavyBlue,opacity=0.6] (rand*0.25,rand*0.25) circle[radius=0.02];
        }
    \end{scope}

    \begin{scope}[shift={(3.25,3)}]
      \draw[line width=2,blue,opacity=0.8] (-0.5,0.12) arc(165:195:0.5);
      \draw[opacity=0.8,fill=black] (-0.52,0) circle[x radius=0.03,y radius=0.04];
      \draw[line width=1] (-0.6,0.15) -- (0,0) -- (-0.6,-0.15);
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec10.tex
modified: 2019-02-25 04:03:57
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-4,
        xmax=4.5,
        ymin=0,
        ymax=1.1,
        enlargelimits=false,
        width=2.25in,
        height=1.5in,
        xlabel={$\omega-\omega_{0}$},
        ylabel={$P(\omega)$},
        ytick={0},
        yticklabels=\empty,
        xtick={0},
        xticklabels=\empty,
        % xticklabels{0,,$a$,,a$},
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
      ]
      \addplot[
        DarkGreen,
        domain=-4:4,
        samples=201,
        line width=1.5pt,
      ]
      {1 / (1 + x^2))};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec10.tex
modified: 2019-02-25 04:03:57
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-4,
        xmax=4,
        ymin=0,
        ymax=1.25,
        enlargelimits=false,
        width=5in,
        height=2.5in,
        xlabel={$\Omega = \omega-\omega_{0}$},
        ylabel={$P(\Omega)$},
        ytick={0},
        yticklabels=\empty,
        xtick={0},
        xticklabels=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
      ]
      \addplot[
        DarkGreen,
        domain=-4:4,
        samples=201,
        line width=3pt,
      ]
      {1 / (1 + x^2))};

      \addplot[
        DarkRed,
        domain=-4:4,
        samples=201,
        line width=2,
        dashed
      ]
      {exp(-ln(2)*x*x)};
      \node[anchor=north east] at (4,1.25) {%
        $\displaystyle P(\Omega)\sim
          \frac{1}{1+(2\tau_{L}\Omega)^{2}} $  };
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec10.tex
modified: 2019-02-25 04:03:57
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[shift={(0,0)}]
      \draw (0,0) node[anchor=east]{$\ket{g}$} --(1,0);
      \draw[line width=3,gray] (0,2) node[anchor=east,black]{$\ket{e}$} --
      (1,2);
      \draw[photon,DarkGreen,->] (0.5,2) --node[anchor=west]{\;$\omega_{0}$} (0.5,0);
    \end{scope}

    \begin{scope}[shift={(1.5,0)}]
      \draw (0,0) -- (1,0);
      \draw[dashed] (0,-0.1) -- ++(1,0);
      \draw[line width=2,gray] (0,2) -- (1,2);
      \draw[dashed] (0,2.1) -- ++ (1,0);
      \draw[photon,DarkGreen,->] (0.5,2.1) --
      node[anchor=west]{\quad$\omega'_{0} > \omega_{0}$} (0.5,-0.1);
      \node[anchor=north] at (0.5,-0.2){during collision};
    \end{scope}

    \onslide<4->{
      \begin{scope}[shift={(1,-4)}]
        \node at (1,1) {\includegraphics[width=5cm]{decay-bump}};
        \node[DarkGreen,font=\small] at (1.7,0.2) {collision};
        \node[DarkGreen] at (1.7,2) {$E(t) = E_{0} e^{-t/2\tau_{L}}
            e^{-i\omega_{0}t} \textcolor{DarkRed}{e^{ i\phi(t)}}$};
      \end{scope}
    }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec10.tex
modified: 2019-02-25 04:03:57
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \onslide<5->{
      \begin{scope}[shift={(0,0)}]
        \draw[<->] (0,2) node[anchor=east]{\textcolor{DarkRed}{$\phi(t)$}} -- (0,0) -- (4,0)
        node[anchor=north]{$t$};

        % \coordinate (current point) at (0,1);
        % \foreach \i in {1,2,...,10}{
        %   \coordinate (dx) at (0.25*(1+rand),0);
        %   \coordinate (dy) at (0,1+rand);
        %   \draw (current point) -- ++(dx) -- ++(dy) coordinate (current point);
        %   }
        \draw[DarkSlateGray,line width=1.5] (0,1) -- ++(0.5,0) -- ++(0,0.3)
        -- ++(0.4,0) -- ++ (0,-0.4)
        -- ++(0.3,0) -- ++ (0,-0.5)
        -- ++(0.5,0) -- ++ (0,0.2)
        -- ++(0.2,0) -- ++ (0,0.8)
        -- ++(0.4,0) -- ++ (0,-0.4)
        -- ++(0.5,0) -- ++ (0,-0.8)
        -- ++(0.25,0) -- ++ (0,1.5) -- ++(0.3,0);
      \end{scope}
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec11.tex
modified: 2019-03-02 23:57:45
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-4,
        xmax=4.5,
        ymin=0,
        ymax=1.1,
        enlargelimits=false,
        width=2.25in,
        height=1.5in,
        xlabel={$\omega-\omega_{0}$},
        ylabel={$\Four{P}(\omega)$},
        ytick={0},
        yticklabels=\empty,
        xtick={0},
        xticklabels=\empty,
        % xticklabels{0,,$a$,,a$},
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
      ]
      \addplot[
        DarkGreen,
        domain=-4:4,
        samples=201,
        line width=1.5pt,
      ]
      {1 / (1 + x^2))};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec11.tex
modified: 2019-03-02 23:57:45
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-4,
        xmax=4,
        ymin=0,
        ymax=1.25,
        enlargelimits=false,
        width=5in,
        height=2.5in,
        xlabel={$\Omega = \omega-\omega_{0}$},
        ylabel={$\Four{P}(\Omega)$},
        ytick={0},
        yticklabels=\empty,
        xtick={0},
        xticklabels=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
      ]
      \addplot[
        DarkGreen,
        domain=-4:4,
        samples=201,
        line width=3pt,
      ]
      {1 / (1 + x^2))};

      \addplot[
        DarkRed,
        domain=-4:4,
        samples=201,
        line width=2,
        dashed
      ]
      {exp(-ln(2)*x*x)};
      \node[anchor=north east] at (4,1.25) {%
        $\displaystyle \Four{P}(\Omega)\sim
          \frac{1}{1+(2\tau_{L}\Omega)^{2}} $  };
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec11.tex
modified: 2019-03-02 23:57:45
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[opacity=0.5,gray] (0,0) circle[radius=0.2];
    \node at (0,0) {\includegraphics[width=0.9\textwidth]{onebrew1}};
    \begin{scope}[DarkRed,line width=2pt]
      \draw (-5,0.3) circle[radius=0.2] coordinate (c);
      \draw[<-] ($(c) + (0,0.3cm)$) -- ++ (90:1.45) node[anchor=south] {$r = \SI{60}{cm}, R =
          99.9\%$};
      \draw[<-,DarkGreen] (-4.55,-0.1) -- ++(225:1.25) node[anchor=east]{$V
          = +\SI{1450}{V}$};
      \draw[<-] (-1,0.4) -- ++(90:1.25) node[anchor=south,text
        width=2cm,font=\small,align=center]{Ne (0.1 Torr) He (0.7 Torr) $d =
          \SI{2}{mm}$};
      \draw (3.35,0.3) circle[radius=0.3];
      \draw[<-] (3.35,0.7) -- ++(90:1.25) node[anchor=south]{$r =
          \SI{45}{cm}, T = 1.5\%$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec11.tex
modified: 2019-03-02 23:57:45
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=2pt,gray] (0,0) arc(180:200:4) coordinate (a);
    \draw[line width=2pt,gray] (0,0) arc(180:160:4);
    \draw (.04,0) arc(180:200:3.96);
    \draw (.04,0) arc(180:160:3.96);

    \node[anchor=north] at (a) {high reflector};

    \draw[line width=2pt,gray] (8,0) arc(0:20:3);
    \draw[line width=2pt,gray] (8,0) arc(0:-20:3) coordinate (b);
    \node[anchor=north,text width=3cm] at (b) {output coupler  transmission $T$};

    % edges of the gaussian beam
    \draw[DarkRed] (0.2,1) .. controls (4,0.3) and (5,0.3)  .. (7.9,0.7);
    \draw[DarkRed] (0.2,-1) .. controls (4,-0.3) and (5,-0.3)  .. (7.9,-0.7);

    \onslide<1>{\node[anchor=south,DarkRed] at (4.5,0.5) {gaussian beam};}

    \onslide<2>{
      % atoms
      \excited{(1,0.5)}{0.5}{0.5}
      \excited{(3,-0.25)}{0.5}{0.5}
      \excited{(7,0.25)}{0.5}{0.5}
      \emitted{(5,0)}{0.5}{0.5}
      \emitted{(2,-0.5)}{0.5}{0.5}
      \emitted{(4,0.4)}{0.5}{0.5}

      % output beam
      \foreach \n in {-3,-2,...,3} {
          \draw[photon,->,line width=1] (8.3,\n * 0.25) -- ++(2*\n:2.5);
        }
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec11.tex
modified: 2019-03-02 23:57:45
domain: p134
source:
  \begin{tikzpicture}[scale=0.667]
    \draw[line width=2pt,gray] (0,0) arc(180:200:4) coordinate (a);
    \draw[line width=2pt,gray] (0,0) arc(180:160:4);
    \draw (.04,0) arc(180:200:3.96);
    \draw (.04,0) arc(180:160:3.96);

    \node[anchor=north] at (a) {high reflector};

    \draw[line width=2pt,gray] (8,0) arc(0:20:3);
    \draw[line width=2pt,gray] (8,0) arc(0:-20:3) coordinate (b);
    \node[anchor=north,text width=3cm,DarkGreen] at (b) {output coupler  transmission $T$};

    % edges of the gaussian beam
    \draw[DarkRed] (0.2,1) .. controls (4,0.3) and (5,0.3)  .. (7.9,0.7);
    \draw[DarkRed] (0.2,-1) .. controls (4,-0.3) and (5,-0.3)  .. (7.9,-0.7);


    % atoms
    \excited{(1,0.5)}{0.5}{0.5}
    \excited{(3,-0.25)}{0.5}{0.5}
    \excited{(7,0.25)}{0.5}{0.5}
    \emitted{(5,0)}{0.5}{0.5}
    \emitted{(2,-0.5)}{0.5}{0.5}
    \emitted{(4,0.4)}{0.5}{0.5}

    % output beam
    \foreach \n in {-3,-2,...,3} {
        \draw[photon,->,line width=1] (8.3,\n * 0.25) -- ++(2*\n:2.5);
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec11.tex
modified: 2019-03-02 23:57:45
domain: p134
source:
  \begin{tikzpicture}[scale=1,font=\large]
    \node[draw,rounded corners,text width=3cm,fill=gray!10,align=center] at
    (0,0) {rate atoms emit into mode};
    \node[font=\Huge] at (2.25,0){$\ge$};
    \node[draw, rounded corners, text width=3cm,fill=gray!10,align=center,anchor=west] at
    (3,0) {rate atoms in lower state absorb photons from mode};
    \node[font=\Huge] at (6.75,0){$+$};
    \node[draw, rounded corners, text width=3cm,fill=gray!10,align=center,anchor=west] at
    (7.25,0) {rate mirrors and cavity optics remove/scatter photons from
      mode};

    \begin{scope}[shift={(0,-2)}]
      \emitted{(-1,0)}{.5}{.5}
      \emitted{(0,0.5)}{.5}{.5}
      \emitted{(0,-0.5)}{.5}{.5}
      \emitted{(1,0)}{.5}{.5}
    \end{scope}

    \begin{scope}[shift={(5,-2.5)}]
      \absorbed{(-1,0)}{.5}{.5}
      \absorbed{(0,0.5)}{.5}{.5}
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec11.tex
modified: 2019-03-02 23:57:45
domain: p134
source:
  \begin{tikzpicture}[scale=0.8]
    \draw[line width=2pt,gray] (0,0) arc(180:200:4) coordinate (a);
    \draw[line width=2pt,gray] (0,0) arc(180:160:4);
    \draw (.04,0) arc(180:200:3.96);
    \draw (.04,0) arc(180:160:3.96);

    \draw[line width=2pt,gray] (8,0) arc(0:20:3);
    \draw[line width=2pt,gray] (8,0) arc(0:-20:3) coordinate (b);

    % edges of the gaussian beam
    \draw[DarkRed] (0.2,1) .. controls (4,0.3) and (5,0.3)  .. (7.9,0.7);
    \draw[DarkRed] (0.2,-1) .. controls (4,-0.3) and (5,-0.3)  .. (7.9,-0.7);

    \draw[photon,->] (0.2,-0.2) -- (7.8,-0.2);
    \draw[photon,->] (7.9,0.2) -- (0.1,0.2);
    \draw[photon,->] (8.1,0) -- ++(0:2);

    \begin{scope}[DarkGreen,line width=1.5]
      \draw[dashed] (0,0) -- (0,2);
      \draw[dashed] (8,0) -- (8,2);
      \draw[<->] (0,1.75) --node[fill=white]{$L$} ++(0:8);
    \end{scope}

    \node[anchor=north,text width=7cm,align=center,font=\large] at (4,-1)
    { Need $\displaystyle L = N \frac{\lambda_{N}}{2} $ for constructive
      interference, where $N \in \mathbb{Z}$ };

    \pause
    \node at (4,-3.75){\includegraphics[width=6cm]{He-Ne}};

    \node[anchor=north, text width=4cm, align=center,DarkRed,draw,rounded corners] at (4,-4.5) {
      For our He-Ne lasers, $L \approx \SI{35}{cm}$; $N \approx \SI{1.1}{million}$
    };
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec11.tex
modified: 2019-03-02 23:57:45
domain: p134
source:
  \begin{tikzpicture}[scale=0.5]
    \draw[line width=2pt,gray] (0,0) arc(180:200:4) coordinate (a);
    \draw[line width=2pt,gray] (0,0) arc(180:160:4);
    \draw (.04,0) arc(180:200:3.96);
    \draw (.04,0) arc(180:160:3.96);


    \draw[line width=2pt,gray] (8,0) arc(0:20:3);
    \draw[line width=2pt,gray] (8,0) arc(0:-20:3) coordinate (b);

    \node[anchor=north] at (a) {$r_{1}$};
    \node[anchor=north] at (b) {$r_{2}$};

    % edges of the gaussian beam
    \draw[DarkRed] (0.2,1) .. controls (4,0.3) and (5,0.3)  .. (7.9,0.7);
    \draw[DarkRed] (0.2,-1) .. controls (4,-0.3) and (5,-0.3)  .. (7.9,-0.7);

    \draw[photon,->] (0.2,-0.2) -- (7.8,-0.2);
    \draw[photon,->] (7.9,0.2) -- (0.1,0.2);
    \draw[photon,->] (8.1,0) -- ++(0:2);

    \begin{scope}[DarkGreen,line width=1.5]
      \draw[dashed] (0,0) -- (0,2);
      \draw[dashed] (8,0) -- (8,2);
      \draw[<->] (0,1.75) --node[fill=white]{$L$} ++(0:8);
    \end{scope}


    \begin{scope}[shift={(0,-8)}]
      %    \onslide<2>{
      % If you want no plot frame, just arrows for axes
      % use axis x line=bottom, axis y line=left, axis line style={line width=1.25}
      % and maybe xtick=\empty, ytick=\empty
      \def\R{0.94}
      \begin{axis}[
          xmin=-800,
          xmax=800,
          ymin=0,
          % ymax=1,
          %enlargelimits=false,
          width=5in,
          height=2.5in,
          xlabel={$\phi$},
          ylabel={$\mathcal{T}$},
          ytick={},
          yticklabel=\empty,
          xtick={-720,-360,0,360,720},
          xticklabels={$-4\pi$,$-2\pi$,$0$,$2\pi$,$4\pi$},
          % xticklabels{0,,$a$,,a$},
          axis x line=bottom,
          axis y line=center
        ]
        \addplot[
          DarkGreen,
          domain=-800:800,
          samples=1001,
          line width=1pt,
        ]
        {(1-\R)^2 /( (1-\R)^2 + 4*\R*(sin(x/2)^2))};
        \addplot[
          DarkBlue,
          domain=-800:800,
          samples=1001,
          line width=1pt,
        ]
        {(1-2*\R)^2 /( (1-2*\R)^2 + 4*2*\R*(sin(x/2)^2))};
        \addplot[
          DarkRed,
          domain=-800:800,
          samples=1001,
          line width=1pt,
        ]
        {(1-1.5*\R)^2 /( (1-1.5*\R)^2 + 4*1.5*\R*(sin(x/2)^2))};

      \end{axis}
      %      }
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec11.tex
modified: 2019-03-02 23:57:45
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \draw[->] (-6,0) -- (6,0) node[anchor=north east]{$\nu$};
    \foreach \x in {-5,-4,...,5}{
        \draw[line width=2,DarkRed] (\x,0) -- ++(0,2);
      }
    \foreach \n in {1, 2, ..., 5} {
        \node at (\n,-0.3) {$n+\n$};
        \node at (-\n,-0.3){$n-\n$};
      }
    \node at (0,-0.3) {$n$};
    \node at (0,-1){$n \approx 1,100,000$};

    \node[DarkRed,draw,font=\Large] at (4,-1.5){$\nu_{n} = \frac{c}{2L} n$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec05.tex
modified: 2019-02-07 00:11:45
domain: p134
source:
  \begin{tikzpicture}[scale=0.67]
    \draw (-5,0) -- (5,0); % symmetry line
    \draw[gray,line width=3,<->] (0,-2) -- (0,2);
    \newcommand*{\f}{1.5}

    \draw[<->,DarkGreen] (0,-0.3) -- node[anchor=north]{$f$} (\f,-0.3);
    \fill[DarkGreen] (\f,0) circle[radius=0.05];
    \fill[DarkGreen] (-\f,0) circle[radius=0.05];
    \draw[<->,DarkGreen] (-\f,-0.3) -- node[anchor=north]{$f$} (0,-0.3);


    \foreach \y in {-1, -0.5, ..., 1}{
        \draw[DarkGreen,->] (-3*\f,1) -- (0,\y) -- ($(0,\y)!1.5!(1.5*\f,-0.5)$);
        \draw[DarkGreen,line width=3,<-] (-3*\f,1) -- ++(-90:1);
        \draw[DarkGreen,line width=1.5,<-] (1.5*\f,-.5) --++(90:0.5);
      }
    \draw[dashed] (-3*\f,0) -- (-3*\f,-1.5);
    \draw[|->] (0,-1.25) -- node[anchor=north]{$o$} (-3*\f,-1.25);
    \draw[dashed] (1.5*\f,-0.7) -- ++(-90:0.8);
    \draw[|->] (0,-1.25) -- node[anchor=north]{$i$} (1.5*\f,-1.25);

    \draw[DarkRed,<-,line width=1.5] (1.6*\f,-0.7) --
    ++(-45:1.2) node[anchor=north,
      font=\scriptsize,
      text width=1in]{Rays emerge from image just like an object and
      could be imaged by a downstream lens};

    \begin{scope}[shift={(1,-5)}]
      \fill[DarkSlateBlue!25!white] (0.2,1.5) arc(16:-16:5.442) --
      (-0.2,-1.5) arc(204:156:3.688) -- cycle;
      \draw (-6,0) -- (4,0);
      \draw[->] (3.169,0) -- node[anchor=south]{$R_{1}$} ++(164:3.688);
      \draw[->] (-5.031,0) -- node[anchor=north]{$R_{2}$} ++ (-12:5.442);
      \draw[dashed] (-5.031,0) -- ++(16:5.442);
      \draw[dashed] (3.169,0) -- ++(204:3.688);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec05.tex
modified: 2019-02-07 00:11:45
domain: p134
source:
  \begin{tikzpicture}[scale=1.,
      kvec/.style={->,line width=1.25pt,color=DarkBlue},
    ]
    \def\len{3}
    \def\wid{4}
    \def\ang{40}
    \def\refr{59}
    \def\tlen{2.25}
    \def\bgnd{yellow!30!white} % background color of upper medium
    \def\Bgnd{green!30}            % background color of lower medium

    % arcs for the k vectors
    \fill[fill=\bgnd] (-\wid,0) rectangle (\wid,\len);
    \fill[fill=\Bgnd] (-\wid,0) rectangle (\wid,-\len);
    \draw[color=DarkRed,dashed] (\len,0) arc[radius=\len,start angle=0,end
        angle=180];
    \draw[color=DarkRed,dashed] (\len*0.75,0) arc[radius=\len*0.75,start angle=0,end angle=-180];

    % axes and materials

    \draw[color=black!50!white,->] (-\wid,0) -- (\wid+0.25,0)
    node[anchor=west]{$x$};
    \draw[color=SlateBlue!70,dashed,->] (0,-\len) -- (0,\len+0.25)
    node[anchor=south]{$z$};

    \node at (-0.85*\wid,0.9*\len) {$\mu_{1}, \epsilon_{1}$};
    \node at (-0.85*\wid,-0.9*\len) {$\mu_{2}, \epsilon_{2}$};
    \node at (0.9*\wid,-0.9*\len) {TE};

    \draw[dashed] (-1.93, 0.85*\len) -- (-1.93, -0.4);
    \draw[DarkRed,->,line width=1] (-1.93,-0.02) --node[anchor=north]{$k_{x}$}
    (0,-0.02);



    % incident beam


    \coordinate (A) at (90+\ang:0.75*\len); % field anchor
    \node[anchor=west,fill=\bgnd] at (A) {\;\;$E_{\rm i}$};
    \draw[kvec,<-] (0,0) --node[anchor=east]{$k_{\rm i}$} ++(90+\ang:\len);
    \draw[force] (A) -- ++(\ang:1) node[anchor=south,fill=\bgnd] {$H_{\rm  i}$};
    \filldraw[fill=\bgnd] (A) circle[radius=0.15];
    \draw[line width=1.5] (A) +(45:0.15) -- ++(225:0.15) (A) +(135:0.15) -- ++(-45:0.15);


    % reflected beam
    \draw[kvec] (0,0) --node[anchor=north west]{$k_{\rm r}$} ++(90-\ang:\len)
    coordinate (kr);
    \coordinate (B) at (90-\ang:0.75*\len);
    \draw[force] (B) -- ++(180-\ang:1) node[anchor=south,fill=\bgnd] {$H_{\rm  r}$};
    \filldraw[fill=\bgnd] (B) circle[radius=0.15];
    \draw[line width=1.5] (B) +(45:0.15) -- ++(225:0.15) (B) +(135:0.15) --
    ++(-45:0.15);

    \node[anchor=east] at (B) {$E_{\rm r}$\;\;};
    \draw[DarkRed,<-,line width=1] (kr) -- node[fill=\bgnd,anchor=west]{$w_{1}$}
    ++(-90:2.3);

    % refracted beam
    \draw[kvec] (0,0) -- ++(-90+\refr:\tlen) node[anchor=north]{$k_{\rm t}$}
    coordinate (kt);
    \coordinate (C) at (-90+\refr:0.35*\len);
    \draw[force] (C) -- ++(\refr:1) node[anchor=west] {$H_{\rm  t}$};
    \filldraw[fill=\Bgnd] (C) circle[radius=0.15];
    \draw[line width=1.5] (C) +(45:0.15) -- ++(225:0.15) (C) +(135:0.15) -- ++(-45:0.15);
    \node[anchor=north east] at (C) {$E_{\rm t}$};

    \draw[DarkRed,<-|,line width=1] (kt) --
    node[fill=\Bgnd,anchor=west]{$w_{2}$} ++(90:1.165);

    % label angles
    \def\arcrad{0.4}
    \draw (90:\arcrad) arc(90:130:\arcrad);
    \node at (110:\arcrad+0.3) {$\theta_{\rm i}$};
    \draw (-90:\arcrad) arc(-90:-35:\arcrad);
    \node at (-60:\arcrad+0.2) {$\theta_{\rm t}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec05.tex
modified: 2019-02-07 00:11:45
domain: p134
source:
  \begin{tikzpicture}[scale=.67,
      blabel/.style= {DarkRed,font=\sffamily},
      olabel/.style={DarkGreen,font=\sffamily},
      beam/.style={DarkRed,line width=2pt}
    ]

    \def\beam{2cm}
    \def\bsthick{0.25cm}

    % source
    \begin{scope}[shift={(-2.5*\beam,0.5)}]
      \node[star, star points=12,star point height=0.5,star point
        ratio=3,fill,DarkRed] at (0,0){};
      \node[DarkRed,anchor=south] at (0,0.75) {\textsf{source}};
    \end{scope}
    \node[blabel,anchor=south west] at (-2*\beam,0.65) {$\mathbf{E}_{\rm in}(t)$};

    \draw[beam] (-2*\beam,0.5) -- (2.5*\beam,0.5) ; % incident beam
    \draw[beam,->] (-1.25*\beam,0.5) -- +(0:.25); % arrows for incident beam
    \draw[beam,->] (1.5*\beam,0.5) --+(0:.25);
    \draw[beam] (0.5,0.5) -- (0.5,2*\beam);  % towards top mirror
    \draw[beam,->] (0.5,\beam) -- +(90:0.5);

    % beamsplitter
    \begin{scope}[shift={(-1.414*\bsthick,0)},rotate=45]
      \filldraw[fill=gray!20,opacity=0.5] (-1*\beam,0) rectangle (1.*\beam,-\bsthick);
      \draw[line width=1.5pt] (-\beam,-\bsthick) -- (\beam,-\bsthick);
      \draw[olabel,<-] (-1.1*\beam,0) -- ++(180:0.6) node[anchor=north east] {beam splitter};
    \end{scope}

    \onslide<2->{
      % beams

      % top mirror
      \filldraw[fill=gray!30] (-\beam,2*\beam) rectangle (\beam,2*\beam+\bsthick);
      \draw[line width=2] (-\beam,2*\beam) -- +(0:2*\beam);
      \node[anchor=west] at (\beam,2*\beam+0.5*\bsthick) {\large $M_{2}$};

      % right mirror
      \begin{scope}[shift={(2.5*\beam,0)}]
        \filldraw[fill=gray!30] (0,-\beam) rectangle (\bsthick,\beam);
        \draw[line width=2] (0,-\beam) -- ++(90:2*\beam);
        \node[anchor=south] at (0.5*\bsthick, \beam) {\large $M_{1}$};
      \end{scope}


    }

    % reflected beams
    \onslide<3->{

      \draw[beam,->] (-0.5,2*\beam) -- ++(-90:4*\beam) node[blabel,anchor=north]
      {$\mathbf{E}_{\rm out}$}; % from top mirror
      \draw[beam,->] (2.5*\beam,-0.2) -- (-2*\beam,-0.2); % from M1
      \draw[beam,->] (-0.5,\beam) -- ++(-90:0.25);
      \draw[beam,->] (1.5*\beam,-0.2) -- +(180:0.25);
      \draw[beam,->] (-0.2,-0.2) -- (-0.2,-2*\beam);
    }

    % translatable mirror
    \onslide<4->{
      \draw[beam,->] (-0.5,-0.5) -- (-2*\beam,-0.5);

      \begin{scope}[shift={(2*\beam,0)},opacity=0.25]
        \filldraw[fill=gray!30] (0,-\beam) rectangle (\bsthick,\beam);
        \draw[line width=2] (0,-\beam) -- ++(90:2*\beam);
      \end{scope}

      \draw[DarkGreen,|->] (2*\beam,-1.25*\beam) -- node[anchor=north]{$d$}
      (2.5*\beam,-1.25*\beam);

      % labels

      \begin{scope}[shift={(2.7*\beam,0)},rotate=90]
        \node[olabel,anchor=north,rotate=90] at (0,0) {translatable mirror};
      \end{scope}
    }

    % compensator
    \onslide<5->{
      \begin{scope}[shift={(1.5,0)},rotate=45]
        \filldraw[fill=gray!20,opacity=0.5] (-1.*\beam,0) rectangle (1.*\beam,-\bsthick);
        \draw[olabel,<-] (\beam,0.2) --++(45:0.6) node[anchor=south] {compensator};
      \end{scope}
    }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec05.tex
modified: 2019-02-07 00:11:45
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0,
        xmax=4,
        ymin=0,
        ymax=1.1,
        enlargelimits=false,
        width=2.5in,
        xlabel={$d$},
        ylabel={$I_{\rm out}$},
        ytick={0,1},
        xtick={0,1,2,3,4},
        xticklabels={0,$\lambda$,$2\lambda$,$3\lambda$,$4\lambda$},
      ]
      \addplot[
        domain=0:5,
        samples=801,
        line width=1pt,
        DarkRed
      ]
      {sin(360*x)^2};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec07.tex
modified: 2019-02-17 18:18:25
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-3,
        xmax=3,
        ymin=0,
        ymax=1,
        enlargelimits=false,
        width=2in,
        height=2.5in,
        xlabel={$\omega_{0}$},
        ylabel={},
        ytick={0,1},
        yticklabel=\empty,
        xtick={},
        xticklabel=\empty,
        % xticklabels{0,,$a$,,a$},
      ]
      \addplot[
        domain=-3:3,
        samples=201,
        line width=0pt,
        fill=DarkRed!25!white
      ]
      {exp(-x^2)} \closedcycle;

      \addplot[domain=1:1.2, samples=25,fill=blue!25!white,line width=0pt]
      {exp(-x^2)} \closedcycle;
      \addplot[domain=0.8:1, samples=25,fill=green!25!white,line width=0pt]
      {exp(-x^2)} \closedcycle;
      \addplot[
        domain=-3:3,
        samples=201,
        line width=2pt,
        DarkRed,
      ]
      {exp(-x^2)};

    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec07.tex
modified: 2019-02-17 18:18:25
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-100,
        xmax=100,
        ymin=-0.4,
        ymax=1.05,
        enlargelimits=false,
        width=3in,
        height=1.5in,
        xlabel={},%$\Omega$},
        ylabel={$\mathrm{sinc}(\Omega T/2)$},
        ytick={0},
        yticklabel=\empty,
        xtick={0},
        %xticklabel=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
      ]
      \addplot[
        domain=-100:-10,
        samples=101,
        line width=0.5pt,
        DarkRed
      ]
      {sin(x*180/3.14159)/x};

      \addplot[
        domain=-10:10,
        samples=100,
        line width=0.5pt,
        DarkRed
      ]
      {sin(x*180/3.14159)/x};
      \addplot[
        domain=10:100,
        samples=101,
        line width=0.5pt,
        DarkRed
      ]
      {sin(x*180/3.14159)/x};

      \draw[<-,NavyBlue] (3.14,0) --  (10,0.5) node[anchor=west]{$\frac{\pi}{T} $};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec07.tex
modified: 2019-02-17 18:18:25
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-3,
        xmax=3,
        ymin=0,
        ymax=1.05,
        enlargelimits=false,
        width=3.in,
        height=1.5in,
        xlabel={$\Omega$},
        ylabel={$|A(\Omega)|$},
        ytick={},
        yticklabel=\empty,
        xtick={0},
        %xticklabel=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
      ]
      \addplot[
        domain=-3:3,
        samples=201,
        line width=0pt,
        fill=DarkRed!10!white
      ]
      {exp(-x^2)} \closedcycle;

      \addplot[domain=0.8:1, samples=25,fill=green!25!white,line width=0pt]
      {exp(-x^2)} \closedcycle;

      \addplot[
        domain=-3:3,
        samples=201,
        line width=1pt,
        DarkRed,
      ]
      {exp(-x^2)};

      \draw[<-,DarkGreen] (0.8,0.1) -- (0.5,0.1) node[anchor=east]{$\Delta\Omega$};
      \draw[<-,DarkGreen] (1,0.1) -- (1.3,0.1);
      \draw[<-,DarkGreen] (0.9, 0.25) -- (1.5,0.6)
      node[anchor=south,text width=2cm,font=\scriptsize,
        align=center]{Averages to zero
        unless centered at 0};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec06.tex
modified: 2019-02-11 23:33:19
domain: p134
source:
  \begin{tikzpicture}[scale=1,
      energy/.style= {DarkGreen},
      Na/.style={yellow!75!black}
    ]
    \draw (0,0) -- ++(0:1) node[anchor=west]{$3s_{1/2}$};
    \node[energy,anchor=east] at (-0.25,0) {$-5.14$};

    \draw (1,4) -- ++(0:1) node[anchor=west]{$3p_{1/2}$};
    \draw (1,4.5) -- ++(0:1) node[anchor=west]{$3p_{3/2}$};

    \draw[->,Na,line width=2] (1.25,4.5)
    --node[fill=white,rotate=78]{$\SI{589.0}{nm}$}  (0.25,0);
    \draw[->,Na,line width=2] (1.75,4)
    --node[fill=white,rotate=78]{$\SI{589.6}{nm}$}  (0.75,0);

    \node[energy, anchor=east] at (-0.25,4.25) {$-3.04$};
    \draw[dashed] (0,4.25) -- ++(0:1);
    \node[rotate=90,energy] at (-0.75,2.125){Energy (eV)};

    \draw[<->,DarkGreen] (3.25,4) -- node[anchor=west,text
      width=2cm,font=\scriptsize]{spin-orbit splitting = \SI{2.1}{meV}}
    ++(90:0.5);

    \node[DarkRed, anchor=west,
      fill=DarkRed!10!white,
      draw,
      rounded corners,
      text width=3cm,
      font=\tiny] at (2.5,3.25) {There are 4 $3p_{3/2}$ states and 2
      $3p_{1/2}$ states, but the ratio of the line intensities is not 2:1. Why
      might that be?};

    \node[anchor=west,DarkRed,draw] at (2.,1)
    {\includegraphics[width=4cm]{Na_doublet_plot}};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec06.tex
modified: 2019-02-11 23:33:19
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
      xmin=0, xmax=100, ymin=0, ymax=1, enlargelimits=false,
      width=2.5in, height=2in,
      xlabel={$\tau$}, ylabel={$I_{\rm out}/I_{0}$}, ytick={0,1}, xtick={0},
      % xticklabel=\empty, xticklabels{0,,$a$,,a$},
      % axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \fill[gray!50] (48,0) rectangle (52,1);
      \addplot[DarkGreen, domain=0:100, samples=2000, line width=0.5pt,]
      {0.5*(1-cos(180*x)*cos(x))};
      \addplot[DarkRed,dashed,line width=1pt,domain=0:100,samples=50]
      {0.5*(1+cos(x))};
      \addplot[DarkRed,dashed,line width=1pt,domain=0:100,samples=50]
      {0.5*(1-cos(x))};
      \draw[<-,DarkRed,line width=1.5] (50,0.82) -- (70,0.82) node[anchor=west]{$I_{\rm out}^{(\rm
              max)}$};
      \draw[<-,DarkRed,line width=1.5] (50,0.18) -- (70,0.18) node[anchor=west]{$I_{\rm out}^{(\rm min)}$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec06.tex
modified: 2019-02-11 23:33:19
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-3,
        xmax=3,
        ymin=0,
        ymax=1.05,
        enlargelimits=false,
        width=3.in,
        height=2.5in,
        xlabel={$\Omega$},
        ylabel={$|A(\Omega)|$},
        ytick={},
        yticklabel=\empty,
        xtick={0},
        %xticklabel=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
      ]
      \addplot[
        domain=-3:3,
        samples=201,
        line width=0pt,
        fill=DarkRed!10!white
      ]
      {exp(-x^2)} \closedcycle;

      \addplot[domain=0.8:1, samples=25,fill=green!25!white,line width=0pt]
      {exp(-x^2)} \closedcycle;

      \addplot[
        domain=-3:3,
        samples=201,
        line width=1pt,
        DarkRed,
      ]
      {exp(-x^2)};

      \draw[<-,DarkGreen] (0.8,0.1) -- (0.5,0.1) node[anchor=east]{$\Delta\Omega$};
      \draw[<-,DarkGreen] (1,0.1) -- (1.3,0.1);
      \draw[<-,DarkGreen] (0.9, 0.25) -- (1.5,0.6)
      node[anchor=south,text width=2cm,font=\scriptsize,
        align=center]{Averages to zero
        unless centered at 0};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec12.tex
modified: 2019-03-04 22:33:49
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    % \onslide<1>{\atom{1}{(0,0)}{2}}
    \foreach \n in {1,2,3,4,5}{
        \onslide<\n>{\atom{\n}{(0,0)}{2}}
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec12.tex
modified: 2019-03-04 22:33:49
domain: p134
source:
  \begin{tikzpicture}[scale=0.8]

    % atoms
    \onslide<1>{
      \atom{1}{(1,0.5)}{0.5}
      \atom{1}{(3,-0.25)}{0.5}
      \atom{1}{(7,0.25)}{0.5}
      \atom{1}{(5,0)}{0.5}
      \atom{1}{(2,-0.5)}{0.5}
      \atom{1}{(4,0.4)}{0.5}
    }

    \onslide<2->{
      \atom{1}{(1,0.5)}{0.5}
      \atom{3}{(3,-0.25)}{0.5}
      \atom{3}{(7,0.25)}{0.5}
      \atom{3}{(5,0)}{0.5}
      \atom{4}{(2,-0.5)}{0.5}
      \atom{5}{(4,0.4)}{0.5}
    }

    \onslide<3->{
      \draw[line width=2pt,gray] (0,0) arc(180:200:4) coordinate (a);
      \draw[line width=2pt,gray] (0,0) arc(180:160:4);
      \draw (.04,0) arc(180:200:3.96);
      \draw (.04,0) arc(180:160:3.96);

      \node[anchor=north] at (a) {high reflector};

      \draw[line width=2pt,gray] (8,0) arc(0:20:3);
      \draw[line width=2pt,gray] (8,0) arc(0:-20:3) coordinate (b);


      % edges of the gaussian beam
      \draw[DarkRed] (0.2,1) .. controls (4,0.3) and (5,0.3)  .. (7.9,0.7);
      \draw[DarkRed] (0.2,-1) .. controls (4,-0.3) and (5,-0.3)  .. (7.9,-0.7);
    }

    \onslide<3>{
      \node[anchor=south,DarkRed] at (5,1) {gaussian beam};
      \fill[DarkRed,opacity=0.7] (5.75,1) .. controls (5.75, 0.5)
      and (6.25,0.25) .. (6.25,0) .. controls (6.25,-0.25) and
      (5.75,-0.5) .. (5.75, -1) -- cycle;
    }

    \onslide<4>{
      \node[anchor=north,text width=3cm] at (b) {output coupler  transmission $T$};
      % output beam
      \foreach \n in {-3,-2,...,3} {
          \draw[photon,->,line width=1] (8.3,\n * 0.25) -- ++(2*\n:2.5);
        }
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec12.tex
modified: 2019-03-04 22:33:49
domain: p134
source:
  \begin{tikzpicture}[scale=1.25]
    \draw[line width=2pt,gray] (0,0) arc(180:200:4) coordinate (a);
    \draw[line width=2pt,gray] (0,0) arc(180:160:4);
    \draw (.04,0) arc(180:200:3.96);
    \draw (.04,0) arc(180:160:3.96);


    %      \node[anchor=north] at (a) {high reflector};
    \node[anchor=south, rotate=90] at (0,0) {high reflector};

    \draw[line width=2pt,gray] (8,0) arc(0:20:3);
    \draw[line width=2pt,gray] (8,0) arc(0:-20:3) coordinate (b);
    \node[anchor=north,text width=3cm, rotate=90] at (8,0)
    {output coupler  transmission $T$};

    % edges of the gaussian beam
    \draw[DarkRed] (0.2,1) .. controls (4,0.3) and (5,0.3)  .. (7.9,0.7);
    \draw[DarkRed] (0.2,-1) .. controls (4,-0.3) and (5,-0.3)  .. (7.9,-0.7);

    % standing waves?
    % they go between 0 and 8
    \onslide<2->{
      \standing{0}{20}{DarkGreen}
      \node[DarkGreen] at (4,-1) {$\displaystyle n \frac{\lambda}{2} = L \SO
          \lambda_{n} = \frac{2L}{n} $};
    }
    \onslide<3->{
      \standing{0.3}{21}{DarkBlue}
      \standing{-0.3}{19}{DarkRed}
    }


  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec12.tex
modified: 2019-03-04 22:33:49
domain: p134
source:
  \begin{tikzpicture}[scale=0.5]
    \begin{scope}[shift={(0,0)}]
      %    \onslide<2>{
      % If you want no plot frame, just arrows for axes
      % use axis x line=bottom, axis y line=left, axis line style={line width=1.25}
      % and maybe xtick=\empty, ytick=\empty
      \def\R{0.94}
      \begin{axis}[
          xmin=-800,
          xmax=800,
          ymin=0,
          % ymax=1,
          %enlargelimits=false,
          width=5in,
          height=2.5in,
          xlabel={$\phi$},
          ylabel={$\mathcal{T}$},
          ytick={},
          yticklabel=\empty,
          xtick={-720,-360,0,360,720},
          xticklabels={$-4\pi$,$-2\pi$,$0$,$2\pi$,$4\pi$},
          % xticklabels{0,,$a$,,a$},
          axis x line=bottom,
          axis y line=center
        ]
        \addplot[
          DarkGreen,
          domain=-800:800,
          samples=1001,
          line width=1pt,
        ]
        {(1-\R)^2 /( (1-\R)^2 + 4*\R*(sin(x/2)^2))};
        \addplot[
          DarkBlue,
          domain=-800:800,
          samples=1001,
          line width=1pt,
        ]
        {(1-2*\R)^2 /( (1-2*\R)^2 + 4*2*\R*(sin(x/2)^2))};
        \addplot[
          DarkRed,
          domain=-800:800,
          samples=1001,
          line width=1pt,
        ]
        {(1-1.5*\R)^2 /( (1-1.5*\R)^2 + 4*1.5*\R*(sin(x/2)^2))};

      \end{axis}
      %      }
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec03a.tex
modified: 2019-01-27 15:18:31
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \node[anchor=south west, inner sep=0] at (0,0) {
      \includegraphics[width=0.675\textwidth]{lec04fit02} };
    \draw[DarkRed,ultra thick,rounded corners] (3.6,5.95) rectangle
    +(3.6,0.8);
    \node[DarkRed,anchor=north west,text width=4cm] at (7.5,6.75) {Select the wave containing the uncertainties};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: scrap.tex
modified: 2019-02-10 20:26:42
domain: p134
source:
  \begin{tikzpicture}[scale=1.25]
    \def\ang{25}
    \def\rad{3}
    \def\right{6}
    \fill[color=gray!25!white] (0,0) arc(180:180-\ang:\rad)
    -- ++(0:\right) coordinate (A) -- (\right,0) -- cycle;
    \fill[color=gray!25!white] (0,0) arc(180:180+\ang:\rad)
    -- ++(0:\right) coordinate (B) -- (\right,0) -- cycle;
    \fill[color=gray!25!white] (\right,0) -- (A) -- (B) -- cycle;
    \draw (-3,0) -- (\right+0.5,0);

    % Show center of curvature
    \draw[dashed] (\rad,0) -- ++(160.5:5.5);

    \coordinate (a) at (0.2,1);
    \draw[DarkRed,->,line width=1.5] (-3,1) -- (a) -- (5,0);
    \begin{scope}[shift={(a)}]
      \draw (180:1) arc(180:160:1);
      \node at (170:1.35){$\theta_{1}$};
      \draw[dashed,DarkSlateGray] (0,0) -- ++(0:3);
      \draw (-20:2.25) arc(-20:-12:2.25);
      \node at (-16:2.5) {$\theta_{2}$};
      \draw (0:1.75) arc(0:-12:1.75);
      \node[anchor=west] at (-6:1.9) {$\theta_{1}-\theta_{2}$};
    \end{scope}

    \node[anchor=south east] at (B) {$n_{2}$};
    \node at (-2.5,-1.2) {$n_{1}$};

    \draw[coord] (-2.5,0) --node[anchor=east]{$y$} (-2.5,1);
    \node at (1.4,0.4){$R$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec08.tex
modified: 2019-02-18 23:08:10
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-3,
        xmax=3.3,
        ymin=0,
        ymax=1.1,
        enlargelimits=false,
        width=2in,
        height=2in,
        xlabel={$\tau$},
        ylabel={$\half[1 - \Re \gone]$},
        ytick={\empty},
        xtick={0},
        xticklabel={0},
        % xticklabels{0,,$a$,,a$},
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1}
      ]
      \addplot[
        DarkRed,
        domain=-3:3,
        samples=201,
        line width=1pt,
      ]
      {(1+exp(-0.5*x^2))/2};
      \addplot[
        DarkRed,
        domain=-3:3,
        samples=201,
        line width=1pt,
      ]
      {(1-exp(-0.5*x^2))/2};
      \addplot[DarkSlateBlue,
        domain=-3:3,
        samples=2001,
        line width=0.5pt,
      ]
      {0.5 + 0.5*cos(2000*x)*exp(-0.5*x*x)};

      %       \draw[DarkGreen,<->,line width=1.5] (-0.886,0.6)
      %       --node[anchor=north]{$\tau_{\rm coh} $} (0.886,0.6);
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec08.tex
modified: 2019-02-18 23:08:10
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-3,
        xmax=3.3,
        ymin=0,
        ymax=1.1,
        enlargelimits=false,
        width=3in,
        height=1.5in,
        xlabel={},
        ylabel={$V(\tau)$},
        ytick={\empty},
        xtick={\empty},
        xticklabel=\empty,
        % xticklabels{0,,$a$,,a$},
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
      ]
      \addplot[
        DarkRed,
        domain=-3:3,
        samples=201,
        line width=1pt,
      ]
      {exp(-0.5*x^2)};

      \draw[DarkGreen,<->,line width=1.5] (-0.886,0.6)
      --node[anchor=north]{$\tau_{\rm coh} $} (0.886,0.6);
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/lec
filename: lec09.tex
modified: 2019-02-20 22:26:59
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) node[anchor=east]{$\ket{g}$} --(1,0);
    \draw[line width=3,gray] (0,2) node[anchor=east,black]{$\ket{e}$} --
    (1,2);
    \draw[DarkGreen,line width=3,->] (0.5,0) -- (0.5,2);
    \node at (0.5,-0.6) {$t = 0$};

    \begin{scope}[shift={(2.5,0)}]
      \draw (0,0) node[anchor=east]{$\ket{g}$} --(1,0);
      \draw[line width=3,gray] (0,2) node[anchor=east,black]{$\ket{e}$} --
      (1,2);
      \draw[DarkGreen,photon,->] (0.5,2) --node[anchor=west]{$\omega$} (0.5,0);
      \node at (0.5,-0.6) {$t$};

    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/notes
filename: coherence.tex
modified: 2019-02-17 16:14:42
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \def\rad{2}
    \draw[->,DarkSlateBlue] (180:1.15*\rad) -- (0:1.15*\rad) node[anchor=north]{$x$} ;
    \draw[->,DarkSlateBlue] (0,0) -- (90:1.15*\rad) node[anchor=east]{$y$};
    \fill (0,0) circle[radius=0.05];
    %    \draw[dashed] (0:\rad) arc(0:180:\rad);
    \draw[line width=1.5,opacity=0.5,gray] (180:\rad) -- (180:0.1)
    arc(180:360:0.1)
    -- (0:\rad) arc(0:180:\rad);
    \draw[->,DarkGreen] (0,0) --node[anchor=south east]{$R$} (30:\rad);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/notes
filename: coherence.tex
modified: 2019-02-17 16:14:42
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-100,
        xmax=100,
        ymin=-0.4,
        ymax=1.05,
        enlargelimits=false,
        width=4in,
        height=1.5in,
        xlabel={},%$\Omega$},
        ylabel={$\mathrm{sinc}(\Omega T/2)$},
        ytick={0},
        yticklabel=\empty,
        xtick={0},
        %xticklabel=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
      ]
      \addplot[
        domain=-100:-10,
        samples=101,
        line width=0.5pt,
        DarkRed
      ]
      {sin(x*180/3.14159)/x};

      \addplot[
        domain=-10:10,
        samples=100,
        line width=0.5pt,
        DarkRed
      ]
      {sin(x*180/3.14159)/x};
      \addplot[
        domain=10:100,
        samples=101,
        line width=0.5pt,
        DarkRed
      ]
      {sin(x*180/3.14159)/x};

      \draw[<-,NavyBlue] (3.14,0) --  (10,0.5) node[anchor=west]{$\frac{\pi}{T} $};
    \end{axis}



    % If you want no plot frame, just arrows for axes
    % use axis x line=bottom, axis y line=left, axis line style={line width=1.25}
    % and maybe xtick=\empty, ytick=\empty
    \begin{scope}[shift={(0,-3)}]
      \begin{axis}[
          xmin=-3,
          xmax=3,
          ymin=0,
          ymax=1.05,
          enlargelimits=false,
          width=4.in,
          height=1.5in,
          xlabel={$\Omega$},
          ylabel={$|A(\Omega)|$},
          ytick={},
          yticklabel=\empty,
          xtick={0},
          %xticklabel=\empty,
          axis x line=bottom,
          axis y line=left,
          axis line style={line width=1.25}
        ]
        \addplot[
          domain=-3:3,
          samples=201,
          line width=0pt,
          fill=DarkRed!10!white
        ]
        {exp(-x^2)} \closedcycle;

        \addplot[domain=0.8:1, samples=25,fill=green!25!white,line width=0pt]
        {exp(-x^2)} \closedcycle;

        \addplot[
          domain=-3:3,
          samples=201,
          line width=1pt,
          DarkRed,
        ]
        {exp(-x^2)};

        \draw[<-,DarkGreen] (0.8,0.1) -- (0.5,0.1) node[anchor=east]{$\Delta\Omega$};
        \draw[<-,DarkGreen] (1,0.1) -- (1.3,0.1);
        \draw[<-,DarkGreen] (0.9, 0.25) -- (1.5,0.6)
        node[anchor=south,text width=2cm,font=\scriptsize,
          align=center]{Averages to zero
          unless centered at 0};
      \end{axis}
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2019/notes
filename: statistics.tex
modified: 2019-01-13 04:16:06
domain: p134
source:
  \begin{tikzpicture}[scale=0.9]
    \begin{axis}[
        ymin=0,
        ymax=0.5,
        enlargelimits=false,
        height=2in,
        width=3in,
        xlabel={$x$},
        ylabel={$P(x)$},
        xticklabels={,,}
      ]
      \addplot[domain=1:7, samples=80, line width=0pt, fill=red!60!white]
      {1/sqrt(2*pi) / exp((x-4)^2 / 2)} \closedcycle;

      \addplot[domain=2:6, samples=60, line width=0pt, fill=red!40!white]
      {1/sqrt(2*pi) / exp((x-4)^2 / 2)} \closedcycle;

      \addplot[domain=3:5, samples=40, line width=0pt, fill=red!20!white]
      {1/sqrt(2*pi) / exp((x-4)^2 / 2)} \closedcycle;

      \draw[dashed,color=gray] (5,0) -- (5,0.4)
      node[anchor=south]{\color{black}$\scriptsize{\mu+\sigma}$} ;
      \draw[dashed,color=gray] (3,0) -- (3,0.4)
      node[anchor=south]{\color{black} $\scriptsize{\mu-\sigma}$};
      \draw[dashed,color=gray] (6,0) -- (6,0.325)
      node[anchor=south]{\color{black}$\scriptsize{\mu+2\sigma}$} ;
      \draw[dashed,color=gray] (2,0) -- (2,0.325)
      node[anchor=south]{\color{black} $\scriptsize{\mu-2\sigma}$};
      \draw[dashed,color=gray] (4,0) -- (4,0.4)
      node[anchor=south]{\color{black}$\mu$};

      \addplot[
        domain=0:8,
        samples=100,
        line width=1pt,
        color=red!65!black
      ]
      {1/sqrt(2*pi) / exp((x-4)^2 / 2)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec02.tex
modified: 2020-01-25 03:14:23
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \node[anchor=south west,inner sep=0] at (0,0) {
      \includegraphics[width=0.6\textwidth]{lec04fit01}
    };

    \onslide<2>{
      \coordinate (A) at (1.,5.8);
      \draw[DarkRed,ultra thick,rounded corners] (A) rectangle +(2.9,0.4);
      \node[anchor=north east,text width=4cm,DarkRed] at (0.5,6)
      {\small Either select a function from the menu, or click to define a
        \textbf{New Fit Function\ldots}};
      \draw[DarkGreen,ultra thick,rounded corners] (1.4,4.4) rectangle +(2.,0.4);
      \draw[DarkGreen,ultra thick,rounded corners] (2.1,2.45) rectangle +(3.2,1);
    }

    \onslide<3>{
      \draw[DarkRed,ultra thick,rounded corners] (3.5,6.5) rectangle +(1.4,0.4);
      \node[DarkRed,anchor=west,text width=4cm] at (6.5,5.5) {\small Select the
        dependent variable and the independent variable (or \_calculated\_)};
    }

    \onslide<4>{
      \coordinate (A) at (5.8,6.55);
      \draw[DarkBlue,ultra thick,rounded corners] (A) rectangle +(1.5,0.4);
      \node[DarkBlue,anchor=west,text width=4cm] at (6.5,5.3) {\small
        Checking \textbf{From Target} limits the waves you can pick to those on
        the top graph};
    }


  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec02.tex
modified: 2020-01-25 03:14:23
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \node[anchor=south west, inner sep=0] at (0,0) {
      \includegraphics[width=0.675\textwidth]{lec04fit04}};
    \draw[DarkRed,ultra thick,rounded corners] (0.8,5.75) rectangle +(3,0.35);
    \draw[DarkRed,ultra thick,rounded corners] (1.3,5.25) rectangle
    +(2.5,0.35);
    \node[DarkRed,text width=4cm] at (10.2,5.5) {
      Be sure to add a textbox and set the Textbox Preferences to include the
      function name.
    };
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec14.tex
modified: 2020-02-21 07:19:34
domain: p134
source:
  \begin{tikzpicture}[scale=1.25]
    \draw[line width=2pt,gray] (0,0) arc(180:200:4) coordinate (a);
    \draw[line width=2pt,gray] (0,0) arc(180:160:4);
    \draw (.04,0) arc(180:200:3.96);
    \draw (.04,0) arc(180:160:3.96);


    % %      \node[anchor=north] at (a) {high reflector};
    \node[anchor=south, rotate=90] at (0,0) {high reflector};
    \draw[line width=2pt,gray] (8,0) arc(0:20:3);
    \draw[line width=2pt,gray] (8,0) arc(0:-20:3) coordinate (b);
    \node[anchor=north,text width=3cm, rotate=90] at (8,0)
    {output coupler  transmission $T$};

    % edges of the gaussian beam
    \draw[DarkRed] (0.2,1) .. controls (4,0.3) and (5,0.3)  .. (7.9,0.7);
    \draw[DarkRed] (0.2,-1) .. controls (4,-0.3) and (5,-0.3)  .. (7.9,-0.7);

    %       % standing waves?
    %       % they go between 0 and 8
    \onslide<2->{

      \standing{0}{20}{DarkGreen}

      \node[DarkGreen] at (4,-1) {$\displaystyle n \frac{\lambda}{2} = L \SO
          \lambda_{n} = \frac{2L}{n} $};
    }
    \onslide<3->{
      \standing{0.3}{21}{DarkBlue}
      \standing{-0.3}{19}{DarkRed}
    }


  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec14.tex
modified: 2020-02-21 07:19:34
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \draw[->] (-6,0) -- (6,0) node[anchor=north east]{$\nu$};
    \foreach \x in {-5,-4,...,5}{
        \draw[line width=2,Red] (\x,0) -- ++(0,2);
      }
    \foreach \n in {1, 2, ..., 5} {
        \node at (\n,-0.3) {$n+\n$};
        \node at (-\n,-0.3){$n-\n$};
      }
    \node at (0,-0.3) {$n$};
    \node at (0,-1){$n \approx 1,100,000$};

    \node[Red,draw,font=\Large] at (-4,-1.5){$\nu_{n} = \frac{c}{2L} n$};
    \node[Red,draw,font=\Large] at (4,-1.5){$\Delta\nu_{\rm FSR} =
        \frac{c}{2L} \approx \SI{500}{MHz}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec14.tex
modified: 2020-02-21 07:19:34
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[shift={(0,0)}]
      \def\R{0.94}
      \begin{axis}[
          xmin=-800,
          xmax=800,
          ymin=0,
          % ymax=1,
          % enlargelimits=false,
          width=\columnwidth,
          height=1.5in,
          xlabel={$\phi$},
          ylabel={$\mathcal{T}$},
          ytick={},
          yticklabel=\empty,
          xtick={-720,-360,0,360,720},
          xticklabels={$-4\pi$,$-2\pi$,$0$,$2\pi$,$4\pi$},
          % xticklabels{0,,$a$,,a$},
          axis x line=bottom,
          axis y line=center
        ]
        \addplot[
          DarkGreen,
          domain=-800:800,
          samples=1001,
          line width=1pt,
        ]
        {(1-\R)^2 /( (1-\R)^2 + 4*\R*(sin(x/2)^2))};
        \addplot[
          blue,
          domain=-800:800,
          samples=1001,
          line width=1pt,
        ]
        {(1-2*\R)^2 /( (1-2*\R)^2 + 4*2*\R*(sin(x/2)^2))};
        \addplot[
          Red,
          domain=-800:800,
          samples=1001,
          line width=1pt,
        ]
        {(1-1.5*\R)^2 /( (1-1.5*\R)^2 + 4*1.5*\R*(sin(x/2)^2))};
      \end{axis}
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: geometric-notes.tex
modified: 2020-01-17 18:43:47
domain: p134
source:
  \begin{tikzpicture}[scale=0.6]
    \shade[shading=radial,inner color=blue!50!white] (0,0)
    circle[radius=2];
    \fill[color=red] (0,0) circle[radius=0.1];
    \shade[shading=radial,inner color=blue!50!white] (-0.1,0)
    circle[radius=2];
    \fill[color=red] (0.1,0) circle[radius=0.1];
    \draw[->,line width=3,gray] (-1,2) -- +(0:2) node[anchor=south]{$E$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: geometric-notes.tex
modified: 2020-01-17 18:43:47
domain: p134
source:
  \begin{tikzpicture}[scale=1.25]
    \fill[red] (0,0) circle[radius=0.1];
    \foreach \a in {0,30,...,330} {
        \node[blue,font=\tiny] at (\a:0.2){$-$};
        \node[red,font=\tiny] at (\a:0.8){$+$};
        \draw[DarkGreen, ->] (\a:0.3) -- ++(\a:0.4);
      }
    \node at (0,-1.25) {$\rho_{\rm b} = -\div\vb{P}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: geometric-notes.tex
modified: 2020-01-17 18:43:47
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    % metal plates
    \def\wid{5}
    \node[anchor=west] at (\wid,1) {$\vb{E}_{\rm in} = \frac{\vb{E}_{\rm
            app}}{\epsilon}$};
    \draw[gray!50!white,line width=4pt] (0,0) -- (\wid,0) (0,2) -- (\wid,2) coordinate (A);
    \fill [yellow!20!white] (0,0.3) rectangle (\wid,1.7);
    \foreach \x in {0.25,0.5,...,4.75}{
        \node[color=red,font=\small] at (\x,2) {$+$};
        \node[color=blue,font=\small] at (\x,0) {$-$};
        \node[color=blue,font=\tiny] at (\x,1.6){$-$};
        \node[color=red,font=\tiny] at (\x,0.4){$+$};
        \draw[->,DarkGreen!50,line width=1.5pt] (\x,1.4) -- (\x,0.6);
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: geometric-notes.tex
modified: 2020-01-17 18:43:47
domain: p134
source:
  \begin{tikzpicture}[scale=1.,
      kvec/.style={->,line width=1.25pt,color=DarkBlue},
    ]
    \def\len{3}
    \def\wid{4}
    \def\ang{40}
    \def\refr{59}
    \def\tlen{2.25}
    \def\bgnd{yellow!20!white} % background color of upper medium
    \def\Bgnd{green!20}            % background color of lower medium

    % arcs for the k vectors
    \fill[fill=\bgnd] (-\wid,0) rectangle (\wid,\len);
    \fill[fill=\Bgnd] (-\wid,0) rectangle (\wid,-\len);

    \draw[color=DarkRed,dashed] (\len,0) arc[radius=\len,start angle=0,end
        angle=180];

    \draw[color=DarkRed,dashed] (\len*0.75,0) arc[radius=\len*0.75,start angle=0,end angle=-180];

    % axes and materials

    \draw[color=black!50!white,->] (-\wid,0) -- (\wid+0.25,0)
    node[anchor=west]{$x$};
    \draw[color=SlateBlue!70,dashed,->] (0,-\len) -- (0,\len+0.25)
    node[anchor=south]{$z$};

    \node at (-0.85*\wid,0.9*\len) {$\mu_{1}, \epsilon_{1}$};
    \node at (-0.85*\wid,-0.9*\len) {$\mu_{2}, \epsilon_{2}$};

    \draw[dashed] (-1.93, 0.85*\len) -- (-1.93, -0.4);
    \draw[DarkRed,->,line width=1] (-1.93,-0.02) --node[anchor=north]{$k_{x}$}
    (0,-0.02);

    % incident beam

    \coordinate (A) at (90+\ang:0.75*\len); % field anchor

    \draw[kvec,<-] (0,0) --node[anchor=east]{$k_{\rm i}$} ++(90+\ang:\len);

    % reflected beam
    \draw[kvec] (0,0) --node[anchor=north west]{$k_{\rm r}$} ++(90-\ang:\len)
    coordinate (kr);
    \coordinate (B) at (90-\ang:0.75*\len);

    % refracted beam

    \draw[kvec] (0,0) -- node[anchor=north]{$k_{\rm t}$} ++(-90+\refr:\tlen)
    coordinate (kt);
    \coordinate (C) at (-90+\refr:0.35*\len);

    \draw[kvec,DarkRed] (0,0) -- node[anchor=south]{$k_{x}$} (1.93,0);
    \draw[dashed] (kr) -- ++(-90:4);  % marking k_x

    % label angles
    \def\arcrad{0.4}
    \draw (90:\arcrad) arc(90:130:\arcrad);
    \node at (110:\arcrad+0.3) {$\theta_{\rm i}$};

    \draw (-90:\arcrad) arc(-90:-35:\arcrad);
    \node at (-60:\arcrad+0.2) {$\theta_{\rm t}$};
    \draw[DarkRed,<-,line width=1] (kr) -- node[fill=\bgnd,anchor=west]{$w_{1}$}
    ++(-90:2.3);

    \draw[DarkRed,<-|,line width=1] (kt) --
    node[fill=\Bgnd,anchor=west]{$w_{2}$} ++(90:1.165);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: geometric-notes.tex
modified: 2020-01-17 18:43:47
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    % the lens
    \fill[DarkSlateBlue!25!white] (0.1,2) arc(12:-12:9.62) --
    (-0.1,-2) arc(192:168:9.62) -- cycle;

    % the optical axis
    \draw (-5,0) -- (5,0);

    % lens arrow
    % \draw[gray,line width=3,<->] (0,-2.5) -- (0,2.5);
    \draw[gray, <->] (0,-2.5) -- (0,2.5);

    % kink point
    \coordinate (A) at (0,1.5);
    \draw[DarkRed,line width=1.5] (-4,0) --  (A) -- (2.5,0);

    % arrows
    \draw[DarkRed,line width=1.5,->] (-4,0) -- (-2,0.75);
    \draw[DarkRed,line width=1.5,->] (A) -- (1.25,0.75);

    \draw (-3,0) arc(0:20:1);
    \node at (-2.7,0.2){$\alpha_{1}$};
    \draw (1.8,0) arc(180:148:0.7);
    \node at (1.5,0.2){$\alpha_{2}$};
    \node[anchor=east] at (0,0.8){$y$};
    \draw[<->,DarkGreen] (-4,-0.3) -- node[anchor=north]{$o$} (0,-0.3);
    \draw[<->,DarkGreen] (0,-0.3) -- node[anchor=north]{$i$} (2.5,-0.3);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: geometric-notes.tex
modified: 2020-01-17 18:43:47
domain: p134
source:
  \begin{tikzpicture}[scale=0.85]
    \draw (-5,0) -- (5,0); % symmetry line
    \draw[gray,line width=3,<->] (0,-2) -- (0,2);
    \def\f{1.5}

    \foreach \y in {0.25,0.5,...,1.25}{
        \draw[DarkRed,->] (-4,\y) -- (0,\y) -- ($(0,\y)!1.5!(\f,0)$);
      }
    \begin{scope}[shift={(\f,0)}]
      \draw[<-,DarkRed] (45:0.1) -- ++(45:0.5) node[anchor=west]{image focal
        point};
    \end{scope}
    \draw[<->,DarkGreen] (0,1.3) -- node[anchor=south]{$f$} (\f,1.3);


    \foreach \y in {0.25,0.5,...,1.25}{
        \draw[DarkBlue,->] (-\f,0) -- (0,-\y) -- (4,-\y);
      }
    \draw[<->,DarkGreen] (-\f,-1.3) -- node[anchor=north]{$f$} (0,-1.3);
    \draw[DarkGreen,dashed] (-\f,.25) -- ++(-90:1.75);
    \draw[DarkGreen,dashed] (\f, -0.25) -- ++ (90:1.75);

    % focal points
    \foreach \x in {-\f,\f}{ \filldraw[fill=yellow] (\x,0) circle[radius=0.05]; }

    \begin{scope}[shift={(-\f,0)}]
      \draw[<-,DarkGreen] (-135:0.1) -- ++(-135:0.5)
      node[anchor=east]{object focal point};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: geometric-notes.tex
modified: 2020-01-17 18:43:47
domain: p134
source:
  \begin{tikzpicture}[scale=0.85]
    \def\f{1.5}
    %   \begin{scope}[shift={(0,-4.5)}]

    \draw (-5,0) -- (5,0); % symmetry line
    \draw[gray,line width=3,<->] (0,-2) -- (0,2);


    % principal rays
    \foreach \y in {-0.5, 0, 1}{
        \draw[DarkGreen,->,line width=1.25] (-3*\f,1) -- (0,\y) -- ($(0,\y)!1.5!(1.5*\f,-0.5)$);
      }
    % focal points
    \foreach \x in {-\f,\f}{
        \filldraw[fill=yellow] (\x,0) circle[radius=0.05];
      }

    \draw[DarkGreen,line width=3,<-] (-3*\f,1) -- ++(-90:1);
    \draw[DarkGreen,line width=1.5,<-] (1.5*\f,-.5) --++(90:0.5);

    \draw[dashed] (-3*\f,0) -- (-3*\f,-1.5);
    \draw[|->] (0,-1.25) -- node[anchor=north]{$o$} (-3*\f,-1.25);
    \draw[dashed] (1.5*\f,-0.7) -- ++(-90:0.8);
    \draw[|->] (0,-1.25) -- node[anchor=north]{$i$} (1.5*\f,-1.25);

    \draw[DarkRed,<-,line width=1.5] (1.6*\f,-0.7) --
    ++(-60:1.2) node[anchor=north,
      font=\small,
      text width=1.2in]{Rays emerge from image just like an object and
      could be imaged by a downstream lens};
    %  \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: geometric-notes.tex
modified: 2020-01-17 18:43:47
domain: p134
source:
  \begin{tikzpicture}[
      scale=1,
      ray/.style={DarkRed, line width=1.5pt,->}
    ]
    \def\f{1.5} % focal length
    \draw (-2,0) -- (3,0); % symmetry line

    % "lens"
    \draw[gray,line width=3,<->] (0,-2) -- (0,2);



    % \foreach \y in {-1, -0.5, ..., 1.}{
    %   \draw[DarkGreen,->] (-3*\f,1) -- (0,\y) -- ($(0,\y)!1.5!(1.5*\f,-0.5)$);
    %   \draw[DarkGreen,line width=3,<-] (-3*\f,1) -- ++(-90:1);
    %   \draw[DarkGreen,line width=1.5,<-] (1.5*\f,-.5) --++(90:0.5);
    %    }
    %    \draw[dashed] (-3*\f,0) -- (-3*\f,-1.5);
    %    \draw[|->] (0,-1.25) -- node[anchor=north]{$o$} (-3*\f,-1.25);
    %    \draw[dashed] (1.5*\f,-0.7) -- ++(-90:0.8);
    %    \draw[|->] (0,-1.25) -- node[anchor=north]{$i$} (1.5*\f,-1.25);

    % object distance
    \draw[|->,DarkSlateGray] (0,-0.25) -- node[anchor=north]{$o$} ++(180:0.5*\f);
    \draw[|->,DarkSlateGray] (0,-0.75) -- node[anchor=north]{$-|i|$} ++(180:\f);

    \draw[|->,DarkSlateGray] (0,-2.2) -- node[anchor=north]{positive $o$}
    ++(180:2.5);
    \draw[|->,DarkSlateGray] (0,-2.2) -- node[anchor=north]{positive $i$}
    ++(0:2.5);
    % Object
    \draw[ray,line width=2pt] (-\f/2,0) -- ++(90:0.75) coordinate (a);


    % ray through the center of the lens
    \draw[ray] (a) -- ($(a)!3!(0,0)$);
    % ray parallel to the optic axis
    \draw[ray] (a) -- (0,0.75) -- ($(0,0.75)!2!(\f,0)$);

    % ray passing through object focus
    \draw[ray] (a) -- (0,1.5) -- ++(0:3);
    \draw[DarkRed,dashed] (a) -- (-\f,0);
    % extending the lines

    \draw[DarkRed!50!white,line width=3,->]  (-\f,0) -- ++(90:1.5);
    \draw[DarkRed,->,line width=1.5] (a) -- (0,1.5) -- ++(0:3);
    \draw[DarkRed,->,line width=1.5] (a) -- (0,0.75) --($(0,0.75)!2!(\f,0)$);
    \draw[DarkRed,->,line width=1.5] (a) -- ($(a)!3!(0,0)$);
    \draw[DarkRed,dashed] (0,1.5) -- (-\f,1.5) -- (-\f/2,0.75)
    (-\f,1.5) -- (0,0.75);

    % focal points
    \foreach \x in {-\f,\f}{ \filldraw[fill=yellow] (\x,0) circle[radius=0.05];  }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: geometric-notes.tex
modified: 2020-01-17 18:43:47
domain: p134
source:
  \begin{tikzpicture}[scale=1,
      ray/.style={->,DarkRed,line width=1.5pt}]
    \newcommand*{\f}{3}

    \draw (-5,0) -- (3.5,0);
    % lens
    \draw[gray,line width=3] (0,-2) -- (0,2) -- ++(70:0.4)
    (0,2) -- ++(110:0.4)
    (0,-2) -- ++(290:0.4)
    (0,-2) -- ++(250:0.4);

    \draw[|->,DarkSlateGray] (0,-2.5) -- node[anchor=north]{positive $o$}
    ++(180:2.5);
    \draw[|->,DarkSlateGray] (0,-2.5) -- node[anchor=north]{positive $i$}
    ++(0:2.5);

    % object
    \draw[DarkRed,line width=3pt,->] (-1.5*\f,0) -- ++(90:1.5)
    coordinate (c);

    % principal rays
    \draw[ray] (c) -- ($(c)!1.5!(0,0)$);
    \draw[ray] (c) -- ++(0:1.5*\f) coordinate (d) -- ++(1.5,0.75);
    \draw[ray] (c) -- (0,0.6) -- ++(0:2);
    \draw[DarkRed,dashed] (d) -- (-\f,0)
    (0,0.6) -- (\f,0)
    (0,0.6) -- (-0.6*\f,0.6);


    % focal points
    \foreach \x in {-\f,\f}{ \filldraw[fill=yellow] (\x,0) circle[radius=0.05];  }

    \draw[<-,DarkGreen] (-\f,-0.1) -- ++(-90:0.25)
    node[anchor=north]{image focal point};
    \draw[<-,DarkGreen] (\f,0) ++ (135:0.1) -- ++(135:1)
    node[anchor=south]{object focal point};

    \draw[DarkRed!50!white,line width=2,->] (-0.6*\f,0) -- ++(90:0.6);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: geometric-notes.tex
modified: 2020-01-17 18:43:47
domain: p134
source:
  \begin{tikzpicture}[scale=1.125,
      kvec/.style={->,line width=1.25pt,color=DarkBlue},
    ]
    \def\len{3}
    \def\wid{4}
    \def\ang{40}
    \def\refr{59}
    \def\tlen{2.25}
    \def\bgnd{yellow!20!white} % background color of upper medium
    \def\Bgnd{green!20}            % background color of lower medium

    % arcs for the k vectors
    \fill[fill=\bgnd] (-\wid,0) rectangle (\wid,\len);
    \fill[fill=\Bgnd] (-\wid,0) rectangle (\wid,-\len);
    \draw[color=DarkRed,dashed] (\len,0) arc[radius=\len,start angle=0,end
        angle=180];
    \draw[color=DarkRed,dashed] (\len*0.75,0) arc[radius=\len*0.75,start angle=0,end angle=-180];

    % axes and materials

    \draw[color=black!50!white,->] (-\wid,0) -- (\wid+0.25,0)
    node[anchor=west]{$x$};
    \draw[color=SlateBlue!70,dashed,->] (0,-\len) -- (0,\len+0.25)
    node[anchor=south]{$z$};

    \node at (-0.85*\wid,0.9*\len) {$\mu_{1}, \epsilon_{1}$};
    \node at (-0.85*\wid,-0.9*\len) {$\mu_{2}, \epsilon_{2}$};
    \node at (0.9*\wid,-0.9*\len) {TE};

    \draw[dashed] (-1.93, 0.85*\len) -- (-1.93, -0.4);
    \draw[DarkRed,->,line width=1] (-1.93,-0.02) --node[anchor=north]{$k_{x}$}
    (0,-0.02);

    % incident beam

    \coordinate (A) at (90+\ang:0.75*\len); % field anchor
    \node[anchor=west,fill=\bgnd] at (A) {\;\;$E_{\rm i}$};
    \draw[kvec,<-] (0,0) --node[anchor=east]{$k_{\rm i}$} ++(90+\ang:\len);
    \draw[force] (A) -- ++(\ang:1) node[anchor=south,fill=\bgnd] {$H_{\rm  i}$};
    \filldraw[fill=\bgnd] (A) circle[radius=0.15];
    \draw[line width=1.5] (A) +(45:0.15) -- ++(225:0.15) (A) +(135:0.15) -- ++(-45:0.15);


    % reflected beam
    \draw[kvec] (0,0) --node[anchor=north west]{$k_{\rm r}$} ++(90-\ang:\len)
    coordinate (kr);
    \coordinate (B) at (90-\ang:0.75*\len);
    \draw[force] (B) -- ++(180-\ang:1) node[anchor=south,fill=\bgnd] {$H_{\rm  r}$};
    \filldraw[fill=\bgnd] (B) circle[radius=0.15];
    \draw[line width=1.5] (B) +(45:0.15) -- ++(225:0.15) (B) +(135:0.15) --
    ++(-45:0.15);

    \node[anchor=east] at (B) {$E_{\rm r}$\;\;};
    \draw[DarkRed,<-,line width=1] (kr) -- node[fill=\bgnd,anchor=west]{$w_{1}$}
    ++(-90:2.3);

    % refracted beam
    \draw[kvec] (0,0) -- ++(-90+\refr:\tlen) node[anchor=north]{$k_{\rm t}$}
    coordinate (kt);
    \coordinate (C) at (-90+\refr:0.35*\len);
    \draw[force] (C) -- ++(\refr:1) node[anchor=west] {$H_{\rm  t}$};
    \filldraw[fill=\Bgnd] (C) circle[radius=0.15];
    \draw[line width=1.5] (C) +(45:0.15) -- ++(225:0.15) (C) +(135:0.15) -- ++(-45:0.15);
    \node[anchor=north east] at (C) {$E_{\rm t}$};

    \draw[DarkRed,<-|,line width=1] (kt) --
    node[fill=\Bgnd,anchor=west]{$w_{2}$} ++(90:1.165);

    % label angles
    \def\arcrad{0.4}
    \draw (90:\arcrad) arc(90:130:\arcrad);
    \node at (110:\arcrad+0.3) {$\theta_{\rm i}$};
    \draw (-90:\arcrad) arc(-90:-35:\arcrad);
    \node at (-60:\arcrad+0.2) {$\theta_{\rm t}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: geometric-notes.tex
modified: 2020-01-17 18:43:47
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[shift={(-0.75,1.5)}]
      \fill[gray!5!white] (0,0) rectangle(3,1);
      \fill[gray!25!white] (0,0) rectangle(3,-1);
      \node[anchor=south west] at (0,-1) {$n=1.5$};
      \node[anchor=north east] at (3,1) {$n = 1$};
      \draw (0,0) -- (3,0);
      \draw[dashed] (1.5,-1) -- (1.5,1);
      \draw[DarkRed,<-,line width=1.5] (1.5,0) -- ++(135:1.25);
      \draw[DarkRed,->,line width=1.5] (1.5,0) -- ++(-60:1);
      \draw(1.5,0.5) arc(90:135:0.5) (1.5,-0.5) arc(-90:-60:0.5);
      \node at (1.2,0.7){$\theta_{\rm i}$};
      \node at (1.7,-0.8){$\theta_{\rm t}$};
    \end{scope}

    \node at (0,0)
    {\includegraphics[width=\columnwidth]{ReflectionCoefficient}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: geometric-notes.tex
modified: 2020-01-17 18:43:47
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[shift={(-2,.4)}]
      \fill[gray!5!white] (0,0) rectangle(3,1);
      \fill[gray!25!white] (0,0) rectangle(3,-1);
      \node[anchor=south west] at (0,-1) {$n=1.5$};
      \node[anchor=north east] at (3,1) {$n = 1$};
      \draw (0,0) -- (3,0);
      \draw[dashed] (1.5,-1) -- (1.5,1);
      \draw[DarkRed,<-,line width=1.5] (1.5,0) -- ++(135:1.25);
      \draw[DarkRed,->,line width=1.5] (1.5,0) -- ++(-60:1);
      \draw(1.5,0.5) arc(90:135:0.5) (1.5,-0.5) arc(-90:-60:0.5);
      \node at (1.2,0.7){$\theta_{\rm i}$};
      \node at (1.7,-0.8){$\theta_{\rm t}$};
    \end{scope}

    \node at (0,0)
    {\includegraphics[width=\columnwidth]{Reflectivity}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec04.tex
modified: 2020-01-29 04:06:32
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \node[anchor=south] at (0,0)
    {\includegraphics[width=\wid\columnwidth]{Ibn_Sahl_manuscript}};
    \node[anchor=north,text width=1.5in] at (0,0){Manuscript of Ibn Sahl,
      Persian mathematician, circa 984};
    \begin{scope}[shift={(5,0)}]
      \node[anchor=south] at (0,0)
      {\includegraphics[width=\wid\columnwidth]{Willebrord_Snel}};
      \node at (0, -1){Willebrord Snel van Royen};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec10.tex
modified: 2020-02-12 15:16:57
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-3,
        xmax=3.3,
        ymin=0,
        ymax=1.1,
        enlargelimits=false,
        width=2in,
        height=1.5in,
        xlabel={$\tau$},
        ylabel={$\half[1 - \Re \gone]$},
        ytick={\empty},
        xtick={0},
        xticklabel={0},
        % xticklabels{0,,$a$,,a$},
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1}
      ]
      \addplot[
        DarkRed,
        domain=-3:3,
        samples=201,
        line width=1pt,
      ]
      {(1+exp(-0.5*x^2))/2};
      \addplot[
        DarkRed,
        domain=-3:3,
        samples=201,
        line width=1pt,
      ]
      {(1-exp(-0.5*x^2))/2};
      \addplot[DarkSlateBlue,
        domain=-3:3,
        samples=2001,
        line width=0.5pt,
      ]
      {0.5 + 0.5*cos(2000*x)*exp(-0.5*x*x)};

      %       \draw[DarkGreen,<->,line width=1.5] (-0.886,0.6)
      %       --node[anchor=north]{$\tau_{\rm coh} $} (0.886,0.6);
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec11.tex
modified: 2020-02-14 17:23:40
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-4,
        xmax=4.5,
        ymin=0,
        ymax=1.1,
        enlargelimits=false,
        width=2.25in,
        height=1.5in,
        xlabel={$\Omega = \omega-\omega_{0}$},
        ylabel={$\Pw(\omega)$},
        ytick={0},
        yticklabels=\empty,
        xtick={0},
        xticklabels=\empty,
        % xticklabels{0,,$a$,,a$},
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
      ]
      \addplot[
        DarkGreen,
        domain=-4:4,
        samples=201,
        line width=1.5pt,
      ]
      {1 / (1 + x^2))};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec11.tex
modified: 2020-02-14 17:23:40
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-4,
        xmax=4,
        ymin=0,
        ymax=1.25,
        enlargelimits=false,
        width=5in,
        height=2.5in,
        xlabel={$\Omega = \omega-\omega_{0}$},
        ylabel={$\Pw(\Omega)$},
        ytick={0},
        yticklabels=\empty,
        xtick={0},
        xticklabels=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
      ]
      \addplot[
        DarkGreen,
        domain=-4:4,
        samples=201,
        line width=3pt,
      ]
      {1 / (1 + x^2))};

      \addplot[
        DarkRed,
        domain=-4:4,
        samples=201,
        line width=2,
        dashed
      ]
      {exp(-ln(2)*x*x)};
      \node[anchor=north east] at (4,1.25) {%
        $\displaystyle \Pw(\Omega)\sim
          \frac{1}{1+(2\tau_{L}\Omega)^{2}} $  };
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec07.tex
modified: 2020-02-05 05:03:34
domain: p134
source:
  \begin{tikzpicture}[scale=.67,
      blabel/.style= {DarkRed,font=\sffamily},
      olabel/.style={DarkGreen,font=\sffamily},
      beam/.style={DarkRed,line width=2pt}
    ]

    \def\beam{2cm}
    \def\bsthick{0.25cm}

    % source
    \begin{scope}[shift={(-2.5*\beam,0.5)}]
      \node[star, star points=12,star point height=0.5,star point
        ratio=3,fill,DarkRed] at (0,0){};
      \node[DarkRed,anchor=south] at (0,0.75) {\textsf{source}};
    \end{scope}
    \node[blabel,anchor=south west] at (-2*\beam,0.65) {$\mathbf{E}_{\rm in}(t)$};

    \draw[beam] (-2*\beam,0.5) -- (2.5*\beam,0.5) ; % incident beam
    \draw[beam,->] (-1.25*\beam,0.5) -- +(0:.25); % arrows for incident beam
    \draw[beam,->] (1.5*\beam,0.5) --+(0:.25);
    \draw[beam] (0.5,0.5) -- (0.5,2*\beam);  % towards top mirror
    \draw[beam,->] (0.5,\beam) -- +(90:0.5);

    % beam splitter
    \begin{scope}[shift={(-1.414*\bsthick,0)},rotate=45]
      \filldraw[fill=gray!20,opacity=0.5] (-1*\beam,0) rectangle (1.*\beam,-\bsthick);
      \draw[line width=1.5pt] (-\beam,-\bsthick) -- (\beam,-\bsthick);
      \draw[olabel,<-] (-1.1*\beam,0) -- ++(180:0.6) node[anchor=north east] {beam splitter};
    \end{scope}

    \onslide<2->{
      % beams

      % top mirror
      \filldraw[fill=gray!30] (-\beam,2*\beam) rectangle (\beam,2*\beam+\bsthick);
      \draw[line width=2] (-\beam,2*\beam) -- +(0:2*\beam);
      \node[anchor=west] at (\beam,2*\beam+0.5*\bsthick) {\large $M_{2}$};

      % right mirror
      \begin{scope}[shift={(2.5*\beam,0)}]
        \filldraw[fill=gray!30] (0,-\beam) rectangle (\bsthick,\beam);
        \draw[line width=2] (0,-\beam) -- ++(90:2*\beam);
        \node[anchor=south] at (0.5*\bsthick, \beam) {\large $M_{1}$};
      \end{scope}


    }

    % reflected beams
    \onslide<3->{

      \draw[beam,->] (-0.5,2*\beam) -- ++(-90:4*\beam) node[blabel,anchor=north]
      {$\mathbf{E}_{\rm out}$}; % from top mirror
      \draw[beam,->] (2.5*\beam,-0.2) -- (-2*\beam,-0.2); % from M1
      \draw[beam,->] (-0.5,\beam) -- ++(-90:0.25);
      \draw[beam,->] (1.5*\beam,-0.2) -- +(180:0.25);
      \draw[beam,->] (-0.2,-0.2) -- (-0.2,-2*\beam);
    }

    % translatable mirror
    \onslide<4->{
      \draw[beam,->] (-0.5,-0.5) -- (-2*\beam,-0.5);

      \begin{scope}[shift={(2*\beam,0)},opacity=0.25]
        \filldraw[fill=gray!30] (0,-\beam) rectangle (\bsthick,\beam);
        \draw[line width=2] (0,-\beam) -- ++(90:2*\beam);
      \end{scope}

      \draw[DarkGreen,|->] (2*\beam,-1.25*\beam) -- node[anchor=north]{$d$}
      (2.5*\beam,-1.25*\beam);

      % labels

      \begin{scope}[shift={(2.7*\beam,0)},rotate=90]
        \node[olabel,anchor=north,rotate=90] at (0,0) {translatable mirror};
      \end{scope}
    }

    % compensator
    \onslide<5->{
      \begin{scope}[shift={(1.5,0)},rotate=45]
        \filldraw[fill=gray!20,opacity=0.5] (-1.*\beam,0) rectangle (1.*\beam,-\bsthick);
        \draw[olabel,<-] (\beam,0.2) --++(45:0.6) node[anchor=south] {compensator};
      \end{scope}
    }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec07.tex
modified: 2020-02-05 05:03:34
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \def\wid{6}
    \draw[gray] (-1,0) --node[anchor=north]{$L$} (\wid,0);
    \foreach \x in {0, -0.5} {
        \fill[DarkRed] (\x,0) circle[radius=0.05];
        \draw[DarkRed,line width=0.5] (\x,0) -- (\wid,1);
      }
    \draw[gray](\wid,2) -- (\wid,-1);
    \draw (\wid,0) -- node[anchor=west]{$x$} (\wid,1);
    \node[anchor=north] at (-0.25,0) {$2d$};
    \node[DarkRed] at (3,0.35){$s_{1}$};
    \node[DarkRed] at (2,0.6){$s_{2}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec07.tex
modified: 2020-02-05 05:03:34
domain: p134
source:
  \begin{tikzpicture}[scale=1.2]
    \begin{axis}[
        xmin=0,
        xmax=4,
        ymin=0,
        ymax=1.1,
        enlargelimits=false,
        width=2.5in,
        xlabel={$d$},
        ylabel={$\expval{I_{\rm out}}$},
        ytick={0,1},
        xtick={0,1,2,3,4},
        xticklabels={0,$\lambda$,$2\lambda$,$3\lambda$,$4\lambda$},
        yticklabels={0, $\expval{I\inc}$},
      ]
      \addplot[
        domain=0:5,
        samples=801,
        line width=1pt,
        DarkRed
      ]
      {sin(360*x)^2};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec06.tex
modified: 2020-02-02 23:25:10
domain: p134
source:
  \begin{tikzpicture}[scale=0.9,
      kvec/.style={->,line width=1.25pt,color=DarkBlue},
    ]
    \def\len{3}
    \def\wid{4}
    \def\ang{40}
    \def\refr{59}
    \def\tlen{2.25}
    \def\bgnd{yellow!40!white} % background color of upper medium
    \def\Bgnd{green!40}            % background color of lower medium

    % media
    \fill[fill=\bgnd] (-\wid,0) rectangle (\wid,\len);
    \fill[fill=\Bgnd] (-\wid,0) rectangle (\wid,-0.25*\len);

    % arcs for the k vectors
    \draw[color=DarkRed,dashed] (\len,0) arc[radius=\len,start angle=0,end
        angle=180];

    % axes and materials

    \draw[color=black!50!white,->] (-\wid,0) -- (\wid+0.25,0)
    node[anchor=west]{$x$};
    \draw[color=SlateBlue!70,dashed,->] (0,-0.3*\len) -- (0,\len+0.25)
    node[anchor=south]{$z$};

    \node at (-0.85*\wid,0.9*\len) {$\mu_{1}, \epsilon_{1}$};
    \node at (-0.85*\wid,-0.2*\len) {$\mu_{2}, \epsilon_{2}$};


    %  \draw[dashed] (-1.93, 0.85*\len) -- (-1.93, -0.4);
    %  \draw[DarkRed,->,line width=1] (-1.93,-0.02) --node[anchor=north]{$k_{x}$}
    %  (0,-0.02);

    % incident beam

    \coordinate (A) at (90+\ang:0.75*\len); % field anchor
    \draw[kvec,<-] (0,0) --node[anchor=east]{$k_{\rm i}$} ++(90+\ang:\len);
    % show the electric field
    \onslide<2->{
      \node[anchor=north east, fill=\bgnd] at (A) {\;\;$E_{\rm i}$};
      \filldraw[fill=\bgnd] (A) circle[radius=0.15];
      \draw[line width=1.5] (A) +(45:0.15) -- ++(225:0.15) (A) +(135:0.15) --
      ++(-45:0.15);
    }
    \onslide<5->{\draw[force] (A) -- ++(\ang:1) node[anchor=south,fill=\bgnd] {$H_{\rm  i}$};}



    % label angles
    \def\arcrad{0.4}
    \draw (90:\arcrad) arc(90:130:\arcrad);
    \node at (110:\arcrad+0.3) {$\theta_{\rm i}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec06.tex
modified: 2020-02-02 23:25:10
domain: p134
source:
  \begin{tikzpicture}[scale=1.125,
      kvec/.style={->,line width=1.25pt,color=DarkBlue},
    ]
    \def\len{3}
    \def\wid{4}
    \def\ang{40}
    \def\refr{59}
    \def\tlen{2.25}
    \def\bgnd{yellow!40!white} % background color of upper medium
    \def\Bgnd{green!40}            % background color of lower medium

    % arcs for the k vectors
    \fill[fill=\bgnd] (-\wid,0) rectangle (\wid,\len);
    \fill[fill=\Bgnd] (-\wid,0) rectangle (\wid,-\len);
    \draw[color=DarkRed,dashed] (\len,0) arc[radius=\len,start angle=0,end
        angle=180];
    \draw[color=DarkRed,dashed] (\len*0.75,0) arc[radius=\len*0.75,start angle=0,end angle=-180];

    % axes and materials

    \draw[color=black!50!white,->] (-\wid,0) -- (\wid+0.25,0)
    node[anchor=west]{$x$};
    \draw[color=SlateBlue!70,dashed,->] (0,-\len) -- (0,\len+0.25)
    node[anchor=south]{$z$};

    \node at (-0.85*\wid,0.9*\len) {$\mu_{1}, \epsilon_{1}$};
    \node at (-0.85*\wid,-0.9*\len) {$\mu_{2}, \epsilon_{2}$};
    \node at (0.9*\wid,-0.9*\len) {TE};

    \draw[dashed] (-1.93, 0.85*\len) -- (-1.93, -0.4);
    \draw[DarkRed,->,line width=1] (-1.93,-0.02) --node[anchor=north]{$k_{x}$}
    (0,-0.02);



    % incident beam


    \coordinate (A) at (90+\ang:0.75*\len); % field anchor
    \node[anchor=west,fill=\bgnd] at (A) {\;\;$E_{\rm i}$};
    \draw[kvec,<-] (0,0) --node[anchor=east]{$k_{\rm i}$} ++(90+\ang:\len);
    \draw[force] (A) -- ++(\ang:1) node[anchor=south,fill=\bgnd] {$H_{\rm  i}$};
    \filldraw[fill=\bgnd] (A) circle[radius=0.15];
    \draw[line width=1.5] (A) +(45:0.15) -- ++(225:0.15) (A) +(135:0.15) -- ++(-45:0.15);


    % reflected beam
    \draw[kvec] (0,0) --node[anchor=north west]{$k_{\rm r}$} ++(90-\ang:\len)
    coordinate (kr);
    \coordinate (B) at (90-\ang:0.75*\len);
    \draw[force] (B) -- ++(180-\ang:1) node[anchor=south,fill=\bgnd] {$H_{\rm  r}$};
    \filldraw[fill=\bgnd] (B) circle[radius=0.15];
    \draw[line width=1.5] (B) +(45:0.15) -- ++(225:0.15) (B) +(135:0.15) --
    ++(-45:0.15);

    \node[anchor=east] at (B) {$E_{\rm r}$\;\;};
    \draw[DarkRed,<-,line width=1] (kr) -- node[fill=\bgnd,anchor=west]{$w_{1}$}
    ++(-90:2.3);

    % refracted beam
    \draw[kvec] (0,0) -- ++(-90+\refr:\tlen) node[anchor=north]{$k_{\rm t}$}
    coordinate (kt);
    \coordinate (C) at (-90+\refr:0.35*\len);
    \draw[force] (C) -- ++(\refr:1) node[anchor=west] {$H_{\rm  t}$};
    \filldraw[fill=\Bgnd] (C) circle[radius=0.15];
    \draw[line width=1.5] (C) +(45:0.15) -- ++(225:0.15) (C) +(135:0.15) -- ++(-45:0.15);
    \node[anchor=north east] at (C) {$E_{\rm t}$};

    \draw[DarkRed,<-|,line width=1] (kt) --
    node[fill=\Bgnd,anchor=west]{$w_{2}$} ++(90:1.165);

    % label angles
    \def\arcrad{0.4}
    \draw (90:\arcrad) arc(90:130:\arcrad);
    \node at (110:\arcrad+0.3) {$\theta_{\rm i}$};
    \draw (-90:\arcrad) arc(-90:-35:\arcrad);
    \node at (-60:\arcrad+0.2) {$\theta_{\rm t}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: fodder.tex
modified: 2020-02-02 05:01:08
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[shift={(-2,.4)}]
      \fill[gray!5!white] (0,0) rectangle(3,1);
      \fill[gray!25!white] (0,0) rectangle(3,-1);
      \node[anchor=south west] at (0,-1) {$n=1.5$};
      \node[anchor=north east] at (3,1) {$n = 1$};
      \draw (0,0) -- (3,0);
      \draw[dashed] (1.5,-1) -- (1.5,1);
      \draw[DarkRed,<-,line width=1.5] (1.5,0) -- ++(135:1.25);
      \draw[DarkRed,->,line width=1.5] (1.5,0) -- ++(-60:1);
      \draw(1.5,0.5) arc(90:135:0.5) (1.5,-0.5) arc(-90:-60:0.5);
      \node at (1.2,0.7){$\theta_{\rm i}$};
      \node at (1.7,-0.8){$\theta_{\rm t}$};
    \end{scope}

    % \onslide<2>{\node at (0,0)
    {\includegraphics[width=\textwidth]{Reflectivity}};}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: fodder.tex
modified: 2020-02-02 05:01:08
domain: p134
source:
  \begin{tikzpicture}[scale=0.8]
    \begin{scope}[shift={(0.5,.4)}]
      \fill[gray!5!white] (0,0) rectangle(3,-1);
      \fill[gray!25!white] (0,0) rectangle(3,1);
      \node[anchor=south west] at (0,-1) {$n=1$};
      \node[anchor=north east] at (3,1) {$n = 1.5$};
      \draw (0,0) -- (3,0);
      \draw[dashed] (1.5,-1) -- (1.5,1);
      \draw[DarkRed,<-,line width=1.5] (1.5,0) -- ++(135:1.25);
      \draw[DarkRed,->,line width=1.5] (1.5,0) -- ++(-15:1.5);
      \draw(1.5,0.5) arc(90:135:0.5) (1.5,-0.5) arc(-90:-15:0.5);
      \node at (1.2,0.7){$\theta_{\rm i}$};
      \node at (2,-0.7){$\theta_{\rm t}$};
    \end{scope}

    % \onslide<2>{
    \node at (0,0)
    {\includegraphics[width=\textwidth]{ReflectivityInternal}};
    }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: fodder.tex
modified: 2020-02-02 05:01:08
domain: p134
source:
  \begin{tikzpicture}[scale=.67,
      blabel/.style= {DarkRed,font=\sffamily},
      olabel/.style={DarkGreen,font=\sffamily},
      beam/.style={DarkRed,line width=2pt}
    ]

    \def\beam{2cm}
    \def\bsthick{0.25cm}

    % source
    \begin{scope}[shift={(-2.5*\beam,0.5)}]
      \node[star, star points=12,star point height=0.5,star point
        ratio=3,fill,DarkRed] at (0,0){};
      \node[DarkRed,anchor=south] at (0,0.75) {\textsf{source}};
    \end{scope}
    \node[blabel,anchor=south west] at (-2*\beam,0.65) {$\mathbf{E}_{\rm in}(t)$};

    \draw[beam] (-2*\beam,0.5) -- (2.5*\beam,0.5) ; % incident beam
    \draw[beam,->] (-1.25*\beam,0.5) -- +(0:.25); % arrows for incident beam
    \draw[beam,->] (1.5*\beam,0.5) --+(0:.25);
    \draw[beam] (0.5,0.5) -- (0.5,2*\beam);  % towards top mirror
    \draw[beam,->] (0.5,\beam) -- +(90:0.5);

    % beamsplitter
    \begin{scope}[shift={(-1.414*\bsthick,0)},rotate=45]
      \filldraw[fill=gray!20,opacity=0.5] (-1*\beam,0) rectangle (1.*\beam,-\bsthick);
      \draw[line width=1.5pt] (-\beam,-\bsthick) -- (\beam,-\bsthick);
      \draw[olabel,<-] (-1.1*\beam,0) -- ++(180:0.6) node[anchor=north east] {beam splitter};
    \end{scope}

    % \onslide<2->{
    % beams

    % top mirror
    \filldraw[fill=gray!30] (-\beam,2*\beam) rectangle (\beam,2*\beam+\bsthick);
    \draw[line width=2] (-\beam,2*\beam) -- +(0:2*\beam);
    \node[anchor=west] at (\beam,2*\beam+0.5*\bsthick) {\large $M_{2}$};

    % right mirror
    \begin{scope}[shift={(2.5*\beam,0)}]
      \filldraw[fill=gray!30] (0,-\beam) rectangle (\bsthick,\beam);
      \draw[line width=2] (0,-\beam) -- ++(90:2*\beam);
      \node[anchor=south] at (0.5*\bsthick, \beam) {\large $M_{1}$};
    \end{scope}


    }

    % reflected beams
    % \onslide<3->{

    \draw[beam,->] (-0.5,2*\beam) -- ++(-90:4*\beam) node[blabel,anchor=north]
    {$\mathbf{E}_{\rm out}$}; % from top mirror
    \draw[beam,->] (2.5*\beam,-0.2) -- (-2*\beam,-0.2); % from M1
    \draw[beam,->] (-0.5,\beam) -- ++(-90:0.25);
    \draw[beam,->] (1.5*\beam,-0.2) -- +(180:0.25);
    \draw[beam,->] (-0.2,-0.2) -- (-0.2,-2*\beam);
    }

    % translatable mirror
    % \onslide<4->{
    \draw[beam,->] (-0.5,-0.5) -- (-2*\beam,-0.5);

    \begin{scope}[shift={(2*\beam,0)},opacity=0.25]
      \filldraw[fill=gray!30] (0,-\beam) rectangle (\bsthick,\beam);
      \draw[line width=2] (0,-\beam) -- ++(90:2*\beam);
    \end{scope}

    \draw[DarkGreen,|->] (2*\beam,-1.25*\beam) -- node[anchor=north]{$d$}
    (2.5*\beam,-1.25*\beam);

    % labels

    \begin{scope}[shift={(2.7*\beam,0)},rotate=90]
      \node[olabel,anchor=north,rotate=90] at (0,0) {translatable mirror};
    \end{scope}
    }

    % compensator
    % \onslide<5->{
    \begin{scope}[shift={(1.5,0)},rotate=45]
      \filldraw[fill=gray!20,opacity=0.5] (-1.*\beam,0) rectangle (1.*\beam,-\bsthick);
      \draw[olabel,<-] (\beam,0.2) --++(45:0.6) node[anchor=south] {compensator};
    \end{scope}
    }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: scrap.tex
modified: 2020-02-19 15:00:46
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \fill[DarkGreen] (0,0) sin ++(.5, .2) cos ++(.5, -.2)
    sin ++(-.5, -.2) cos ++(-.5, .2);

    \standing{0.3}{20}{Red}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec08.tex
modified: 2020-02-07 14:59:35
domain: p134
source:
  \begin{tikzpicture}[scale=0.5,
      beam/.style={titlecolor,line width=1.5pt},
      olabel/.style={titlecolor,font=\scriptsize},
      factor/.style={DarkGreen,font=\scriptsize},
    ]
    \def\beam{2cm}
    \def\bsthick{0.25cm}

    % source
    \node[olabel,anchor=south west] at (-2*\beam,0.1) {$\mathbf{E}_{\rm in}(t)$};

    \draw[beam] (-2*\beam,0) -- (2*\beam,0) ; % incident beam
    \draw[beam,->] (-1.25*\beam,0) -- +(0:.25); % arrows for incident beam
    \draw[beam,->] (0,1.5*\beam) -- (0,-1.5*\beam)
    node[olabel,anchor=west]{$\vb{E}\out$};  % from top mirror

    % beamsplitter
    \begin{scope}[shift={(-1.414*\bsthick,0)},rotate=45]
      \filldraw[fill=gray!20,opacity=0.5] (-1*\beam,0) rectangle (1.*\beam,-\bsthick);
      \draw[line width=1.5pt] (-\beam,-\bsthick) -- (\beam,-\bsthick);
    \end{scope}

    % top mirror
    \filldraw[fill=gray!30] (-\beam,1.5*\beam) rectangle (\beam,1.5*\beam+\bsthick);
    \draw[line width=1] (-\beam,1.5*\beam) -- +(0:2*\beam);
    \node[anchor=west] at (\beam,1.5*\beam+0.5*\bsthick) {\scriptsize $M_{2}$};

    % right mirror
    \begin{scope}[shift={(2*\beam,0)}]
      \filldraw[fill=gray!30] (0,-\beam) rectangle (\bsthick,\beam);
      \draw[line width=1] (0,-\beam) -- ++(90:2*\beam);
      \node[anchor=south] at (0.5*\bsthick, \beam) {\scriptsize $M_{1}$};
    \end{scope}


    % compensator
    \begin{scope}[shift={(1.5,0)},rotate=45]
      \filldraw[fill=gray!20,opacity=0.25] (-1.*\beam,0) rectangle (1.*\beam,-\bsthick);
    \end{scope}



    % factors
    \draw[factor, ->] (165:0.8) arc(-90:0:0.5) -- ++(90:0.5)
    node[anchor=east]{$\frac{1}{\sqrt{2}}$};
    \draw[factor,->] (-0.25,-0.5) -- node[anchor=north east]{$\frac{1}{\sqrt{2}}$}
    ++(-90:1);
    \draw[factor,->] (0.25,2.5) -- node[anchor=west]{$e^{i\pi}$} ++(-90:0.75);
    \draw[factor,->] (0.75,0.25) -- node[anchor=south]{$\frac{1}{\sqrt{2}}$}
    ++(0:1.5);

    \draw[factor,->] (3.5,-0.25) -- node[anchor=north]{$e^{i(\pi+\omega\tau) }$} ++(180:1);
    \draw[factor,->] (0.75,-0.25) arc(90:180:0.5) -- ++(-90:0.5)
    node[anchor=west]{$-\frac{1}{\sqrt{2}} $};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec08.tex
modified: 2020-02-07 14:59:35
domain: p134
source:
  \begin{tikzpicture}[scale=0.8]
    \begin{axis}[
        xmin=0,
        xmax=4,
        ymin=0,
        ymax=1.1,
        enlargelimits=false,
        width=2.5in,
        xlabel={$d$},
        ylabel={$\expval{I_{\rm out}}$},
        ytick={0,1},
        xtick={0,1,2,3,4},
        xticklabels={0,$\lambda$,$2\lambda$,$3\lambda$,$4\lambda$},
      ]
      \addplot[
        domain=0:5,
        samples=801,
        line width=1pt,
        titlecolor
      ]
      {sin(360*x)^2};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec08.tex
modified: 2020-02-07 14:59:35
domain: p134
source:
  \begin{tikzpicture}[scale=1,
      energy/.style= {DarkGreen},
      Na/.style={yellow!75!black}
    ]
    \draw (0,0) -- ++(0:1) node[anchor=west]{$3s_{1/2}$};
    \node[energy,anchor=east] at (-0.25,0) {$-5.14$};

    \draw (1,4) -- ++(0:1) node[anchor=west]{$3p_{1/2}$};
    \draw (1,4.5) -- ++(0:1) node[anchor=west]{$3p_{3/2}$};

    \draw[->,Na,line width=2] (1.25,4.5)
    --node[fill=white,rotate=78]{$\SI{589.0}{nm}$}  (0.25,0);
    \draw[->,Na,line width=2] (1.75,4)
    --node[fill=white,rotate=78]{$\SI{589.6}{nm}$}  (0.75,0);

    \node[energy, anchor=east] at (-0.25,4.25) {$-3.04$};
    \draw[dashed] (0,4.25) -- ++(0:1);
    \node[rotate=90,energy] at (-0.75,2.125){Energy (eV)};

    \draw[<->,DarkGreen] (3.25,4) -- node[anchor=west,text
      width=2cm,font=\scriptsize]{spin-orbit splitting = \SI{2.1}{meV}}
    ++(90:0.5);

    \node[titlecolor, anchor=west,
      fill=titlecolor!10!white,
      draw,
      rounded corners,
      text width=3cm,
      font=\tiny] at (2.5,3.25) {There are 4 $3p_{3/2}$ states and 2
      $3p_{1/2}$ states, but the ratio of the line intensities is not 2:1. Why
      might that be?};

    \node[anchor=west,titlecolor,draw] at (2.,1)
    {\includegraphics[width=4cm]{Na_doublet_plot}};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec08.tex
modified: 2020-02-07 14:59:35
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
      xmin=0, xmax=100, ymin=0, ymax=1, enlargelimits=false,
      width=2.5in, height=2in,
      xlabel={$\tau$}, ylabel={$I_{\rm out}/I_{0}$}, ytick={0,1}, xtick={0},
      % xticklabel=\empty, xticklabels{0,,$a$,,a$},
      % axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \fill[gray!50] (48,0) rectangle (52,1);
      \addplot[DarkGreen, domain=0:100, samples=2000, line width=0.5pt,]
      {0.5*(1-cos(180*x)*cos(x))};
      \addplot[titlecolor,dashed,line width=1pt,domain=0:100,samples=50]
      {0.5*(1+cos(x))};
      \addplot[titlecolor,dashed,line width=1pt,domain=0:100,samples=50]
      {0.5*(1-cos(x))};
      \draw[<-,titlecolor,line width=1.5] (50,0.82) -- (70,0.82) node[anchor=west]{$I_{\rm out}^{(\rm
              max)}$};
      \draw[<-,titlecolor,line width=1.5] (50,0.18) -- (70,0.18) node[anchor=west]{$I_{\rm out}^{(\rm min)}$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec08.tex
modified: 2020-02-07 14:59:35
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-3,
        xmax=3,
        ymin=0,
        ymax=1,
        enlargelimits=false,
        width=2in,
        height=2.5in,
        xlabel={$\omega_{0}$},
        ylabel={},
        ytick={0,1},
        yticklabel=\empty,
        xtick={},
        xticklabel=\empty,
        % xticklabels{0,,$a$,,a$},
      ]
      \addplot[
        domain=-3:3,
        samples=201,
        line width=0pt,
        fill=titlecolor!25!white
      ]
      {exp(-x^2)} \closedcycle;

      \addplot[domain=1:1.2, samples=25,fill=blue!25!white,line width=0pt]
      {exp(-x^2)} \closedcycle;
      \addplot[domain=0.8:1, samples=25,fill=green!25!white,line width=0pt]
      {exp(-x^2)} \closedcycle;
      \addplot[
        domain=-3:3,
        samples=201,
        line width=2pt,
        titlecolor,
      ]
      {exp(-x^2)};

    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: lec09.tex
modified: 2020-02-12 02:58:47
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-100,
        xmax=100,
        ymin=-0.4,
        ymax=1.05,
        enlargelimits=false,
        width=3in,
        height=1.5in,
        xlabel={},%$\Omega$},
        ylabel={$\mathrm{sinc}(\Omega T/2)$},
        ytick={0},
        yticklabel=\empty,
        xtick={0},
        %xticklabel=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
      ]
      \addplot[
        domain=-100:-10,
        samples=101,
        line width=0.5pt,
        DarkRed
      ]
      {sin(x*180/3.14159)/x};

      \addplot[
        domain=-10:10,
        samples=100,
        line width=0.5pt,
        DarkRed
      ]
      {sin(x*180/3.14159)/x};
      \addplot[
        domain=10:100,
        samples=101,
        line width=0.5pt,
        DarkRed
      ]
      {sin(x*180/3.14159)/x};

      \draw[<-,NavyBlue] (3.14,0) --  (10,0.5) node[anchor=west]{$\frac{2\pi}{T} $};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: michelson-notes.tex
modified: 2020-02-10 03:38:25
domain: p134
source:
  \begin{tikzpicture}[scale=.67,
      blabel/.style= {DarkRed,font=\sffamily},
      olabel/.style={DarkGreen,font=\sffamily},
      beam/.style={DarkRed,line width=2pt}
    ]

    \def\beam{2cm}
    \def\bsthick{0.25cm}

    % source
    \begin{scope}[shift={(-2.5*\beam,0.5)}]
      \node[star, star points=12,star point height=0.5,star point
        ratio=3,fill,DarkRed] at (0,0){};
      \node[DarkRed,anchor=south] at (0,0.75) {\textsf{source}};
    \end{scope}
    \node[blabel,anchor=south west] at (-2*\beam,0.65) {$\mathbf{E}_{\rm in}(t)$};

    \draw[beam] (-2*\beam,0.5) -- (2.5*\beam,0.5) ; % incident beam
    \draw[beam,->] (-1.25*\beam,0.5) -- +(0:.25); % arrows for incident beam
    \draw[beam,->] (1.5*\beam,0.5) --+(0:.25);
    \draw[beam] (0.5,0.5) -- (0.5,2*\beam);  % towards top mirror
    \draw[beam,->] (0.5,\beam) -- +(90:0.5);

    % beamsplitter
    \begin{scope}[shift={(-1.414*\bsthick,0)},rotate=45]
      \filldraw[fill=gray!20,opacity=0.5] (-1*\beam,0) rectangle (1.*\beam,-\bsthick);
      \draw[line width=1.5pt] (-\beam,-\bsthick) -- (\beam,-\bsthick);
      \draw[olabel,<-] (-1.1*\beam,0) -- ++(180:0.6) node[anchor=north east] {beam splitter};
    \end{scope}

    % beams

    % top mirror
    \filldraw[fill=gray!30] (-\beam,2*\beam) rectangle (\beam,2*\beam+\bsthick);
    \draw[line width=2] (-\beam,2*\beam) -- +(0:2*\beam);
    \node[anchor=west] at (\beam,2*\beam+0.5*\bsthick) {\large $M_{2}$};

    % right mirror
    \begin{scope}[shift={(2.5*\beam,0)}]
      \filldraw[fill=gray!30] (0,-\beam) rectangle (\bsthick,\beam);
      \draw[line width=2] (0,-\beam) -- ++(90:2*\beam);
      \node[anchor=south] at (0.5*\bsthick, \beam) {\large $M_{1}$};
    \end{scope}


    % reflected beams
    \draw[beam,->] (-0.5,2*\beam) -- ++(-90:4*\beam) node[blabel,anchor=north]
    {$\mathbf{E}_{\rm out}$}; % from top mirror
    \draw[beam,->] (2.5*\beam,-0.2) -- (-2*\beam,-0.2); % from M1
    \draw[beam,->] (-0.5,\beam) -- ++(-90:0.25);
    \draw[beam,->] (1.5*\beam,-0.2) -- +(180:0.25);
    \draw[beam,->] (-0.2,-0.2) -- (-0.2,-2*\beam);

    % translatable mirror
    \draw[beam,->] (-0.5,-0.5) -- (-2*\beam,-0.5);

    \begin{scope}[shift={(2*\beam,0)},opacity=0.25]
      \filldraw[fill=gray!30] (0,-\beam) rectangle (\bsthick,\beam);
      \draw[line width=2] (0,-\beam) -- ++(90:2*\beam);
    \end{scope}

    \draw[DarkGreen,|->] (2*\beam,-1.25*\beam) -- node[anchor=north]{$d$}
    (2.5*\beam,-1.25*\beam);

    % labels

    \begin{scope}[shift={(2.7*\beam,0)},rotate=90]
      \node[olabel,anchor=north,rotate=90] at (0,0) {translatable mirror};
    \end{scope}


    % compensator
    \begin{scope}[shift={(1.5,0)},rotate=45]
      \filldraw[fill=gray!20,opacity=0.5] (-1.*\beam,0) rectangle (1.*\beam,-\bsthick);
      \draw[olabel,<-] (\beam,0.2) --++(45:0.6) node[anchor=south] {compensator};
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: michelson-notes.tex
modified: 2020-02-10 03:38:25
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \def\wid{6}
    \draw[gray] (-1,0) --node[anchor=north]{$L$} (\wid,0);
    \foreach \x in {0, -0.5} {
        \fill[DarkRed] (\x,0) circle[radius=0.05];
        \draw[DarkRed,line width=0.5] (\x,0) -- (\wid,1);
      }
    \draw (\wid,0) -- node[anchor=west]{$x$} (\wid,1);
    \node[anchor=north] at (-0.25,0) {$2d$};
    \node[DarkRed] at (3,0.35){$s_{1}$};
    \node[DarkRed] at (2,0.6){$s_{2}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: michelson-notes.tex
modified: 2020-02-10 03:38:25
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0,
        xmax=4,
        ymin=0,
        ymax=1.1,
        enlargelimits=false,
        width=2.5in,
        xlabel={$d$},
        ylabel={$\expval{I_{\rm out}}$},
        ytick={0,1},
        xtick={0,1,2,3,4},
        xticklabels={0,$\lambda$,$2\lambda$,$3\lambda$,$4\lambda$},
        yticklabels={0, $\expval{I\IN}$},
      ]
      \addplot[
        domain=0:5,
        samples=801,
        line width=1pt,
        DarkRed
      ]
      {sin(360*x)^2};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: michelson-notes.tex
modified: 2020-02-10 03:38:25
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
      xmin=0, xmax=100, ymin=0, ymax=1, enlargelimits=false,
      width=3in, height=2.25in,
      xlabel={$\tau$}, ylabel={$\expval{I_{\rm out}}/I_{0}$}, ytick={0,1}, xtick={0},
      % xticklabel=\empty, xticklabels{0,,$a$,,a$},
      % axis x line=bottom, axis y line=left, axis line style={line width=1} % for no frame
      ]
      \fill[gray!50] (48,0) rectangle (52,1);
      \addplot[DarkGreen, domain=0:100, samples=2000, line width=0.5pt,]
      {0.5*(1-cos(180*x)*cos(x))};
      \addplot[DarkRed,dashed,line width=1pt,domain=0:100,samples=50]
      {0.5*(1+cos(x))};
      \addplot[DarkRed,dashed,line width=1pt,domain=0:100,samples=50]
      {0.5*(1-cos(x))};
      \draw[<-,DarkRed,line width=1.5] (50,0.82) -- (70,0.82) node[anchor=west]{$I_{\rm out}^{(\rm
              max)}$};
      \draw[<-,DarkRed,line width=1.5] (50,0.18) -- (70,0.18) node[anchor=west]{$I_{\rm out}^{(\rm min)}$};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: michelson-notes.tex
modified: 2020-02-10 03:38:25
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-3,
        xmax=3,
        ymin=0,
        ymax=1.05,
        enlargelimits=false,
        width=3.in,
        height=1.5in,
        xlabel={$\Omega$},
        ylabel={$|\Four{A}(\Omega)|$},
        ytick={},
        yticklabel=\empty,
        xtick={0},
        %xticklabel=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
      ]
      \addplot[
        domain=-3:3,
        samples=201,
        line width=0pt,
        fill=DarkRed!10!white
      ]
      {exp(-x^2)} \closedcycle;

      \addplot[domain=0.8:1, samples=25,fill=green!25!white,line width=0pt]
      {exp(-x^2)} \closedcycle;

      \addplot[
        domain=-3:3,
        samples=201,
        line width=1pt,
        DarkRed,
      ]
      {exp(-x^2)};

      \draw[<-,DarkGreen] (0.8,0.1) -- (0.5,0.1) node[anchor=east]{$\Delta\Omega$};
      \draw[<-,DarkGreen] (1,0.1) -- (1.3,0.1);
      \draw[<-,DarkGreen] (0.9, 0.25) -- (1.5,0.6)
      node[anchor=south,text width=2cm,font=\scriptsize,
        align=center]{Averages to zero
        unless centered at 0};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec
filename: michelson-notes.tex
modified: 2020-02-10 03:38:25
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-3,
        xmax=3.3,
        ymin=0,
        ymax=1.1,
        enlargelimits=false,
        width=0.8*\columnwidth,
        height=2in,
        xlabel={$\tau$},
        ylabel={$\half[1 - \Re \gone]$},
        ytick={\empty},
        xtick={0},
        xticklabel={0},
        % xticklabels{0,,$a$,,a$},
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1}
      ]
      \addplot[
        Red,
        domain=-3:3,
        samples=201,
        line width=1pt,
        opacity=0.5
      ]
      {(1+exp(-0.5*x^2))/2};
      \addplot[
        Red,
        domain=-3:3,
        samples=201,
        line width=1pt,
        opacity=0.5
      ]
      {(1-exp(-0.5*x^2))/2};
      \addplot[DarkSlateBlue,
        domain=-3:3,
        samples=2001,
        line width=0.25pt,
      ]
      {0.5 + 0.5*cos(3000*x)*exp(-0.5*x*x)};

      %       \draw[DarkGreen,<->,line width=1.5] (-0.886,0.6)
      %       --node[anchor=north]{$\tau_{\rm coh} $} (0.886,0.6);
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec/frames/lec13
filename: 07-Gaussian_beams.tex
modified: 2020-02-02 02:03:55
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \def\wzero{1}
    \def\zr{3}
    \begin{axis}[width=6cm,height=4cm,enlargelimits=false,
        xmin=-0.5, xmax=8, ymin=-3, ymax=3,
        xlabel={$z$},ylabel={},xtick=\empty,ytick=\empty,
        axis x line=middle, axis y line=middle]
      \addplot[gray,domain=-0.5:8, samples=51] { \wzero * sqrt(1 + (x/\zr)^2)
      };
      \addplot[gray,domain=-0.5:8, samples=51] { -\wzero * sqrt(1 + (x/\zr)^2) };
      \draw[dashed,SlateBlue] (0,0) -- (8,2.85);
      \draw[dashed,SlateBlue] (0,0) -- (8,-2.85);
    \end{axis}

    \begin{scope}[shift={(-1,2.15)},rotate={-90}]
      \begin{axis}[
          xmin=-2.5,
          xmax=2.5,
          ymin=0,
          ymax=1.5,
          enlargelimits=false,
          width=3.5cm,
          height=2cm,
          xlabel={},
          ylabel={},
          ytick=\empty,
          xtick=\empty,
          xticklabel=\empty,
          yticklabel=\empty,
          axis x line=bottom,
          axis y line=middle
        ]
        \addplot[
          DarkRed,
          domain=-1.8:1.8,
          samples=51,
          line width=1pt,
        ]
        {exp(-x*x)};
      \end{axis}
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec/frames/lec13
filename: 10-Rectangular_aperture.tex
modified: 2020-02-02 02:03:55
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \def\image{5}

    \fill (-4,1,0) coordinate (S) circle[radius=0.04] node[anchor=south east]{$S(x_{s}, y_{s}, z_{s})$};

    % aperture plane
    \filldraw[fill=gray!5] (0,-1.5,-2.5) -- (0,1.5,-2.5) -- (0,1.5,2.5) --
    (0,-1.5,2.5) -- cycle;
    \filldraw[fill=white] (0,-0.5,-2) -- (0,-0.5,2) -- (0,0.5,2) -- (0,0.5,-2)
    -- cycle;
    \draw[DarkGreen,->] (0,0,0) -- (\image+2,0,0) node[anchor=north] {$z$ };
    \begin{scope}[shift={(\image,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) -- (0,0,3) node[anchor=north] {$y$ };
    \draw[DarkGreen,->] (\image,0,0) -- (\image+2,0,0) node[anchor=north] {$z$ };

    \draw[DarkBlue,->] (S) -- node[anchor=north] {$\vb{s}_{0}$} (0,0);
    \fill (\image,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 (0,2.5,0) {aperture plane};
    \node at (\image,2.5,0) {image plane};

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

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec/frames/lec13
filename: 09-Expanding_vbs.tex
modified: 2020-02-02 02:03:55
domain: p134
source:
  \begin{tikzpicture}[scale=0.8]
    \def\image{5}

    \fill (-4,1,0) coordinate (S) circle[radius=0.04] node[anchor=south east]{$S(x_{s}, y_{s}, z_{s})$};

    % aperture plane
    \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) -- (\image+2,0,0) node[anchor=north] {$z$ };
    \begin{scope}[shift={(\image,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,->] (\image,0,0) -- (\image+2,0,0) node[anchor=north] {$z$ };

    \draw[DarkBlue,->] (S) -- node[anchor=north] {$\vb{s}_{0}$} (0,0);
    \fill (\image,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 (0,2.5,0) {aperture plane};
    \node at (\image,2.5,0) {image plane};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec/frames/lec13
filename: 05-Mode_locking_mechanisms.tex
modified: 2020-02-02 02:03:55
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=2,DarkRed,->] (0,0) --(5,0);
    \filldraw[fill=gray!20] (0,0) -- (0,0.5) -- (0.3,0.5) .. controls (0.2,0)
    and (0.2,0) .. (0.3,-0.5) --  (0,-0.5) -- cycle;
    \begin{scope}[shift={(4,0)},rotate=180]
      \filldraw[fill=gray!20] (0,0) -- (0,0.5) -- (0.3,0.5) .. controls (0.2,0)
      and (0.2,0) .. (0.3,-0.5) --  (0,-0.5) -- cycle;
    \end{scope}
    \node[fill=red!5,draw] at (1.5,0) {gain};
    \node[fill=white,font=\scriptsize,draw,rotate=90] at (3,0) {Q-switch};

    \onslide<2>{
      \begin{scope}[shift={(0,-3)}]
        \draw[line width=2,DarkRed,->] (0,0) --(5,0);
        \filldraw[fill=gray!20] (0,0) -- (0,0.5) -- (0.3,0.5) .. controls (0.2,0)
        and (0.2,0) .. (0.3,-0.5) --  (0,-0.5) -- cycle;
        \begin{scope}[shift={(4,0)},rotate=180]
          \filldraw[fill=gray!20] (0,0) -- (0,0.5) -- (0.3,0.5) .. controls (0.2,0)
          and (0.2,0) .. (0.3,-0.5) --  (0,-0.5) -- cycle;
        \end{scope}
        \node[fill=red!5,draw] at (1.5,0) {gain};
        \node[fill=white,font=\scriptsize,draw,rotate=90] at (3,0) {Q-switch};
        \filldraw[opacity=0.5,fill=green!20,draw=gray] (0.4,-0.3) rectangle
        (0.5,0.3);
        \draw[<-,DarkGreen] (0.45,-0.35) -- ++(-90:0.35)
        node[anchor=north,DarkGreen,font=\scriptsize]    {saturable absorber};

        \node[DarkGreen] at (2,-1.5) {Lowers pulse duration to 20--30 ps};
      \end{scope}
    }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec/frames/lec13
filename: 08-Fresnel-Kirchhoff_scalar_diffraction_theory.tex
modified: 2020-02-02 02:03:55
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \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 (0,2.5,0) {aperture plane};
    \node at (4,2.5,0) {image plane};

    \node at (0,-3,0) {$\displaystyle E(P) = \underset {\text{over 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[anchor=east,DarkSlateGray,font=\scriptsize] at (7.5,-3.5) {see Born \&
      Wolf, Ch.\ 8};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2020/lec/frames/lec13
filename: 11-Single_slit.tex
modified: 2020-02-02 02:03:55
domain: p134
source:
  \begin{tikzpicture}[scale=.8]
    \begin{axis}[
        xmin=-10, xmax=11, ymin=0, ymax=1.1, enlargelimits=false,
        width=3.5in, height=3in,
        xlabel={$\alpha$}, ylabel={Intensity}, ytick={0},xtick=\empty,
        axis x line=bottom, axis y line=left, axis line style={line width=1,gray} % for no frame
      ]
      \addplot[DarkGreen, domain=-10:10, samples=300, line width=2pt,]
      {(sin(x*180/3.14159)/x)^2};
    \end{axis}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec
filename: MichelsonInterferometer.tex
modified: 2018-01-29 01:31:50
domain: p134
source:
  \begin{tikzpicture}[scale=.6,
      blabel/.style= {DarkRed,font=\sffamily},
      olabel/.style={DarkGreen,font=\sffamily},
      beam/.style={DarkRed,line width=2pt}
    ]

    \def\beam{2cm}
    \def\bsthick{0.25cm}

    % source
    \begin{scope}[shift={(-2.5*\beam,0.5)}]
      \node[star, star points=12,star point height=0.5,star point
        ratio=3,fill,DarkRed] at (0,0) {};
      \node[DarkRed,anchor=south] at (0,0.75) {\textsf{source}};
    \end{scope}

    % beams
    \draw[beam] (-2*\beam,0.5) -- (2.5*\beam,0.5) ; % incident beam
    \draw[beam,->] (-1*\beam,0.5) -- +(0:.25); % arrows for incident beam
    \draw[beam,->] (1.5*\beam,0.5) --+(0:.25);

    \draw[beam] (0.5,0.5) -- (0.5,2*\beam);  % towards top mirror
    \draw[beam,->] (0.5,\beam) -- +(90:0.5);

    \draw[beam,->] (-0.5,2*\beam) -- ++(-90:4*\beam) node[blabel,anchor=south east]
    {$\mathbf{E}_{\rm out}$}; % from top mirror
    \draw[beam,->] (-0.5,\beam) -- ++(-90:0.25);

    \draw[beam,->] (2.5*\beam,-0.2) -- (-2*\beam,-0.2);
    \draw[beam,->] (1.5*\beam,-0.2) -- +(180:0.25);

    \draw[beam,->] (-0.2,-0.2) -- (-0.2,-2*\beam);
    \draw[beam,->] (-0.5,-0.5) -- (-2*\beam,-0.5);



    % beamsplitter
    \begin{scope}[shift={(-1.414*\bsthick,0)},rotate=45]
      \filldraw[fill=gray!20,opacity=0.5] (-1*\beam,0) rectangle (1.*\beam,-\bsthick);
      \draw[line width=1.5pt] (-\beam,-\bsthick) -- (\beam,-\bsthick);
      \draw[olabel,<-] (-1.1*\beam,0) -- ++(180:0.6) node[anchor=north east] {beam splitter};
    \end{scope}

    % compensator
    \begin{scope}[shift={(1.5,0)},rotate=45]
      \filldraw[fill=gray!20,opacity=0.5] (-1.*\beam,0) rectangle (1.*\beam,-\bsthick);
      \draw[olabel,<-] (\beam,0.2) --++(45:0.6) node[anchor=south] {compensator};
    \end{scope}

    % top mirror
    \filldraw[fill=gray!30] (-\beam,2*\beam) rectangle (\beam,2*\beam+\bsthick);
    \draw[line width=2] (-\beam,2*\beam) -- +(0:2*\beam);
    \node[anchor=west] at (\beam,2*\beam+0.5*\bsthick) {\large $M_{2}$};

    % right mirror
    \begin{scope}[shift={(2*\beam,0)},opacity=0.25]
      \filldraw[fill=gray!30] (0,-\beam) rectangle (\bsthick,\beam);
      \draw[line width=2] (0,-\beam) -- ++(90:2*\beam);
    \end{scope}

    \begin{scope}[shift={(2.5*\beam,0)}]
      \filldraw[fill=gray!30] (0,-\beam) rectangle (\bsthick,\beam);
      \draw[line width=2] (0,-\beam) -- ++(90:2*\beam);
      \node[anchor=south] at (0.5*\bsthick, \beam) {\large $M_{1}$};
    \end{scope}

    % detector
    \begin{scope}[shift={(-0.35,-2.2*\beam)}]
      \draw[line width=2] (0.4,0.4) -- (0.4,0) -- (0,0) -- (0,-0.4) -- (0,0)
      -- (-0.4,0) -- (-0.4,0.4);
      \node[anchor=north] at (0,-0.4) {\large $D$};
    \end{scope}

    \draw[DarkGreen,|->] (2*\beam,-1.25*\beam) -- node[anchor=north]{$d$}
    (2.5*\beam,-1.25*\beam);

    % labels
    \node[blabel,anchor=south west] at (-2*\beam,0.5) {$\mathbf{E}_{\rm in}(t)$};
    \begin{scope}[shift={(2.7*\beam,0)},rotate=90]
      \node[olabel,anchor=north,rotate=90] at (0,0) {translatable mirror};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec13
filename: lec13.tex
modified: 2018-02-14 17:46:40
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-4,
        xmax=4.5,
        ymin=0,
        ymax=1.1,
        enlargelimits=false,
        width=2.75in,
        height=2.5in,
        xlabel={$\omega-\omega_{0}$},
        ylabel={$P(\omega)$},
        ytick={0},
        yticklabels=\empty,
        xtick={0},
        xticklabels=\empty,
        % xticklabels{0,,$a$,,a$},
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
      ]
      \addplot[
        DarkGreen,
        domain=-4:4,
        samples=201,
        line width=1.5pt,
      ]
      {1 / (1 + x^2))};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec13
filename: lec13.tex
modified: 2018-02-14 17:46:40
domain: p134
source:
  \begin{tikzpicture}[scale=0.8]
    \draw[line width=2pt,gray] (0,0) arc(180:200:4) coordinate (a);
    \draw[line width=2pt,gray] (0,0) arc(180:160:4);
    \draw (.04,0) arc(180:200:3.96);
    \draw (.04,0) arc(180:160:3.96);


    \draw[line width=2pt,gray] (8,0) arc(0:20:3);
    \draw[line width=2pt,gray] (8,0) arc(0:-20:3) coordinate (b);

    % edges of the gaussian beam
    \draw[DarkRed] (0.2,1) .. controls (4,0.3) and (5,0.3)  .. (7.9,0.7);
    \draw[DarkRed] (0.2,-1) .. controls (4,-0.3) and (5,-0.3)  .. (7.9,-0.7);

    \draw[photon,->] (0.2,-0.2) -- (7.8,-0.2);
    \draw[photon,->] (7.9,0.2) -- (0.1,0.2);
    \draw[photon,->] (8.1,0) -- ++(0:2);

    \begin{scope}[DarkGreen,line width=1.5]
      \draw[dashed] (0,0) -- (0,2);
      \draw[dashed] (8,0) -- (8,2);
      \draw[<->] (0,1.75) --node[fill=white]{$L$} ++(0:8);
    \end{scope}

    \node[anchor=north,text width=7cm,align=center,font=\large] at (4,-1)
    { Need $\displaystyle L = m \frac{\lambda}{2} $ for constructive
      interference, $m \in \mathbb{Z}$ }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec14
filename: lec14.tex
modified: 2018-02-16 19:38:52
domain: p134
source:
  \begin{tikzpicture}[scale=0.5]
    \draw[line width=2pt,gray] (0,0) arc(180:200:4) coordinate (a);
    \draw[line width=2pt,gray] (0,0) arc(180:160:4);
    \draw (.04,0) arc(180:200:3.96);
    \draw (.04,0) arc(180:160:3.96);


    \draw[line width=2pt,gray] (8,0) arc(0:20:3);
    \draw[line width=2pt,gray] (8,0) arc(0:-20:3) coordinate (b);

    \node[anchor=north] at (a) {$r_{1}$};
    \node[anchor=north] at (b) {$r_{2}$};

    % edges of the gaussian beam
    \draw[DarkRed] (0.2,1) .. controls (4,0.3) and (5,0.3)  .. (7.9,0.7);
    \draw[DarkRed] (0.2,-1) .. controls (4,-0.3) and (5,-0.3)  .. (7.9,-0.7);

    \draw[photon,->] (0.2,-0.2) -- (7.8,-0.2);
    \draw[photon,->] (7.9,0.2) -- (0.1,0.2);
    \draw[photon,->] (8.1,0) -- ++(0:2);

    \begin{scope}[DarkGreen,line width=1.5]
      \draw[dashed] (0,0) -- (0,2);
      \draw[dashed] (8,0) -- (8,2);
      \draw[<->] (0,1.75) --node[fill=white]{$L$} ++(0:8);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec14
filename: lec14.tex
modified: 2018-02-16 19:38:52
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \def\R{0.94}
    \begin{axis}[
        xmin=-800,
        xmax=800,
        ymin=0,
        % ymax=1,
        %enlargelimits=false,
        width=2.5in,
        height=1.5in,
        xlabel={$\phi$},
        ylabel={$\mathcal{T}$},
        ytick={},
        yticklabel=\empty,
        xtick={-720,-360,0,360,720},
        xticklabels={$-4\pi$,$-2\pi$,$0$,$2\pi$,$4\pi$},
        % xticklabels{0,,$a$,,a$},
        axis x line=bottom,
        axis y line=center
      ]
      \addplot[
        DarkGreen,
        domain=-800:800,
        samples=1001,
        line width=1pt,
      ]
      {(1-\R)^2 /( (1-\R)^2 + 4*\R*(sin(x/2)^2))};
    \end{axis}
    %      }

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec15
filename: lec15.tex
modified: 2018-02-19 19:12:06
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=390, xmax=1050, ymin=0, ymax=1.2, enlargelimits=false,
        width=\textwidth, height=2in,
        xlabel={$\lambda$ (nm)}, ylabel={Normalized Intensity}, ytick={0,1}, xtick={400,500,600,700,800,900,1000},
        % xticklabel=\empty, xticklabels{0,,$a$,,a$},
        % axis x line=bottom, axis y line=left axis line style={line width=1.25} % for no frame
      ]
      \addplot[DarkGreen,line width=2,smooth] table {Tisapphabs.dat};
      \addplot[DarkRed,line width=2,smooth] table {Tisapphemit.dat};
      \node[DarkGreen] at (axis cs:510,1.1) {absorption};
      \node[DarkRed] at (axis cs:800,1.1) {emission};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec15
filename: lec15.tex
modified: 2018-02-19 19:12:06
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \def\image{5}

    \fill (-4,1,0) coordinate (S) circle[radius=0.04] node[anchor=south east]{$S(x_{s}, y_{s}, z_{s})$};

    % aperture plane
    \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) -- (\image+2,0,0) node[anchor=north] {$z$ };
    \begin{scope}[shift={(\image,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,->] (\image,0,0) -- (\image+2,0,0) node[anchor=north] {$z$ };

    \draw[DarkBlue,->] (S) -- node[anchor=north] {$\vb{s}_{0}$} (0,0);
    \fill (\image,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 (0,2.5,0) {aperture plane};
    \node at (\image,2.5,0) {image plane};

    \node at (0,-3,0) {$\displaystyle E(P) = \underset{
          \mathclap{
            \substack{\text{over} \\ \text{aperture}}
          }
        }{\iint} \dd{x}\dd{y} \;
        \underbrace{\frac{A e^{i(ks-\omega t)}}{s}}_{\substack{\text{source} \\
            \text{spherical} \\ \text{wave}}} \frac{e^{ikr}}{r} \frac{e^{i\pi/2}}{\lambda}
        \underbrace{\frac{\vu{s} \vdot \vu{z} + \vu{r} \vdot \vu{z}
          }{2}}_{\substack{\text{obliquity} \\ \text{factor}}}   $};

    \node[anchor=east,DarkSlateGray,font=\scriptsize] at (7.5,-3.5) {see Born \&
      Wolf, Ch.\ 8};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec15
filename: lec15.tex
modified: 2018-02-19 19:12:06
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-10, xmax=11, ymin=0, ymax=1.1, enlargelimits=false,
        width=3.5in, height=3in,
        xlabel={$\alpha$}, ylabel={$I$}, ytick={0},xtick=\empty,
        % xticklabel=\empty, xticklabels{0,,$a$,,a$},
        axis x line=bottom, axis y line=left, axis line style={line width=1,gray} % for no frame
      ]
      \addplot[DarkGreen, domain=-10:10, samples=300, line width=2pt,]
      {(sin(x*180/3.14159)/x)^2};
    \end{axis}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec06
filename: lec06.tex
modified: 2018-01-29 17:26:15
domain: p134
source:
  \begin{tikzpicture}[scale=0.8]
    \begin{axis}[
        xmin=0,
        xmax=4,
        ymin=0,
        ymax=1.1,
        enlargelimits=false,
        width=2.5in,
        xlabel={$d$},
        ylabel={$I_{\rm out}$},
        ytick={0,1},
        xtick={0,1,2,3,4},
        xticklabels={0,$\lambda$,$2\lambda$,$3\lambda$,$4\lambda$},
      ]
      \addplot[
        domain=0:5,
        samples=801,
        line width=1pt,
        DarkRed
      ]
      {sin(360*x)^2};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec08
filename: lec08.tex
modified: 2018-02-02 19:12:36
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-3,
        xmax=3,
        ymin=0,
        ymax=1.05,
        enlargelimits=false,
        width=3.in,
        height=2.5in,
        xlabel={$\Omega$},
        ylabel={$|A(\Omega)|$},
        ytick={},
        yticklabel=\empty,
        xtick={0},
        %xticklabel=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
      ]
      \addplot[
        domain=-3:3,
        samples=201,
        line width=0pt,
        fill=DarkRed!10!white
      ]
      {exp(-x^2)} \closedcycle;

      \addplot[domain=0.8:1, samples=25,fill=green!25!white,line width=0pt]
      {exp(-x^2)} \closedcycle;

      \addplot[
        domain=-3:3,
        samples=201,
        line width=1pt,
        DarkRed,
      ]
      {exp(-x^2)};

      \draw[<-,DarkGreen] (0.8,0.1) -- (0.5,0.1) node[anchor=east]{$\Delta\Omega$};
      \draw[<-,DarkGreen] (1,0.1) -- (1.3,0.1);
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec09
filename: lec09.tex
modified: 2018-02-05 23:25:27
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-100,
        xmax=100,
        ymin=-0.4,
        ymax=1.05,
        enlargelimits=false,
        width=2.5in,
        height=1.5in,
        xlabel={},%$\Omega$},
        ylabel={$\mathrm{sinc}(\Omega T/2)$},
        ytick={0},
        yticklabel=\empty,
        xtick={0},
        %xticklabel=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
      ]
      \addplot[
        domain=-100:-10,
        samples=101,
        line width=0.5pt,
        DarkRed
      ]
      {sin(x*180/3.14159)/x};

      \addplot[
        domain=-10:10,
        samples=100,
        line width=0.5pt,
        DarkRed
      ]
      {sin(x*180/3.14159)/x};
      \addplot[
        domain=10:100,
        samples=101,
        line width=0.5pt,
        DarkRed
      ]
      {sin(x*180/3.14159)/x};

      \draw[<-,NavyBlue] (3.14,0) --  (10,0.5) node[anchor=west]{$\frac{\pi}{T}
        $};

    \end{axis}
    \node at (4.25,-0.25) {$\Omega$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec09
filename: lec09.tex
modified: 2018-02-05 23:25:27
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=-3,
        xmax=3,
        ymin=0,
        ymax=1.05,
        enlargelimits=false,
        width=3.in,
        height=1.5in,
        xlabel={$\Omega$},
        ylabel={$|A(\Omega)|$},
        ytick={},
        yticklabel=\empty,
        xtick={0},
        %xticklabel=\empty,
        axis x line=bottom,
        axis y line=left,
        axis line style={line width=1.25}
      ]
      \addplot[
        domain=-3:3,
        samples=201,
        line width=0pt,
        fill=DarkRed!10!white
      ]
      {exp(-x^2)} \closedcycle;

      \addplot[domain=0.8:1, samples=25,fill=green!25!white,line width=0pt]
      {exp(-x^2)} \closedcycle;

      \addplot[
        domain=-3:3,
        samples=201,
        line width=1pt,
        DarkRed,
      ]
      {exp(-x^2)};

      \draw[<-,DarkGreen] (0.8,0.1) -- (0.5,0.1) node[anchor=east]{$\Delta\Omega$};
      \draw[<-,DarkGreen] (1,0.1) -- (1.3,0.1);
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec07
filename: lec07.tex
modified: 2018-02-01 03:50:08
domain: p134
source:
  \begin{tikzpicture}[scale=1,
      energy/.style= {DarkGreen},
      Na/.style={yellow!75!black}
    ]
    \draw (0,0) -- ++(0:1) node[anchor=west]{$3s_{1/2}$};
    \node[energy,anchor=east] at (-0.25,0) {$-5.14$};

    \draw (1,4) -- ++(0:1) node[anchor=west]{$3p_{1/2}$};
    \draw (1,4.5) -- ++(0:1) node[anchor=west]{$3p_{3/2}$};

    \draw[->,Na,line width=2] (1.25,4.5)
    --node[fill=white,rotate=78]{$\SI{589.0}{nm}$}  (0.25,0);
    \draw[->,Na,line width=2] (1.75,4)
    --node[fill=white,rotate=78]{$\SI{589.6}{nm}$}  (0.75,0);

    \node[energy, anchor=east] at (-0.25,4.25) {$-3.04$};
    \draw[dashed] (0,4.25) -- ++(0:1);
    \node[rotate=90,energy] at (-0.75,2.125){Energy (eV)};

    \draw[<->,DarkGreen] (3.25,4) -- node[anchor=west,text
      width=2cm,font=\scriptsize]{spin-orbit splitting = \SI{2.1}{meV}} ++(90:0.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec17
filename: lec17.tex
modified: 2018-02-23 21:46:37
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed,DarkSlateGray] (-5.5,0) -- (4,0);
    \foreach \y in {-3,-2,...,3}{
        \draw[DarkRed,->] (-5,\y*0.2) -- ++(0:2);
        \only<1>{
          \draw[DarkRed,->] (-1.5,\y*0.2) -- ++(15:5);
        }
      }
    \only<1>{
      \draw (3.25,0) arc(0:15:2.4);
      \node[anchor=west] at (3.25,0.35) {$\theta$};
    }
    \draw[line width=2] (-2,0.5) -- ++(90:2);
    \draw[line width=2] (-2,-0.5) -- ++(-90:2);

    \node[anchor=west,text width=1.5in] at (4,2) {%
      Far-field behavior assumes rays emerge parallel from the aperture.};

    \only<2>{
      \draw[] (-1,0) arc(180:150:6) coordinate (A);
      \draw (-1,0) arc(180:210:6) coordinate (B);
      \fill[fill=gray,opacity=0.25,black] (B) arc(210:150:6) -- cycle;
      \draw (A) -- (B);
      \draw[gray,line width=2] (3.5,2) -- (3.5,-2); % screen
      \coordinate (C) at (3.5,1);
      \foreach \y in {-3,-2,...,3}{
          \draw[DarkRed] (-1.5,\y*0.2) -- ++(15:0.5) -- (C);
        };
      \draw[->,line width=1.5,DarkGreen] (-.5,-1) --
      node[anchor=south]{$f$} (3.5,-1);
      \node[DarkGreen,text width=1.5in,anchor=west] at (4,-1) {%
        A lens focuses parallel rays at its focal plane, producing the
        Fraunhofer diffraction pattern there.};
    }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec17
filename: lec17.tex
modified: 2018-02-23 21:46:37
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \coordinate (R) at (10,0);
    \draw (-1.5,0) coordinate(S) -- (R);
    \node[anchor=north] at (-.75,0) {$s_{0}$};
    \fill[DarkRed] (S) circle[radius = 0.05];
    \draw[line width=2] (0,-2) -- (0,0.5);
    \draw[<-] (-.1,-2.1) -- ++(225:1.25) node[anchor=north]{razor};
    \draw[line width=1.5,DarkRed] (S) -- (0,1) -- (R);
    \node[anchor=west] at (R) {$P$};
    \node[anchor=north] at (5,0) {$r_{0}$};
    \draw[DarkGreen,->] (0.2,0) -- node[anchor=west]{$\xi$} (0.2,1);
    \draw[DarkGreen,->] (-0.2,0) -- node[anchor=east]{$x$} (-0.2,0.5);

    \node[anchor=north,text width=3in] at (5,-1) {%
    $$ E_{P} \sim \int_{-\infty}^{\infty} \dd{\eta} \int_{x}^{\infty} \dd{\xi} e^{i k
          f(\xi,\eta)} $$

    $$ f(\xi,\eta) = \frac{\xi^{2} + \eta^{2}}{2} \qty(\frac{1}{s_{0}} +
      \frac{1}{r_{0}})  $$

    $$ u^{2} \equiv \frac{2(s_{0}+r_{0})}{\lambda s_{0} r_{0}} \xi^{2}
      \qquad
      v^{2} \equiv \frac{2(s_{0}+r_{0})}{\lambda s_{0} r_{0}} \eta^{2}
    $$
    };
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec10
filename: lec10.tex
modified: 2018-02-07 19:04:40
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \draw[->] (0,-1) -- (5,-1) node[anchor=north east]{$t$};
    \foreach \i in {0,1,...,6}
      {
        \node at (2+rand*2,rand) {\includegraphics[width=2cm,height=0.5cm]{decay}};
      }

    \node[anchor=west,text width=2in] at (6,0) {atoms emitting after stimulation at random times};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec05
filename: NaDoubletTikz.tex
modified: 2018-01-26 19:52:20
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \def\lamone{.589}
    \def\lamtwo{.5896}
    \begin{axis}[
        xmin=0,
        xmax=10,
        ymin=0,
        ymax=2.1,
        enlargelimits=false,
        width=2.5in,
        xlabel={$d$\ (\textmu m)},
        ylabel={$I_{\rm out}$},
        ytick={0,1},
        %      xtick={0,1,2,3,4},
        %      xticklabels={0,$\lambda$,$2\lambda$,$3\lambda$,$4\lambda$},
      ]
      \addplot[
        domain=0:10,
        samples=2001,
        line width=0.5pt,
        DarkRed
      ]
      {sin(360*x/\lamone)^2 + sin(360*x/\lamtwo)^2};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec05
filename: NaDoubletTikz.tex
modified: 2018-01-26 19:52:20
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \def\lamone{.589}
    \def\lamtwo{.5896}
    \begin{axis}[
        xmin=0,
        xmax=200,
        ymin=0,
        ymax=2.1,
        enlargelimits=false,
        width=2.5in,
        xlabel={$d$\ (\textmu m)},
        ylabel={$I_{\rm out}$},
        ytick={0,1},
        %      xtick={0,1,2,3,4},
        %      xticklabels={0,$\lambda$,$2\lambda$,$3\lambda$,$4\lambda$},
      ]
      \addplot[
        domain=0:200,
        samples=10001,
        line width=0.5pt,
        DarkRed
      ]
      {sin(360*x/\lamone)^2 + sin(360*x/\lamtwo)^2};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec05
filename: lec05.tex
modified: 2018-01-29 01:35:44
domain: p134
source:
  \begin{tikzpicture}[scale=.67,
      blabel/.style= {DarkRed,font=\sffamily},
      olabel/.style={DarkGreen,font=\sffamily},
      beam/.style={DarkRed,line width=2pt}
    ]

    \def\beam{2cm}
    \def\bsthick{0.25cm}

    % source
    \begin{scope}[shift={(-2.5*\beam,0.5)}]
      \node[star, star points=12,star point height=0.5,star point
        ratio=3,fill,DarkRed] at (0,0){};
      \node[DarkRed,anchor=south] at (0,0.75) {\textsf{source}};
    \end{scope}

    % beams
    \draw[beam] (-2*\beam,0.5) -- (2.5*\beam,0.5) ; % incident beam
    \draw[beam,->] (-1.25*\beam,0.5) -- +(0:.25); % arrows for incident beam
    \draw[beam,->] (1.5*\beam,0.5) --+(0:.25);

    \draw[beam] (0.5,0.5) -- (0.5,2*\beam);  % towards top mirror
    \draw[beam,->] (0.5,\beam) -- +(90:0.5);

    \draw[beam,->] (-0.5,2*\beam) -- ++(-90:4*\beam) node[blabel,anchor=north]
    {$\mathbf{E}_{\rm out}$}; % from top mirror
    \draw[beam,->] (-0.5,\beam) -- ++(-90:0.25);

    \draw[beam,->] (2.5*\beam,-0.2) -- (-2*\beam,-0.2);
    \draw[beam,->] (1.5*\beam,-0.2) -- +(180:0.25);

    \draw[beam,->] (-0.2,-0.2) -- (-0.2,-2*\beam);
    \draw[beam,->] (-0.5,-0.5) -- (-2*\beam,-0.5);


    % beamsplitter
    \begin{scope}[shift={(-1.414*\bsthick,0)},rotate=45]
      \filldraw[fill=gray!20,opacity=0.5] (-1*\beam,0) rectangle (1.*\beam,-\bsthick);
      \draw[line width=1.5pt] (-\beam,-\bsthick) -- (\beam,-\bsthick);
      \draw[olabel,<-] (-1.1*\beam,0) -- ++(180:0.6) node[anchor=north east] {beam splitter};
    \end{scope}

    % compensator
    \begin{scope}[shift={(1.5,0)},rotate=45]
      \filldraw[fill=gray!20,opacity=0.5] (-1.*\beam,0) rectangle (1.*\beam,-\bsthick);
      \draw[olabel,<-] (\beam,0.2) --++(45:0.6) node[anchor=south] {compensator};
    \end{scope}

    % top mirror
    \filldraw[fill=gray!30] (-\beam,2*\beam) rectangle (\beam,2*\beam+\bsthick);
    \draw[line width=2] (-\beam,2*\beam) -- +(0:2*\beam);
    \node[anchor=west] at (\beam,2*\beam+0.5*\bsthick) {\large $M_{2}$};

    % right mirror
    \begin{scope}[shift={(2*\beam,0)},opacity=0.25]
      \filldraw[fill=gray!30] (0,-\beam) rectangle (\bsthick,\beam);
      \draw[line width=2] (0,-\beam) -- ++(90:2*\beam);
    \end{scope}

    \begin{scope}[shift={(2.5*\beam,0)}]
      \filldraw[fill=gray!30] (0,-\beam) rectangle (\bsthick,\beam);
      \draw[line width=2] (0,-\beam) -- ++(90:2*\beam);
      \node[anchor=south] at (0.5*\bsthick, \beam) {\large $M_{1}$};
    \end{scope}


    \draw[DarkGreen,|->] (2*\beam,-1.25*\beam) -- node[anchor=north]{$d$}
    (2.5*\beam,-1.25*\beam);

    % labels
    \node[blabel,anchor=south west] at (-2*\beam,0.5) {$\mathbf{E}_{\rm in}(t)$};
    \begin{scope}[shift={(2.7*\beam,0)},rotate=90]
      \node[olabel,anchor=north,rotate=90] at (0,0) {translatable mirror};
    \end{scope}

    \onslide<2->{\node at (-5,4) {\key};}
    \onslide<3>{\node at (7,-4) {\key};}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec04
filename: lec04.tex
modified: 2018-01-24 05:41:26
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \node[anchor=south west,inner sep=0] at (0,0) {
      \includegraphics[width=0.675\textwidth]{lec04fit01} };
    \draw<2>[DarkRed,ultra thick,rounded corners] (1,5.75) rectangle
    (3.5,6.15);
    \node<2>[anchor=north east,text width=4cm,DarkRed] at (1.5,5.6) {\small Either select
      a function from the menu, or click to define a \textbf{New Fit Function\ldots}};
    \draw<2>[DarkRed,ultra thick,rounded corners] (2,2) rectangle (5,3.5);
    \draw<3>[DarkRed,ultra thick,rounded corners] (3.7,5.75) rectangle
    (5.5,6.15);
    \draw<3>[DarkRed,ultra thick,rounded corners] (3.7,4.6) rectangle (5.5,5);
    \node<3>[DarkRed,anchor=west,text width=4cm] at (6,5) {\small Select the
      dependent variable and the independent variable (or \_calculated\_)};
    \draw<4>[DarkRed,ultra thick,rounded corners] (6,6) rectangle (7.25,6.5);
    \node<4>[DarkRed,anchor=west,text width=3cm] at (7.25,6.5) {\small
      Checking \textbf{From Target} limits the waves you can pick to those in
      the top graph};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec04
filename: lec04.tex
modified: 2018-01-24 05:41:26
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \node[anchor=south west, inner sep=0] at (0,0) {
      \includegraphics[width=0.675\textwidth]{lec04fit02} };
    \draw[DarkRed,ultra thick,rounded corners] (3.2,5.35) rectangle
    (6.5,6);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec04
filename: lec04.tex
modified: 2018-01-24 05:41:26
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \node[anchor=south west, inner sep=0] at (0,0) {
      \includegraphics[width=0.675\textwidth]{lec04fit04}};
    \draw[DarkRed,ultra thick,rounded corners] (0.8,5.75) rectangle (3.8,6.1);
    \draw[DarkRed,ultra thick,rounded corners] (0.8,5) rectangle (3.8,5.4);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/lec/lec04
filename: lec04.tex
modified: 2018-01-24 05:41:26
domain: p134
source:
  \begin{tikzpicture}[scale=1]

    \node[anchor=south west,inner sep=0] at (0,0) {
      \includegraphics[width=0.8\textwidth]{lec04fig01}};
    \node<1-> at (-1.5,6) {\small \textbf{Lec04.pxp}};
    \node<2->[anchor=south west,inner sep=0,fill=gray!15!white] at (-1.25,1){
      \includegraphics[width=5.5cm]{Fraunhofer}};
    \node<3->[anchor=south west,fill=DarkGreen!15,text width=4cm] at (6,1)
    {\small Plot the data, fit to the AiryDisk function, and see what
      conclusions you can draw. };
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/reports/cadams@hmc/3-write_up_exp2
filename: Adams-3-PNS.tex
modified: 2018-04-22 17:55:21
domain: p134
source:
  \begin{tikzpicture}[scale = 2, >=stealth',pos=.8, photon/.style={decorate,decoration={snake,post length=1mm}}]
    \draw[color = orange, fill = orange, line width = 0.7pt] (0,0) circle(1);
    \draw[->, color = black] (0,0) -- (-0.7071067812,0.7071067812);
    \draw[->,photon, color = red] (1,0) -- (1,-1);
    \draw[->,photon, color = orange] (0,-1) -- (0,-1.5);
    \draw[->,photon, color = blue] (-1,0) -- (-1,-1);
    \draw[->,>=stealth',semithick] (10:1.1) arc[radius=1.2, start angle=10, end angle=70] ;
    \draw[->, color = black] (1,0) -- (1,0.3);
    \draw[->, color = black] (0.,-1.) -- (0,-1-0.25);
    \draw[->, color = black] (0,-1) -- (0.3,-1);
    \node at (0, 1.3) {{\emph{Top View of Sol}}};
    \node at (1.,-1.12) {$\lambda_R  < \lambda$};
    \node at (-1.,-1.12) {$\lambda_L  >\lambda$};
    \node at (0,-1.6) {$\lambda$};
    \node at (0.95, 0.9){$\omega$};
    \node at (-0.7071067812/2 +0.1 , 0.7071067812/2 + 0.1) {$R$};
    \node at (0, -1.9) {[\textsc{Observer Here}]};
    \node at (1.1,0.1) {$ \mathbf{v}$};
    \node at (-0.1,-1.-0.11) {$ \mathbf{\hat n}$};
    \node at (0.35,-1) {$ \mathbf{v}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/2018/reports/cadams@hmc/3-write_up_exp2/tikz
filename: test.tex
modified: 2018-03-27 04:56:54
domain: p134
source:
  \begin{tikzpicture}[>=stealth',pos=.8, photon/.style={decorate,decoration={snake,post length=1mm}}]]
    \draw[color = orange, fill = orange, line width = 0.7pt] (0,0) circle(1);
    \draw[->,photon] (1,0) -- (1,-1);
    \draw[->,photon] (0,-1) -- (0,-2);
    \draw[->,photon] (-1,0) -- (-1,-1);
    \draw[->,>=stealth',semithick] (10:1.1) arc[radius=1.2, start angle=10, end angle=70] ;
    \node at (0, 1.5) {Top View};
    \node at (1.,-1.12) {$\lambda_R  < \lambda$};
    \node at (-1.,-1.12) {$\lambda_R  >\lambda$};
    \node at (0,-2.2) {$\lambda$};
    \node at (0.95, 0.9){$\omega$};
    \node at (0, 0) {Sol};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/p134
filename: Exp6bell.tex
modified: 2018-02-08 19:39:24
domain: p134
source:
  \begin{tikzpicture}[scale=0.85]

    \def\thick{0.25}
    \def\height{1}
    \def\diverge{8} % degrees
    \def\PBS{\filldraw[fill=gray!5,opacity=0.5] (-0.2,-0.2) rectangle (0.2,0.2); \draw
      (-0.2,-0.2) -- (0.2,0.2); }
    \draw[uvbeam] (10,0) -- (-2,0);
    \filldraw[fill=DarkOrchid!25] (10,-0.5) rectangle (13,0.5);
    \node[color=DarkOrchid] at (11.5,0){\large\textbf{Laser 405 nm}};

    % beam dump
    \fill (-2,0.5\height) rectangle (-2.5,-0.5\height);
    \node[anchor=east,text width=1cm] at (-2.75,0) {Beam dump};
    % HWP
    \filldraw[hwp] (9,-\height) rectangle(9+\thick,\height);
    \node[anchor=south] at (9+\thick/2,\height){$\lambda/2$};

    % quartz plate
    \begin{scope}[shift={(8,0)},rotate=15]
      \filldraw[fill=gray!30,opacity=0.5] (0,-\height) rectangle(\thick,\height);
      \node[anchor=south,text width=1cm,align=center] at
      (\thick/2,\height){quartz\par plate};
      \begin{scope}[shift={(\thick/2-0.125,0.2)}]
        \draw[->,line width=1pt] (120:0.2) arc(120:420:0.4);
      \end{scope}
    \end{scope}

    % SPD crystals
    \begin{scope}[shift={(7,0)}]
      \filldraw[fill=gray!40,opacity=0.5] (0,-0.5*\height) rectangle
      (0.15,0.5*\height);
      \filldraw[fill=gray!40,opacity=0.5] (0.15,-0.5*\height) rectangle
      (0.3,0.5*\height);
      \node[anchor=south] at (0.15, 0.6\height) {SPD};
      \node[anchor=north] at (0.15, -0.6\height) {crystals};
    \end{scope}

    % IR photons
    \draw[beam] (7.15,0) --node[rotate=-\diverge,anchor=south]{signal} ++(180-\diverge:8);
    \draw[beam] (7.15,0) --node[rotate=\diverge,anchor=north]{idler} ++(180+\diverge:8);
    \begin{scope}[shift={(0,1)},rotate=90-\diverge]
      \draw[beam] (0,0) -- ++(0:0.8);
      \detector{(90:0.8)}{90}
      \node[anchor=east] at (90:1.25){$T$};
      \detector{(0:0.8)}{0}
      \node[anchor=south] at (0:1.25){$R$};
      \PBS
      \filldraw[hwp] (-0.3,-0.8) rectangle (0.3,-0.9);
      \node[anchor=south] at (0.3,-0.85){$\lambda/2$};
    \end{scope}

    \begin{scope}[shift={(0,-1)},rotate=90+\diverge]
      \draw[beam] (0,0) -- ++(180:0.8);
      \detector{(90:0.8)}{90}
      \node[anchor=east] at (90:1.25){$G$};
      \detector{(180:0.8)}{180}
      \node[anchor=north] at (180:1.25){$G'$};
      \begin{scope}[rotate=90]
        \PBS
        \filldraw[hwp] (-0.8,-0.3) rectangle (-0.9,0.3);
        \node[anchor=north] at (-0.85,0.35){$\lambda/2$};
      \end{scope}
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/p134
filename: Exp8.tex
modified: 2019-01-09 20:18:49
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \def\h{2}
    \def\w{3}
    \def\inang{40}
    \def\outang{25}
    \fill[fill=gray!10] (-\w,0) rectangle (\w,\h) ;
    \fill[fill=gray!30] (-\w,0) rectangle (\w,-\h) ;
    \draw (-\w,0) -- (\w,0);  % interface
    \draw[dashed] (0,-\h) -- (0,\h);
    \node[anchor=south west] at (-\w, 0) {$n_{1}$};
    \node[anchor=north west] at (-\w, 0) {$n_{2}$};
    % angles
    \draw[color=gray] (0,0) -- (90+\inang:2.5);
    \draw[color=gray] (0,0) -- (90-\inang:2.5);
    \draw[color=gray] (0,0) -- (-90+\outang:2.2);
    \draw (0,0.5) arc (90:90+\inang:0.5);
    \draw (0,0.5) arc (90:90-\inang:0.5);
    \draw (0,-0.65) arc (-90:-90+\outang:0.65);
    \node at (90+\inang * 0.5:0.85) {$\theta_{1}$};
    \node at (90-\inang * 0.5:0.85) {$\theta_{1}$};
    \node at (-90+\outang * 0.5:1.2) {$\theta_{2}$};

    % k vectors
    \draw[force] (90+\inang:2) -- node[anchor=north east]{$\vb{k}_{\rm i}$}
    ++(-90+\inang:1);
    \draw[force] (90-\inang:1) -- node[anchor=north west]{$\vb{k}_{\rm refl}$}
    ++(90-\inang:1);
    \draw[force] (-90+\outang:0.8) -- node[anchor=south west]{$\vb{k}_{\rm refr}$} ++(-90+\outang:1.3);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/p134
filename: Exp8.tex
modified: 2019-01-09 20:18:49
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \def\w{5}
    \def\h{3}
    % Normal to the plane of interface
    \draw[dashed,color=blue!40!black] (0, 0) -- (0, 1.1*\h) node[anchor=south]{N};
    \draw[dashed,color=blue!40!white] (0, -1.1*\h) -- (0, 0);
    \draw (-\w, 0) -- (\w, 0);
    % planes
    \filldraw[fill=gray!20,opacity=0.2] (-\w,-\h,0) rectangle (\w,\h,0) ;
    \filldraw[fill=gray!60,opacity=0.4] (-\w,-\h,0) rectangle (\w,0,0) ;
    \filldraw[fill=gray!20,opacity=0.2] (-\w,-\h,0) rectangle (\w,\h,0) ;
    \filldraw[fill=gray!20,opacity=0.3] (-\w,0, \h) -- (\w, 0, \h) --  (\w,0,-\h)
    -- (-\w, 0, -\h)  -- cycle;
    \node[anchor=north west] at (-\w,\h) {\small\textsf{Plane of incidence}};
    \begin{scope}[cm={1,0,0.8,0.8,(0,0)}] % Sets the coordinate transfo matrix entries.
      \node[transform shape,color=DarkGreen] at (-\w*0.5,0,0.9*\h) {\small\textsf{Plane of interface}};
    \end{scope}
    \node[anchor=north east] at (\w,-0.4){$n_{\rm t}$};
    \node[anchor=south east] at (\w,0.2){$n_{\rm i}$};
    % k vector lines
    \draw[color=gray,dashed] (0,0) -- (160:6) (0,0)  -- (20:6)
    (0,0) -- (-40:5);
    % angle definitions
    \draw (0,0.5) arc(90:160:0.5);
    \draw (0, -0.5) arc(270:320:0.5);
    \node at (125:0.8){$\theta_{\rm i}$};
    \node at (295:0.8){$\theta_{\rm t}$};
    % incident wave
    \begin{scope}[shift={(160:4)}]
      \draw[force] (0,0) -- ++(-20:1) node[anchor=north]{$\vb{k}_{\rm inc}$};
      \draw[field] (0,0) -- ++(70:1) node[anchor=west]{$\vb{E}_{\rm ||, inc}$};
      \draw[field] (0,0) -- ++(-135:0.75) node[anchor=north]{$\vb{E}_{\rm \perp, inc}$};
    \end{scope}

    % reflected wave
    \begin{scope}[shift={(20:3.5)}]
      \draw[force] (0,0) -- ++(20:1) node[anchor=north west]{$\vb{k}_{\rm refl}$};
      \draw[field] (0,0) -- ++(110:1) node[anchor=west]{$\vb{E}_{\rm ||, refl}$};
      \draw[field] (0,0) -- ++(-135:0.75) node[anchor=north]{$\vb{E}_{\rm \perp, refl}$};
    \end{scope}

    % transmitted wave
    \begin{scope}[shift={(-40:2)}]
      \draw[force] (0,0) -- ++(-40:1.35) node[anchor=south west]{$\vb{k}_{\rm trans}$};
      \draw[field] (0,0) -- ++(50:1) node[anchor=west]{$\vb{E}_{\rm ||, trans}$};
      \draw[field] (0,0) -- ++(-135:0.75) node[anchor=north]{$\vb{E}_{\rm \perp, trans}$};
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/p134
filename: scrap.tex
modified: 2017-12-01 05:37:29
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \def\w{5}
    \def\h{3}
    % Normal to the plane of interface
    \draw[dashed,color=blue!40!black] (0, 0) -- (0, 1.1*\h) node[anchor=south]{N};
    \draw[dashed,color=blue!40!white] (0, -1.1*\h) -- (0, 0);
    \draw (-\w, 0) -- (\w, 0);
    % planes
    \filldraw[fill=gray!20,opacity=0.2] (-\w,-\h,0) rectangle (\w,\h,0) ;
    \filldraw[fill=gray!20,opacity=0.3] (-\w,0, \h) -- (\w, 0, \h) --  (\w,0,-\h)
    -- (-\w, 0, -\h)  -- cycle;
    \node[anchor=north west] at (-\w,\h) {\small\textsf{Plane of incidence}};
    \begin{scope}[cm={1,0,1,1,(0,0)}] % Sets the coordinate trafo matrix entries.
      \node[transform shape,color=DarkGreen] at (-\w*0.5,0,0.8*\h) {\small\textsf{Plane of interface}};
    \end{scope}
    % k vector lines
    \draw[color=gray,dashed] (0,0) -- (160:6) (0,0)  -- (20:6)
    (0,0) -- (-40:5);
    % incident wave
    \begin{scope}[shift={(160:4)}]
      \draw[force] (0,0) -- ++(-20:1) node[anchor=north]{$k_{\rm inc}$};
      \draw[field] (0,0) -- ++(70:1) node[anchor=west]{$\VEC{E}_{\rm ||, inc}$};
      \draw[field] (0,0) -- ++(-135:0.75) node[anchor=north]{$\VEC{E}_{\rm \perp, inc}$};
    \end{scope}

    % reflected wave
    \begin{scope}[shift={(20:4)}]
      \draw[force] (0,0) -- ++(20:1) node[anchor=north]{$k_{\rm refl}$};
      \draw[field] (0,0) -- ++(110:1) node[anchor=west]{$\VEC{E}_{\rm ||, refl}$};
      \draw[field] (0,0) -- ++(-135:0.75) node[anchor=north]{$\VEC{E}_{\rm \perp, refl}$};
    \end{scope}

    % transmitted wave
    \begin{scope}[shift={(-40:2)}]
      \draw[force] (0,0) -- ++(-40:1.35) node[anchor=south west]{$k_{\rm trans}$};
      \draw[field] (0,0) -- ++(50:1) node[anchor=west]{$\VEC{E}_{\rm ||, trans}$};
      \draw[field] (0,0) -- ++(-135:0.75) node[anchor=north]{$\VEC{E}_{\rm \perp, trans}$};
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/p134
filename: scrap.tex
modified: 2017-12-01 05:37:29
domain: p134
source:
  \begin{tikzpicture}[scale=1.25]
    \def\w{3}
    \def\pt{0.05}
    \draw[->] (-\w,0) -- (\w,0) node[anchor=north]{$1/d\obj$};
    \draw[->] (0,-\w) -- (0,\w) node[anchor=west]{$1/d\img$};
    \draw[dashed,DarkBlue] (-\w/2,\w) -- (\w,-\w/2);
    \draw[dashed,DarkBlue] (-\w,\w/2) -- (\w/2,-\w);
    \fill (\w/2,0) circle[radius=\pt] node[anchor=south west]{$1/f\conv$};
    \fill (0,\w/2) circle[radius=\pt] node[anchor=south west]{$1/f\conv$};
    \fill (-\w/2,0) circle[radius=\pt] node[anchor=north east]{$1/f\divg$};
    \fill (0,-\w/2) circle[radius=\pt] node[anchor=north east]{$1/f\divg$};
    \node[text width=1in,align=center] at (.75*\w,.75*\w){\small\textsf{real
        object and real image}};
    \node[text width=1in,align=center] at (-.75*\w,.75*\w){\small\textsf{virtual
        object and real image}};
    \node[text width=1in,align=center] at (-.75*\w,-.75*\w){\small\textsf{virtual
        object and virtual image}};
    \node[text width=1in,align=center] at (.75*\w,-.75*\w){\small\textsf{real object and virtual image}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/p134
filename: Exp5.tex
modified: 2020-01-23 20:19:42
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin=0,
        ymax=2,
        enlargelimits=false,
        height=2in,
        width=4in,
        xlabel={$\tau = 2d/c$},
        ylabel={$I(\tau) / \avg{I}$},
        ytick={0,1,2},
        xtick={0,100,200,300,400,500}
      ]
      \addplot[
        domain=0:500,
        samples=500,
        line width=1pt,
        color=DarkGreen
      ]
      {1 + cos(12*x) / exp(0.004*x)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/p134
filename: Exp5.tex
modified: 2020-01-23 20:19:42
domain: p134
source:
  \begin{tikzpicture}
    \begin{axis}[
        ymin=0,
        ymax=1,
        enlargelimits=false,
        height=2in,
        width=4in,
        xlabel={$\tau = 2d/c$},
        ylabel={$V(\tau)$},
        ytick={0,1},
        xtick={0,100,200,300,400,500}
      ]
      \addplot[
        domain=0:500,
        samples=100,
        line width=1pt,
        color=DarkGreen
      ]
      {1 / exp(0.004*x)};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/p134
filename: Exp3.tex
modified: 2019-05-03 16:30:29
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \def\redge{7} % right edge of lines
    \def\blueshift{DarkOrange!80!black}
    \draw (-4,0) -- (\redge,0);
    \node at (-2,0.35) {$2p^{5}\; 3p$ (Paschen $2p_{4}$)};
    \node at (-2, -0.35){$j=2$, $g_{2} = 1.301$};
    \foreach \y in {-2, -1, ..., 2} {
        \draw (0,0) -- (1.5,\y) -- (\redge,\y);
        \node[anchor=west] at (1.75,\y+0.25) {$m_{j} = \y$};
      }
    \draw (-4,5) -- (\redge,5);
    \node at (-2,5.35) {$2p^{5}\; 5s$ (Paschen $3 s_{2}$)};
    \node at (-2, 4.65){$j=1$, $g_{1} = 1.295$};
    \foreach \y in {-1, 0, 1} {
        \draw (0,5) -- (1.5, 5+\y) -- (\redge,5+\y);
        \node[anchor=west] at (1.75,\y+5.25) {$m_{j} = \y$};
      }
    \draw[<->] (\redge-0.5,5) --node[anchor=west]{$\Delta E = g_{1} \muB B$} ++(0,1);
    \foreach \n in {1, 0, -1} {
        \draw[transition] (5-\n,5+\n) -- ++(0,-4);
        \draw[transition,\blueshift] (5.25-\n,5+\n) -- ++ (0,-6);
      }
    \node[DarkRed, anchor=west] at (\redge-0.5,3.25) {$\Delta m_{j} = + 1$};
    \node[\blueshift, anchor=west] at (\redge-0.5,2.75) {$\Delta m_{j} = - 1$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/homework
filename: ps2-2020-sol.tex
modified: 2020-05-21 15:30:45
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=100, ymin=0, ymax=1, enlargelimits=false,
        width=5in, height=2in,
        xlabel={$\omega$}, ylabel={$\Four{P}(\omega)$}, ytick=\empty, xtick={20,70},
        xticklabels={$\omega_{1}$, $\omega_{2}$}, yticklabels={},
        axis x line=bottom, axis y line=left, axis x discontinuity=parallel,
        axis line style={line width=0.75,DarkSlateGray} % for no frame
      ]
      \addplot[Brown, domain=10:30, samples=101, line width=1pt]
      {exp(-0.1*(x-20)^2)};
      \addplot[Brown, domain=60:80, samples=101, line width=1pt]
      {exp(-0.1*(x-70)^2)};
    \end{axis}
    \begin{scope}[shift={(5,0)}]
      \def\ww{0.06} \def\hh{0.25}
      \draw[white,line width=2] (-\ww,0) -- (\ww,0);
      \draw (-\ww,\hh) -- (-\ww,-\hh);
      \draw (\ww,\hh) -- (\ww,-\hh);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/homework
filename: ps2-2020-sol.tex
modified: 2020-05-21 15:30:45
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=100, ymin=0, ymax=1.2, enlargelimits=false,
        width=5in, height=2.5in,
        xlabel={$\tau$}, ylabel={$I(\tau)$}, 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
      ]
      \begin{scope}[DarkGreen,opacity=0.5,samples=101,line width=1pt,domain=0:100]
        \addplot[line width=1pt]{ 0.5 * (1 + exp(-0.0001*x*x)) };
        \addplot[line width=1pt]{ 0.5 * (1 - exp(-0.0001*x*x)) };
        \draw[<-,opacity=1] (axis cs:65,0.84) -- (axis cs:70,0.95)
        node[anchor=west,text width=2.5cm,align=center] {decays like $\exp(-\sigma_{\omega}^2 \tau^2/2)$};
      \end{scope}

      \begin{scope}[DarkRed,line width=1,domain=0:100,samples=201,opacity=0.5]
        \addplot[line width=1] {0.5 * (1 - exp(-0.0001*x*x)*cos(15*x))};
        \addplot[line width=1] {0.5 * (1 + exp(-0.0001*x*x)*cos(15*x))};
        \draw[opacity=1,<-] (axis cs:28,0.8) -- (axis cs:35,1.05) node[anchor=west]
        {oscillates at $\cos\qty(\frac{\Delta \omega \tau}{2}) $};
      \end{scope}

      \begin{scope}[gray!70!black,line width=0.5]
        \addplot[domain=0:100,samples=2000] {0.5 * (1 -
          exp(-0.0001*x*x)*cos(15*x)* cos(400*x) )};
        \draw[<-] (axis cs:49,0.2) -- (axis cs:58,0.1)
        node[anchor=west]{fast fringes at $\overline{\omega}$};
      \end{scope}
    \end{axis}

    \node[DarkRed] at (5,-1.3) {Note: \emph{definitely \textbf{not} to scale}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/homework
filename: ps2-2020-sol.tex
modified: 2020-05-21 15:30:45
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=100, ymin=0, ymax=1.1, enlargelimits=false,
        width=5in, height=2in,
        xlabel={$\tau$}, ylabel={$\mathcal{V}(\tau)$}, 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
      ]

      \begin{scope}[DarkGreen,opacity=0.5,samples=101,line width=1pt,domain=0:100]
        \addplot[line width=1pt]{ exp(-0.0001*x*x) };
        \draw[<-,opacity=1] (axis cs:65,0.67) -- (axis cs:78,0.8)
        node[anchor=west,text width=2.5cm,align=center]
        {envelope decays like $\exp(-\sigma_{\omega}^2 \tau^2/2)$};
      \end{scope}

      \begin{scope}[DarkRed,line width=1,domain=0:100,samples=201]
        \addplot[line width=1] {exp(-0.0001*x*x)*abs(cos(15*x))};
        \draw[opacity=1,<-] (axis cs:27,0.8) -- (axis cs:35,1) node[anchor=west]
        {oscillates at $\qty|\cos\qty(\frac{\Delta \omega \tau}{2})|$};
      \end{scope}
    \end{axis}

    \node[DarkRed] at (5,-1.3) {Again: \emph{definitely \textbf{not} to scale}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/homework
filename: ps1-2019-sol.tex
modified: 2019-02-19 18:05:29
domain: p134
source:
  \begin{tikzpicture}[scale=1]

    \fill[fill=gray,opacity=0.25] (2,0.5) -- (-1,0.5) -- (-2,-0.5) -- (1,-0.5)
    -- cycle;
    % \filldraw[fill=yellow!20!white] (-1.5,0) --
    % (1.5,0) -- (1.5,1) -- (-1.5, 1) -- cycle;
    % \filldraw[fill=yellow!40!white] (1.5,0) -- (1.5,1) -- (1.8,1.5) --
    % (1.8,0.7) -- cycle;
    % \filldraw[fill=yellow!20!white, opacity = 0.5] (-1.5,1) --
    % (-0.8,1.5) -- (1.8,1.5) -- (1.5,1) -- cycle;

    \filldraw[fill=blue!50!white, opacity=0.5] (0,-0.1)
    circle[x radius=1, y radius=0.2];
    \filldraw[fill=gray!50!white, opacity=0.5] (0,0.1)
    circle[x radius=1, y radius=0.2];
    \fill[gray, opacity=0.5] (-1,0.1) arc[start angle=180, end
        angle=360, x radius=1, y radius = 0.2] -- ++(0,-0.2)
    arc[start angle=360, end angle=180, x radius=1, y radius = 0.2]
    -- cycle;
    \draw[dashed,opacity=0.75] (0,0) circle[x radius=1, y radius = 0.2];

    \draw[force] (0,0.1) -- ++(90:.75) node[anchor=east]{$D_{1\perp}$};
    \draw[force,<-] (0,-0.1) -- ++(-90:.75)
    node[anchor=east]{$D_{2\perp}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/homework
filename: ps1-2019-sol.tex
modified: 2019-02-19 18:05:29
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=yellow!20!white] (-1.5,0) rectangle (1.5,0.4);
    \filldraw[fill=red!20!white] (-1.5,0) rectangle (1.5,-0.4);
    \draw[dashed] (-1,-0.1) rectangle (1,0.1);
    \draw[dashed,->] (-0.1,-0.1) -- (0.1,-0.1);
    \draw[dashed,->] (0.1,0.1) -- (-0.1,0.1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/homework
filename: ps2-2018-sol.tex
modified: 2018-03-19 18:28:42
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        xmin=0, xmax=100, ymin=0, ymax=1, enlargelimits=false,
        width=5in, height=2in,
        xlabel={$\omega$}, ylabel={$P(\omega)$}, ytick=\empty, xtick={20,70},
        xticklabels={$\omega_{1}$, $\omega_{2}$}, yticklabels={},
        axis x line=bottom, axis y line=left, axis x discontinuity=parallel,
        axis line style={line width=0.75,DarkSlateGray} % for no frame
      ]
      \addplot[Brown, domain=10:30, samples=101, line width=1pt]
      {exp(-0.1*(x-20)^2)};
      \addplot[Brown, domain=60:80, samples=101, line width=1pt]
      {exp(-0.1*(x-70)^2)};
    \end{axis}
    \begin{scope}[shift={(5,0)}]
      \def\ww{0.06} \def\hh{0.25}
      \draw[white,line width=2] (-\ww,0) -- (\ww,0);
      \draw (-\ww,\hh) -- (-\ww,-\hh);
      \draw (\ww,\hh) -- (\ww,-\hh);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/Writing
filename: revtex-template.tex
modified: 2020-01-21 04:04:41
domain: p134
source:
  \begin{tikzpicture}[scale=1.25]
    \def\w{3}
    \def\pt{0.05}
    \def\obj{_{\rm obj}}
    \def\img{_{\mathrm{img}}}
    \def\conv{_{\mathrm{conv}}}
    \def\divg{_{\mathrm{div}}}
    \draw[->] (-\w,0) -- (\w,0) node[anchor=north]{$1/d\obj$};
    \draw[->] (0,-\w) -- (0,\w) node[anchor=west]{$1/d\img$};
    \draw[dashed,DarkBlue] (-\w/2,\w) -- (\w,-\w/2);
    \draw[dashed,DarkBlue] (-\w,\w/2) -- (\w/2,-\w);
    \fill (\w/2,0) circle[radius=\pt] node[anchor=south west]{$1/f\conv$};
    \fill (0,\w/2) circle[radius=\pt] node[anchor=south west]{$1/f\conv$};
    \fill (-\w/2,0) circle[radius=\pt] node[anchor=north east]{$1/f\divg$};
    \fill (0,-\w/2) circle[radius=\pt] node[anchor=north east]{$1/f\divg$};
    \node[text width=1in,align=center] at (.75*\w,.75*\w){\small\textsf{real
        object and real image}};
    \node[text width=1in,align=center] at (-.75*\w,.75*\w){\small\textsf{virtual
        object and real image}};
    \node[text width=1in,align=center] at (-.75*\w,-.75*\w){\small\textsf{virtual
        object and virtual image}};
    \node[text width=1in,align=center] at (.75*\w,-.75*\w){\small\textsf{real object and virtual image}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p134/Writing
filename: revtex-template.tex
modified: 2020-01-21 04:04:41
domain: p134
source:
  \begin{tikzpicture}[scale=1]
    \def\w{5}
    \def\h{3}
    \def\VEC#1{\mathbf{#1}}
    % Normal to the plane of interface
    \draw[dashed,color=blue!40!black] (0, 0) -- (0, 1.1*\h) node[anchor=south]{N};
    \draw[dashed,color=blue!40!white] (0, -1.1*\h) -- (0, 0);
    \draw (-\w, 0) -- (\w, 0);
    % planes
    \filldraw[fill=gray!20,opacity=0.2] (-\w,-\h,0) rectangle (\w,\h,0) ;
    \filldraw[fill=gray!60,opacity=0.4] (-\w,-\h,0) rectangle (\w,0,0) ;
    \filldraw[fill=gray!20,opacity=0.2] (-\w,-\h,0) rectangle (\w,\h,0) ;
    \filldraw[fill=gray!20,opacity=0.3] (-\w,0, \h) -- (\w, 0, \h) --  (\w,0,-\h)
    -- (-\w, 0, -\h)  -- cycle;
    \node[anchor=north west] at (-\w,\h) {\small\textsf{Plane of incidence}};
    \begin{scope}[cm={1,0,0.8,0.8,(0,0)}] % Sets the coordinate transfo matrix entries.
      \node[transform shape,color=DarkGreen] at (-\w*0.5,0,0.9*\h) {\small\textsf{Plane of interface}};
    \end{scope}
    \node[anchor=north east] at (\w,-0.4){$n_{\rm t}$};
    \node[anchor=south east] at (\w,0.2){$n_{\rm i}$};
    % k vector lines
    \draw[color=gray,dashed] (0,0) -- (160:6) (0,0)  -- (20:6)
    (0,0) -- (-40:5);
    % angle definitions
    \draw (0,0.5) arc(90:160:0.5);
    \draw (0, -0.5) arc(270:320:0.5);
    \node at (125:0.8){$\theta_{\rm i}$};
    \node at (295:0.8){$\theta_{\rm t}$};
    % incident wave
    \begin{scope}[shift={(160:4)}]
      \draw[force] (0,0) -- ++(-20:1) node[anchor=north]{$\VEC{k}_{\rm inc}$};
      \draw[field] (0,0) -- ++(70:1) node[anchor=west]{$\VEC{E}_{\rm ||, inc}$};
      \draw[field] (0,0) -- ++(-135:0.75) node[anchor=north]{$\VEC{E}_{\rm \perp, inc}$};
    \end{scope}

    % reflected wave
    \begin{scope}[shift={(20:3.5)}]
      \draw[force] (0,0) -- ++(20:1) node[anchor=north west]{$\VEC{k}_{\rm refl}$};
      \draw[field] (0,0) -- ++(110:1) node[anchor=west]{$\VEC{E}_{\rm ||, refl}$};
      \draw[field] (0,0) -- ++(-135:0.75) node[anchor=north]{$\VEC{E}_{\rm \perp, refl}$};
    \end{scope}

    % transmitted wave
    \begin{scope}[shift={(-40:2)}]
      \draw[force] (0,0) -- ++(-40:1.35) node[anchor=south west]{$\VEC{k}_{\rm trans}$};
      \draw[field] (0,0) -- ++(50:1) node[anchor=west]{$\VEC{E}_{\rm ||, trans}$};
      \draw[field] (0,0) -- ++(-135:0.75) node[anchor=north]{$\VEC{E}_{\rm \perp, trans}$};
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}[scale=1.5,>=stealth']
    \coordinate (AB) at (0,0);
    \coordinate (AC) at (2,0);
    \coordinate (BC) at (1.4,1);

    \draw[->,blue,line width=1pt] (AB) -- ($ (AB)!0.5!(AC) $) node[below] {$\mathbf{A}$} -- (AC);
    \draw[->,red,line width=1pt] (AB) -- ($ (AB)!0.5!(BC) $) node[anchor=south] {$\mathbf{B}$} -- (1.4,1);
    \draw[->,darkgray,line width=1pt] (AC) -- ($ (AC)!0.5!(BC) $) node[right] {$\mathbf{C = B - A}$}  -- (BC);

    % Now the arc

    \draw ($ (AB)!0.25!(AC) $) arc[ radius=0.5,start angle=0,end angle=35];
    \node at (0.67,0.2) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}[scale=1.75,>=stealth']
    \draw (0,0) circle (1);
    % draw the axes
    \draw[<->] (1.25,0) node[below] {$x$} -- (0,0) -- (0,1.25) node[left] {$y$};
    % draw the radial vector and label
    \draw[->,line width=1.5pt] (0,0) -- node[above] {$\mathbf{r}$}  (30:1);
    % draw the arc and theta
    \draw (0.35,0) arc (0:30:0.35);
    \draw (0.5,0.125) node {$\theta$};
    % draw the velocity vector
    \draw[blue,line width=1.5pt,->] (30:1) -- ++(120:0.75) node[anchor=west] {$ \mathbf{v} $};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}
    \draw[fill=blue!20] (0,0) rectangle (1,0.75) rectangle(2,0);
    \draw[very thick, ->] (2,0.375) -- (2.7,0.375) node[anchor=west]
    {$\displaystyle \frac{c}{5}$};
    \draw[fill=blue!20] (4,0) rectangle (5,0.75) rectangle (6,0) rectangle (7,0.75)
    rectangle (8,0);
    \draw[very thick, ->] (8, 0.375) -- (8.7,0.375) node[anchor=west] {$
        \displaystyle \frac{c}{10} $};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}
    \draw[fill=blue!20] (0,0) rectangle (1,0.75) rectangle(2,0);
    \draw[very thick, ->] (2,0.375) -- (2.7,0.375) node[anchor=west]
    {$\displaystyle \frac{c}{10}$};
    \draw[fill=blue!20] (4,0) rectangle (5,0.75) rectangle (6,0) rectangle (7,0.75)
    rectangle (8,0);
    \draw[very thick, ->] (8, 0.375) -- (8.7,0.375) node[anchor=west] {$
        \displaystyle \vv $};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}[scale=2,>=stealth']
    \coordinate (AA) at ($ (0.125,0) + (20:0.8) $);
    % draw the incident ball
    \draw[->,line width=2pt] (-1,0) -- (-0.3,0);
    % draw the ball
    \shade[ball color=lightgray] (-0.125,0) circle (0.125) ++(90:0.1) node[anchor=south] {$m$};
    % draw the original position of the pin
    \filldraw[fill=blue!10!white, dash pattern=on 2pt off 2pt] (0.125,0) circle(0.0625);
    % draw a continuation line in the forward direction
    \draw[ dash pattern=on 2pt off 2pt] (0.25,0) -- (1,0);
    % draw the pin moving off at 60 degrees
    \draw[blue,->,line width=1.5pt] (0.125,0) ++(-60:.15) -- ++(-60:.5);
    \filldraw[fill=blue!50!white] (0.125,0) ++(-60:.75) circle(0.0625) node[anchor=north] {$m/3$};
    \draw (0.525,0) arc(0:-60:0.4);
    \draw (0.7,-0.25) node {$60^{\circ}$} ;
    % draw the arrow
    \draw[gray,->,line width=1.5pt] (0.125,0) ++(20:0.1)-- ++(20:0.5);
    % draw the ball heading off

    \shade[ball color=gray] (AA) circle (0.125);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}
    \shade[ball color=lightgray] (0,0) circle (0.1) ++(-0.5,0) node
      {1 kg};
    \shade[ball color=lightgray] (2,0) circle (0.15) ++(0.5,0) node {2
        kg};
    \shade[ball color=lightgray] (2,2) circle (0.2) ++(0.75,0) node {3
        kg};
    \shade[ball color=lightgray] (0,2) circle (0.25) ++(-0.75,0) node
      {4 kg};
    \draw[line width=0.75pt,color=gray,dashed] (0,0) -- (0,2) -- (2,2)
    -- (2,0) -- (0,0);
    \node at (-0.5,1) {2 m};
    \node at (1,-0.5) {2 m};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=2pt] (0,0) arc(-90:90:1cm);
    \draw[->] (0,1) -- node[anchor=south] {$R$} ++(30:0.9);
    \node at (1.35,0.8) {$M$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}
    \filldraw[fill=gray!30!white, draw=black] (-1,0)  arc(180:360:1cm)-- (-1,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}[scale=1.5,>=stealth']
    \filldraw[fill=gray!30!white, draw=black] (-1,0)
    arc(180:360:1cm)-- (-1,0);
    \draw[<->] (1.25,0) node[anchor=north] {$x$}-- (0,0) -- (0,0.5) node[anchor=east] {$y$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}[scale=1.5,>=stealth']
    \filldraw[fill=gray!30!white, draw=black] (-1,0)
    arc(180:360:1cm)-- (-1,0);
    \draw[<->] (1.25,0) node[anchor=north] {$x$}-- (0,0) -- (0,0.5)
    node[anchor=east] {$y$};
    \filldraw[fill=blue!50!white,draw=blue] (0,-0.6) -- (0.8,-0.6)
    arc(-36.87:-40:1) -- ++(-1.532,0) arc(220:216.87 :1) -- (0,-0.6);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}[scale=1.5,>=stealth']
    \filldraw[fill=gray!30!white, draw=black] (-1,0)
    arc(180:360:1cm)-- (-1,0);
    \draw[<->] (1.25,0) node[anchor=north] {$x$}-- (0,0) -- (0,0.5)
    node[anchor=east] {$y$};
    \draw (0,0) -- (-40:1);
    \draw (0,0) -- (-50:1);
    \draw (0:0.6) arc(360:180:0.6);
    \draw (0:0.7) arc(360:180:0.7);
    \filldraw[fill=blue!50!white,draw=blue] (-40:0.6) -- (-40:0.7)
    arc(-40:-50:0.7) -- (-50:0.6) arc (-50:-40:0.6);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}[
      scale=1,
      >=stealth',
      photon/.style={line width=1.5pt,
          color=blue,->,
          decorate,
          decoration={snake,post length=0.1in}},
      arrowy/.style={color=black,|->,line width=1pt},
      accel/.style={->,line width=3pt,color=gray}
    ]
    \draw[photon] (0,0) --(2,0);
    \node at (1,0.5) {$E_{0}$};
    \draw[arrowy] (5,0) -- +(180:1.5) node[anchor=north]{$v_{0}$};
    \shade[ball color=red!30!white] (5,0) circle(0.25);
    \node at (5,0.5){$m_{0}$};
    \draw[dashed] (6,-1) -- (6,1);
    \draw[photon] (8.5,0) -- +(180:2);
    \node at (7.5,0.5) {$E$};
    \draw[arrowy] (10.5,0) -- +(0:1.5) node[anchor=north]{$v$};
    \shade[ball color=red!30!white] (10.5,0) circle(0.25);
    \node at (10.5,0.5){$m$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}
    \draw[line width=3pt,color=brown] (0,0) -- (3,0);
    \draw (0,-0.3) circle(0.15)  (3,-0.3) circle(0.15);
    \node at (0,-0.7) {$A$};
    \node at (3, -0.7) {$B$};
    \node at (1.5,-0.3) {$L$};
    \node at (1.5,0.3) {$M$};
    \draw[->] (3.3,0) -- (3.6,0) node[anchor=south] {$\vv_{0}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
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[force] (0,-0.25) -- ++(-90:1.5)
    node[anchor=west]{$mg$};
    \draw[coord] (0.75,0) -- ++(-90:1.) node[anchor=west]{$x$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
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 (-2.2,0) -- (2.2,0);  % ground
    \draw (2,0) arc(0:180:2);  % hemisphere
    \draw[green!30!black,->] (0,0) -- (0,1) node[anchor=east]{$R$} --
    (0,2);
    \draw[green!30!black,->] (0,0) -- (60:2);
    \draw[green!30!black](60:0.75)    arc(60:90:0.75);
    \node[green!30!black] at (75:1.1) {$\theta$};
    %
    % Now the pig
    \draw[red!30!white, fill] (90:2.1) circle [x radius=0.2, y radius=0.1];
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
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[rotate=-30,color=red!30!white,fill] (0,0) circle[x radius=0.4,
        y radius=0.2] ;
    \draw[force] (0,0) -- ++(-90:1) node[anchor=west]{$mg$};
    \draw[force] (0,0) -- ++(60:1) node[anchor=east]{$N$};
    \draw[coord] (-30:1.6) node[anchor=north] {$\uth$} -- ++(150:1.4) -- ++(60:1.4) node[anchor=west]{$\ur$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
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},
      traj/.style={dashed,color=gray, line width=1pt}
    ]
    \node at (-1,0.15) {$R$};
    \draw (-2,0) -- (0,0) node[anchor=west]{Hook};
    \fill (0,0) circle[radius=0.03];
    \draw (-2,0) circle[x radius = 0.05, y radius = 0.05];
    \draw[traj] (-2,0) arc(180:270:2) arc(-90:110:0.8);
    \draw[fill] (0,-0.4) circle[x radius=0.02,y radius = 0.02]
    node[anchor=south]{A};
    \draw[coord,->] (-0.2,0) -- ++(-90:0.6) node[anchor=east] {$d$} --
    ++(-90:0.6);
    \fill (0,-1.2) circle[x radius=0.02,y radius=0.02];
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}[decoration={coil,aspect=0.3,segment length=3mm,amplitude=3mm},>=stealth']
    \draw [decorate] (0.,0) -- (2.1,0);
    \node at (1,0.6) {$k$};
    \filldraw[fill=lightgray,draw=black] (2,-0.5) rectangle (3,0.5);
    \node at (2.5,0) {$m$};
    \filldraw[fill=blue!10!white] (3,-1) rectangle (5,1);
    \node at (4,0) {$M$};
    \draw[->] (3,1.25) -- ++(0:1.25);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}[scale=1.5,>=stealth']
    \draw (0,0) -- node[anchor=south]{2} (1,0) -- node[anchor=south]{1} (2,0);
    \shadedraw[ball color=lightgray] (0,0) circle(0.2);
    \shadedraw[ball color=lightgray] (1,0) circle(0.2);
    \shadedraw[ball color=lightgray] (2,0) circle(0.2);
    \node at (0,-.4) {$m_{3}$};
    \node at (1,-0.4) {$m_{2}$};
    \node at (2,-0.4) {$m_{1}$};
    \draw[->] (2.2,0) -- ++(0.4,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}[scale=1.,>=stealth']
    \filldraw (0,0) circle (0.15);
    \node at (0,-0.35) {$m_{3}$};
    \draw[|->] (0,0.5) -- node[above] {$x_{3}$} ++(0:1);
    \draw[->,line width=1pt] (0.2,0) -- node[below] {$T_{0}/4$}    ++(0:1.5);
    \filldraw (5,0) circle (0.15);
    \node at (5,-0.35) {$m_{2}$};
    \draw[|->] (5,0.5) -- node[above] {$x_{2}$} ++(0:1);
    \draw[->,line width=1pt] (5.2,0) -- node[below] {$T_{0}/2$}    ++(0:1.5);
    \draw[->,line width=1pt] (4.8,0) -- node[below] {$T_{0}/4$}  ++(180:1.5);
    \filldraw (10,0) circle (0.15);
    \draw[|->] (10,0.5) -- node[above] {$x_{1}$} ++(0:1);
    \node at (10,-0.35) {$m_{1}$};
    \draw[->,line width=1pt] (10.2,0) -- node[below] {$T_{0}$}    ++(0:1.5);
    \draw[->,line width=1pt] (9.8,0) -- node[below] {$T_{0}/2$}  ++(180:1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}[
      scale=0.5,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray}
    ]
    \filldraw (0,0) circle(0.25);
    \draw[coord] (0.6,0) -- ++(90:2) node[anchor=west]{ $y$ };
    \draw[force] (-90:0.2) -- ++(-90:1.5)
    node[anchor=east]{ $mg$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}[>=stealth',scale=1,
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->}
    ]
    \draw (0,0) circle(0.5);
    \draw[force] (0,0) -- ++(90:1.5) node[anchor=east]{
      $F_{0}$ };
    \draw[force] (0.5,0) -- ++(-90:1.5)
    node[anchor=west]{$T_{2}$};
    \draw[force] (-0.5,0) -- ++(-90:1.5)
    node[anchor=east]{$T_{1}$};
    \draw[coord] (0.75,0) -- ++(90:1.5) node[anchor=west]{$x_{p}$};
    % now mass 1
    \draw (-3.25,-.25) rectangle(-2.75,.25);
    \node at (-3.75,0) {$m_{1}$};
    \draw[force] (-3,-0.25) -- (-3,-1.75) node[anchor=east]{$m_{1}g$};
    \draw[force] (-3, 0.25) -- (-3,1.75) node[anchor=east]{$T_{1}$};
    \draw[coord] (-2.5,0) -- (-2.5,1.5) node[anchor=west]{$x_{1}$};
    % now mass 2
    \draw (3.25,-.25) rectangle(2.75,.25);
    \node at (3.75,-0.5) {$m_{2}$};
    \draw[force] (3,-0.25) -- (3,-1.75) node[anchor=east]{$m_{2}g$};
    \draw[force] (3, 0.25) -- (3,1.75) node[anchor=east]{$T_{2}$};
    \draw[force] (2.9,-0.25) -- ++(90:1.) node[anchor=east]{$N$};
    \draw[coord] (3.5,0) -- (3.5,1.5) node[anchor=west]{$x_{2}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}[scale=0.75,>=stealth',
      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=west]{$mg$};
    \draw[force] (0,0) ++(60:0.25) -- ++(60:1.5)
    node[anchor=west]{$T$};
    \draw[dashed,line width=0.75pt] (0,0.25) -- ++(90:1);
    \draw (0,0.8) arc(90:75:0.8) node[anchor=south]{$\theta$}
    arc(75:60:0.8);
    \draw[->,line width=3pt,color=gray] (0.75,0) -- ++(0:1) node[anchor=south]{$a$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
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 (-2,0) -- (2,0);
    \draw (-1,0) rectangle (1,2) (0,1) node {$M$};
    \draw (-0.5,2) rectangle (0.25,2.75) (-0.125,2.375) node {$M/2$} ;
    \draw[force] (-1.75,2.375) node[anchor=south]{$F_{0}$} -- ++(0:1.25);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
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) rectangle (1,1) ;
    \draw[force] (-1,0.5) node[anchor=south]{$F_{0}$} -- ++(0:1);
    \draw[force] (0.5,0) -- (180:0.75) node[anchor=north]{$f$};
    \draw[force] (0.5,0.5) -- ++(-90:1) node[anchor=west]{$\frac{Mg}{2}$};
    \draw[force] (0.6,0) -- ++(90:1.5) node[anchor=east]{$n$};
    \draw[coord,->] (0.5,1.75) -- ++(0:1) node[anchor=north]{$x$};
    \draw[coord,->] (0.5,1.75) -- ++(90:1) node[anchor=east]{$y$};

    \draw (3,0) rectangle ++(1,1) ;
    \draw[force] (3.5,1) -- ++(0:1) node[anchor=north]{$f$};
    \draw[force] (3.5,0.5) -- ++(-90:1) node[anchor=west]{$Mg$};
    \draw[force] (3.6,0) -- ++(90:1.5) node[anchor=east]{$N$};
    \draw[force] (3.3,1) -- ++(-90:1.2) node[anchor=east]{$n$};
    \draw[coord] (3.5,1.75) -- ++(0:1) node[anchor=north]{$X$};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
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[line width=1.5pt] (4,0) -- (0,0) -- ++(60:2) -- cycle;
    \draw[<->] (0.6,0) arc(0:60:0.6);
    \node at (30:1) {$60^{\circ}$};
    \draw[<->] (3,0) arc(180:150:1);
    \node at (2.6,0.4) {$\dg{30}$};

    \draw[rotate=60] (0:1) rectangle ++(0.35,0.35) node[anchor=east]{$m$};
    \draw[rotate around={-30:(4,0)}] (2,0) rectangle ++(0.35,0.35) node[anchor=west]{$m$};
    \draw[brown, line width=1.5pt] (60:1.35) ++(150:0.2) -- ++(60:0.6)
    arc(150:60:0.3) -- ++(-30:1.35);
    \node at (-0.5, 1.5) {\# 1};
    \node at (3,1.5) {\# 2};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}[
      scale=0.5,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,<->},
      accel/.style={->,line width=3pt,color=gray}
    ]
    \draw[rotate=60] (-0.5,-0.5) rectangle (0.5,0.5) ;
    \draw[force] (0,0) -- (-90:2) node[anchor=east] {$mg$};
    \draw[force] (0,0) ++(-30:0.5) -- ++(150:2) node[anchor=east] {$N_{1}$};
    \draw[force] (0,0) ++(-30:0.5) -- ++(60:2) node[anchor=west]{
      $f_{1}$};
    \draw[force] (0,0) ++ (60:0.5) -- ++(60:2) node[anchor=east]{ $T$ };
    \draw[coord] (0,0) ++(150:4.5) node[anchor=east]{$y_{1}$} -- ++(-30:1.5) -- ++(240:1.5) node[anchor=east] {$x_{1}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}[
      scale=0.5,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,<->},
      accel/.style={->,line width=3pt,color=gray}
    ]
    \draw[rotate=60] (-0.5,-0.5) rectangle (0.5,0.5) ;
    \draw[force] (0,0) -- (-90:2) node[anchor=east] {$mg$};
    \draw[force] (0,0) ++(-30:0.5) -- ++(150:2) node[anchor=east] {$T$};
    \draw[force] (0,0) ++(-120:0.5) -- ++(-30:2) node[anchor=west]{
      $f_{2}$};
    \draw[force] (0,0) ++ (60:-0.5) -- ++(60:2) node[anchor=west]{ $N_{2}$ };
    \draw[coord] (0,0) ++(60:4) node[anchor=east]{$y_{2}$} --
    ++(240:1.5) -- ++(150:1.5) node[anchor=east] {$x_{2}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24
filename: tikz.tex
modified: 2013-01-05 23:35:33
domain: p24
source:
  \begin{tikzpicture}[
      scale=0.67,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,|->},
      accel/.style={->,line width=3pt,color=gray}
    ]
    \draw[->] (0,-2) -- (0, 5) node[anchor=east]{$U$};
    \draw[->] (0,0) -- (6,0) node[anchor=north]{$x$};
    \draw[line width=2pt, blue] (0.15,5) .. controls (0.8, -2) and
    (2,-1.5) .. (2.8, -1.0) .. controls (4,-0.3) .. (5.5,-0.2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013
filename: MathIn24.tex
modified: 2013-06-09 03:07:13
domain: p24
source:
  \begin{tikzpicture}[
      scale=5,
      >=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[fill=gray,rotate=30] (0,-0.25) rectangle (0.1,0.25);
    \draw[coord,<->,rotate=30] (0, 0.3) -- node[anchor=south]{$\DD r$}
    +(0:0.1);
    \draw[force,rotate=30] (0,0) -- +(180:0.15)
    node[anchor=north]{$T(r)$};
    \draw[force,rotate=30] (0.1,0) -- +(0:0.15) node[anchor=south]{$T(r +
          \DD r)$};
    \draw[accel,rotate=30] (-0.1,0.2) --+(180:0.2) node[anchor=south]{$a$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/lec13
filename: lec04note.tex
modified: 2013-02-04 07:07:34
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[fill=gray!40!white,rotate=30] (0,-0.25) rectangle (6,0.25);
    \filldraw[fill=gray,rotate=30] (3,-0.25) rectangle (3.2,0.25);
    \fill (0,0) circle(0.05);
    \draw[->] (28:6.5) arc(28:36:6.5) node[anchor=south]{$\omega$};
    \draw[coord,rotate=30] (0,0.5) -- +(0:3) node[anchor=south]{$r$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/lec13/lec14
filename: lec14tz.tex
modified: 2013-03-12 05:37:44
domain: p24
source:
  \begin{tikzpicture}[
      scale=1.,
      >=stealth',
      vel/.style={->,line width=2pt,color=DarkBlue},
      force/.style={line width=2pt,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}
    ]
    \foreach \i in {0,20,...,340}
    \draw (0,0) -- (\i:1);
    \draw[line width=4pt,color=gray] (0,0) circle(1);
    \draw[force] (0,0) -- ++(-90:1.5) node[anchor=east]{$mg$};
    \draw[force] (-1,0) -- ++(180:0.75) node[anchor=north]{$F$};
    \draw[force] (0,0) -- (0.75,1.5) node[anchor=west]{$N$};
    \filldraw[fill=red] (0,0) circle(0.1);

    \begin{scope}[xshift=4cm]
      \foreach \i in {0,20,...,340}
      \draw (0,0) -- (\i:1);
      \draw[line width=4pt,color=gray] (0,0) circle(1);
      \draw[force] (0,0) -- ++(-90:1.5) node[anchor=east]{$mg$};
      \draw[force] (-1,0) -- ++(-90:0.5) node[anchor=east]{$F$};
      \draw[force] (1,0) -- ++(-90:0.5) node[anchor=west]{$F$};
      \draw[force] (0,0) -- (0,2.5) node[anchor=west]{$N$};
      \filldraw[fill=red] (0,0) circle(0.1);
    \end{scope}

    \begin{scope}[xshift=8cm]
      \foreach \i in {0,20,...,340}
      \draw (0,0) -- (\i:1);
      \draw[line width=4pt,color=gray] (0,0) circle(1);
      \draw[force] (0,0) -- ++(-90:1.5) node[anchor=east]{$mg$};
      \draw[force] (-0.2,0) -- ++(90:1.) node[anchor=south east]{$5F$};
      \draw[force] (1,0) -- ++(90:0.2) node[anchor=west]{$F$};
      \draw[force] (0,0) -- (0,0.3) node[anchor=west]{$N$};
      \filldraw[fill=red] (0,0) circle(0.1);
    \end{scope}

    \begin{scope}[yshift=-4.5cm]
      \foreach \i in {0,20,...,340}
      \draw (0,0) -- (\i:1);
      \draw[line width=4pt,color=gray] (0,0) circle(1);
      \draw[force] (0,0) -- ++(-90:1.5) node[anchor=east]{$mg$};
      \draw[force] (-1,0) -- ++(-90:0.75) node[anchor=east]{$F$};
      \draw[force] (0,0) -- (0,2.25) node[anchor=west]{$N$};
      \filldraw[fill=red] (0,0) circle(0.1);
    \end{scope}

    \begin{scope}[yshift=-4.5cm,xshift=4cm]
      \foreach \i in {0,20,...,340}
      \draw (0,0) -- (\i:1);
      \draw[line width=4pt,color=gray] (0,0) circle(1);
      \draw[force] (0,0) -- ++(-90:1.5) node[anchor=east]{$mg$};
      \draw[force] (-1,0) -- ++(-90:0.75) node[anchor=east]{$F$};
      \draw[force] (1,0) -- ++(90:0.75) node[anchor=east]{$F$};
      \draw[force] (0,0) -- (0,1.5) node[anchor=west]{$N$};
      \filldraw[fill=red] (0,0) circle(0.1);
    \end{scope}

    \begin{scope}[yshift=-4.5cm,xshift=8cm]
      \foreach \i in {0,20,...,340}
      \draw (0,0) -- (\i:1);
      \draw[line width=4pt,color=gray] (0,0) circle(1);
      \draw[force] (0,0) -- ++(-90:1.5) node[anchor=east]{$mg$};
      \draw[force] (-0.4,0) -- ++(90:0.5) node[anchor=east]{$F$};
      \draw[force] (1,0) -- ++(90:0.5) node[anchor=east]{$F$};
      \draw[force] (0,0) -- (0,0.5) node[anchor=west]{$N$};
      \filldraw[fill=red] (0,0) circle(0.1);
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/lec13/lec14
filename: lec14tz.tex
modified: 2013-03-12 05:37:44
domain: p24
source:
  \begin{tikzpicture}[
      scale=1.,
      >=stealth',
      vel/.style={->,line width=2pt,color=DarkBlue},
      force/.style={line width=2pt,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}
    ]
    \foreach \i in {0,20,...,340}
    \draw (0,0) -- (\i:1);
    \draw[line width=4pt,color=gray] (0,0) circle(1);
    \draw[force] (0,0) -- ++(-90:1.5) node[anchor=west]{$mg$};
    \draw[force] (15:1) -- ++(60:0.75) node[anchor=west]{$F_{1}$};
    \draw[force] (210:1) -- ++(-90:0.75) node[anchor=north east]{$F_{2}$};
    \draw[force] (0,0) -- (110:1.75) node[anchor=east]{$N$};
    \filldraw[fill=red] (0,0) circle(0.1);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/hw13
filename: hw13.tex
modified: 2013-03-01 03:29:02
domain: p24
source:
  \begin{tikzpicture}[
      scale=3,
      >=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[fill=gray!30!white] (0,0,0) -- (0,1,0) -- (0,1,1) -- (0,0,1) --(0,0,0);
    \draw (0.2,0,0) -- (0.2,1,0) -- (0.2,1,1) -- (0.2,0,1)
    --(0.2,0,0);
    \draw (0,0,0) -- ++(0.2,0,0);
    \draw (0,1,0) -- ++(0.2,0,0);
    \draw (0,1,1) -- ++(0.2,0,0);
    \draw (0,0,1) -- ++(0.2,0,0);
    \node at (0.2,0, 1.2) {$ \vv \dd t $};
    \node at (-0.3, 0.5, 0.5) {$A$};
    \draw[vel] (0,0.5,0.5) -- ++(0.6,0,0) node[anchor=north] {$\vv$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/hw13
filename: sup1.tex
modified: 2014-01-11 21:03:50
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}
    ]
    \draw[force] (0,0) -- node[anchor=south]{$k\vv$} +(180:1.5);
    \draw[force] (-1.5,0) --node[anchor=south]{$\kappa\vv^{2}$} +(180:1.5);
    \filldraw (0,0) circle(0.1);
    \draw[coord] (0,-0.3) -- +(0:1.5) node[anchor=north]{$x$};
    \node at (45:0.4){$m$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/exams13
filename: quiz2_solution.tex
modified: 2013-03-09 21:47:43
domain: p24
source:
  \begin{tikzpicture}[
      scale=0.625,
      >=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[dashed,color=gray] (0,3) -- ++(180:4);
    \draw[<->] (-1,3) arc(180:210:1);
    \node at (-1.5,2.65){$\theta$};
    % Draw the incident pig
    \draw[color=gray,line width=1.5] (0,3) -- ++(-90:2.75);
    \draw (0,3) ++(210:3) -- ++(90:4);
    \draw[line width=3] (0,3) ++(210:3) ++(0,4) -- ++(0.5,0) -- ++(-1,0);
    \draw[line width=2] (0,3) -- ++(210:3);
    \fill (0,3) circle(0.1) node[anchor=south west]{P};
    \draw[dashed, color=gray] (0,0) arc(-90:-220:3);
    \shade[ball color=red] (0,3) ++(210:3) circle(0.25);
    \node at (-3,1.2) {$m$};
    \draw[<-] (-2.6,1) -- ++(0,-1.5) node[anchor=north]{\textsf{incident
        pig}};
    \draw[<-] (-2.5, 4) -- ++(1,0) node[anchor=west]{\textsf{string}};

    \draw[dashed,color=gray] (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 (-1.2,1.95) {$R$};

    \shade[ball color=blue] (0.5,0) circle(0.25);
    \node at (0.75,0.4) {$M$};
    \draw[<-] (0.85,0) -- ++(1.5,0) node[anchor=west]{\textsf{target pig}};
    \draw[<-,line width=1] (0.25,0) -- ++(135:1) node[anchor=south,fill=white]{\textsf{explosive}};

    % draw the floor and ramp
    \draw[brown, line width=2pt] (-1,-0.3) -- ++(0:1.5) -- ++(-90:3) --
    ++(0:5.6) -- ++(-75:0.75) -- ++(-90:0.5) ++(0.5,0) --++(0,0.5) -- ++(75:0.75) -- ++(0:1.5);

    \draw[coord,<->] (0,-0.25) -- node[fill=white]{$R$} ++(-90:3);
    \draw[coord,<->] (0.5,-3) -- node[fill=white]{$2R$} ++(0:6);

    \filldraw[fill=gray] (7,5) rectangle (8,5.4);
    \node at (7.5,5.7){laser};
    \draw[line width=2pt,color=red] (6.5,5.2) -- ++(180:0.3) ++(180:0.3)
    -- ++(180:0.3) ++(180:0.3) -- ++(180:0.3) ++(180:0.3)
    ++(-3,0) -- ++(-0.3,0) ++(-0.3,0) -- ++(-0.3,0) ++(-0.3,0) --
    ++(-0.3,0) ++(-0.3,0);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/exams13
filename: quiz2_solution.tex
modified: 2013-03-09 21:47:43
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[fill=red!50!white] (0,0) circle(0.2);
    \draw[force] (0,0) -- ++(0,-1) node[anchor=west]{$Mg$};
    \draw[coord,<->] (2,0) node[anchor=south]{$x$} -- ++(-1,0) --
    ++(0,-1) node[anchor=west]{$y$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/exams13
filename: quiz2_solution.tex
modified: 2013-03-09 21:47:43
domain: p24
source:
  \begin{tikzpicture}[
      scale=1.5,
      >=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, color=gray] (0,-2) arc(-90:-180:2);
    \draw (-2,0) -- (0,0) -- (0,-2);
    \draw (0,0) -- node[anchor=north]{$R$} ++(210:2);
    \draw[line width=1pt] (210:2) -- +(90:1);
    \node[fill=white] at (-2.2,-0.5) {$R \sin\theta$};
    \draw (210:2) -- ++(0:1.732);
    \draw (-0.5,0) node[anchor=north east]{$\theta$} arc
    (180:210:0.5);
    \draw[coord,<->] (0.25,-1) -- node[fill=white] {$R - R\sin\theta$}  (0.25,-2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/exams13
filename: quiz1.tex
modified: 2013-01-31 07:08:39
domain: p24
source:
  \begin{tikzpicture}[scale=1.25,decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm},>=stealth']
    \draw[decorate] (15:0.25) -- (15:3.7);
    \shade[ball color=gray] (0,0) circle(0.25);
    \node at (0,-0.5){$m$};
    \node at (-0.3, 0.4) {A};
    \shade[ball color=gray] (15:4) circle(0.35);
    \node at (6:4.2) {$M$};
    \node at (22:4.2){B};
    \node at (28:2.05) {$k$};
    %\draw[->] (24:5) arc(24:36:5) node[anchor=south]{$\omega$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/exams13
filename: quiz1.tex
modified: 2013-01-31 07:08:39
domain: p24
source:
  \begin{tikzpicture}[scale=1.25,
      decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm},>=stealth']
    \draw[decorate] (15:0.25) -- (15:3.7);
    \shade[ball color=gray] (0,0) circle(0.25);
    \shade[ball color=gray] (105:0.5) circle (0.25);
    \node at (0.2, -0.4) {A};
    \node at (0.3,0.7){C};
    \shade[ball color=gray] (15:4) circle(0.35);
    %\node at (6:4.2) {$M$};
    \node at (22:4.2){B};
    \node at (28:2.05) {$k$};
    \draw[->,>=stealth', line width=1.5] (-0.3,-0.4) -- ++(105:0.75);
    \draw[->,>=stealth', line width=1.5] (20:4.5) -- ++(-75:0.75);
    %\node at (0,-0.5){$m$};
    %\draw[->] (24:5) arc(24:36:5) node[anchor=south]{$\omega$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/exams13
filename: quiz2_v1.tex
modified: 2013-03-04 01:45:21
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},
      decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm}
    ]
    \draw[dashed,color=gray] (0,3) -- ++(180:4);
    \draw[<->] (-1,3) arc(180:210:1);
    \node at (-1.25,2.65){$\theta$};
    % Draw the incident pig
    \draw[color=gray,line width=1.5] (0,3) -- ++(-90:2.75);
    \draw (0,3) ++(210:3) -- ++(90:4);
    \draw[line width=3] (0,3) ++(210:3) ++(0,4) -- ++(0.5,0) -- ++(-1,0);
    \draw[line width=2] (0,3) -- ++(210:3);
    \fill (0,3) circle(0.1) node[anchor=south west]{P};
    \draw[dashed, color=gray] (0,0) arc(-90:-220:3);
    \shade[ball color=red] (0,3) ++(210:3) circle(0.25);
    \node at (-3,1.2) {$m$};
    \draw[<-] (-2.6,1) -- ++(0,-1.5) node[anchor=north]{\textsf{incident pig}};

    \draw[dashed,color=gray] (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 (-1.2,1.95) {$R$};

    \shade[ball color=blue] (0.5,0) circle(0.25);
    \node at (0.75,0.4) {$M$};
    \draw[<-] (0.85,0) -- ++(1.5,0) node[anchor=west]{\textsf{target pig}};
    \draw[<-,line width=1] (0.25,0) -- ++(135:1) node[anchor=south,fill=white]{\textsf{explosive}};

    % draw the floor and ramp
    \draw[brown, line width=2pt] (-1,-0.3) -- ++(0:1.5) -- ++(-90:3) --
    ++(0:5.6) -- ++(-75:0.75) -- ++(-90:0.5) ++(0.5,0) --++(0,0.5) -- ++(75:0.75) -- ++(0:1.5);

    \draw[coord,<->] (0,-0.25) -- node[fill=white]{$R$} ++(-90:3);
    \draw[coord,<->] (0.5,-3) -- node[fill=white]{$2R$} ++(0:6);

    \filldraw[fill=gray] (7,5) rectangle (8,5.4);
    \node at (7.5,5.7){laser};
    \draw[line width=2pt,color=red] (6.5,5.2) -- ++(180:0.3) ++(180:0.3)
    -- ++(180:0.3) ++(180:0.3) -- ++(180:0.3) ++(180:0.3)
    ++(-3,0) -- ++(-0.3,0) ++(-0.3,0) -- ++(-0.3,0) ++(-0.3,0) --
    ++(-0.3,0) ++(-0.3,0);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/exams13
filename: quiz1-post-mortem.tex
modified: 2013-02-11 07:12:17
domain: p24
source:
  \begin{tikzpicture}[
      scale=0.8,
      >=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[force] (0,0) -- node[anchor=south]{$F_{\rm s}$} +(15:2);
    \shade[ball color=gray] (0,0) circle(0.25);
    \node at (0,-0.5){$m$};
    \draw[accel] (0,1) node[anchor=south] {$a$} -- +(15:1);

    \node at (3,0.25){ or };
    \draw[force] (4,0) -- node[anchor=south]{$F_{\rm s}$} +(15:2);
    \shade[ball color=gray] (4,0) circle(0.25);
    \node at (4,-0.5){$m$};
    \draw[coord,<-] (3.8,0.75) node[anchor=south]{$r$} -- +(15:2.5);

    \draw (-0.5, -1) rectangle (6.5,2);
    \node at (3,1.5){ correct };
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/exams13
filename: quiz2_v3.tex
modified: 2013-03-04 21:02:05
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},
      decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm}
    ]
    \draw[dashed,color=gray] (0,3) -- ++(180:4);
    \draw[<->] (-1,3) arc(180:210:1);
    \node at (-1.25,2.65){$\theta$};
    % Draw the incident pig
    \draw[color=gray,line width=1.5] (0,3) -- ++(-90:2.75);
    \draw (0,3) ++(210:3) -- ++(90:4);
    \draw[line width=3] (0,3) ++(210:3) ++(0,4) -- ++(0.5,0) -- ++(-1,0);
    \draw[line width=2] (0,3) -- ++(210:3);
    \fill (0,3) circle(0.1) node[anchor=south west]{P};
    \draw[dashed, color=gray] (0,0) arc(-90:-220:3);
    \shade[ball color=red] (0,3) ++(210:3) circle(0.25);
    \node at (-3,1.2) {$m$};
    \draw[<-] (-2.6,1) -- ++(0,-1.5) node[anchor=north]{\textsf{incident
        pig}};
    \draw[<-] (-2.5, 4) -- ++(1,0) node[anchor=west]{\textsf{string}};

    \draw[dashed,color=gray] (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 (-1.2,1.95) {$R$};

    \shade[ball color=blue] (0.5,0) circle(0.25);
    \node at (0.75,0.4) {$M$};
    \draw[<-] (0.85,0) -- ++(1.5,0) node[anchor=west]{\textsf{target pig}};
    \draw[<-,line width=1] (0.25,0) -- ++(135:1) node[anchor=south,fill=white]{\textsf{explosive}};

    % draw the floor and ramp
    \draw[brown, line width=2pt] (-1,-0.3) -- ++(0:1.5) -- ++(-90:3) --
    ++(0:5.6) -- ++(-75:0.75) -- ++(-90:0.5) ++(0.5,0) --++(0,0.5) -- ++(75:0.75) -- ++(0:1.5);

    \draw[coord,<->] (0,-0.25) -- node[fill=white]{$R$} ++(-90:3);
    \draw[coord,<->] (0.5,-3) -- node[fill=white]{$2R$} ++(0:6);

    \filldraw[fill=gray] (7,5) rectangle (8,5.4);
    \node at (7.5,5.7){laser};
    \draw[line width=2pt,color=red] (6.5,5.2) -- ++(180:0.3) ++(180:0.3)
    -- ++(180:0.3) ++(180:0.3) -- ++(180:0.3) ++(180:0.3)
    ++(-3,0) -- ++(-0.3,0) ++(-0.3,0) -- ++(-0.3,0) ++(-0.3,0) --
    ++(-0.3,0) ++(-0.3,0);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/exams13
filename: p24_mt1_2013_v2 (original).tex
modified: 2013-02-17 00:06:18
domain: p24
source:
  \begin{tikzpicture}[
      scale=1.3,
      >=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] (0,0) -- (8,0);
    \draw (4,0) arc(0:10:2);
    \node at (4.25,0.15) {$\alpha$};
    % Draw the downslope
    %    \draw[line width=1.5pt] (0,0)  arc(-90:-110:1) -- ++(160:6);
    \draw[line width=1.5pt] (0,0) -- ++(0:2) arc (-90:-80:1) -- ++(10:8);
    \draw[line width=4pt,color=gray] (3,0.12) -- ++(10:7.25);
    % the truck
    \filldraw[rotate=0] (0,0.05) circle (0.05);
    \filldraw[rotate=0] (0.6,0.05) circle (0.05);
    \filldraw[rotate=0] (0.8,0.05) circle (0.05);
    \filldraw[rotate=0,fill=yellow!70!white] (-0.2,0.1) rectangle
    (0.7,0.4);
    \filldraw[rotate=0,fill=red!50!black] (0.7,0.1) rectangle
    (0.9,0.35);
    \draw[vel] (0,.75) -- node[anchor=south]{$\vv_{0}$}++(0:1.);
    \draw[coord] (2.9,1) -- node[anchor=south]{$d$} ++(10:7.25);
    \node[rotate=10] at (6.5,0.45) {gravel};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/exams13
filename: p24_mt1_2013_v3.tex
modified: 2013-02-18 20:51:51
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}
    ]
    \draw[dashed] (0,0) -- (8,0);
    \draw (4,0) arc(0:10:2);
    \node at (4.25,0.2) {$\alpha$};
    % Draw the downslope
    \draw[line width=1.5pt] (0,0)  arc(-90:-110:1) -- ++(160:6);
    \draw[line width=1.5pt] (0,0) -- ++(0:2) arc(-90:-80:1) --
    ++(10:8);
    \draw[line width=4pt,color=gray] (2,0) arc(-90:-80:1) -- ++(10:8);
    % the truck
    \draw[vel,rotate=-20] (-6,0.75) -- node[above=0.05in]{$\vv_{0}$} ++(0:1);
    \filldraw[rotate=-20] (-6.1,0.05) circle (0.05);
    \filldraw[rotate=-20] (-5.5,0.05) circle (0.05);
    \filldraw[rotate=-20] (-5.65,0.05) circle (0.05);
    \filldraw[rotate=-20,fill=yellow!70!white] (-6.2,0.1) rectangle
    (-5.6,0.4);
    \filldraw[rotate=-20,fill=red!50!black] (-5.6,0.1) rectangle
    (-5.4,0.35);
    \draw[coord,<->,rotate=-20] (-5.8,-0.5) -- node[anchor=north]{$L$}
    (-0.25,-0.5);
    %    \draw[coord] (2,1) -- node[anchor=south]{$d$} ++(10:8);
    \node[rotate=10] at (6.5,0.45) {gravel};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/exams13
filename: p24_mt1_2013_v3.tex
modified: 2013-02-18 20:51:51
domain: p24
source:
  \begin{tikzpicture}[
      scale=1.3,
      >=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] (0,0) -- (8,0);
    \draw (4,0) arc(0:10:2);
    \node at (4.25,0.15) {$\alpha$};
    % Draw the downslope
    %    \draw[line width=1.5pt] (0,0)  arc(-90:-110:1) -- ++(160:6);
    \draw[line width=1.5pt] (0,0) -- ++(0:2) arc(-90:-80:1) --
    ++(10:8);
    \draw[line width=4pt,color=gray] (3,0.12) -- ++(10:7.25);
    % the truck
    \filldraw[rotate=10] (9,-0.3) circle (0.05);
    \filldraw[rotate=10] (9.6,-0.3) circle (0.05);
    \filldraw[rotate=10] (9.8,-0.3) circle (0.05);
    \filldraw[rotate=10,fill=yellow!70!white] (8.8,-0.3) rectangle
    (9.7,0);
    \filldraw[rotate=10,fill=red!50!black] (9.7,-0.3) rectangle
    (9.9,-0.05);
    \node[rotate=10] at (6.5,0.45) {gravel};

    % now the tow truck
    \fill[rotate=10] (2.4,-0.3) circle (0.05);
    \fill[rotate=10] (2.7,-0.3) circle (0.05);
    \filldraw[fill=gray,rotate=10] (2.3,-0.3) rectangle (2.8,-0.1);
    \draw[line width=1.5,color=brown,rotate=10] (2.8,-0.2) -- ++(0:6);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/exams13
filename: p24_mt1_2013_v3.tex
modified: 2013-02-18 20:51:51
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[fill=gray!50!white] (0,0) -- (2,1.2) -- (2,-1.2) --
    cycle ;
    \filldraw[fill=gray!50!white] (-2,0) -- (0,1.2) -- (0,-1.2) --
    cycle ;
    \draw[dashed,color=blue] (0.03,-2) -- (0.03,2);
    \draw[coord,<->] (4,0) node[anchor=north]{$x$} -- (3,0) -- (3,1)
    node [anchor=east]{$y$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/exams13
filename: p24_mt1_2013_v3.tex
modified: 2013-02-18 20:51:51
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}
    ]
    \draw[step=0.5,color=gray!25!white] (-2.5,-2) grid (2.5,2);
    \draw[color = gray!50!white,line width=0.5pt] (-2.5,0) -- (2.5,0);
    \draw (0,0) -- (2,1.2) -- (2,-1.2) --
    cycle ;
    \draw (-2,0) -- (0,1.2) -- (0,-1.2) --
    cycle ;
    \draw[dashed,color=blue] (0.03,-2) -- (0.03,2);
    \draw[coord,<->] (4,0) node[anchor=north]{$x$} -- (3,0) -- (3,1)
    node [anchor=east]{$y$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/exams13
filename: p24_mt1_2013_v3.tex
modified: 2013-02-18 20:51:51
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}
    ]
    \draw[color = gray!50!white,line width=0.5pt] (-2.5,0) -- (2.5,0);
    \draw (0,0) -- (2,1.2) -- (2,-1.2) --
    cycle ;
    \draw (-2,0) -- (0,1.2) -- (0,-1.2) --
    cycle ;
    \draw[dashed,color=blue] (0.03,-2) -- (0.03,2);
    \draw[coord,<->] (4,0) node[anchor=north]{$x$} -- (3,0) -- (3,1)
    node [anchor=east]{$y$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/exams13
filename: p24_mt1_2013_v1 (original).tex
modified: 2013-02-13 08:00:31
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[fill=gray!50!white] (0,0) node[anchor=east]{A} -- (2,1.2) -- (2,-1.2) --
    cycle ;
    \filldraw (0,0) circle (0.05);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/exams13
filename: p24_mt1_2013_v1 (original).tex
modified: 2013-02-13 08:00:31
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[dashed] (-1.8,0.4) -- ++(0:3);
    \draw [->,line width=1.5pt,red!50!black] (-1.8,0.4) -- ++(0:0.5)
    node[anchor=north]{$\vv_{0}$};
    \draw[coord, <->] (-0.2,0) -- (-0.2, 0.4);
    \draw (-0.4,0.2) node {$b$};
    \node at (-1,-0.2) {top view};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2013/exams13
filename: p24_mt1_2013_v1 (original).tex
modified: 2013-02-13 08:00:31
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);
    \draw (0,1.8) arc (90:60:0.3);
    \node at (-0.45, 1.8) {$30^{\circ}$};
    \node at (0.45, 1.8) {$30^{\circ}$};
    \draw[dashed] (0,1.5) circle (1);
    \draw (0, 1.5) -- ++(-135:1);
    \node at (-0.55,1.2) {$R$};

    \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/p24/2013/exams13
filename: p24_mt1_2013_v1 (original).tex
modified: 2013-02-13 08:00:31
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=1.5pt, color=blue!50!white},
      ground/.style={line width=1.5pt, color=brown}
    ]
    \draw[ground] (-3,-0.025) -- (3.5,-0.025);
    \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[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,-] (0,0) -- (0,0.75) node[anchor=west,fill=white]{$\frac{3}{2} R$};
    % \draw[coord,->] (0,0.75)--(0,1.5);

    % \node at (-2.8,1.25) {$h$};
    % \node at (2.8,1.2) {P};
    % \draw[coord,<->] (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/p24/2013/rec13
filename: prob5.tex
modified: 2013-02-05 21:38:23
domain: p24
source:
  \begin{tikzpicture}[>=stealth',scale=0.75]
    \draw[blue] (-3,0) -- (0,-0.1) -- (3,0);
    \node[blue] at (-1.5,-0.4){$\ell/2$};
    \node[blue] at (1.5,-0.4){$\ell/2$};
    \filldraw[Brown] (0,0) circle(0.1);
    \node at (-3,-0.5){$m$};
    \draw[->,line width=1.25pt] (-3,0.15) -- ++(90:1) node[anchor=west]{$\vv_{0}$};
    \node at (3,-0.5){$2m$};
    \draw[->,line width=1.25pt] (3,0.15) -- ++(90:1) node[anchor=west]{$\vv_{0}$};
    \filldraw[gray] (-3,0) circle(0.15);
    \filldraw[gray] (3,0) circle(0.25);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/lec14
filename: lec13note.tex
modified: 2014-03-07 05:53:44
domain: p24
source:
  \begin{tikzpicture}[scale=1,rotate=30]
    \fill (0,0) circle (0.05);
    \draw (0,0) -- (180:8);
    \fill (-8,0) circle (0.25);
    \node at (-8,-0.5){$m$};
    \filldraw[fill=gray!50!white,dashed] (-4,0) circle (0.35);
    \node at (-4, 0.75) {$4m$};
    \draw[->] (175:8.75) arc (175:185:8.75) node[anchor=east]{$\omega_{0}$};
    \draw[coord] (-8,-1.25) -- ++(-90:1) node[anchor=west]{$x$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/lec14
filename: lec13note.tex
modified: 2014-03-07 05:53:44
domain: p24
source:
  \begin{tikzpicture}[scale=1,rotate=30]
    \fill (0,0) circle (0.05);
    \draw (0,0) -- (180:8);
    \fill (-8,0) circle (0.25);
    \node at (-8,-0.5){$m$};
    \filldraw[fill=gray!50!white,dashed] (-4,0) circle (0.35);
    \node at (-4, 0.75) {$4m$};
    \draw[->] (175:8.75) arc (175:185:8.75) node[anchor=east]{$\omega_{0}$};
    \draw[coord] (-8,-1.25) -- ++(-90:1) node[anchor=west]{$x$};
    \draw[force] (0,0) -- ++(-90:3) node[anchor=west]{$\VEC{F}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: hw17-sol.tex
modified: 2014-03-25 20:18:03
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}
      \filldraw [fill=brown!50!white] (-0.25,-0.25) rectangle (0.25, 0.25);
      \draw[force] (0,0.25) --node[anchor=east]{$T_{1}$} ++(0,1);
      \draw[force] (0,0) -- node[anchor=west]{$m_{1}g$} ++(-90:1);
      \draw[coord] (-0.75,0) -- node[anchor=east]{$x_{1}$} ++(90:1);
    \end{scope}

    \begin{scope}[shift={(8,0)}]
      \filldraw [fill=brown!50!white] (-0.25,-0.25) rectangle (0.25, 0.25);
      \draw[force] (0,0.25) --node[anchor=east]{$T_{2}$} ++(0,1);
      \draw[force] (0,0) -- node[anchor=west]{$m_{2}g$} ++(-90:1);
      \draw[coord] (-0.75,0) -- node[anchor=east]{$x_{2}$} ++(-90:1);
    \end{scope}

    \begin{scope}[shift={(4,0)}]
      \draw (0,0) circle[radius=.75] circle[radius=1.5];
      \draw[force] (-0.75,0) --node[anchor=east]{$T_{1}$} ++(0,-1);
      \draw[force] (1.5,0) -- node[anchor=west]{$T_{2}$} ++(-90:1);
      \draw[force] (0,0) -- node[anchor=west]{$F$} ++ (90:2);
      \draw[coord] (60:2)arc(60:30:2);
      \node at (45:2.25) {$\theta$} ;
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: hw17-sol.tex
modified: 2014-03-25 20:18:03
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[shift={(4,0)}]
      \filldraw [fill=brown!50!white] (-0.25,-0.25) rectangle (0.25, 0.25);
      \draw[force] (0,0.25) --node[anchor=east]{$T$} ++(0,1);
      \draw[force] (0,0) -- node[anchor=west]{$mg$} ++(-90:1);
      \draw[coord] (-0.75,0) -- node[anchor=east]{$x$} ++(-90:1);
    \end{scope}

    \begin{scope}
      \draw (0,0) circle[radius=1.5];
      \draw[force] (1.5,0) -- node[anchor=west]{$T$} ++(-90:1.5);
      \draw[force] (0,0) -- node[anchor=west]{$F$} ++ (90:2);
      \draw[force] (0,0) -- node[anchor=east]{$Mg$} ++(-90:1);
      \draw[coord] (60:2)arc(60:30:2);
      \node at (45:2.25) {$\theta$} ;
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: 14SUP7.tex
modified: 2014-01-13 06:43:49
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=4,color=gray] (0,0) -- (0,1);
    \draw[dashed] (0,0) -- (0,-4);
    \draw (0,0) -- node[anchor=west]{$L$} (-75:3);
    \filldraw[fill=blue!50!black] (-75:3) circle(0.25);
    \node at (-65:3.2) {$M$};
    \draw[->] (-90:2) arc(-90:-75:2);
    \node at (-82:2.4) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: tmp.tex
modified: 2014-08-18 00:55:31
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/p24/2014/hw14
filename: tmp.tex
modified: 2014-08-18 00:55:31
domain: p24
source:
  \begin{tikzpicture}[scale=.75]
    \filldraw[fill=yellow] (0,0) circle(0.3);
    \draw[dashed,color=gray] (0,0) circle(3) circle(2);
    \filldraw[fill=blue!75!white] (0:2) circle(0.1);
    \filldraw[fill=red!75!white] (44.35:3) circle(0.1);
    \draw[green!75!black,->] (2,0) arc[x radius=2.5,y radius=2.4, start angle=0,
        end angle=180];
    \node at (90:4) {Launch from Earth};
    \node at (-90:4){$t = 0$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: tmp.tex
modified: 2014-08-18 00:55:31
domain: p24
source:
  \begin{tikzpicture}[scale=.75]
    \filldraw[fill=yellow] (0,0) circle(0.3);
    \draw[dashed,color=gray] (0,0) circle(3) circle(2);
    \filldraw[fill=blue!20!white,draw=gray] (0:2) circle(0.1);
    \filldraw[fill=red!20!white,draw=gray] (44.35:3) circle(0.1);
    \filldraw[fill=blue!75!white] (255.2:2) circle(0.1);
    \filldraw[fill=red!75!white] (180:3) circle(0.1);
    \draw[green!75!black] (2,0) arc[x radius=2.5,y radius=2.4, start angle=0,
        end angle=180];
    \node at (90:4) {Arrival on Mars};
    \node at (-90:4){$t = \tau$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: tmp.tex
modified: 2014-08-18 00:55:31
domain: p24
source:
  \begin{tikzpicture}[scale=.75]
    \filldraw[fill=yellow] (0,0) circle(0.3);
    \draw[dashed,color=gray] (0,0) circle(3) circle(2);
    \filldraw[fill=blue!75!white] (342.6:2) circle(0.1);
    \filldraw[fill=red!75!white] (57.9:3) circle(0.1);
    \begin{scope}[rotate=57.9]
      \draw[green!75!black,->] (3,0) arc[x radius=2.5,y radius=2.4, start angle=0,
          end angle=180];
    \end{scope}
    \node at (90:4) {Launch from Mars};
    \node at (-90:4){$t = \tau + t_{\rm W}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: tmp.tex
modified: 2014-08-18 00:55:31
domain: p24
source:
  \begin{tikzpicture}[scale=.75]
    \filldraw[fill=yellow] (0,0) circle(0.3);
    \draw[dashed,color=gray] (0,0) circle(3) circle(2);
    \filldraw[fill=blue!20!white,draw=gray] (342.6:2) circle(0.1);
    \filldraw[fill=red!20!white,draw=gray] (57.9:3) circle(0.1);
    \filldraw[fill=blue!75!white] (237.8:2) circle(0.1);
    \filldraw[fill=red!75!white] (193.5:3) circle(0.1);
    \begin{scope}[rotate=57.9]
      \draw[green!75!black] (3,0) arc[x radius=2.5,y radius=2.4, start angle=0,
          end angle=180];
    \end{scope}
    \node at (90:4) {Return to Earth};
    \node at (-90:4){$t = 2\tau+t_{\rm W}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: hw20-sol.tex
modified: 2014-03-19 21:40:57
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=4,color=gray] (0,0) -- (0,1);
    \draw[dashed] (0,0) -- (0,-4);
    \draw (0,0) -- node[anchor=west]{$L$} (-75:3);
    \filldraw[fill=blue!30!white] (-75:3) circle(0.25);
    \draw[force] (-75:3) -- ++(-90:1.5) node[anchor=west]{$ Mg $};
    \draw[force] (-75:2.75) -- ++(105:1.5);
    \draw[->] (-90:2) arc(-90:-75:2);
    \node at (-82:2.4) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: hw06-sol.tex
modified: 2014-02-11 01:22:41
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}
    ]
    \draw (0,0) rectangle (1,0.5);
    \draw[force] (0.5,0) -- ++(180:1.5)
    node[anchor=south]{$f$};
    \draw[force] (0.5,0.25) -- ++(-90:1.5)
    node[anchor=east]{$mg$};
    \draw[force] (0.5,0) -- ++(90:1.5)
    node[anchor=west]{$n$};
    \draw[accel](1.5,1)  node[anchor=south]{$a$} -- ++(0:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: hw06-sol.tex
modified: 2014-02-11 01:22:41
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}
    ]
    \draw[rotate=30] (0,0) rectangle (1,0.5);
    \draw[force,rotate=30] (0.5,0) -- ++(180:1.5)
    node[anchor=south]{$f$};
    \draw[force,rotate=30] (0.5,0.25) -- ++(-120:1.5)
    node[anchor=east]{$mg$};
    \draw[force,rotate=30] (0.5,0) -- ++(90:1.5)
    node[anchor=west]{$n$};
    \draw[accel,rotate=30](1.5,1) node[anchor=south]{$a$} -- ++(0:1);
    \draw[color=green!40!black] (0,0) -- +(0:1.5) (0:0.75) arc (0:30:0.75);
    \node at (15:1.1) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: hw04-sol.tex
modified: 2014-01-31 17:45:21
domain: p24
source:
  \begin{tikzpicture}[
      scale=2,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black},
      cable/.style={line width=5pt,color=DarkRed},
      accel/.style={->,line width=3pt,color=gray}
    ]
    \draw[cable] (0,0) -- node[anchor=south]{$dm$} (1,0);
    \draw[force] (-0.1,0) -- +(180:0.5) node[anchor=east]{$T$};
    \draw[force] (1.1,0) -- +(0:0.5) node[anchor=west]{$T + dT$};
    \draw[coord] (0,-0.15) -- +(270:0.25) node[anchor=north]{\vphantom{d}$x$};
    \draw[coord] (1,-0.15) -- +(270:0.25)
    node[anchor=north]{$x+dx$};
    \draw[accel] (0.75,0.5) -- node[anchor=south]{$\;\;\VEC{a}$} +(180:0.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: hw04-sol.tex
modified: 2014-01-31 17:45:21
domain: p24
source:
  \begin{tikzpicture}[
      scale=2,
      >=stealth',
      force/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black},
      cable/.style={line width=5pt,color=DarkRed},
      accel/.style={->,line width=3pt,color=gray}
    ]
    \draw[cable] (0,0) -- node[anchor=south]{$dm$} (1,0);
    \draw[force] (-0.1,0) -- +(180:0.5) node[anchor=east]{$T(x)$};
    \draw[force] (1.1,0) -- +(0:0.5) node[anchor=west]{$T(x+\DD x)$};
    \draw[coord] (0,-0.15) -- +(270:0.25) node[anchor=north]{\vphantom{d}$x$};
    \draw[coord] (1,-0.15) -- +(270:0.25)
    node[anchor=north]{$x+ \DD x$};
    \draw[accel] (0.75,0.5) -- node[anchor=south]{$\;\;\VEC{a}$} +(180:0.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: hw15-sol.tex
modified: 2014-03-16 03:23:57
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[color=gray,line width=4] (0,0) -- (60:4);
    \draw[force] (0,0) -- ++(90:1) node[anchor=east]{$F_{y}$};
    \draw[force] (0,0) -- ++(0:1) node[anchor=north]{$F_{x}$};
    \draw[force] (60:2) -- ++(-90:1) node[anchor=west]{$\ds\frac{Mg}{2}$};
    \draw[force] (60:4) -- ++(-90:1) node[anchor=west]{$T_{2}$};
    \draw[force] (60:4) -- ++(180:1) node[anchor=south]{$T_{1}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: hw15-sol.tex
modified: 2014-03-16 03:23:57
domain: p24
source:
  \begin{tikzpicture}[scale=0.5]
    \draw[dashed,color=gray] (0,0) -- ++(9,0) -- (9,12);
    \draw[color=gray,line width=4] (0,0) -- (9,12);
    \draw[force] (0,0) -- ++(90:2) node[anchor=east]{$N$};
    \draw[force] (0,0) -- ++(0:2) node[anchor=north]{$F_{s}$};
    \draw[force] (4.5,6) -- ++(-90:2) node[anchor=west]{$W$};
    \draw[force] (9,12) -- ++(180:2) node[anchor=south]{$R$};
    \draw[force] (3,4) -- ++(-90:4) node[anchor=west]{$W_{w}$};
    \node[color=gray] at (5.5,-0.5) {9 ft};
    \node[color=gray] at (10,6) {12 ft};
    \node at (-0.5,-0.5) {P};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: hw23-sol.tex
modified: 2014-04-17 00:28:42
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[red, line width=2,shift={(0.05,0)}] (-0.1,-0.1) -- (0.1,0.1)
    (-0.1,0.1) -- (0.1,-0.1);
    \fill[fill=gray] (0,-2.5) rectangle (0.1,-4);
    \draw (0,0) rectangle (0.1,-4);
    \draw[coord,<->] (1,0) -- node[fill=white]{$d$} ++(-90:4);
    \draw[coord,<->] (0.5,0) -- node[fill=white]{$\alpha d$} ++(-90:2.5);
    \draw[coord] (-0.5,0) -- node[fill=white]{$x$} ++(-90:3.25);
    \draw[force] (-1.,-3.25) --node[anchor=north]{\VEC{\Delta p}} ++(0:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: hw19-sol.tex
modified: 2014-04-04 22:08:45
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=brown!30!white] (0,0) -- (4,0) --(4,2.5) --cycle ;
    \draw[force] (2.7,0.9) -- node[anchor=west]{$mg$} ++(-90:1.5);
    \draw[force] (4,2.5) --node[anchor=south]{$T$} ++(180:2);
    \draw[force] (0,0) -- node[anchor=east]{$F_{y}$} (90:1.5);
    \draw[force] (0,0) -- node[anchor=north]{$F_{x}$} (0:2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: hw18-sol.tex
modified: 2014-03-31 18:09:12
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) circle[radius=1];
    \draw[dashed] (0,0) circle[radius=0.5];
    \draw[force] (-0.5,0) -- ++(90:1.5) node[anchor=east]{$T$};
    \draw[force] (0,0) -- ++(-90:2) node[anchor=west]{$mg$};
    \draw[coord] (1.25,0) -- ++(-90:1) node[anchor=west]{$x$};
    \draw[coord] (60:1.25) arc(60:30:1.25) node[anchor=west]{$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: hw18-sol.tex
modified: 2014-03-31 18:09:12
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw (2,0) arc(0:180:2);
    \draw (0,0) -- (0,2) (0,0) --node[anchor=west]{$R$} (60:2);
    \draw (0,1) arc(90:60:1);
    \node at (75:1.25){$\theta$};
    \filldraw[fill=red!30!white] (60:2.2) circle[radius=0.2];
    \draw[coord] (60:3) -- ++(60:0.75) node[anchor=west]{$\ur$};
    \draw[coord] (60:3) -- ++(-30:0.75) node[anchor=south]{$\uth$};
    \draw[force] (60:2.2) -- ++(-90:1) node[anchor=west]{$mg$};
    \draw[force] (60:2) -- ++(60:0.75) node[anchor=east]{$N$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: hw08-sol.tex
modified: 2014-02-14 00:44:36
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!20!white] (-1,-0.5) rectangle (1,0.5);
    \node at (0.5,0.) {$M$};
    \draw[force] (0,-0.5) -- ++(180:1.5) node[anchor=north]{$f$};
    \draw[force] (0,0) -- ++(270:1.5) node[anchor=east]{$Mg$};
    \draw[force] (-0.1,-0.5) -- ++(90:1.5) node[anchor=east]{$N$};
    \draw[force] (1,0.25) -- ++(20:1.5) node[anchor=south]{$F$};
    \draw[dashed] (1,0.25) -- ++(0:1.5);
    \draw (2,0.25) arc (0:20:1);
    \node at (2.35,0.45){$\small\theta$};
    \draw[coord] (3,0) -- ++(0:1) node[anchor=north]{$x$};
    \draw[coord] (3,0) -- ++(90:1) node[anchor=east]{$y$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: hw08-sol.tex
modified: 2014-02-14 00:44:36
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw (3,0) -- node[anchor=north]{1} ++(180:3) --
    node[anchor=south,rotate=25]{$\sqrt{1+\mu_{k}^{2}}$} (3,1.5) --
    node[anchor=west]{$\mu_{k}$} (3,0);
    \draw (1,0) arc (0:25:1);
    \node at (12.5:1.5) {$\theta_{\rm min}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/hw14
filename: hw08-sol.tex
modified: 2014-02-14 00:44:36
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[rotate=30,color=red!30!white,fill] (0,0) circle[x radius=0.4,
        y radius=0.2] ;
    \draw[force] (0,0) -- ++(-90:1) node[anchor=west]{$mg$};
    \draw[force] (0,0) -- ++(120:1) node[anchor=east]{$N$};
    \draw[coord, rotate=30] (0:1.6) node[anchor=north] {$\uth$} -- ++(180:1.4) -- ++(90:1.4) node[anchor=west]{$\ur$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/p18-14
filename: class01-stud.tex
modified: 2014-01-28 06:01:28
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) -- node[anchor=north]{$\ell$} (0:2)
    -- node[anchor=west]{$\ell$} +(120:2)
    -- node[anchor=east]{$\ell$} (0,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/p18-14
filename: class11-p18.tex
modified: 2014-04-16 04:46:18
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \shade[ball color=blue!50!white] (0,1) circle(1);
    \node at (-1.25,2) {$m, R$};
    \draw[vel] (0,1) -- ++(0:1.5) node[anchor=south]{$v_{0}$};
    \draw[line width=1.5] (-1,0) -- (12,0);
    \begin{scope}[shift={(10,2.5)}]
      \draw[color=gray!50!white,line width=3] (0,0) -- +(-60:2.5);
      \draw[color=gray,line width=3] (0,0) -- +(-90:2.5);
      \draw (0,-1) arc(-90:-60:1);
      \node at (0.35,-1.25){$\theta$};
      \fill (0,0) circle (0.05);
      \draw[coord,<->] (-0.5,0) -- node[fill=white]{$d$} ++(-90:2.5);
      \draw[coord,<-] (45:0.1) --++(45:1)
      node[anchor=west,text width=0.7in,font=\scriptsize]{frictionless pivot};
      \node at (135:0.45){$3m$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/p18-14
filename: class11-p18.tex
modified: 2014-04-16 04:46:18
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \shade[ball color=blue!50!white] (0,1) circle(1);
    \node at (-1.25,2) {$m, R$};
    \draw[vel] (0,1) -- ++(0:1.5) node[anchor=south]{$v_{0}$};
    \draw[line width=1.5] (-1,0) -- (12,0);
    \draw[line width=4,color=DarkRed!60!white] (2,-0.05) -- +(6,0);
    \begin{scope}[shift={(10,2.5)}]
      \draw[color=gray!50!white,line width=3] (0,0) -- +(-60:2.5);
      \draw[color=gray,line width=3] (0,0) -- +(-90:2.5);
      \draw (0,-1) arc(-90:-60:1);
      \node at (0.35,-1.25){$\theta$};
      \fill (0,0) circle (0.05);
      \draw[coord,<->] (-0.5,0) -- node[fill=white]{$d$} ++(-90:2.5);
      \draw[coord,<-] (45:0.1) --++(45:1)
      node[anchor=west,text width=0.7in,font=\scriptsize]{frictionless pivot};
      \node at (135:0.45){$3m$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/p18-14
filename: class02-prof.tex
modified: 2014-02-02 21:44:26
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed] (-2,0) -- (2,0);
    \draw[force] (0,0) -- ++(15:1.5) node[anchor=south]{$T$} ;
    \draw[force] (0,0) -- ++(165:1.5) node[anchor=south]{$T$} ;
    \draw[force] (0,0) -- ++(-90:0.5) node[anchor=east]{$F_{0}$} ;
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/p18-14
filename: class03-prof.tex
modified: 2014-02-10 02:49:17
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}
    ]
    \draw[rotate=-30] (0,0) rectangle (1,0.5);
    \draw[force,rotate=-30] (0.5,0) -- ++(180:1.5)
    node[anchor=south]{$f$};
    \draw[force,rotate=-30] (0.5,0.25) -- ++(-60:1.5)
    node[anchor=east]{$mg$};
    \draw[force,rotate=-30] (0.5,0) -- ++(90:1.5)
    node[anchor=west]{$n$};
    \draw[force,rotate=-30] (1,0.25) -- ++(0:1.5)
    node[anchor=west]{$T$};
    \draw[accel,rotate=-30](1.5,1) -- node[anchor=south]{$a$}  ++(0:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/p18-14
filename: class03-prof.tex
modified: 2014-02-10 02:49:17
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}
    ]
    \draw[rotate=-30] (0,0) rectangle (1,0.5);
    \draw[force,rotate=-30] (0.5,0) --
    node[anchor=north]{$F$} ++(180:1.5);
    \draw[force,rotate=-30] (0.5,0.25) -- ++(-60:1.5)
    node[anchor=east]{$Mg$};
    \draw[force,rotate=-30] (0.5,0) -- ++(90:1.5)
    node[anchor=west]{$N$};
    \draw[force,rotate=-30] (0,0.25) --
    node[anchor=south]{$T$} ++(180:1.5);
    \draw[accel,rotate=-30](1.5,1) -- node[anchor=south]{$a$}  ++(0:1);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/p18-14
filename: class12-p18.tex
modified: 2014-04-21 23:49:27
domain: p24
source:
  \begin{tikzpicture}
    \begin{axis}[xlabel={$x$}, ylabel={$U(x)$}]
      \addplot[domain=0.95:1.5, samples=100]
      {1/x^12 - 1/x^6};
      \addplot[red,domain=0.95:1.3,samples=100,dashed]
      {-0.25 + 4.5*2^(2/3) * (x-2^(1/6))^2};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-quiz3-2013.tex
modified: 2014-04-16 04:41:55
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \shade[ball color=blue!50!white] (0,1) circle(1);
    \node at (-1.25,2) {$m, R$};
    \draw[vel] (0,1) -- ++(0:1.5) node[anchor=south]{$V_{0}$};
    \draw[line width=1.5] (-1,0) -- (12,0);
    \draw[line width=4,color=DarkRed!60!white] (2,-0.05) -- +(6,0);
    \begin{scope}[shift={(10,2.5)}]
      \draw[color=gray!50!white,line width=3] (0,0) -- +(-60:2.5);
      \draw[color=gray,line width=3] (0,0) -- +(-90:2.5);
      \draw (0,-1) arc(-90:-60:1);
      \node at (0.35,-1.25){$\theta$};
      \fill (0,0) circle (0.05);
      \draw[coord,<->] (-0.5,0) -- node[fill=white]{$d$} ++(-90:2.5);
      \draw[coord,<-] (45:0.1) --++(45:1)
      node[anchor=west,text width=0.7in,font=\scriptsize]{frictionless pivot};
      \node at (135:0.45){$3m$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-mt1-2014-online.tex
modified: 2014-08-24 06:21:15
domain: p24
source:
  \begin{tikzpicture}[scale=0.65]
    \draw (0,0) circle[radius=2];
    \draw[dashed] (0,2.5) -- (0,-2.5) (0,0) -- (-45:2);
    \draw (0,-0.75) arc(-90:-45:0.75);
    \node at (-67.5:1){$\theta$};
    \fill (-45:2) circle[radius=0.1] node[anchor=north west]{$m$};
    \draw[->] (-0.2,2.35) arc[x radius=0.4, y radius=0.1,
        start angle=120, end angle=420];
    \node at (0.75,2.35){$\omega$};
    \draw[accel] (2.75,0) -- ++(-90:1) node[anchor=west]{$g$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-mt1-2014-online.tex
modified: 2014-08-24 06:21:15
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw (0,0) circle(0.05);
    \draw[force] (0,0) -- ++(-90:1.5) node[anchor=west] {$mg$};
    \draw[force] (0,0) -- ++(120:2) node[anchor=north east] {$N$};
    \draw[accel] (-0.5,0) -- ++(180:1) node[anchor=north]{$a$};
    \draw[dashed] (0,0) -- (0,2);
    \draw (0,0.75) arc(90:120:0.75);
    \node at (105:1.1) {$\theta$};
    \draw[coord] (0.5,0) -- ++(0:1.5) node[anchor=north]{$x$};
    \draw[coord] (0.5,0) -- ++(90:1.5) node[anchor=west]{$y$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-mt1-2014-online.tex
modified: 2014-08-24 06:21:15
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=blue!30!white] (0,0) -- ++(0,-6) -- (8,-6) -- cycle;
    \draw (7,-6) arc(180:143.13:1);
    \node at (6.7,-5.7){$\phi$};
    \filldraw[fill=gray!50!white] (0,0) circle (0.25);
    \fill (0,0) circle(0.05);
    \draw (-0.25,0) -- ++(-90:2);
    \filldraw[fill=DarkGreen] (-0.375,-2) rectangle (-0.125,-2.5)
    (-0.375,-1) rectangle (-0.125,-1.5);
    \node at (-0.75,-1.25){$m$};
    \node at (-0.75,-2.25){$m$};

    \begin{scope}[rotate=-36.869897646]
      \draw (0,0.25) -- ++(0:9);
      \draw[<-] (9.3,-0.05) -- ++(200:1.5) node[anchor=east] {$\mu_k$};
      \filldraw[fill=DarkRed] (9,0) rectangle (9.75,0.5);
      \node at (9.375, 0.75){$M$};
    \end{scope}

    % Now the laser beam
    \draw[line width=1.5,color=red,->] (-3,-4.5) -- ++(0:2.5);
    \node at (-2.25,-4.2)[color=red]{laser beam};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-mt1-2014-online.tex
modified: 2014-08-24 06:21:15
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[accel] (0.5,0) -- ++(-90:1) node[anchor=west]{$a_{1}$};
    \filldraw[fill=DarkGreen!50!white] (-0.125,0) rectangle (0.125,-0.5);
    \node at (-0.75,0){$2m$};
    \draw[force] (0,-0.25) -- ++(-90:1) node[anchor=east]{$2mg$};
    \draw[force] (0,0) -- ++(90:1) node[anchor=east]{$T$};

    \begin{scope}[shift = {(3,0)}]
      \filldraw[fill=DarkRed!30!white,rotate=-36.87] (0,0) rectangle (0.75,0.5);
      \draw[accel,rotate=-36.87] (0,1) -- ++(180:1)
      node[anchor=south]{$a_{1}$};
      \draw[force,rotate=-36.87] (0,0.25) -- ++ (180:1)
      node[anchor=east]{$T$};
      \draw[force,rotate=-36.87] (0.375,0.25) -- ++(-53.13:1)
      node[anchor=east]{$Mg$};
      \draw[force,rotate=-36.87] (0.375,0) -- ++ (90:1)
      node[anchor=west]{$N$};
      \draw[force,rotate=-36.87] (0.375,0) -- ++(0:1) node[anchor=north]{$F_{k}$};
    \end{scope}

    \node at (1.5,2.5){\textsf{first portion}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-mt1-2014-online.tex
modified: 2014-08-24 06:21:15
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[accel] (0.5,0) -- ++(-90:1) node[anchor=west]{$a_{2}$};
    \filldraw[fill=DarkGreen!50!white] (-0.125,0) rectangle (0.125,-0.5);
    \node at (-0.75,0){$m$};
    \draw[force] (0,-0.25) -- ++(-90:1) node[anchor=east]{$mg$};
    \draw[force] (0,0) -- ++(90:1) node[anchor=east]{$T'$};

    \begin{scope}[shift = {(3,0)}]
      \filldraw[fill=DarkRed!30!white,rotate=-36.87] (0,0) rectangle (0.75,0.5);
      \draw[accel,rotate=-36.87] (0,1) -- ++(180:1)
      node[anchor=south]{$a_{2}$};
      \draw[force,rotate=-36.87] (0,0.25) -- ++ (180:1)
      node[anchor=east]{$T'$};
      \draw[force,rotate=-36.87] (0.375,0.25) -- ++(-53.13:1)
      node[anchor=east]{$Mg$};
      \draw[force,rotate=-36.87] (0.375,0) -- ++ (90:1)
      node[anchor=west]{$N$};
      \draw[force,rotate=-36.87] (0.375,0) -- ++(0:1) node[anchor=north]{$F_{k}$};
    \end{scope}

    \node at (1.5,2.5){\textsf{second portion}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-quiz3-2014-online.tex
modified: 2014-08-17 05:30:10
domain: p24
source:
  \begin{tikzpicture}[scale=0.67]
    \filldraw[fill=gray!50!white] (0,0) circle(3);
    \node at (45:2.2){$M,R$};
    \foreach \i in {0,120,240}
      {
        \filldraw[fill=black] (\i:2.9) circle(0.2);
        \node at (\i:3.5) {$m$};
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-quiz3-2014-online.tex
modified: 2014-08-17 05:30:10
domain: p24
source:
  \begin{tikzpicture}[scale=0.67]
    \filldraw[fill=gray!25!white] (0,0) circle(3);
    \node at (45:2.2){$M,R$};
    \filldraw[fill=black] (0:2.9) circle(0.2);
    \node at (0:3.5){$M$};
    \draw[dashed] (0,0) -- (3,0);
    \draw[color=red,line width=2,shift={(1.5,0)}] (45:0.2) --(225:0.2)
    (135:0.2) -- (-45:0.2);
    \node at (1.5,-0.5) {CM};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-quiz2-2014-v4.tex
modified: 2014-03-11 22:51:56
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},
      tightspring/.style={decorate,decoration={coil,aspect=0.3,segment length=1mm,amplitude=2mm}}
    ]

    % draw the floor and ramp
    \draw[brown!70!black, line width=2pt] (-5,0) -- ++(0:7) -- (9, 1) -- ++(0:2);
    \draw[dashed] (2,0) -- (11,0);

    \draw (5,0) arc(0:12:2);
    \node at (5.25,0.22) {$\alpha$};

    % the two masses and the compressed spring
    \filldraw[fill=red!70!black] (-2,0) rectangle (-1.5,0.5);
    \node at (-1.75,0.75){$M$};
    \draw[color=brown,line width=2pt](-1.5,0.25) -- (-0.5,0.25);
    \draw[tightspring] (-1.5,0.25) -- (-0.25,0.25);
    \node at (-1.,0.65){$k$};
    \filldraw[fill=blue!70!black] (-0.5,0) rectangle (0,0.5);
    \node at (-0.25,0.75){$ m $};

    \draw[coord,<->] (10.5,0) -- (10.5,1);
    \node at (10.8,0.5) {$b$};

    % The bouncer spring
    \begin{scope}[shift={(-4.5,0)}]
      \draw[tightspring,color=gray] (-0.5,0.25) -- (0,0.25);
      \filldraw[fill=gray!50!white] (0,0) rectangle (0.1,0.5);
      %\filldraw[fill=gray!50!white] (-0.5,0) rectangle (-1,0.5);
      %\node at (-0.25,1) {\textsf{For part (e)}};
      \draw[color=brown!70!black,line width=4pt](-0.5,0) -- ++(90:1);
    \end{scope}


  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-quiz2-2014-v4.tex
modified: 2014-03-11 22:51:56
domain: p24
source:
  \begin{tikzpicture}[scale=0.75,rotate=15]
    \filldraw[fill=blue!30!white] (-0.5,-0.5) rectangle (0.5, 0.5);
    \draw[force] (0,0) -- ++(-105:2) node[anchor=west]{$mg$};
    \draw[force] (0,-0.5) -- ++(90:2) node[anchor=east]{$N$};
    \draw[force] (0,-0.5) -- ++(180:1) node[anchor=north]{$F_{k}$};
    \draw[dashed] (-0.5,-0.5) -- +(-15:2)  (-0.5,-0.5) -- +(0:2);
    \draw (0.75,-0.5) arc (0:-15:1.25);
    \node at (1.15,-0.75){$\alpha$};
    \draw[coord] (1.5,0) -- ++(0:1) node[anchor=north]{$x$};
    \draw[coord] (1.5,0) -- ++(90:1) node[anchor=west]{$y$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-quiz2-2014-v4.tex
modified: 2014-03-11 22:51:56
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},
      tightspring/.style={decorate,decoration={coil,aspect=0.3,segment length=1mm,amplitude=2mm}}
    ]

    % draw the floor and ramp
    \draw[brown!70!black, line width=2pt] (-5,0) -- ++(0:7) -- (9, 1) -- ++(0:2);
    \draw[dashed] (2,0) -- (11,0);

    \draw (5,0) arc(0:12:2);
    \node at (5.25,0.22) {$\alpha$};

    % the two masses and the compressed spring
    \filldraw[fill=red!70!black] (0,0) rectangle (0.5,0.5);
    \node at (0.25,0.75){$r m$};
    \draw[vel] (0.75,0.25) -- ++(0:0.5) node[anchor=south]{$v'$};
    \filldraw[fill=blue!30!white] (9,1) rectangle (9.5,1.5);
    \node at (9.25,1.75){$ m $};

    \draw[coord,<->] (10.5,0) -- (10.5,1);
    \node at (10.8,0.5) {$b$};

    % The bouncer spring
    \begin{scope}[shift={(-4,0)}]
      \draw[tightspring] (-0.5,0.25) -- (0,0.25);
      \filldraw[fill=gray!50!black] (0,0) rectangle (0.1,0.5);
      \filldraw[fill=gray!50!black] (-0.5,0) rectangle (-1,0.5);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-mt2-2014-sol.tex
modified: 2014-08-24 22:13:17
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[left color=white, right color=gray!80!white] (0,0) rectangle
    (3,6);
    \draw[dashed, line width=1.5] (0,-0.5) -- (0, 6.5);
    \draw[coord] (0,-0.5) --node[fill=white]{$w$} ++(0:3);
    \draw[coord] (-0.5,0) --node[fill=white]{$h$} ++(90:6);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-mt2-2014-sol.tex
modified: 2014-08-24 22:13:17
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[left color=white, right color=gray!80!white] (0,0) rectangle
    (3,6);
    \draw[coord] (0,-0.5) --node[fill=white]{$w$} ++(0:3);
    \draw[coord] (-0.5,0) --node[fill=white]{$h$} ++(90:6);
    \fill (0,3) circle[radius=0.1];
    \begin{scope}[shift={(0,3)}]
      \draw[->] (-25:4) arc(-25:25:4) node[anchor=west]{$\omega$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-mt2-2014-sol.tex
modified: 2014-08-24 22:13:17
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[left color=white, right color=gray!80!white] (0,0) rectangle
    (3,6);
    \draw[coord] (0,0.5) --node[fill=white]{$w$} ++(0:3);
    \draw[coord] (0.5,0) --node[fill=white]{$h$} ++(90:6);
    \fill (0,3) circle[radius=0.1];
    \draw[force,line width=2] (0,6) -- +(-120:3)
    node[anchor=east]{$F$};
    \draw (0,5) arc(-90:-120:1);
    \node at (-0.3,4.75) {$\dg{30}$};
    \begin{scope}[shift={(3.5,3)}]
      \draw[accel] (0,0.5) -- node[anchor=west]{$~g$} (0,-0.5);
    \end{scope}

    \draw[force] (2.2,3) -- ++(-90:1.5) node[anchor=east]{$Mg$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-quiz1-2014-v4.tex
modified: 2014-02-04 21:34:05
domain: p24
source:
  \begin{tikzpicture}[scale=1,decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm},>=stealth']
    \draw (15:0.25) -- (15:3.7);
    \shade[ball color=gray] (0,0) circle(0.25);
    \node at (0,-0.5){$m$};
    \node at (-0.3, 0.4) {A};
    \shade[ball color=gray] (15:4) circle(0.35);
    \node at (6:4.2) {$M$};
    \node at (22:4.2){B};
    \draw[<->,rotate=15] (0,0.5) -- node[fill=white]{$L$} (4,0.5);
    \draw[rotate=15,->,line width=1.5] (-5:5) arc(-5:5:5);
    \draw[->,line width=1.5,rotate=15] (160:1) arc (180:190:4);
    %\draw[->] (24:5) arc(24:36:5) node[anchor=south]{$\omega$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-quiz1-2014-v4.tex
modified: 2014-02-04 21:34:05
domain: p24
source:
  \begin{tikzpicture}[scale=1,decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm},>=stealth']
    \draw (15:0.25) -- (15:3.7);

    \shade[ball color=gray] (0,0) circle(0.25);
    \shade[ball color=blue] (290:0.5) circle(0.25);
    \node[color=blue] at (-30:0.65){C};
    \node[color=blue] at (-60:0.9){$m$};
    \node at (-0.5,0){$m$};
    \node at (-0.3, 0.4) {A};
    \shade[ball color=gray] (15:4) circle(0.35);

    \node at (6:4.2) {$M$};
    \node at (22:4.2){B};
    \draw[<->,rotate=15] (0,0.5) -- node[fill=white]{$L$} (4,0.5);
    \draw[rotate=15,->,line width=1.5] (-5:5) arc(-5:5:5);
    \draw[->,line width=1.5,rotate=15] (160:1) arc (180:190:4);
    %\draw[->] (24:5) arc(24:36:5) node[anchor=south]{$\omega$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-quiz1-2014-sol.tex
modified: 2014-02-05 18:15:05
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray] (0,0) circle (0.25);
    \node at (0,0.5) {A};
    \filldraw[fill=gray] (4,0) circle (0.25);
    \draw[coord] (0,0) -- ++(5,0) node[anchor=north]{$r$};
    \draw (2.9,0.1) -- (3.1,-0.1) (3.1, 0.1) -- (2.9, -0.1);
    \node at (3, -0.3) {CM};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-quiz1-2014-sol.tex
modified: 2014-02-05 18:15:05
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray] (0,0) circle (0.25);
    \node at (0,-0.5){$m$};
    \draw[force] (0.25,0) -- ++(0:1) node[anchor=north]{$T$};
    \draw[accel] (0,0.5) -- ++(0:1) node[anchor=south]{$a_{\rm A}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-quiz1-2014-sol.tex
modified: 2014-02-05 18:15:05
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray] (0,0) circle (0.25);
    \node at (0,-0.5){$M$};
    \draw[force] (-0.25,0) -- ++(180:1) node[anchor=north]{$T$};
    \draw[accel] (0,0.5) -- ++(180:1) node[anchor=south]{$a_{\rm B}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-quiz1-2014-sol.tex
modified: 2014-02-05 18:15:05
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray] (0,0) circle(0.25);
    \draw[vel,rotate=15] (0,-0.3) -- ++(-90:1) node[anchor=west]{$\VEC{v}$};
    \node at (0,1){\textsf{before}};
    \begin{scope}[shift={(4,0)}]
      \filldraw[fill=gray] (0,0) circle(0.25);
      \filldraw[fill=blue,rotate=15] (0,-0.5) circle(0.25);
      \draw[vel,rotate=15] (0,-0.8) -- ++(-90:0.5) node[anchor=west]{$\VEC{v}/2$};
      \node at (0,1){\textsf{after}};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014.tex
modified: 2015-04-27 02:30:44
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw (-1,-0.6) -- (5,-0.6);
    \draw (0,0) rectangle (4,2);
    \filldraw[fill=gray!20!white] (0.5,-0.3) circle(0.3);
    \filldraw[fill=gray!20!white] (3.5,-0.3) circle(0.3);
    \draw[accel] (4,1) -- ++(0:1) node[anchor=north]{$a$};
    \draw[accel] (-0.75,1.5) -- ++(-90:1) node[anchor=east]{$g$};
    \draw[dashed] (2,2) -- (2,0);
    \filldraw (2,2) -- ++(-120:1.5) circle(0.125);
    \draw (2,1.5) arc(-90:-120:0.5);
    \node at (1.8, 1.25) {$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014.tex
modified: 2015-04-27 02:30:44
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw (-2,2) arc(180:270:2);
    \filldraw[fill=gray] (-2,2) rectangle (-1.8,1.8) node [anchor=west]{$m$};
    \draw[line width=2.5,color=DarkRed] (0,-0.05) -- node[anchor=south]{$\mu_{k}
        = ~? $} ++(3,0);
    \draw[coord,<->] (0,-0.5) --node[fill=white]{$L$} ++(3,0);
    \draw[accel] (3.5,2) -- node[anchor=east]{$g$} ++(-90:1.5);
    \draw[coord,<->] (-2.3,2) -- node[anchor=east]{$R$} ++(-90:2);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014.tex
modified: 2015-04-27 02:30:44
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[coord,->] (0,-0.5) -- (0,4);
    \draw[coord,->] (-0.5,0) -- (6,0) node[anchor=north]{$x$};
    \draw[line width=1.5] plot[smooth] coordinates { (0.5,4) (1.5,1) (2.5,0.5)
        (3.75,2)  (5.5,2.5)};
    \draw[dashed] (0,3) -- ++(0:6);
    \node at (-0.5,3) {$E$};
    \node at (1.1,4){$U(x)$};
    \draw[dashed] (0.8,3) -- (0.8,-0.25) node[anchor=north]{$x_{1}$};
    \draw[dashed] (1.3,1.5) -- (1.3,-0.25) node[anchor=north]{$x_{2}$};
    \draw[dashed] (2.25,0.45) -- (2.25,-0.25) node[anchor=north]{$x_{3}$};
    \draw[dashed] (3.25,1.5) -- (3.25,-0.25) node[anchor=north]{$x_{4}$};
    \draw[dashed] (4.5,2.25) -- (4.5,-0.25) node[anchor=north]{$x_{5}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014.tex
modified: 2015-04-27 02:30:44
domain: p24
source:
  \begin{tikzpicture}[scale=0.5]
    \draw (0,-3) -- (0,6) ;
    \foreach \i in {-5,0,5,10}
      {
        \draw(-0.2,\i/2) -- (0.2,\i/2);
        \node at (-0.75,\i/2) {$\i$};
      }
    \draw (0,0) -- (9,0);
    \foreach \i in {2,4,6,8}
      {
        \draw (\i,-0.2) -- (\i,0.2);
        \node at (\i, -0.7) {$\i$};
      }
    \node at (4,-1.5){$x$ (m)};
    \node[rotate=90] at (-1.5,1.5){$F$ (N)};
    \draw[line width=2] (0,5) -- (2,5) -- (4,0) -- (6,0) -- (8,-2.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014.tex
modified: 2015-04-27 02:30:44
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=5,color=brown] (-5,0) -- (0,0) -- (0,-3) ;
    \draw (-3,0.1) rectangle (-2,0.8);
    \node at (-2.5,0.45){$\SI{5}{kg}$};

    \draw (0.3,0.3) circle(0.15);
    \draw (-2,0.45) -- (0.3,0.45);
    \draw (0.45,0.3) -- (0.45,-1.5);
    \filldraw[fill=gray!50!white] (0,0) -- (-0.2,0) -- (0.3,0.3) -- (0,-0.2) --
    (0,0);
    \fill (0.3,0.3) circle[radius=0.05];
    \draw (0.15,-1.5) rectangle (0.75,-2.5);
    \node[rotate=-90] at (0.45,-2) {$\SI{5}{kg}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014.tex
modified: 2015-04-27 02:30:44
domain: p24
source:
  \begin{tikzpicture}[scale=0.75]
    \filldraw[fill=gray!30!white,dashed] (0,0) circle[radius=3];
    \filldraw[fill=gray!50!white,dashed] (0,0) circle[radius=1];
    \draw[rotate=-30] (-4,-1) -- (7,-1);
    \draw[->,line width=1.5] (0,0) -- (45:1);

    \filldraw[fill=gray!30!white,opacity=0.5] (-0.1,0.1) circle[radius=3];
    \node at (0:0.75){$R/3$};
    \draw[->,line width=1.5] (0,0) -- (135:3.1);
    \node at (120:2) {$R$};
    \fill (0,0) circle[radius=0.1];
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014.tex
modified: 2015-04-27 02:30:44
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=5,color=gray] (-2,2) -- (2,2);
    \draw (0,2) -- (0,0);
    \draw[dashed] (0,0) -- (0,-2);
    \draw[line width=4,color=gray!50!white] (0,0) -- (-135:2);
    \draw (0,-0.75) arc(-90:-135:0.75);
    \node at (-112.5:1.1){$\dg{45}$};
    \begin{scope}[rotate=-135]
      \draw[line width=5,color=gray!50!black] (1.9,0) ellipse[x radius=0.5, y radius=1.95];
      \filldraw[fill=gray!50!white] (2,0) ellipse[x radius=0.5, y radius=2];
      \draw[->,line width=1.5]
      (2.25,1.1) arc[x radius=0.3, y radius= 1.3, start angle=60, end angle=315];
      \draw[line width=4,color=gray!30!white] (2,0) -- (4.5,0);
      \draw[vel] (4.7,0) --  (6,0);
      \node at (5.3,0.4) {$\omega$};
    \end{scope}
    \draw[force] (-135:2) --node[anchor=west]{$mg$} ++(-90:3);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Clinic
filename: LaTeX-Guide.tex
modified: 2020-09-25 19:26:37
domain: Clinic
source:
  \begin{tikzpicture}[scale=1]
    \node[anchor=north west] at (0,0) {\includegraphics[width=5in]{noise/noise-db}};
    \node[anchor=north west] at (-2,2)
    {\includegraphics[width=3.75in]{noise/noise-db-inset}};
    \node[anchor=north west,rotate=90] at (0.2,-9) {Counts};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014.tex
modified: 2015-04-27 02:30:44
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed] (0,3) -- (0,-1.5) ;
    \filldraw[fill=gray,rotate=33] (3.3,0) rectangle (3.5,0.2);
    \draw (0,2) ellipse[x radius=3, y radius=0.4];
    \draw (3,1.95) -- (0,0) -- (-3,1.95);
    \draw (0,0.75) arc(90:147:0.75);
    \node at (120:1.05) {$\theta$};
    \draw[<->] (0,2) -- node[fill=white]{$R$} (-3,2);

    \draw[->,rotate=33] (3.1,0.1) -- +(180:1);
    \node at (3.25,1.9){$m$};
    \draw[accel] (-2,0.5) -- +(-90:1.25) node[anchor=west]{$g$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Clinic/Director/2017-2018/CLGP 2017-18/Manuscript
filename: fig_iv_full_cell.tex
modified: 2020-12-15 03:43:24
domain: Clinic
source:
  \begin{tikzpicture}[
      circuit ee IEC,
      every info/.style={font=\small}, % footnotesize
      small circuit symbols,
      set resistor graphic=var resistor IEC graphic,
      set diode graphic=var diode IEC graphic,
      scale=1]
    \def\dx{1.5}
    \def\dy{1.25}

    % the circuit diagram %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \begin{scope}[
        shift={(-0.5,2.75)},
        font=\large
      ]
      \node [contact] (left contact 1) at (0,0) {};
      \node [contact] (right contact 1) at (3,0) {};

      \draw (right contact 1) to [
        diode={info=$I_{\rm diode}$},
        current direction={near end}
      ] (left contact 1);

      \draw (right contact 1) -- ++(down:\dy) to
      [resistor={info'={$R_{\rm shunt}$},info={$I_{\rm shunt}$}}, current
      direction={near end}]
      ++(left:3) to (left contact 1);
      \draw (left contact 1) -- ++(up:\dy) to
      [current source={light dependent,info'={$I_{\rm photo}$}}, current
      direction={near end}] ++(right:3) to (right contact 1);
      \draw (right contact 1) to [resistor={info'={$R_{\rm series}$},info={$I_{\rm
                out}$}},current direction={at end}]  ++(right:2);
      %    \draw[->] (right contact 1) --node[anchor=south]{$I_{\rm out}$} ++(0:1);
      \draw (left contact 1) to [current direction'={info={$I_{\rm in}$}}]
      ++(left:1);
    \end{scope}

    % Plot %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \begin{scope}[shift={(0,0)}]
      \begin{axis}[
          width={5in},
          height={3in},
          xlabel={$V$ (V)},
          %ylabel={$I$ (A)},
          axis x line=bottom,
          axis y line=center,
          axis line style={line width=1},
          xmin=-0.8,
          xmax=0.8,
          ymin=0,
          ymax=10.5,
          xtick={-0.6,0,0.6},
          ytick={2, 4, 6, 8}, %\empty,
        ]
        %    \fill[green!15!white] (0.005,0.05) rectangle (0.75,10.5);
        %    \fill[red!25!white] (-0.005,0.05) rectangle (-0.75,10.5);
        \addplot [DarkBlue, line width=2,opacity=0.5] table {kw.dat};
        %\addplot [DarkBlue, line width=2,opacity=0.5] table {ipvcurve.dat};
        %\addplot [red, opacity=0.5] table {ku265.dat};
        \draw[dashed, line width=1] (0.638,0) --
        node[rotate=-87,anchor=south]{slope $\approx -1/R_{\rm series}$} (0.565,10);
        \draw[dashed,line width=1] (-0.639,9.3272) -- (0.63,9.2);
        \node at (-0.5,10) {slope $\approx -1/R_{\rm shunt}$};
        \node[font=\small,anchor=west] at (0.02,1) {cell generates power};
        \node[font=\small,anchor=east] at (-0.05,1) {cell absorbs power};
        \node[anchor=east] at (0,10) {$I$ (A)};
      \end{axis}
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014.tex
modified: 2015-04-27 02:30:44
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed] (0,3) -- (0,-1.5) ;
    \filldraw[fill=gray,rotate=33] (3.3,0) rectangle (3.5,0.2);
    \draw (0,2) ellipse[x radius=3, y radius=0.4];
    \draw (3,1.95) -- (0,0) -- (-3,1.95);
    \draw (0,0.75) arc(90:147:0.75);
    \node at (120:1.05) {$\theta$};
    \draw[<->] (0,2) -- node[fill=white]{$R$} (-3,2);
    \draw[->] (2.9,2) arc[x radius=2.9, y radius=0.35, start angle=5,
        end angle=60] node[anchor=north]{$v_{0}$};
    \node at (3.25,1.9){$m$};
    \draw[accel] (-2,0.5) -- +(-90:1.25) node[anchor=west]{$g$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Clinic/Director/2017-2018/CLGP 2017-18/Manuscript/Graphics
filename: tikz_figures.tex
modified: 2020-12-15 03:20:21
domain: Clinic
source:
  \begin{tikzpicture}[
      circuit ee IEC,
      every info/.style={font=\footnotesize},
      small circuit symbols,
      set resistor graphic=var resistor IEC graphic,
      set diode graphic=var diode IEC graphic,
      scale=1]
    \def\dx{1.5}
    \def\dy{1.25}

    \node [contact] (bottom contact 1) at (0,0) {};
    \node [contact] (top contact 1) at (0,3) {};
    \draw (bottom contact 1) to [circuit handle symbol={draw,shape=circle}]  (-2, 0)
    to [voltage source={info=$V_{\rm app}$}] (-2,3)
    to [diode={info'={diode}}] (top contact 1);
    % \draw (top contact 1) to [diode={info'=$I_{\rm diode}$}, current
    % direction={near end}]
    % (-2,3) to [voltage source={info=$V_{\rm app}$}] (-2,0) -- (bottom contact 1);

    %   \draw (right contact 1) -- ++(down:\dy) to
    %     [resistor={info'={$R_{\rm shunt}$},info={$I_{\rm shunt}$}}, current direction={near end}] ++(left:3) to (left contact 1);
    %     \draw (left contact 1) -- ++(up:\dy) to
    %     [current source={light dependent,info'={$I_{\rm photo}$}}, current
    %     direction={near end}] ++(right:3) to (right contact 1);
    %     \draw (right contact 1) to [resistor={info'={$R_{\rm series}$},info={$I_{\rm
    %         out}$}},current direction={at end}]  ++(right:2);
    % %    \draw[->] (right contact 1) --node[anchor=south]{$I_{\rm out}$} ++(0:1);
    %   \draw (left contact 1) to [current direction'={info={$I_{\rm in}$}}]
    %   ++(left:1);


  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014.tex
modified: 2015-04-27 02:30:44
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed] (0,3) -- (0,-1.5) ;
    \draw (0,2) ellipse[x radius=3, y radius=0.4];
    \draw (3,1.95) -- (0,0) -- (-3,1.95);
    \draw (0,0.75) arc(90:147:0.75);
    \node at (120:1.05) {$\theta$};
    \draw[<->] (0,2) -- node[fill=white]{$R$} (-3,2);
    \shade[ball color=gray!50!black] (2.9,2.1) circle(0.15);
    \draw[->,rotate=33]  (3.4,0.2) -- +(180:1);
    \node at (3.25,1.9){$m$};
    \draw[accel] (-2,0.5) -- +(-90:1.25) node[anchor=west]{$g$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Clinic/Director/2017-2018/CLGP 2017-18/Manuscript/Graphics
filename: fig_iv_quarter_cell.tex
modified: 2020-12-14 22:01:11
domain: Clinic
source:
  \begin{tikzpicture}[
      circuit ee IEC,
      every info/.style={font=\small}, % footnotesize
      small circuit symbols,
      set resistor graphic=var resistor IEC graphic,
      set diode graphic=var diode IEC graphic,
      scale=1]
    \def\dx{1.5}
    \def\dy{1.25}

    % the circuit diagram %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \begin{scope}[
        shift={(-0.5,2.75)},
        font=\large
      ]
      \node [contact] (left contact 1) at (0,0) {};
      \node [contact] (right contact 1) at (3,0) {};

      \draw (right contact 1) to [
        diode={info=$I_{\rm diode}$},
        current direction={near end}
      ] (left contact 1);

      \draw (right contact 1) -- ++(down:\dy) to
      [resistor={info'={$R_{\rm shunt}$},info={$I_{\rm shunt}$}}, current
      direction={near end}]
      ++(left:3) to (left contact 1);
      \draw (left contact 1) -- ++(up:\dy) to
      [current source={light dependent,info'={$I_{\rm photo}$}}, current
      direction={near end}] ++(right:3) to (right contact 1);
      \draw (right contact 1) to [resistor={info'={$R_{\rm series}$},info={$I_{\rm
                out}$}},current direction={at end}]  ++(right:2);
      %    \draw[->] (right contact 1) --node[anchor=south]{$I_{\rm out}$} ++(0:1);
      \draw (left contact 1) to [current direction'={info={$I_{\rm in}$}}]
      ++(left:1);
    \end{scope}

    % Plot %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    \begin{scope}[shift={(0,0)}]
      \begin{axis}[
          width={5in},
          height={3in},
          xlabel={$V$ (V)},
          %ylabel={$I$ (A)},
          axis x line=bottom,
          axis y line=center,
          axis line style={line width=1},
          xmin=-0.8,
          xmax=0.8,
          ymin=0,
          ymax=2.75,
          xtick={-0.6,0,0.6},
          ytick={1, 2}, %\empty,
        ]
        %    \fill[green!15!white] (0.005,0.05) rectangle (0.75,10.5);
        %    \fill[red!25!white] (-0.005,0.05) rectangle (-0.75,10.5);
        %\addplot [DarkBlue, line width=2,opacity=0.5] table {kw.dat};
        \addplot [DarkBlue, line width=2,opacity=0.5] table {ipvcurve.dat};
        %\addplot [red, opacity=0.5] table {ku265.dat};
        \draw[dashed, line width=1] (0.638,0) --
        node[rotate=-87,anchor=south]{slope $\approx -1/R_{\rm series}$} (0.565,10/4);
        \draw[dashed,line width=1] (-0.639,9.3272/4) -- (0.63,9.2/4);
        \node at (-0.5,10/4) {slope $\approx -1/R_{\rm shunt}$};
        \node[font=\small,anchor=west] at (0.02,1/4) {cell generates power};
        \node[font=\small,anchor=east] at (-0.05,1/4) {cell absorbs power};
        \node[anchor=east] at (0,10/4) {$I$ (A)};
      \end{axis}
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014.tex
modified: 2015-04-27 02:30:44
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed,->] (0,-1) -- (0,5) node[anchor=east]{$z$};
    \draw[dashed] (-4,0) -- (2,0) node[anchor=west]{$z = 0$};
    \draw[dashed] (-3.,4) -- (-4,4);
    \draw (0,4) ellipse[x radius=3, y radius=0.5];
    \draw[<->] (0,4) --node[fill=white]{$R=\sqrt{bh}$} (3,4);
    \draw (0,0) parabola (3,4);
    \draw (0,0) parabola (-3,4);
    \draw[<->] (-3.5,0) --node[fill=white]{$h$} (-3.5,4);

    \begin{scope}[shift={(0,2.5)}]
      \draw[line width=1.5] (0.1,0.1) -- (-0.1,-0.1);
      \draw[line width=1.5] (-0.1,0.1) -- (0.1,-0.1);
    \end{scope}
    \draw[<->] (-0.3,0) --node[fill=white]{$z_{\rm CM}$} ++(90:2.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014.tex
modified: 2015-04-27 02:30:44
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=gray!50] (-0.05,0) rectangle (0.05,6);
    \fill[fill=gray] (0,0) circle (0.2);
    \fill (0,0) circle (0.05);
    \node at (-0.4,3) {$m$};

    \filldraw[fill=gray] (-2.5,6) circle (0.25);
    \node at (-2.5,6.5){$m$};
    \draw[vel] (-2,6) --node[anchor=south]{$v_{0}$} ++(0:1.25);
    \draw[spring] (0.25,6) -- ++(0:1.75);
    \node at (1,6.5){$k$};
    \draw (0.05,6) -- (0.25,6);
    \fill[color=brown] (2,5.25) rectangle (2.5,6.75);
    \draw[line width=1.5] (2,5) -- (2,7);

    \draw[dashed] (2,0) -- (4,0) (4,6) -- (2.5,6);
    \draw[<->] (3.2,0) --node[fill=white]{$D$} (3.2,6);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Clinic/2021
filename: tmp.tex
modified: 2021-10-22 19:18:06
domain: Clinic
source:
  \begin{tikzpicture}[scale=1.5,>=Stealth,vel/.style={->,line width=2pt,color=DarkBlue},
      vector/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,->},
      signal/.style={color=DarkRed,line width=2},
      mp/.style={color=gray},
      note/.style={color=DarkGreen,font=\tiny,anchor=north},
    ]

    \draw[->] node[anchor=east]{$r(t)$} (0,0) -- ++(0.5,0) coordinate (A)
    -- ++(0, 1) -- ++(0.5,0) coordinate (a);
    \draw (a) -- ++(0.4,0);
    \draw (a) ++(0.5,0)  coordinate (b);
    \myotimes{(b)}
    \draw[->] (1.5,0) node[shape=rectangle,draw] {LO} ++(90:0.175) -- node[anchor=west,font=\small]{$2\cos(2\pi f_0 t)$} (1.5,0.9);
    \draw[->] (1.5,-0.175) -- ++(-90:0.15)
    node[anchor=north,font=\tiny,shape=rectangle,draw] {90$^{\circ}$ shift};
    \draw[->] (1.5,-0.6) --node[anchor=west,font=\small]{$-2\sin(2\pi f_{0} t)$} (1.5,-0.9);

    \draw[->] (A) -- ++(0,-1) -- ++(0.5,0) coordinate (ap);
    \draw (ap) -- ++(0.4,0);
    \draw (ap) ++(0.5,0) coordinate (bp);
    \myotimes{(bp)}

    % Now head off to two low-pass filters
    \draw[->] (b) ++(0.1,0) -- (2.5,1) coordinate (c);
    \draw (c) -- ++(1,0) coordinate (d);
    \draw (d) ++(0,-0.25) rectangle ++(.85,0.5);
    \begin{scope}[shift = {(d)},DarkGreen,line width=1.5]
      \draw (0.1,0.15) -- (0.3,0.15) .. controls (0.5, 0.15) .. (0.7,-0.1) --
      ++(-45:0.1);
      \node[font=\scriptsize] at (0.2,-0.15) {LPF};
    \end{scope}

    \draw[->] (bp) ++(0.1,0) -- (2.5,-1) coordinate (cp);
    \draw (cp) -- ++(1,0) coordinate (dp);
    \draw (dp) ++(0,-0.25) rectangle ++(.85,0.5);
    \begin{scope}[shift = {(dp)},DarkGreen,line width=1.5]
      \draw (0.1,0.15) -- (0.3,0.15) .. controls (0.5, 0.15) .. (0.7,-0.1) --
      ++(-45:0.1);
      \node[font=\scriptsize] at (0.2,-0.15) {LPF};
    \end{scope}

    \begin{scope}[shift={(4.35,1)}]
      \draw[->] (0,0) -- node[anchor=south]{$x(t)$} ++(0.75,0);
      \draw (0.75,0) \adc
      \node at (1.75,0) {$x_{n}$};
    \end{scope}
    \begin{scope}[shift={(4.35,-1)}]
      \draw[->] (0,0) -- node[anchor=south]{$y(t)$} ++(0.75,0);
      \draw (0.75,0) \adc
      \node at (1.75,0) {$y_{n}$};

      \node at (1.75,1) {$z_{n} = x_{n} + i y_{n}$};
    \end{scope}

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014.tex
modified: 2015-04-27 02:30:44
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[spring] (0.25,6) -- ++(0:1.75);
    \draw (0.05,6) -- (0.25,6);
    \node at (1,6.5){$k$};

    \filldraw[fill=gray!50] (-0.05,0) rectangle (0.05,6);
    \fill[fill=gray] (0,0) circle (0.2);
    \fill (0,0) circle (0.05);

    \filldraw[fill=gray] (0,6) circle (0.25);
    \foreach \i in {-10,10}
      {
        \begin{scope}[rotate=\i]
          \draw[dashed] (-0.05,0) rectangle (0.05,5.75);
          \draw[dashed] (0,6) circle (0.25);
        \end{scope}
      }
    \draw (0.05,3.5) arc(90:82:3.5);
    \node at (85:3.75){$\theta$};

    \fill[color=brown] (2,5.25) rectangle (2.5,6.75);
    \draw[line width=1.5] (2,5) -- (2,7);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Clinic/2021
filename: lesson06.tex
modified: 2021-10-26 17:10:32
domain: Clinic
source:
  \begin{tikzpicture}[scale=1,>=Stealth,vel/.style={->,line width=2pt,color=DarkBlue},
      vector/.style={line width=1.5pt,color=blue,->},
      coord/.style={color=green!40!black,->},
      signal/.style={color=DarkRed,line width=2},
      sample/.style={color=DarkBlue,fill=yellow}
    ]
    \def\amp{0.5}
    \def\samp{0.05}

    \draw[coord] (-0.2,0) -- (4.4,0) node[anchor=south]{$t$};
    \draw[coord] (0,-0.6) -- (0,1) node[anchor=east] {$V$};

    \draw[signal] (0,\amp)
    cos ++(\amp,-\amp) sin ++(\amp,-\amp) cos ++(\amp,\amp) sin ++(\amp,\amp)
    cos ++(\amp,-\amp) sin ++(\amp,-\amp) cos ++(\amp,\amp) sin ++(\amp,\amp);

    % sample frequently
    %\foreach \x in {0, 0.2, ..., 4} {
    %  \filldraw[sample] (\x, \amp*cos(180*\x)) circle[radius=\samp];
    %}

    % \foreach \x in {0,1,...,4} {
    %   \filldraw[sample] (\x, \amp*cos(180*\x) circle[radius=\samp];
    % }

    % \foreach \x in {0.5,1.5,...,3.5} {
    %   \filldraw[yellow,fill=red,line width=1] (\x, \amp*cos(180*\x)  circle[radius=\samp];
    % }

    \foreach \x in {0,1.5,...,4} {
    \filldraw[sample] (\x, \amp*cos(180*\x) circle[radius=\samp];
    }
    \draw[DarkGreen,line width=1,dashed] (0,\amp)
    cos ++(3*\amp,-\amp) sin ++(3*\amp,-\amp) cos ++(3*\amp,\amp);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014.tex
modified: 2015-04-27 02:30:44
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=1.5] (-5.5,0) -- (1,0);
    \begin{scope}[shift={(0,5)},rotate=-30]
      \draw[<->] (0,-0.75) --node[fill=white]{$L$} (-6,-0.75);
      \draw[<->] (0,-0.25) --node[fill=white]{$d$} (-5,-0.25);
    \end{scope}

    \draw (0,6) arc(90:150:1);
    \node at (-0.7,6.2) {$\theta=\dg{60}$};
    \draw[line width=3] (0,5) -- ++(150:6);
    \draw[spring] (-0.1,7.5) -- (-4,7.5);
    \draw (-4,7.5) -- (-4.4,7.5);
    \draw[color=brown,line width=5] (0,0) -- (0,9);

    \draw[color=DarkGreen,line width=3] (-4,1) -- (-2,1)
    (-3,1) -- (-3,0)
    (-3.4,0.05) -- (-2.6,0.05);

    % time for the wine bottle!

    \begin{scope}[shift={(-2.75,1.05)}]
      \filldraw[fill=brown!40!black,draw=DarkGreen!50!black,
        line width=1]
      (0.05,1) -- (0.05,0.75) .. controls (0.05,0.65) and
      (0.15, 0.6) .. (0.15,0.05) .. controls (0.15,0) .. (0.1,0)
      -- (-0.1,0) .. controls (-0.15,0) and (-0.15,0) ..
      (-0.15,0.05) .. controls (-0.15, 0.6) and (-0.05, 0.65) .. (-0.05,0.75) --
      (-0.05, 1) -- cycle;
    \end{scope}

    \draw[color=brown,line width=2,shift={(-5,0)}]
    (0,0) -- ++(0,0.75) -- (-0.15,1.75)
    (0,0.75) -- (0.75,0.75) -- (0.75,0);

    \draw[color=brown,line width=2,shift={(-1,0)}]
    (0,0) -- (0,0.75) -- (0.15,1.75)
    (0,0.75) -- (-0.75,0.75) -- (-0.75,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Clinic/2021
filename: 211114-pairs.tex
modified: 2021-11-15 04:02:52
domain: Clinic
source:
  \begin{tikzpicture}[scale=1,
      coord/.style={color=green!40!black,|->},
      >=Stealth
    ]
    \shade[ball color=blue!50!white, opacity=0.3] (0,0) circle[radius=3];
    % cartesian system
    \draw[coord,->] (0,0) -- (4,0) node[anchor=west]{$y$};
    \draw[coord,->] (0,0,0) -- (0,0,6) node[anchor=north east]{$x$};
    \draw[coord,->] (0,0) -- (0,4) node[anchor=south]{$z$};
    % cover up the z axis underneath an upcoming label
    \draw[gray!35!white] (0,1.7) -- ++(90:0.25);
    % coordinate of the point
    \coordinate (A) at (1.5,2.121, 1.5);
    \draw[line width=1, ->,color=DarkRed] (0,0,0) -- node[anchor=north west]{$r$}  (A);
    % projection to the xy plane
    \draw[dashed,color=DarkBlue] (A) -- (1.5, 0, 1.5) -- (0,0);
    % circle of latitude
    \draw[dashed] (2.2,2) arc[x radius=2.2, y radius=0.5, start angle=0, end
        angle=-180];
    \draw[dashed,opacity=0.2] (2.2,2) arc[x radius=2.2, y radius=0.5, start
        angle=0, end angle=180];
    % circle of longitude
    \draw[dashed,color=black] (0,-3) arc[x radius=1.075, y radius=3, start angle=-90,
        end angle=90];
    \draw[dashed,color=gray, opacity=0.2] (0,-3) arc[x radius=1.1, y radius=3,
        start angle=-90, end angle=-270];
    % definition of phi
    \draw[->] (0,0,0.5) arc[start angle=-135, end angle=-45,
        x radius=0.35, y radius =0.25];
    \node at (0,-0.4){$\phi$};
    % theta definition
    \draw[->] (0,0.6) arc[start angle=90, end angle=50,
        y radius=0.6, x radius = 0.4];
    \node at (0.2, 0.75) {$\theta$};
    % circle of longitude at \phi + d\phi
    \draw[dashed,color=black] (0,-3) arc[x radius=1.4, y radius=3, start angle=-90,
        end angle=90];
    \draw[dashed,color=gray, opacity=0.2] (0,-3) arc[x radius=1.4, y radius=3,
        start angle=-90, end angle=-270];
    % circle of latitude at \theta + d\theta
    \draw[dashed] (2.35,1.8) arc[x radius=2.35, y radius=0.5, start angle=0, end
        angle=-180];
    \draw[dashed,opacity=0.2] (2.35,1.8) arc[x radius=2.35, y radius=0.5, start
        angle=0, end angle=180];
    % label the arcs
    \draw[<-] (1.08,1.6) -- ++(135:0.3) node[anchor=east] {$r \sin\theta
        \dd{\phi}$};
    \draw[<-] (1.28,1.45) -- ++(-30:0.3) node[anchor=west] {$r \dd{\theta}$};
    % draw dA
    \fill[fill=black,opacity=0.2] (A) -- ++(6:0.27) -- ++(-75:0.2) -- ++(186:0.28)
    -- cycle;
    % label dA
    \draw[<-] (1.08,1.48) -- ++(-50:1) node[anchor=west]{$\dd{A} = r^{2} \sin\theta
        \dd{\phi} \dd{\theta}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014.tex
modified: 2015-04-27 02:30:44
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[accel] (-1.25,2) -- node[anchor=east]{$g$} ++(-90:1.25);

    \node at (0,2) {$m$};
    \draw (0,2) circle(0.2);

    % The spring uncompressed
    \draw[line width=1.5,
      decorate,
      decoration={coil,segment length=4pt,aspect=0.15,amplitude=8pt}]
    (0,0) -- (0,1.5);
    \draw[<->] (-0.6,0) --node[fill=white]{$L$} +(90:1.5);

    % The spring compressed
    \draw[line width=1.5,
      shift={(3,0)},
      decorate,
      decoration={coil,segment length=3pt,aspect=0.15,amplitude=8pt}]
    (0,0) -- (0,1);

    \filldraw[fill=white] (3,1.15) circle(0.2);
    \node at (3,1.15) {$m$};
    \draw (1.25,0) -- (2.75,0.9);
    \draw (4.75,0) -- (3.25,0.9);
    \draw (1.75,0) arc(0:32:0.5);
    \node at (2.,0.2){$\theta$};
    \draw (4.25,0) arc(180:148:0.5);
    \node at (4,0.2){$\theta$};


    % The floor
    \fill[fill=gray!33] (-1,0) rectangle (6,-0.6);
    \draw (-1,0) -- (6,0);

    \draw[color=white,line width=8,decorate,
      decoration={coil, segment length=16pt, amplitude=3pt}]
    (0.75,0.25) -- (0.75,-1);

    % dashed lines
    \draw[dashed] (0,1.5) -- (6,1.5) (3.25,1) -- (6,1);
    \draw[<->] (5,1) --node[anchor=west]{$d$} (5,1.5);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Clinic/2021/MITLL-Midyear
filename: theory.tex
modified: 2022-03-25 14:05:45.265644
domain: Clinic
source:
  \begin{tikzpicture}[scale=1.2]
    \draw[coord] (-2.5,0) -- (0:2.5) node[anchor=north]{$\xi$};
    \draw[coord] (0,-1.5) -- (90:1.5) node[anchor=east]{$\eta$};
    \foreach \p/\lab in {(2,-1)/a_1,(1.25,1)/a_2,(-1.25,1)/a_3,(-2,-1)/a_4}{
        \fill[DarkRed,opacity=0.33] \p circle[radius=0.1];
        \draw[line width=1.5,DarkSlateBlue,->] (0,0) -- node[anchor=south]{$\lab$} \p;
      }
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014.tex
modified: 2015-04-27 02:30:44
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[accel] (-1.25,2) -- node[anchor=east]{$g$} ++(-90:1.25);


    % The spring uncompressed
    \draw[line width=1.5,
      decorate,
      decoration={coil,segment length=4pt,aspect=0.15,amplitude=8pt}]
    (0,0) -- (0,1.5);
    \draw[<->] (-0.6,0) --node[fill=white]{$L$} +(90:1.5);

    % The spring stretched
    \draw[line width=1.5,
      shift={(3,0)},
      decorate,
      decoration={coil,segment length=6pt,aspect=0.15,amplitude=8pt}]
    (0,0) -- (0,2.5);

    \filldraw[fill=white] (3,2.35) circle(0.2);
    \node at (3,2.35) {$m$};


    % The floor
    \fill[fill=gray!33] (-1,0) rectangle (6,-0.6);
    \draw (-1,0) -- (6,0);

    \draw[color=white,line width=8,decorate,
      decoration={coil, segment length=16pt, amplitude=3pt}]
    (0.75,0.25) -- (0.75,-1);

    % dashed lines
    \draw[dashed] (0,1.5) -- (6,1.5) (3.25,2.25) -- (6,2.25);
    \draw[<->] (5,1.5) --node[anchor=west]{$x$} (5,2.25);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Clinic/2021/MITLL-Midyear
filename: theory.tex
modified: 2022-03-25 14:05:45.265644
domain: Clinic
source:
  \begin{tikzpicture}[scale=1.25]
    \draw[->] (0,0) -- (3,0) node[anchor=north]{$\xi$};
    \draw[->] (0,0) -- (0,3) node[anchor=east]{$\eta$};
    \draw[->,DarkGreen,line width=1.5] (0,0) -- (20:2) node[anchor=west]{$\vb{A}_1$};
    \draw[->,DarkGreen,line width=1.5] (0,0) -- (70:3) node[anchor=south]{$\vb{A}_2$};
    \draw[->,DarkRed] (0,0) -- (135:2) node[anchor=south east]{$\boldsymbol{\kappa}$};
    \draw[DarkGreen] (0:1) arc(0:20:1) (0:1.5) arc(0:70:1.5) (10:1.2) node{$\theta_1$} (35:1.8) node{$\theta_2$};
    \draw[DarkRed] (0:0.5) arc(0:135:0.5) (105:0.75) node {$\psi$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Clinic/2021/MITLL-Midyear
filename: theory.tex
modified: 2022-03-25 14:05:45.265644
domain: Clinic
source:
  \begin{tikzpicture}[scale=1.5]
    \draw[coord] (0,0) -- (6,0) node[anchor=north]{$x$};
    \draw[coord] (0,0) -- (0,4) node[anchor=east]{$y$};
    \fill[DarkRed,opacity=0.5] (1,1) coordinate (A) circle[radius=0.1];
    \fill[DarkRed,opacity=0.5] (2.5,1) coordinate (B) circle[radius=0.1];
    \draw[coord] (0,0) --node[anchor=south east]{$r_1$} (A);
    \draw[coord] (0,0) --node[anchor=north]{$r_2$} (B);
    % indicate the intersection
    \fill[yellow,opacity=0.25] (33:6.9) coordinate (C) circle[radius=0.1];


    \draw[gray!25] (A) -- ++(30:6) (B) -- ++(40:5);
    \draw[DarkBlue,line width=1.5,->] (A) --node[anchor=south east]{$\uv_{1}$}
    ++(30:1);
    \draw[DarkBlue,line width=1.5,->] (B) --node[anchor=north west]{$\uv_{2}$}
    ++(40:1);

    % draw the baseline
    \draw[DarkRed,line width=1.5,->] (A) -- node[anchor=north]{$\vb{b}$} (B);

    % draw remove
    \draw[DarkGoldenrod,->,line width=1] (A) ++(0.75,0) --node[anchor=south east]{$\vb{s}$} (C);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-mt2-2014-v6.tex
modified: 2015-03-26 04:45:26
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[left color=white, right color=gray!80!white] (0,0) rectangle
    (3,6);
    \draw[coord] (0,0.5) --node[fill=white]{$w$} ++(0:3);
    \draw[coord] (0.5,0) --node[fill=white]{$h$} ++(90:6);
    \fill (0,3) circle[radius=0.1];
    \draw[force,line width=2] (0,6) -- +(-120:3)
    node[anchor=east]{$F$};
    \draw (0,5) arc(-90:-120:1);
    \node at (-0.3,4.75) {$\dg{30}$};
    \begin{scope}[shift={(3.5,3)}]
      \draw[accel] (0,0.5) -- node[anchor=west]{$~g$} (0,-0.5);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Clinic/2018/LLNL/LLNL_Statement-of-work_Final
filename: llnl-statement-of-work.tex
modified: 2018-10-08 18:14:51
domain: Clinic
source:
  \begin{tikzpicture}[node distance=2cm]
    \node (start) [startstop] {Start};
    \node (set-up) [process, below of=start] {Set Up System};
    \node (top) [process, below of=set-up] {Edit Topology File};
    \node (em) [process, below of=top] {Energy Minimization};
    \node (1fs) [process, below of=em] {Relaxation Simulations};
    \node (mksim) [process, below of=1fs] {Make Simulation File};
    \node (runsim) [process, below of=mksim] {Run Bilayer Simulation};
    \node (ana) [process, below of=runsim] {Python Analysis};
    \node (finished) [decision, right of=ana, xshift=2cm] {Another?};
    \node (stop) [startstop, below of=ana]{Stop};

    \node (scr) [process, right of=em, xshift=5cm] {Simulation Script};
    \node (check) [decision, left of=1fs, xshift=-2cm] {Stable?};


    \draw [arrow] (start) -- node[anchor=east] {General Process} (set-up);
    \draw [arrow] (set-up) -- (top);
    \draw [arrow] (top) -- (em);
    \draw [arrow] (em) -- (1fs);
    \draw [arrow] (1fs) -- (check);
    \draw [arrow] (mksim) -- (runsim);
    \draw [arrow] (runsim) -- (ana);
    \draw [arrow] (ana) -- (finished);
    \draw [arrow] (finished) |- node[anchor=west, yshift=0.5cm] {Yes} (stop);
    \draw [arrow] (finished) |- node[anchor=west, yshift=-5cm] {No} (set-up);
    \draw [arrow] (check) |- node[anchor=west, yshift=0.5cm] {Yes} (mksim);
    \draw [arrow] (check) |- node[anchor=west, yshift=-0.5cm] {No} (em);

    \draw [arrow] (start) -| node[anchor = north, yshift=.7cm, xshift = -2.7cm] {With Automated Pipeline} (scr);
    \draw [arrow] (scr) |- (stop);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014-key.tex
modified: 2014-05-13 17:26:24
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[rotate=33]
      \filldraw[fill=gray] (-0.25,-0.25) rectangle (0.25,0.25);
      \draw[force] (0,0) -- ++(-123:1.5) node[anchor=east]{$mg$};
      \draw[force] (0,-0.25) -- ++(90:1.5) node[anchor=east]{$N$};
      \draw[coord,->] (-1.5,0) -- ++(90:1) node[anchor=east]{$y$};
      \draw[coord,->] (-1.5,0) -- ++(180:1) node[anchor=north]{$x$};
      \draw[coord,-,dashed] (-1.5,0) -- ++(-123:1);
      \draw[coord,-] (-1.85,0) arc(-180:-123:0.35);
      \node at (-2,-0.3){$\theta$};
    \end{scope}

    \begin{scope}[shift={(-2,-4.5)}]
      \draw (0,0) -- node[anchor=north west]{$s$} ++(33:3)
      -- node[anchor=south]{$R$} (0,1.633917105) -- node[anchor=east]{$h$} (0,0);
      \draw (33:0.6) arc (33:90:0.6);
      \node at (65:0.85) {$\theta$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/Clinic/2018/LLNL/LLNL_Statement-of-Work_Draft
filename: statement-of-work-v1.tex
modified: 2018-10-03 17:07:30
domain: Clinic
source:
  \begin{tikzpicture}[node distance=2cm]
    \node (start) [startstop] {Start};
    \node (set-up) [process, below of=start] {Set Up System};
    \node (top) [process, below of=set-up] {Edit Topology File};
    \node (em) [process, below of=top] {Energy Minimization};
    \node (mksim) [process, below of=em] {Make Simulation File};
    \node (runsim) [process, below of=mksim] {Run Bilayer Simulation};
    \node (finished) [decision, right of=runsim, xshift=2cm] {Finished?};
    \node (stop) [startstop, below of=runsim]{Stop};

    \node (scr) [process, right of=set-up, xshift=5cm] {Script Simulator};

    \draw [arrow] (start) -- node[anchor=east] {initial} (set-up);
    \draw [arrow] (set-up) -- (top);
    \draw [arrow] (top) -- (em);
    \draw [arrow] (em) -- (mksim);
    \draw [arrow] (mksim) -- (runsim);
    \draw [arrow] (runsim) -- (finished);
    \draw [arrow] (finished) |- node[anchor=west, yshift=0.5cm] {yes} (stop);
    \draw [arrow] (finished) |- node[anchor=west, yshift=-5cm] {no} (set-up);

    \draw [arrow] (start) -| node[anchor = north, yshift=.7cm, xshift = -2.5cm] {with bilayer understanding} (scr);
    \draw [arrow] (scr) |- (stop);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014-key.tex
modified: 2014-05-13 17:26:24
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \begin{scope}[rotate=33]
      \filldraw[fill=gray] (-0.25,-0.25) rectangle (0.25,0.25);
      \draw[force] (0,0) -- ++(-123:1.5) node[anchor=west]{$mg$};
      \draw[force] (0,-0.25) -- ++(90:1.5) node[anchor=east]{$N$};
      \draw[dashed] (0,-0.25) -- ++(180:1.5);
      \draw (-0.7,-0.25) arc (180:237:0.5);
      \node at (215:1) {$\theta$};
    \end{scope}
    \draw[accel] (-1,0) -- ++ (180:1) node[anchor=south]{$a$};
    \draw[coord,->] (2,0) -- ++(90:1) node[anchor=east]{$y$};
    \draw[coord,->] (2,0) -- ++(180:1) node[anchor=north]{$x$};
    % \draw[coord,-,dashed] (-1.5,0) -- ++(-123:1);
    % \draw[coord,-] (-1.85,0) arc(-180:-123:0.35);
    % \node at (-2,-0.3){$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014-key.tex
modified: 2014-05-13 17:26:24
domain: p24
source:
  \begin{tikzpicture}[scale=0.5]
    \draw (0,0) -- node[anchor=west]{$y$} (0,-2)
    -- node[anchor=north east]{$d$} ++(150:4)
    -- node[anchor=south]{$x$} (0,0);
    \draw (0,-1.5) arc(90:150:0.5);
    \node at (-0.35,-1.15){$\theta$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014-key.tex
modified: 2014-05-13 17:26:24
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=3,color=gray] (0,0) -- (150:5);
    \draw[force] (0,0) -- +(90:1.2) node[anchor=west]{$F_{y}$};
    \draw[force] (0,0) -- +(180:1.5) node[anchor=north]{$F_{x}$};
    \draw[force] (150:2.5) -- ++(-90:1.2) node[anchor=east]{$mg$};
    \draw[force] (150:3.5) -- ++(0:1.5) node[anchor=south]{$kx$};
    \fill (0,0) circle(0.1);
    \node at (0.2,-0.2){P};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-final-2014-key.tex
modified: 2014-05-13 17:26:24
domain: p24
source:
  \begin{tikzpicture}[scale=0.6]
    \filldraw[fill=gray] (0,0) circle (0.2);
    \draw[force] (0,0) -- +(-90:1.5) node[anchor=west]{$mg$};
    \draw[force] (0,-0.2) -- +(90:2.5) node[anchor=west]{$kd$};
    \draw[force] (-30:0.2) -- (-30:2.5) node[anchor=west]{$T$};
    \draw[force] (-150:0.2) -- (-150:2.5) node[anchor=east]{$T$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-mt1-2014-v4.tex
modified: 2014-02-17 23:55:04
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw (0,0) circle[radius=2];
    \draw[dashed] (0,2.5) -- (0,-2.5) (0,0) -- (-45:2);
    \draw (0,-0.75) arc(-90:-45:0.75);
    \node at (-67.5:1){$\theta$};
    \fill (-45:2) circle[radius=0.1] node[anchor=north west]{$m$};
    \draw[->] (-0.2,2.35) arc[x radius=0.4, y radius=0.1,
        start angle=120, end angle=420];
    \node at (0.75,2.35){$\omega$};
    \draw[accel] (2.75,0) -- ++(-90:1) node[anchor=west]{$g$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14
filename: p24-mt1-2014-v4.tex
modified: 2014-02-17 23:55:04
domain: p24
source:
  \begin{tikzpicture}[scale=1.5]
    \draw[dashed] (0,0) -- (8,0);
    \draw[color=brown,line width=1.5] (0,0) -- ++(270:3) -- ++(0:8);
    \draw[dashed] (0,0.2) -- ++(180:2);
    \draw (-0.7,0.2) arc (180:210:0.5);
    \node at (-1,0){$\theta$};
    \begin{scope}[rotate=30]
      \draw[line width=2pt] (0,0.25) rectangle (-2,-0.25);
      \draw[spring] (-2,0) -- (-1,0);
      \filldraw[dashed,fill=gray!40!white] (-1,0) circle(0.22);
      \shade[ball color=yellow] (0,0) circle(0.22);
    \end{scope}
    \begin{scope}[shift={(7,-2.96)}]
      \draw[line width=2,color=DarkRed] (0,0) -- ++(0.2, 0) -- ++(75:0.25);
      \draw[line width=2,color=DarkRed] (0,0) -- ++(-0.2, 0) -- ++(105:0.25);
    \end{scope}

    % Now draw the dimension lines
    \draw[dashed,<->] (0,-2) -- node[fill=white]{$L$} ++(7,0);
    \draw[dashed,<->] (7,0) -- node[fill=white]{$h$} ++(-90:2.96);

    \draw[vel] (30:0.4) -- ++(30:0.6) node[anchor=south]{$v_{0}$};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14/old drafts
filename: p24-quiz2-2014-v1.tex
modified: 2014-03-01 06:46:56
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},
      tightspring/.style={decorate,decoration={coil,aspect=0.3,segment length=1mm,amplitude=2mm}}
    ]

    % draw the floor and ramp
    \draw[brown!70!black, line width=2pt] (-5,0) -- ++(0:7) -- (9, 1) -- ++(0:2);
    \draw[dashed] (2,0) -- (11,0);

    \draw (5,0) arc(0:12:2);
    \node at (5.25,0.22) {$\alpha$};

    % the two masses and the compressed spring
    \filldraw[fill=red!70!black] (-2,0) rectangle (-1.5,0.5);
    \node at (-1.75,0.75){$r m$};
    \draw[color=brown,line width=2pt](-1.5,0.25) -- (-0.5,0.25);
    \draw[tightspring] (-1.5,0.25) -- (-0.25,0.25);
    \node at (-1.,0.65){$k$};
    \filldraw[fill=blue!70!black] (-0.5,0) rectangle (0,0.5);
    \node at (-0.25,0.75){$ m $};

    \draw[coord,<->] (10.5,0) -- (10.5,1);
    \node at (10.8,0.5) {$b$};

    % The bouncer spring
    \begin{scope}[shift={(-4,0)}]
      \draw[tightspring] (-0.5,0.25) -- (0,0.25);
      \filldraw[fill=gray!50!black] (0,0) rectangle (0.1,0.5);
      \filldraw[fill=gray!50!black] (-0.5,0) rectangle (-1,0.5);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14/old drafts
filename: p24-quiz2-2014-v3.tex
modified: 2014-03-03 23:37:22
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},
      tightspring/.style={decorate,decoration={coil,aspect=0.3,segment length=1mm,amplitude=2mm}}
    ]

    % draw the floor and ramp
    \draw[brown!70!black, line width=2pt] (-3,0) -- ++(0:5) -- (9, 1) -- ++(0:2);
    \draw[brown!50!white, line width=2pt,dashed] (-5,0) -- (-3,0);
    \draw[dashed] (2,0) -- (11,0);

    \draw (5,0) arc(0:12:2);
    \node at (5.25,0.22) {$\alpha$};

    % the two masses and the compressed spring
    \filldraw[fill=red!70!black] (-2,0) rectangle (-1.5,0.5);
    \node at (-1.75,0.75){$r m$};
    \draw[color=brown,line width=2pt](-1.5,0.25) -- (-0.5,0.25);
    \draw[tightspring] (-1.5,0.25) -- (-0.25,0.25);
    \node at (-1.,0.65){$k$};
    \filldraw[fill=blue!70!black] (-0.5,0) rectangle (0,0.5);
    \node at (-0.25,0.75){$ m $};

    \draw[coord,<->] (10.5,0) -- (10.5,1);
    \node at (10.8,0.5) {$b$};

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14/old drafts
filename: quiz1-v1.tex
modified: 2015-01-28 15:57:25
domain: p24
source:
  \begin{tikzpicture}
    [scale=1.67,
      decoration={coil,aspect=0.3,segment length=2mm,amplitude=2mm},
      >=stealth']
    \filldraw[fill=gray!20!white] (-2, -1) -- ++(-10:4)
    -- ++(50:2) -- ++(-185:3.5) -- cycle;
    \filldraw[fill=gray!40!white] (-2, -1) -- ++(-10:4)
    -- ++(50:2) -- ++(-90:0.1)
    -- ++(230:2) -- ++(90:0.1)
    -- ++ (-90:0.1) --
    ++(170:4) -- cycle;

    % Now the hole in the middle of the table
    \filldraw[fill=white] (0.75,-0.65) circle[x radius=0.1, y radius=0.033,
        rotate=-10];

    \filldraw[fill=gray!50!white] (1.7,-0.5)
    -- ++(0.1,-0.1)
    -- ++(0,0.15)
    -- ++(-0.1, 0.1)
    -- cycle;
    \filldraw[fill=gray!70!white] (1.8,-0.6)
    -- ++(0,0.15)
    -- ++(0.1,0.05)
    -- ++(0,-0.15)
    -- cycle;
    \filldraw[fill=gray!30!white] (1.7,-0.35)
    -- ++(0.1,-0.1)
    -- ++(0.1,0.05)
    -- ++(-0.1,0.1)
    -- cycle;

    \draw (0.75,-0.65) -- ++(10:1);
    \node at (2.15,-0.5){$m_{1}$};

    \draw[dashed] (0.75,-0.65) -- ++(-90:.8);

    % now m2
    \filldraw[fill=gray!30!white] (0.62,-2.15)
    -- ++(0.2,-0.05)
    -- ++(0.05,0.1)
    -- ++(-0.2,0.05)
    -- cycle;
    \filldraw[fill=gray!20!white] (0.62, -2.15)
    -- ++(0,-0.2)
    -- ++(0.2,-0.05)
    -- ++(0,0.2)
    -- ++(-0.2,0.05);
    \filldraw[fill=gray!50!white] (0.82,-2.2)
    -- ++(0,-0.2)
    -- ++(0.05,0.1)
    -- ++(0,0.2)
    -- cycle;
    \draw (0.75,-1.60) -- ++(-90:0.5);
    \node at (1.1,-2.3) {$m_{2}$};


    \draw[line width=1.5,->] (3.,-1.25) -- node[anchor=west]{$g$} ++(-90:0.65);

  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14/old drafts
filename: quiz1-v1.tex
modified: 2015-01-28 15:57:25
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw (-3,-2) rectangle (3,2);
    \draw (0,0) circle (0.05);
    \draw[dotted] (0,0) circle (1.5);
    \draw (0,0) -- node[anchor=north]{$r$} (30:1.5);
    \filldraw[rotate=30,fill=gray!50!white] (1.4,-0.15) rectangle (1.6,0.15);
    \draw[line width=1.5,->] (30:1.5) -- ++(120:0.6);
    \node at (30:2){$m_{1}$};
    \node at (2.25,-1.6) {\small \textsf{top view}};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14/old drafts
filename: p24-mt2-2014-v4.tex
modified: 2014-04-04 03:26:05
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[left color=white, right color=gray!60!white] (0,0) rectangle
    (3,6);
    \draw[dashed, line width=1.5] (0,-0.5) -- (0, 6.5);
    \draw[coord] (0,-0.25) --node[fill=white]{$w$} ++(0:3);
    \draw[coord] (-0.25,0) --node[fill=white]{$h$} ++(90:6);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14/old drafts
filename: p24-mt2-2014-v4.tex
modified: 2014-04-04 03:26:05
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[left color=white, right color=gray!60!white] (0,0) rectangle
    (3,6);
    %\draw[coord] (0,-0.25) --node[fill=white]{$w$} ++(0:3);
    %\draw[coord] (-0.25,0) --node[fill=white]{$h$} ++(90:6);
    \fill (0,3) circle[radius=0.1];
    \begin{scope}[shift={(0,3)}]
      \draw[->] (-25:4) arc(-25:25:4) node[anchor=west]{$\omega$};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14/old drafts
filename: p24-mt2-2014-v5.tex
modified: 2014-04-06 16:07:04
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[left color=white, right color=gray!80!white] (0,0) rectangle
    (3,6);
    %\draw[coord] (0,-0.25) --node[fill=white]{$w$} ++(0:3);
    %\draw[coord] (-0.25,0) --node[fill=white]{$h$} ++(90:6);
    \fill (0,3) circle[radius=0.1];
    \draw[force,line width=2] (0,6) -- +(-120:3)
    node[anchor=east]{$F$};
    \draw (0,5) arc(-90:-120:1);
    \node at (-0.3,4.75) {$\dg{30}$};
    \begin{scope}[shift={(3.5,3)}]
      \draw[accel] (0,0.5) -- node[anchor=west]{$g$} (0,-0.5);
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14/old drafts
filename: p24-mt1-2014-v1.tex
modified: 2014-02-13 16:01:24
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=blue!30!white] (0,0) -- ++(0,-6) -- (8,-6) -- cycle;
    \draw (7,-6) arc(180:143.13:1);
    \node at (6.7,-5.7){$\phi$};
    \filldraw[fill=gray!50!white] (0,0) circle (0.25);
    \fill (0,0) circle(0.05);
    \draw (-0.25,0) -- ++(-90:2);
    \filldraw[fill=DarkGreen] (-0.375,-2) rectangle (-0.125,-2.5)
    (-0.375,-1) rectangle (-0.125,-1.5);
    \node at (-0.75,-1.25){$m$};
    \node at (-0.75,-2.25){$m$};

    \begin{scope}[rotate=-36.869897646]
      \draw (0,0.25) -- ++(0:9);
      \filldraw[fill=DarkRed] (9,0) rectangle (9.75,0.5);
      \node at (9.375, 0.75){$M$};
    \end{scope}

    % Now the laser beam
    \draw[line width=1.5,color=red,->] (-3,-4.5) -- ++(0:2.5);
    \node at (-2.25,-4.2)[color=red]{laser beam};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/exams14/old drafts
filename: p24-mt1-2014-v2-sol.tex
modified: 2014-02-17 16:12:15
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \shade[ball color=yellow] (0,0) circle(0.22);
    \draw[force] (0,0) -- ++(-90:1) node[anchor=east]{$g$};
    \draw[coord] (0.5,0) -- ++ (0:0.75) node[anchor=north]{$x$};
    \draw[coord] (0.5,0) -- ++ (90:0.75) node[anchor=east]{$y$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/rec14
filename: rec27-prof.tex
modified: 2014-04-29 21:19:10
domain: p24
source:
  \begin{tikzpicture}[scale=0.667]
    \draw (0,0) sin (3,0.25) cos (6,0);
    \draw (0,0) sin(3,-0.25) cos (6,0);
    \node at (-0.75,0) {$ n = 1 $};
    \begin{scope}[shift={(0,-1)}]
      \draw (0,0) sin (1.5,0.25) cos (3,0) sin (4.5,0.25) cos(6,0);
      \draw (0,0) sin(1.5,-0.25) cos (3,0) sin (4.5,-0.25) cos (6,0);
      \node at (-0.75,0) {$ n = 2 $};
    \end{scope}
    \begin{scope}[shift={(0,-2)}]
      \draw (0,0) sin (1,0.25) cos (2,0) sin (3,0.25) cos(4,0) sin (5,0.25) cos(6,0);
      \draw (0,0) sin(1,-0.25) cos (2,0) sin (3,-0.25) cos (4,0) sin (5,-0.25)
      cos(6,0);
      \node at (-0.75,0) {$ n = 3 $};
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/rec14
filename: rec27-prof.tex
modified: 2014-04-29 21:19:10
domain: p24
source:
  \begin{tikzpicture}[scale=0.667]
    \draw[line width=2,color=gray!50] (6,-0.5) -- (0,-0.5) -- (0,0.5) -- (6,0.5);
    \draw[line width=1.5] (0,0.5) cos (6,0) (0,-0.5) cos(6,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/rec14
filename: rec18-prof.tex
modified: 2014-05-07 22:45:26
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \filldraw[fill=blue!30!white] (0,0) circle(1);
    \filldraw[fill=red!50!black] (0,0) -- (1,0) arc(0:30:1) -- cycle;
    \begin{scope}[shift={(3,0)}, rotate=60]
      \filldraw[fill=blue!30!white] (0,0) circle(1);
      \filldraw[fill=red!50!black] (0,0) -- (1,0) arc(0:30:1) -- cycle;
    \end{scope}
    \begin{scope}[shift={(7,0)}, rotate=0]
      \filldraw[fill=blue!30!white] (0,0) circle(1);
      \filldraw[fill=red!50!black] (0,0) -- (1,0) arc(0:30:1) -- cycle;
    \end{scope}
    \begin{scope}[shift={(11,-2)}, rotate=60]
      \filldraw[fill=blue!30!white] (0,0) circle(1);
      \filldraw[fill=red!50!black] (0,0) -- (1,0) arc(0:30:1) -- cycle;
    \end{scope}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/rec14
filename: rec20-stud.tex
modified: 2014-04-07 16:15:50
domain: p24
source:
  \begin{tikzpicture}[scale=0.9]
    \draw[color=blue!40!black,line width=3] (0,2) -- (0,-2);
    \node[text width=2.25cm, font=\scriptsize] at (0.25, -2.5){ tower continues down to the ground below };
    \draw[color=gray!50!black,line width=5] (-2,0) -- (6,0);
    \draw[color=brown!50!black] (-2,0.05) -- (-0.05,2)
    (0.05,2) -- (2.67,0.05)
    (6,0) -- (6,-1);
    \filldraw[fill=gray] (5.75,-1) rectangle (6.25,-1.5);
    \node at (6,-1.75){$m_{l}$};
    \fill[fill=white] (0,0) circle[radius=0.05];
    \draw[color=red,line width=2] (-0.15, 0.15) -- (0.15, -0.15);
    \draw[color=red,line width=2] (0.15, 0.15) -- (-0.15, -0.15);
    \fill[color=black] (-2.05,0.3) rectangle (-1.9,-0.075);
    \node at (-2.4,0) {$\frac{5}{3}M$};
    \node at (4,0.35){$M$};
    \draw[coord,<->] (0,-0.5) --node[fill=white]{$\frac{d}{3}$} +(0:2.67);
    \draw[coord,<->] (0,-0.85) --node[fill=white]{$\frac{3d}{4}$} +(0:6);
    \draw[coord,<->] (0,-0.5) --node[fill=white]{$\frac{d}{4}$} +(180:2);
    \draw (-1.5,0) arc(0:45:0.5);
    \node at (-1.2,0.35){$\dg{45}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/rec14
filename: rec02-stud.tex
modified: 2014-01-24 17:40:21
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}
    ]
    \fill[fill=gray] (0,0) -- (-1,0)  arc(180:360:1) -- (0,0);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/hw
filename: hw05-solp.tex
modified: 2015-10-04 17:58:32
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=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/p24/2014/rec14
filename: rec04-prof.tex
modified: 2014-01-31 17:46:42
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \shade[ball color=blue] (0,0) circle(0.5);
    \node at (135:1){$m_{2}$};
    \draw[accel] (0,1) -- ++(0:1) node[anchor=west]{$a$};
    \draw[force] (0.5,0) -- ++(0:1) node[anchor=north]{$k_{2}\Delta x_{2}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/hw
filename: tmp.tex
modified: 2015-12-17 03:36:32
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \draw[line width=3pt,color=DarkBlue] (0,0) -- (0,4);
    \draw[line width=3pt, color=DarkRed!50!white] (2,0) -- (2,4);
    \node at (0,-0.5) {$T_{A}, R_{A}$};
    \node at (2,-0.5) {$T_{B}, R_{B}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/rec14
filename: rec04-prof.tex
modified: 2014-01-31 17:46:42
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \shade[ball color=blue] (0,0) circle(0.5);
    \node at (135:1.){$m_{1}$};
    \draw[accel] (0,1) -- ++(0:1) node[anchor=west]{$a$};
    \draw[force] (0.5,0) -- ++(0:1) node[anchor=north]{$k_{1}\Delta x_{1}$};
    \draw[force] (-0.5,0) -- ++(180:1) node[anchor=north]{$k_{2}\Delta x_{2}$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/rec14
filename: rec09-prof.tex
modified: 2014-02-18 18:01:24
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[fill=gray] (0,0) rectangle (1, 0.5);
    \draw[force] (0.45,0) -- ++(90:2) node[anchor=west]{$N$};
    \draw[force] (0.55,0.25) -- ++(-90:1.25)
    node[anchor=west]{$mg$};
    \draw[accel] (-.5,0.5) -- node[anchor=east]{$a$} ++(90:1.25);
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/hw
filename: hw04-sol.tex
modified: 2015-09-20 19:30:32
domain: p117
source:
  \begin{tikzpicture}[scale=1]
    \begin{axis}[
        ymin=0,
        ymax=3,
        enlargelimits=false,
        ylabel={$\sigma$},
        xlabel={$\kb T / \hw$},
        ytick={0,1,2,3},
        xtick={0,1,2,3,4,5,6},
        % xticklabel=\empty,
      ]
      \addplot[
        trace01,
        domain=0.001:6,
        samples=201,
        line width=2pt,
      ]
      {1/x /(exp(1/x)-1) - ln(1-exp(-1/x))};
    \end{axis}
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p24/2014/rec14
filename: rec15-prof.tex
modified: 2014-03-12 18:24:57
domain: p24
source:
  \begin{tikzpicture}[scale=1]
    \draw[dashed] (0,0) -- (0,-2);
    \draw[line width=1] (0,0) -- (1,-3);
    \draw[line width=4,color=brown] (1,-3) -- (6,-3);
    \node at (1.6,-2.7){$x$};
    \node at (4,-2.7){$\ell-x$};
    \draw[line width=1] (6,-3) -- (10,0);
    \draw[dashed] (10,0) -- (10,-2);
    \draw[dashed] (1,-3) -- (2,-6);
    \draw[dashed] (6,-3) -- (2,-6);
    \draw[dashed] (2,-6) -- (2, -3);
    \draw[force,line width=3] (2,-3) -- node[anchor=west]{$mg$} ++(-90:2);
    \draw[force,line width=3] (1,-3) -- node[anchor=west]{$T_{1}$} ++(-0.5,1.5);
    \draw[force,line width=3] (6,-3) -- node[anchor=north west]{$T_{2}$} ++(2,1.5);
    \draw (0,-1) arc(-90:-70:1);
    \node at (-80:1.4){$\theta$};
    \draw (10,-1) arc(-90:-140:1);
    \begin{scope}[shift={(10,0)}]
      \node at (-115:1.4){$\phi$};
    \end{scope}
    \draw (2,-4.5) arc(90:110:1.5);
    \node at (1.7,-4.2) {$\theta$};
    \draw (2,-4.5) arc(90:40:1.5);
    \node at (2.8,-4.4){$\phi$};
  \end{tikzpicture}


folder: /Users/saeta/Documents/Courses/p117/2015/hw
filename: hw05-sol (original).tex
modified: 2015-10-01 16:03:38
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=3.5in,
        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,
        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,
        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}


