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notebook.tex
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% Default to the notebook output style
% Inherit from the specified cell style.
\documentclass[11pt]{article}
\usepackage[T1]{fontenc}
% Nicer default font (+ math font) than Computer Modern for most use cases
\usepackage{mathpazo}
% Basic figure setup, for now with no caption control since it's done
% automatically by Pandoc (which extracts  syntax from Markdown).
\usepackage{graphicx}
% We will generate all images so they have a width \maxwidth. This means
% that they will get their normal width if they fit onto the page, but
% are scaled down if they would overflow the margins.
\makeatletter
\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth
\else\Gin@nat@width\fi}
\makeatother
\let\Oldincludegraphics\includegraphics
% Set max figure width to be 80% of text width, for now hardcoded.
\renewcommand{\includegraphics}[1]{\Oldincludegraphics[width=.8\maxwidth]{#1}}
% Ensure that by default, figures have no caption (until we provide a
% proper Figure object with a Caption API and a way to capture that
% in the conversion process - todo).
\usepackage{caption}
\DeclareCaptionLabelFormat{nolabel}{}
\captionsetup{labelformat=nolabel}
\usepackage{adjustbox} % Used to constrain images to a maximum size
\usepackage{xcolor} % Allow colors to be defined
\usepackage{enumerate} % Needed for markdown enumerations to work
\usepackage{geometry} % Used to adjust the document margins
\usepackage{amsmath} % Equations
\usepackage{amssymb} % Equations
\usepackage{textcomp} % defines textquotesingle
% Hack from http://tex.stackexchange.com/a/47451/13684:
\AtBeginDocument{%
\def\PYZsq{\textquotesingle}% Upright quotes in Pygmentized code
}
\usepackage{upquote} % Upright quotes for verbatim code
\usepackage{eurosym} % defines \euro
\usepackage[mathletters]{ucs} % Extended unicode (utf-8) support
\usepackage[utf8x]{inputenc} % Allow utf-8 characters in the tex document
\usepackage{fancyvrb} % verbatim replacement that allows latex
\usepackage{grffile} % extends the file name processing of package graphics
% to support a larger range
% The hyperref package gives us a pdf with properly built
% internal navigation ('pdf bookmarks' for the table of contents,
% internal cross-reference links, web links for URLs, etc.)
\usepackage{hyperref}
\usepackage{longtable} % longtable support required by pandoc >1.10
\usepackage{booktabs} % table support for pandoc > 1.12.2
\usepackage[inline]{enumitem} % IRkernel/repr support (it uses the enumerate* environment)
\usepackage[normalem]{ulem} % ulem is needed to support strikethroughs (\sout)
% normalem makes italics be italics, not underlines
% Colors for the hyperref package
\definecolor{urlcolor}{rgb}{0,.145,.698}
\definecolor{linkcolor}{rgb}{.71,0.21,0.01}
\definecolor{citecolor}{rgb}{.12,.54,.11}
% ANSI colors
\definecolor{ansi-black}{HTML}{3E424D}
\definecolor{ansi-black-intense}{HTML}{282C36}
\definecolor{ansi-red}{HTML}{E75C58}
\definecolor{ansi-red-intense}{HTML}{B22B31}
\definecolor{ansi-green}{HTML}{00A250}
\definecolor{ansi-green-intense}{HTML}{007427}
\definecolor{ansi-yellow}{HTML}{DDB62B}
\definecolor{ansi-yellow-intense}{HTML}{B27D12}
\definecolor{ansi-blue}{HTML}{208FFB}
\definecolor{ansi-blue-intense}{HTML}{0065CA}
\definecolor{ansi-magenta}{HTML}{D160C4}
\definecolor{ansi-magenta-intense}{HTML}{A03196}
\definecolor{ansi-cyan}{HTML}{60C6C8}
\definecolor{ansi-cyan-intense}{HTML}{258F8F}
\definecolor{ansi-white}{HTML}{C5C1B4}
\definecolor{ansi-white-intense}{HTML}{A1A6B2}
% commands and environments needed by pandoc snippets
% extracted from the output of `pandoc -s`
\providecommand{\tightlist}{%
\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
\DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}}
% Add ',fontsize=\small' for more characters per line
\newenvironment{Shaded}{}{}
\newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
\newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.56,0.13,0.00}{{#1}}}
\newcommand{\DecValTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\FloatTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\CharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\StringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\CommentTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textit{{#1}}}}
\newcommand{\OtherTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{{#1}}}
\newcommand{\AlertTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
\newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.02,0.16,0.49}{{#1}}}
\newcommand{\RegionMarkerTok}[1]{{#1}}
\newcommand{\ErrorTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
\newcommand{\NormalTok}[1]{{#1}}
% Additional commands for more recent versions of Pandoc
\newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.53,0.00,0.00}{{#1}}}
\newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.73,0.40,0.53}{{#1}}}
\newcommand{\ImportTok}[1]{{#1}}
\newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.73,0.13,0.13}{\textit{{#1}}}}
\newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\VariableTok}[1]{\textcolor[rgb]{0.10,0.09,0.49}{{#1}}}
\newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
\newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.40,0.40,0.40}{{#1}}}
\newcommand{\BuiltInTok}[1]{{#1}}
\newcommand{\ExtensionTok}[1]{{#1}}
\newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.74,0.48,0.00}{{#1}}}
\newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.49,0.56,0.16}{{#1}}}
\newcommand{\InformationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\WarningTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
% Define a nice break command that doesn't care if a line doesn't already
% exist.
\def\br{\hspace*{\fill} \\* }
% Math Jax compatability definitions
\def\gt{>}
\def\lt{<}
% Document parameters
\title{Melting Ice}
% Pygments definitions
\makeatletter
\def\PY@reset{\let\PY@it=\relax \let\PY@bf=\relax%
\let\PY@ul=\relax \let\PY@tc=\relax%
\let\PY@bc=\relax \let\PY@ff=\relax}
\def\PY@tok#1{\csname PY@tok@#1\endcsname}
\def\PY@toks#1+{\ifx\relax#1\empty\else%
\PY@tok{#1}\expandafter\PY@toks\fi}
\def\PY@do#1{\PY@bc{\PY@tc{\PY@ul{%
\PY@it{\PY@bf{\PY@ff{#1}}}}}}}
\def\PY#1#2{\PY@reset\PY@toks#1+\relax+\PY@do{#2}}
\expandafter\def\csname PY@tok@w\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.73,0.73}{##1}}}
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\expandafter\def\csname PY@tok@sd\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
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\expandafter\def\csname PY@tok@ss\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
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\expandafter\def\csname PY@tok@gu\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.50,0.00,0.50}{##1}}}
\expandafter\def\csname PY@tok@gd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.63,0.00,0.00}{##1}}}
\expandafter\def\csname PY@tok@gi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.63,0.00}{##1}}}
\expandafter\def\csname PY@tok@gr\endcsname{\def\PY@tc##1{\textcolor[rgb]{1.00,0.00,0.00}{##1}}}
\expandafter\def\csname PY@tok@ge\endcsname{\let\PY@it=\textit}
\expandafter\def\csname PY@tok@gs\endcsname{\let\PY@bf=\textbf}
\expandafter\def\csname PY@tok@gp\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}}
\expandafter\def\csname PY@tok@go\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.53,0.53}{##1}}}
\expandafter\def\csname PY@tok@gt\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.27,0.87}{##1}}}
\expandafter\def\csname PY@tok@err\endcsname{\def\PY@bc##1{\setlength{\fboxsep}{0pt}\fcolorbox[rgb]{1.00,0.00,0.00}{1,1,1}{\strut ##1}}}
\expandafter\def\csname PY@tok@kc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@kd\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
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\expandafter\def\csname PY@tok@s1\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
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\expandafter\def\csname PY@tok@mf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
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\expandafter\def\csname PY@tok@c1\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\expandafter\def\csname PY@tok@cs\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\def\PYZbs{\char`\\}
\def\PYZus{\char`\_}
\def\PYZob{\char`\{}
\def\PYZcb{\char`\}}
\def\PYZca{\char`\^}
\def\PYZam{\char`\&}
\def\PYZlt{\char`\<}
\def\PYZgt{\char`\>}
\def\PYZsh{\char`\#}
\def\PYZpc{\char`\%}
\def\PYZdl{\char`\$}
\def\PYZhy{\char`\-}
\def\PYZsq{\char`\'}
\def\PYZdq{\char`\"}
\def\PYZti{\char`\~}
% for compatibility with earlier versions
\def\PYZat{@}
\def\PYZlb{[}
\def\PYZrb{]}
\makeatother
% Exact colors from NB
\definecolor{incolor}{rgb}{0.0, 0.0, 0.5}
\definecolor{outcolor}{rgb}{0.545, 0.0, 0.0}
% Prevent overflowing lines due to hard-to-break entities
\sloppy
% Setup hyperref package
\hypersetup{
breaklinks=true, % so long urls are correctly broken across lines
colorlinks=true,
urlcolor=urlcolor,
linkcolor=linkcolor,
citecolor=citecolor,
}
% Slightly bigger margins than the latex defaults
\geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in}
\begin{document}
\maketitle
\section{Modeling and Simulation in
Python}\label{modeling-and-simulation-in-python}
Project 2
Maalvika Bhat \& Richard Gao
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}9}]:} \PY{c+c1}{\PYZsh{} Configure Jupyter so figures appear in the notebook}
\PY{o}{\PYZpc{}}\PY{k}{matplotlib} inline
\PY{c+c1}{\PYZsh{} Configure Jupyter to display the assigned value after an assignment}
\PY{o}{\PYZpc{}}\PY{k}{config} InteractiveShell.ast\PYZus{}node\PYZus{}interactivity=\PYZsq{}last\PYZus{}expr\PYZus{}or\PYZus{}assign\PYZsq{}
\PY{c+c1}{\PYZsh{} import functions from the modsim.py module}
\PY{k+kn}{from} \PY{n+nn}{modsim} \PY{k}{import} \PY{o}{*}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}10}]:} \PY{c+c1}{\PYZsh{} kilogram = UNITS.kilogram}
\PY{c+c1}{\PYZsh{} kelvin = UNITS.kelvin}
\PY{c+c1}{\PYZsh{} watt = UNITS.watt}
\PY{c+c1}{\PYZsh{} joule = UNITS.joule}
\PY{c+c1}{\PYZsh{} degC = UNITS.celsius}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}11}]:} \PY{c+c1}{\PYZsh{} m\PYZus{}solid = .05 * kilogram}
\PY{c+c1}{\PYZsh{} latent\PYZus{}heat\PYZus{}fusion = 3.3 * 10 ** 5 * joule / kilogram}
\PY{n}{m\PYZus{}solid} \PY{o}{=} \PY{o}{.}\PY{l+m+mi}{05}
\PY{n}{latent\PYZus{}heat\PYZus{}fusion} \PY{o}{=} \PY{l+m+mf}{3.3} \PY{o}{*} \PY{l+m+mi}{10} \PY{o}{*}\PY{o}{*} \PY{l+m+mi}{5}
\PY{n}{q} \PY{o}{=} \PY{n}{m\PYZus{}solid} \PY{o}{*} \PY{n}{latent\PYZus{}heat\PYZus{}fusion}\PY{p}{;}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}21}]:} \PY{k}{def} \PY{n+nf}{make\PYZus{}system}\PY{p}{(}\PY{n}{thermal\PYZus{}conductivity\PYZus{}factor}\PY{p}{,} \PY{n}{specific\PYZus{}heat\PYZus{}capacity}\PY{p}{,} \PY{n}{surface\PYZus{}area}\PY{p}{,} \PY{n}{plate\PYZus{}temp}\PY{p}{,} \PY{n}{thickness}\PY{p}{)}\PY{p}{:}
\PY{l+s+sd}{\PYZdq{}\PYZdq{}\PYZdq{}Makes a System object with the given parameters.}
\PY{l+s+sd}{ returns: System object}
\PY{l+s+sd}{ \PYZdq{}\PYZdq{}\PYZdq{}}
\PY{n}{init} \PY{o}{=} \PY{n}{State}\PY{p}{(}\PY{n}{thermal\PYZus{}energy\PYZus{}plate} \PY{o}{=} \PY{n}{q}\PY{p}{,}
\PY{n}{thermal\PYZus{}energy\PYZus{}ice} \PY{o}{=} \PY{l+m+mi}{0}\PY{p}{,}
\PY{n}{temp\PYZus{}plate}\PY{o}{=}\PY{n}{plate\PYZus{}temp}\PY{p}{)}
\PY{n}{t0} \PY{o}{=} \PY{l+m+mi}{0}
\PY{n}{t\PYZus{}end} \PY{o}{=} \PY{l+m+mi}{100}
\PY{n}{dt} \PY{o}{=} \PY{o}{.}\PY{l+m+mi}{01}
\PY{k}{return} \PY{n}{System}\PY{p}{(}\PY{n+nb}{locals}\PY{p}{(}\PY{p}{)}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}22}]:} \PY{k}{def} \PY{n+nf}{update\PYZus{}func}\PY{p}{(}\PY{n}{state}\PY{p}{,} \PY{n}{dt}\PY{p}{,} \PY{n}{system}\PY{p}{)}\PY{p}{:}
\PY{n}{unpack}\PY{p}{(}\PY{n}{system}\PY{p}{)}
\PY{n}{thermal\PYZus{}energy\PYZus{}plate}\PY{p}{,} \PY{n}{thermal\PYZus{}energy\PYZus{}ice}\PY{p}{,} \PY{n}{temp\PYZus{}plate} \PY{o}{=} \PY{n}{state}
\PY{n}{deltaQ} \PY{o}{=} \PY{p}{(}\PY{n}{thermal\PYZus{}conductivity\PYZus{}factor} \PY{o}{*} \PY{n}{surface\PYZus{}area} \PY{o}{*} \PY{n}{temp\PYZus{}plate} \PY{o}{/} \PY{n}{thickness}\PY{p}{)} \PY{o}{*} \PY{n}{dt}
\PY{n}{thermal\PYZus{}energy\PYZus{}plate} \PY{o}{\PYZhy{}}\PY{o}{=} \PY{n}{deltaQ}
\PY{n}{thermal\PYZus{}energy\PYZus{}ice} \PY{o}{+}\PY{o}{=} \PY{n}{deltaQ}
\PY{n}{temp\PYZus{}plate} \PY{o}{\PYZhy{}}\PY{o}{=} \PY{n}{deltaQ} \PY{o}{/} \PY{p}{(}\PY{n}{specific\PYZus{}heat\PYZus{}capacity} \PY{o}{*} \PY{l+m+mi}{1}\PY{p}{)}
\PY{k}{return} \PY{n}{State}\PY{p}{(}\PY{n}{thermal\PYZus{}energy\PYZus{}plate}\PY{o}{=}\PY{n}{thermal\PYZus{}energy\PYZus{}plate}\PY{p}{,} \PY{n}{thermal\PYZus{}energy\PYZus{}ice}\PY{o}{=}\PY{n}{thermal\PYZus{}energy\PYZus{}ice}\PY{p}{,} \PY{n}{temp\PYZus{}plate}\PY{o}{=}\PY{n}{temp\PYZus{}plate}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}23}]:} \PY{k}{def} \PY{n+nf}{run\PYZus{}simulation}\PY{p}{(}\PY{n}{system}\PY{p}{,} \PY{n}{update\PYZus{}func}\PY{p}{)}\PY{p}{:}
\PY{n}{unpack}\PY{p}{(}\PY{n}{system}\PY{p}{)}
\PY{n}{frame} \PY{o}{=} \PY{n}{TimeFrame}\PY{p}{(}\PY{n}{columns}\PY{o}{=}\PY{n}{init}\PY{o}{.}\PY{n}{index}\PY{p}{)}
\PY{n}{frame}\PY{o}{.}\PY{n}{row}\PY{p}{[}\PY{n}{t0}\PY{p}{]} \PY{o}{=} \PY{n}{init}
\PY{n}{steps} \PY{o}{=} \PY{n}{linspace}\PY{p}{(}\PY{n}{t0}\PY{p}{,} \PY{n}{t\PYZus{}end}\PY{p}{,} \PY{n+nb}{int}\PY{p}{(}\PY{n}{t\PYZus{}end} \PY{o}{/} \PY{n}{dt}\PY{p}{)}\PY{p}{)}
\PY{n}{timesteps} \PY{o}{=} \PY{n}{Series}\PY{p}{(}\PY{n}{steps}\PY{p}{)}
\PY{k}{for} \PY{n}{t} \PY{o+ow}{in} \PY{n}{timesteps}\PY{o}{.}\PY{n}{index}\PY{p}{[}\PY{p}{:}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{:}
\PY{n}{frame}\PY{o}{.}\PY{n}{row}\PY{p}{[}\PY{n}{timesteps}\PY{p}{[}\PY{n}{t}\PY{o}{+}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{]} \PY{o}{=} \PY{n}{update\PYZus{}func}\PY{p}{(}\PY{n}{frame}\PY{o}{.}\PY{n}{row}\PY{p}{[}\PY{n}{timesteps}\PY{p}{[}\PY{n}{t}\PY{p}{]}\PY{p}{]}\PY{p}{,} \PY{n}{dt}\PY{p}{,} \PY{n}{system}\PY{p}{)}
\PY{k}{if} \PY{n}{frame}\PY{o}{.}\PY{n}{row}\PY{p}{[}\PY{n}{timesteps}\PY{p}{[}\PY{n}{t}\PY{o}{+}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{]}\PY{o}{.}\PY{n}{thermal\PYZus{}energy\PYZus{}plate} \PY{o}{\PYZlt{}} \PY{l+m+mi}{0}\PY{p}{:}
\PY{k}{break}
\PY{k}{return} \PY{n}{frame}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}24}]:} \PY{c+c1}{\PYZsh{} change surface\PYZus{}area from 3 m to .05 m because it\PYZsq{}s surface area touching}
\PY{c+c1}{\PYZsh{} change material melts a lot slower, this works}
\PY{n}{system} \PY{o}{=} \PY{n}{make\PYZus{}system}\PY{p}{(}\PY{l+m+mi}{204}\PY{p}{,} \PY{l+m+mi}{897}\PY{p}{,} \PY{o}{.}\PY{l+m+mi}{05}\PY{p}{,} \PY{l+m+mi}{23}\PY{p}{,} \PY{o}{.}\PY{l+m+mi}{02}\PY{p}{)} \PY{c+c1}{\PYZsh{}thermal\PYZus{}conductivity\PYZus{}factor, surface\PYZus{}area, plate\PYZus{}temp, thickness}
\PY{n}{results} \PY{o}{=} \PY{n}{run\PYZus{}simulation}\PY{p}{(}\PY{n}{system}\PY{p}{,} \PY{n}{update\PYZus{}func}\PY{p}{)}
\PY{c+c1}{\PYZsh{} results.head()}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}24}]:} thermal\_energy\_plate thermal\_energy\_ice temp\_plate
0.000000 16500.000000 0.000000 23.000000
0.010001 16499.925250 0.074750 22.999917
0.020002 16499.850500 0.149500 22.999833
0.030003 16499.775751 0.224249 22.999750
0.040004 16499.701002 0.298998 22.999667
0.050005 16499.626253 0.373747 22.999583
0.060006 16499.551504 0.448496 22.999500
0.070007 16499.476756 0.523244 22.999417
0.080008 16499.402008 0.597992 22.999333
0.090009 16499.327260 0.672740 22.999250
0.100010 16499.252512 0.747488 22.999167
0.110011 16499.177765 0.822235 22.999083
0.120012 16499.103018 0.896982 22.999000
0.130013 16499.028271 0.971729 22.998917
0.140014 16498.953525 1.046475 22.998833
0.150015 16498.878778 1.121222 22.998750
0.160016 16498.804032 1.195968 22.998667
0.170017 16498.729287 1.270713 22.998583
0.180018 16498.654541 1.345459 22.998500
0.190019 16498.579796 1.420204 22.998417
0.200020 16498.505051 1.494949 22.998333
0.210021 16498.430307 1.569693 22.998250
0.220022 16498.355563 1.644437 22.998167
0.230023 16498.280819 1.719181 22.998083
0.240024 16498.206075 1.793925 22.998000
0.250025 16498.131331 1.868669 22.997917
0.260026 16498.056588 1.943412 22.997833
0.270027 16497.981845 2.018155 22.997750
0.280028 16497.907102 2.092898 22.997667
0.290029 16497.832360 2.167640 22.997583
{\ldots} {\ldots} {\ldots} {\ldots}
99.709971 15768.041110 731.958890 22.183992
99.719972 15767.969012 732.030988 22.183912
99.729973 15767.896915 732.103085 22.183832
99.739974 15767.824817 732.175183 22.183751
99.749975 15767.752720 732.247280 22.183671
99.759976 15767.680623 732.319377 22.183590
99.769977 15767.608526 732.391474 22.183510
99.779978 15767.536430 732.463570 22.183430
99.789979 15767.464334 732.535666 22.183349
99.799980 15767.392238 732.607762 22.183269
99.809981 15767.320142 732.679858 22.183189
99.819982 15767.248047 732.751953 22.183108
99.829983 15767.175952 732.824048 22.183028
99.839984 15767.103857 732.896143 22.182947
99.849985 15767.031762 732.968238 22.182867
99.859986 15766.959668 733.040332 22.182787
99.869987 15766.887574 733.112426 22.182706
99.879988 15766.815480 733.184520 22.182626
99.889989 15766.743387 733.256613 22.182546
99.899990 15766.671293 733.328707 22.182465
99.909991 15766.599200 733.400800 22.182385
99.919992 15766.527108 733.472892 22.182304
99.929993 15766.455015 733.544985 22.182224
99.939994 15766.382923 733.617077 22.182144
99.949995 15766.310831 733.689169 22.182063
99.959996 15766.238739 733.761261 22.181983
99.969997 15766.166648 733.833352 22.181903
99.979998 15766.094557 733.905443 22.181822
99.989999 15766.022466 733.977534 22.181742
100.000000 15765.950375 734.049625 22.181662
[10000 rows x 3 columns]
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}20}]:} \PY{n}{results}\PY{o}{.}\PY{n}{thermal\PYZus{}energy\PYZus{}plate}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{p}{)}
\PY{n}{results}\PY{o}{.}\PY{n}{thermal\PYZus{}energy\PYZus{}ice}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}20}]:} <matplotlib.axes.\_subplots.AxesSubplot at 0x1e48a75bcf8>
\end{Verbatim}
\begin{center}
\adjustimage{max size={0.9\linewidth}{0.9\paperheight}}{output_8_1.png}
\end{center}
{ \hspace*{\fill} \\}
% Add a bibliography block to the postdoc
\end{document}