preamble.sty

% Modify this file to complete your dissertation
\ProvidesPackage{preamble}

\usepackage{amsmath}
\usepackage{ifpdf}

\ifpdf
  \usepackage[pdftex]{graphicx}
\else
  \usepackage[dvips]{graphicx}
\fi

\usepackage{afterpage}
\usepackage{rotating}
\usepackage{physics}
%\usepackage{subfigure}
% Change the CLASS FILE from WSUclass to bookbinding (and edit class file names accordingly) after your thesis is turned in electronically so you can get your dissertation bound and don't forget to change the above from oneside to twoside!!!!!!!!!!!!!!
\usepackage{fancyhdr}
  \fancyfoot[C,CO]{\textbf{\thepage}}
  \pagestyle{plain}
  \renewcommand{\chaptermark}[1]{\markboth{\chaptername \ \thechapter \ \ #1}{}}
  \renewcommand{\sectionmark}[1]{\markright{\thesection \ \ #1}}

% The caption package allows us to change the formatting of figure captions.
% The commands here change to the suggested caption format: single spaced and a bold tag
\usepackage[margin=0.3in,labelfont=bf,labelsep=none]{caption}
 \DeclareCaptionFormat{suggested}{\singlespace#1#2 #3\par\doublespace}
 \captionsetup{format=suggested}

% The cite package cleans up the way citations are handled.  For example, it
% changes the citation [1,2,3,6,7,8,9,10,11] into [1-3,6-11].  If your advisor
% wants superscript citations, use the overcite package instead of the cite package.
%\usepackage{cite}

% The makeidx package makes your index for you.  To make an index entry,
% go to the place in the book that should be referenced and type
%  \index{key}
% An index entry labeled "key" (or whatever you type) will then
% be included and point to the correct page.
\usepackage{makeidx}
\usepackage{siunitx}

\makeindex

% The url package allows for the nice typesetting of URLs.  Since URLs are often
% long with no spaces, they mess up line wrapping.  The command \url{http://www.physics.byu.edu}
% allows LaTeX to break the url across lines at appropriate places: e.g. http://www.physics.byu.edu
\usepackage{url}
\urlstyle{rm}

% The hyperref package provides automatic linking and bookmarking for the table
% of contents, index, equation references, and figure references.
%
% To include a link in your pdf use \href{URL}{Text to be displayed}.  If your
% display text is the URL, you probably should use the \url{} command discussed
% above.
%
% To add a bookmark in the pdf you can use \pdfbookmark.  You can look up its usage
% in the hyperref package documentation
\usepackage[bookmarksnumbered,pdfpagelabels=true,plainpages=false,colorlinks=true,
            linkcolor=black,citecolor=black,urlcolor=blue]{hyperref}

%   \makepreliminarypages : Makes the preliminary pages
%   \clearemptydoublepage : same as \cleardoublepage but doesn't put page numbers
%                           on blank intervening pages
%   \singlespace          : switch to single spaced lines
%   \doublespace          : switch to double spaced lines
\newcommand{\bibs}{DissertationRefs}
\newcommand{\comments}[1]{}

% ==================================================== %
%                                                      %
%   Fill in these fields for the preliminary pages     %
%                                                      %
% ==================================================== %

% For Senior and honors this is the year and month that you submit the thesis
% For Masters and PhD, this is your graduation date
  \Year{2021}
  \Month{December}
  \Author{Kevin H. Evans}
  \University{Washington State University}
  \Department{Department of Physics and Astronomy}
  \degree{Bachelor of Science}
  \DegreeShort{B.S.}

% If you have a long title, split it between two lines. The \TitleBottom field defines the second line
% A two line title should be an "inverted pyramid" with the top line longer than the bottom.
  \TitleTop{Chaos of Bose-Einstein condensates in one-dimension}
  \TitleMiddle{}
  \TitleBottom{ }

% Your research advisor
  \Advisor{Michael Forbes}
  \AdvisorTitle{Ph.D.}

% The representative of the department who will approve your thesis (usually the chair) THIS DOESN'T MATTER FOR WSU
  \DepRep{}
  \DepRepTitle{Advisor}

% Acknowledge those who helped and supported you
  \Acknowledgments{
  	I would like to thank my advisor Michael Forbes for assisting me through this thesis. I would also like to acknowledge Saptarshi Sarkar for giving me an introduction to quantum turbulence and helping me through Python problems.
}


% The text of your abstract
% Known bugs
%   Having a tiny bit of the abstract spill to second page defeats page number removal.
%   Workaround: make the abstract a little longer or a little shorter.
%
  \Abstract{
    The Gross-Pitaevskii equation (GPE) is a nonlinear Schr\"odinger equation used in modeling Bose-Einstein condensates (BECs). Using Lyapunov exponents, chaos was characterized in the GPE in the one-dimensional case. The GPE was simulated using Python using finite-difference methods in space and an adaptive Runge-Kutta solver was used to evolve the equation in time. When an initial state of the GPE with positive coupling constant is perturbed, positive Lyapunov exponents were found. There was a proportionality found between positive Lyapunov exponents and the nonlinear coupling constant of the GPE, $g$. Further research can be done to analyze this proportionality and to extend this research to higher dimensions.
}

% The text of your dedication
% This page is OPTIONAL. To remove, comment out \dedicationpage in diss.tex
%  \Dedication{
%    This thesis is dedicated to my pet dog.
%}


% ------------- These remaining fields are only necessary for masters and PhD ----------------------

% The members of your graduate committee (masters only need A and B, PhD need all 4)
%  \MemberA{}
%  \MemberATitle{}
%  \MemberB{John F.\ Kennedy}
%  \MemberBTitle{Ph.D.}