Some work

prelude.tex

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-\usepackage{graphicx} % support the \includegraphics command and options
+\usepackage{biblatex}
+\addbibresource{references.bib}
 
+\usepackage{graphicx} % support the \includegraphics command and options
 \usepackage[parfill]{parskip} % Activate to begin paragraphs with an empty line rather than an indent
 
 %%% PACKAGES

report.tex

@@ -3,14 +3,15 @@
 
 \input prelude.tex
 
-\title{\textbf{An investigation into things}}
+\title{\textbf{An investigation into things to do with the university}}
 \author{Candidate Number: 24829}
 \affil{Department of Physics, University of Bath}
 \date{March 21, 2023} % Due Date
 
 \begin{document}
+
 \twocolumn[
- \begin{@twocolumnfalse}
+\begin{@twocolumnfalse}
 \maketitle
 \begin{abstract}
 Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor. Aenean massa. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Donec quam felis, ultricies nec, pellentesque eu, pretium quis, sem. Nulla consequat massa quis enim. Donec pede justo, fringilla vel, aliquet nec, vulputate eget, arcu. In enim justo, rhoncus ut, imperdiet a, venenatis vitae, justo. Nullam dictum felis eu pede mollis pretium. Integer tincidunt. Cras dapibus. Vivamus elementum semper nisi. Aenean vulputate eleifend tellus. Aenean leo ligula, porttitor eu, consequat vitae, eleifend ac, enim. Aliquam lorem ante, dapibus in, viverra quis, feugiat a, tellus. Phasellus viverra nulla ut metus varius laoreet. Quisque rutrum. Aenean imperdiet. Etiam ultricies nisi vel augue. 
@@ -22,11 +23,65 @@ Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula
 \medskip
 
 \section*{Introduction}
-Sed ut perspiciatis unde omnis iste natus error sit voluptatem accusantium doloremque laudantium, totam rem aperiam, eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit aut fugit, sed quia consequuntur magni dolores eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci velit, sed quia non numquam eius modi tempora incidunt ut labore et dolore magnam aliquam quaerat voluptatem.
 
-Ut enim ad minima veniam, quis nostrum exercitationem ullam corporis suscipit laboriosam, nisi ut aliquid ex ea commodi consequatur? Quis autem vel eum iure reprehenderit qui in ea voluptate velit esse quam nihil molestiae consequatur, vel illum qui dolorem eum fugiat quo voluptas nulla pariatur? At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
+\section*{Discussion}
+
+Within the DLA model we identify a number of 
+
+We identify three orthogonal characteristics of the system which we can vary to change the behaviour of the system:
+
+\begin{enumerate}
+	\item The sticking behaviour, for example introducing a sticking probability to the system such that a particle will not always stick when moving adjacent to the cluster.
+	\item The random walk behaviour, for instance introducing a different probability distribution, or applying an external force.
+	\item The space which the DLA process is embedded in, most notably its dimension.
+\end{enumerate}
+
+From this we will take the following observables
+
+\begin{enumerate}
+	\item The measured fractal dimension of the cluster.
+	\item TODO the consequent critical exponent of the system
+	\item The surface area of the cluster at various points in its evolution, both total and external.
+	\item The percentage occupation of the cluster in a ball of equal radius.
+\end{enumerate}
+
+\todo{Cavities???}
+
+\todo{We will want to break up that observable discussion into multiple paragraphs, talk about how the critical exponent is related to the fractal dimension, how that relates to the embedding dimension, etc. Why one might be interested in the two other observables we pulled out of our ass.}
+
+\section{General Method}
+
+\todo{What tense should this method be in?}
+
+We will investigate these characteristics in turn as time and computational modelling allows through the following process. Starting with the provided code and working towards a more bespoke and customisable model.
+
+ We first took the initially provided code for DLA modelling \ref{IPC} and make minimal alterations such that it will run with reasonable speed \footnote[1]{When running on macOS systems the rendering code slows down the model by several orders of magnitude making it unsuitable for large scale modelling, hence it is removed and replaced with image generation mitigation as discussed later.} and output data for analysis. This data will be analysed and compared with literature\ref{initial-fractal-dimension-data} to confirm agreement. This will then act as a baseline implementation of the DLA model against which we can compare future alterations to ground them and ensure preservation of correct behaviour. In addition we will be creating a small auxiliary program to generate static images of the final result for manual verification of qualitative characteristics as the rendering code is not suitable for large data collection\footnotemark[1].
+
+\todo{Should we reference git commits here? Or keep them all in one repo. Maybe a combo and have them as submodules in a report branch allowing for a linear history and also concurrent presentation for a report.}
+
+Once this minimal viable alteration is complete we will implement our first proper change to the system, introducing a sticking probability, $p_{stick}$, such that a particle is no longer guaranteed to stick when moving adjacent to the cluster, but instead has a chance of simply passing by. This represents a change in our first identified orthogonal behaviour of the model, and the simplest to implement in the framework of the initially provided code. We will verify behaviour against the minimal viable alteration to ensure it is correct. Once this has been done this data will then be analysed to identify a quantitive relationship between $p_{stick}$ and our observables previously listed.
+
+\todo{Do we want to show that bouncing has no real effect}
+
+\todo{Do we want to talk about testing, for example that we get a uniform offset, etc.}
+
+\todo{Do we have any theory to link for this? Probably in results but worth bearing in mind}
+
+For further alterations a new codebase will be engineered to allow for more efficient alteration of the other two, more systematic, orthogonal characteristics of the system, containing initially the sticking probability alteration. To ensure fidelity of results we will compare the behaviour and observables of this new system to that of the minimal viable alteration, as well as the sticking probability alteration of it \todo{Better word}.
+
+Once accuracy has been determined the model will be embedded in spaces of higher dimensions, with different values of $p_{stick}$, to observe changes in our desired behaviour and compared against literature where possible.
+
+Finally a system for more complex particle motion will be developed such that we can plug in multiple walk modes in addition to a standard random walk, for example by introducing an external force or various varieties.
+
+\section{Specific Method}
+
+\begin{enumerate}
+	\item Choice of maxParticles such that it converges?
+	\item Use of {convergent} eee
+\end{enumerate}
+
+Choice of maxParticles such that it converges?
 
-Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Temporibus autem quibusdam et aut officiis debitis aut rerum necessitatibus saepe eveniet ut et voluptates repudiandae sint et molestiae non recusandae. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat. Sed ut perspiciatis unde omnis iste natus error sit voluptatem accusantium doloremque laudantium, totam rem aperiam, eaque ipsa quae ab illo inventore veritatis et quasi architecto beatae vitae dicta sunt explicabo. Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit aut fugit, sed quia consequuntur magni dolores eos qui ratione
 \section*{Section heading}
 \begin{figure}[t]
 \includegraphics[width=\columnwidth]{newton.png}
@@ -151,12 +206,13 @@ The quick, brown fox jumps over a lazy dog. DJs flock by when MTV ax quiz prog.
 Few quips galvanized the mock jury box. Quick brown dogs jump over the lazy fox. The jay, pig, fox, zebra, and my wolves quack! Blowzy red vixens fight for a quick jump. Joaquin Phoenix was gazed by MTV for luck. A wizard’s job is to vex chumps quickly in fog. Watch "Jeopardy! ", Alex Trebek's fun TV quiz game. Woven silk pyjamas exchanged for blue quartz. Brawny gods just flocked up to quiz and vex him. Adjusting quiver and bow, Zompyc[1] killed the fox. My faxed joke won a pager in the cable TV quiz show. Amazingly few discotheques provide jukeboxes. My girl wove six dozen plaid jackets before she quit. Six big devils from Japan quickly forgot how to waltz. Big July earthquakes confound zany experimental vow.
 
 Foxy parsons quiz and cajole the lovably dim wiki-girl. Have a pick: twenty six letters - no forcing a jumbled quiz! Crazy Fredericka bought many very exquisite opal jewels. Sixty zippers were quickly picked from the woven jute bag. A quick movement of the enemy will jeopardize six gunboats. All questions asked by five watch experts amazed the judge. Jack quietly moved up front and seized the big ball of wax. The quick, brown fox jumps over a lazy dog. DJs flock by when MTV ax quiz prog. Junk MTV quiz graced by fox whelps. Bawds jog, flick quartz, vex nymphs. Waltz, bad nymph, for quick jigs vex! Fox nymphs grab quick-jived waltz. Brick quiz whangs jumpy veldt fox. Bright vixens jump; dozy fowl quack. Quick wafting zephyrs vex bold Jim. Quick zephyrs blow, vexing daft Jim. Sex-charged fop blew my junk TV quiz. How quickly daft jumping zebras vex. Two driven jocks help fax my big quiz. Quick, Baz, get my woven flax jodhpurs! "Now fax quiz Jack! " my brave ghost pled. Five quacking zephyrs jolt my wax bed. Flummoxed by job, kvetching W. zaps Iraq. Cozy sphinx waves quart jug of bad milk. A very bad quack might jinx zippy fowls. Few quips galvanized the mock jury box. Quick brown dogs jump over the lazy fox. The jay, pig, fox, zebra, and my wolves quack! Blowzy red vixens fight for a quick jump. Joaquin Phoenix was gazed by MTV
+
 \section*{References}
-\begin{itemize}
-\item[1]Boyd, P., Mindlin, G., Gilmore, R. and Solari, H. (1994). \textbf{Topological analysis of chaotic orbits: Revisiting Hyperion}. The Astrophysical Journal, 431, p.425
-\end{itemize}
+
+\printbibliography
 
 \section*{Appendix}
-Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor. Aenean massa. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Donec quam felis, ultricies nec, pellentesque eu, pretium quis, sem. Nulla consequat massa quis enim. Donec pede justo, fringilla vel, aliquet nec, vulputate eget, arcu. In enim justo, rhoncus ut, imperdiet a, venenatis vitae, justo. Nullam dictum felis eu pede mollis pretium. Integer tincidunt. Cras dapibus. Vivamus elementum semper nisi. Aenean vulputate eleifend tellus.
+
+Thuis ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor. Aenean massa. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Donec quam felis, ultricies nec, pellentesque eu, pretium quis, sem. Nulla consequat massa quis enim. Donec pede justo, fringilla vel, aliquet nec, vulputate eget, arcu. In enim justo, rhoncus ut, imperdiet a, venenatis vitae, justo. Nullam dictum felis eu pede mollis pretium. Integer tincidunt. Cras dapibus. Vivamus elementum semper nisi. Aenean vulputate eleifend tellus.
 
 \end{document}