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\section*{Appendix}
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?

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@article{botetClusteringClustersProcesses1985,
title = {Clustering of Clusters Processes above Their Upper Critical Dimensionalities},
author = {Botet, R},
date = {1985-04-01},
journaltitle = {Journal of Physics A: Mathematical and General},
shortjournal = {J. Phys. A: Math. Gen.},
volume = {18},
number = {5},
pages = {847--855},
issn = {0305-4470, 1361-6447},
doi = {10.1088/0305-4470/18/5/017},
url = {https://iopscience.iop.org/article/10.1088/0305-4470/18/5/017},
urldate = {2023-02-24},
file = {/Users/joshuacoles/Zotero/storage/CDI267Y4/botet1985.pdf.pdf}
}
@article{botetSizeDistributionClusters1984,
title = {Size Distribution of Clusters in Irreversible Kinetic Aggregation},
author = {Botet, R and Jullien, R},
date = {1984-08-21},
journaltitle = {Journal of Physics A: Mathematical and General},
shortjournal = {J. Phys. A: Math. Gen.},
volume = {17},
number = {12},
pages = {2517--2530},
issn = {0305-4470, 1361-6447},
doi = {10.1088/0305-4470/17/12/022},
url = {https://iopscience.iop.org/article/10.1088/0305-4470/17/12/022},
urldate = {2023-02-24},
file = {/Users/joshuacoles/Zotero/storage/CV6NW42A/botet1984.pdf.pdf}
}
@book{lawlerIntersectionsRandomWalks2013,
title = {Intersections of Random Walks},
author = {Lawler, Gregory F.},
date = {2013},
series = {Modern {{Birkhäuser}} Classics},
publisher = {{Birkhäuser}},
location = {{New York}},
isbn = {978-1-4614-5971-2 978-1-4614-5972-9},
pagetotal = {223},
keywords = {Random walks (Mathematics)},
annotation = {OCLC: ocn812067146},
file = {/Users/joshuacoles/Zotero/storage/C3TSALXD/Lawler - 2013 - Intersections of random walks.pdf}
}
@article{liStorageAddressingScheme2013,
title = {Storage and Addressing Scheme for Practical Hexagonal Image Processing},
author = {Li, Xiangguo},
date = {2013-01-31},
journaltitle = {Journal of Electronic Imaging},
shortjournal = {J. Electron. Imaging},
volume = {22},
number = {1},
pages = {010502},
issn = {1017-9909},
doi = {10.1117/1.JEI.22.1.010502},
url = {http://electronicimaging.spiedigitallibrary.org/article.aspx?doi=10.1117/1.JEI.22.1.010502},
urldate = {2023-03-04},
langid = {english}
}
@article{lyonsSimpleCriterionTransience1983,
title = {A {{Simple Criterion}} for {{Transience}} of a {{Reversible Markov Chain}}},
author = {Lyons, Terry},
date = {1983-05-01},
journaltitle = {The Annals of Probability},
shortjournal = {Ann. Probab.},
volume = {11},
number = {2},
issn = {0091-1798},
doi = {10.1214/aop/1176993604},
url = {https://projecteuclid.org/journals/annals-of-probability/volume-11/issue-2/A-Simple-Criterion-for-Transience-of-a-Reversible-Markov-Chain/10.1214/aop/1176993604.full},
urldate = {2023-03-13},
file = {/Users/joshuacoles/Zotero/storage/65P85MN4/Lyons - 1983 - A Simple Criterion for Transience of a Reversible .pdf}
}
@article{niemeyerFractalDimensionDielectric1984,
title = {Fractal {{Dimension}} of {{Dielectric Breakdown}}},
author = {Niemeyer, L. and Pietronero, L. and Wiesmann, H. J.},
date = {1984-03-19},
journaltitle = {Physical Review Letters},
shortjournal = {Phys. Rev. Lett.},
volume = {52},
number = {12},
pages = {1033--1036},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.52.1033},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.52.1033},
urldate = {2023-03-02},
langid = {english},
file = {/Users/joshuacoles/Zotero/storage/LKJWGEMV/niemeyer1984.pdf.pdf}
}
@article{sanderDiffusionlimitedAggregationKinetic2000,
title = {Diffusion-Limited Aggregation: {{A}} Kinetic Critical Phenomenon?},
shorttitle = {Diffusion-Limited Aggregation},
author = {Sander, Leonard M.},
date = {2000-07},
journaltitle = {Contemporary Physics},
shortjournal = {Contemporary Physics},
volume = {41},
number = {4},
pages = {203--218},
issn = {0010-7514, 1366-5812},
doi = {10.1080/001075100409698},
url = {http://www.tandfonline.com/doi/abs/10.1080/001075100409698},
urldate = {2023-03-02},
langid = {english},
file = {/Users/joshuacoles/Zotero/storage/YV9XD9VR/sander2000.pdf.pdf}
}
@article{tanInfluenceExternalField2000,
title = {Influence of External Field on Diffusion-Limited Aggregation},
author = {Tan, Zhi-Jie and Zou, Xian-Wu and Zhang, Wen-Bing and Jin, Zhun-Zhi},
date = {2000-04},
journaltitle = {Physics Letters A},
shortjournal = {Physics Letters A},
volume = {268},
number = {1-2},
pages = {112--116},
issn = {03759601},
doi = {10.1016/S0375-9601(00)00143-2},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0375960100001432},
urldate = {2023-03-13},
langid = {english}
}
@book{vicsekFractalGrowthPhenomena1992,
title = {Fractal Growth Phenomena},
author = {Vicsek, Tamás},
date = {1992},
edition = {2nd ed},
publisher = {{World Scientific}},
location = {{Singapore ; New Jersey}},
isbn = {978-981-02-0668-0 978-981-02-0669-7},
langid = {english},
pagetotal = {488},
keywords = {Fractals},
file = {/Users/joshuacoles/Zotero/storage/LJP5C4WG/Vicsek - 1992 - Fractal growth phenomena.pdf}
}
@article{wittenDiffusionlimitedAggregation1983,
title = {Diffusion-Limited Aggregation},
author = {Witten, T. A. and Sander, L. M.},
date = {1983-05-01},
journaltitle = {Physical Review B},
shortjournal = {Phys. Rev. B},
volume = {27},
number = {9},
pages = {5686--5697},
issn = {0163-1829},
doi = {10.1103/PhysRevB.27.5686},
url = {https://link.aps.org/doi/10.1103/PhysRevB.27.5686},
urldate = {2023-02-24},
langid = {english},
file = {/Users/joshuacoles/Zotero/storage/ZP38RVBK/ZP38RVBK.pdf}
}

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\input prelude.tex
\addbibresource{references.bib}
\addbibresource{static.bib}
\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}
\newcommand{\singlecolumnabstract}[1]{
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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.
#1
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% What I wish the title was: Development and Testing of a generalised computational model for efficient diffusion limited aggregation modelling and experimentation.
\title{\textbf{Diffusion Limited Aggregation under Novel Conditions using}}
\author{Candidate Number: 24829}
\affil{Department of Physics, University of Bath}
\date{March 21, 2023} % Due Date
\begin{document}
\singlecolumnabstract{
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.
}
\medskip
\section*{Introduction}
Diffusion-limited aggregation (DLA) models processes where the diffusion of small particles into a larger cluster is the limiting factor in a system's growth. It is applicable to a wide range of systems such as,
\begin{enumerate}
\item \todo{think of better workds}
\end{enumerate}
We will model diffusion limited aggregation under a number of novel and unusual conditions to determine the effects of various physical and modelling properties \todo{better word} on the system
% Mention MVA I think so I can reference it in the section on spaces alteration.
\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:
In physical systems modelled by the DLA process the growing aggregate is sitting within a medium through which particles diffuse until "sticking" to the aggregate adding to its extent. A high level description of the DLA algorithm is given as follows,
\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.
\item An initial seed aggregate is placed into the system, without mathematical loss of generality, at the origin. This is normally a single particle.
\item A new particle is then released at some sufficient distance from the seeded aggregate.
\item This particle is allowed to then diffuse until it sticks to the aggregate.
\item At this point the new particle stops moving and becomes part of the aggregate a new particle is released.
\end{enumerate}
From this we will take the following observables
An actual implementation of this system will involve a number of computational parameters determining for example the radius that the particles are spawned at, or defining a "kill circle" past which we consider the particle lost and stop simulating it \cite[p.~27]{sanderDiffusionlimitedAggregationKinetic2000} (this is especially important in $d > 2$ dimensional spaces where random walks are not guaranteed to reoccur \cite{lawlerIntersectionsRandomWalks2013} and could instead tend off to infinity).
\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}
While these are interesting and important to the performant modelling of the system, we aim to choose these such to maximise the fidelity to the original physical system, whilst minimising the computational effort required for simulation. From a modelling perspective however there are a number of interesting orthogonal behaviours within this loose algorithm description which we can vary to potentially provide interesting results.
\todo{Cavities???}
The first is the seed which is used to start the aggregation process. The traditional choice of a single seed models the spontaneous growth of a cluster, but the system could be easily extended to diffusion onto a plate under influence of an external force field \cite{tanInfluenceExternalField2000}, or cluster-cluster aggregation where there are multiple aggregate clusters, which are capable of moving themselves \cite[pp.~210-211]{sanderDiffusionlimitedAggregationKinetic2000}.
\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.}
The next behaviour is in the spawning of the active particle. The choice of spawning location is traditionally made in accordance to a uniform distribution, which bar any physical motivation from a particular system being modelled, seems to intuitive choice. However the choice of a single particle is one which is open to more investigation. This is interesting in both the effect varying this will have on the behaviour of the system, but also if it can be done in a way to minimise the aforementioned effects, as a speed up for long running simulations.
\section{General Method}
Another characteristic behaviour of the algorithm is the choice of diffusion mechanism. Traditionally this is implemented as a
\todo{What tense should this method be in?}
Finally we arrive at the final characteristic we will consider: the space that the DLA process takes place within. Traditionally this is done within a 2D orthogonal gridded space, however other gridded systems, such as hexagonal, can be used to explore any effect the spaces \cite[pp.~210-211]{sanderDiffusionlimitedAggregationKinetic2000}.
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.
%TODO Include a note on long running and exploration simulations in the methodology section?
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].
\subsection*{Method}
\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.}
To this end we designed a generic system such that that these different alterations of the traditional DLA model could be written and explored quickly, collecting sufficient data for statistical measurements.
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.
We first took the initially provided code \cite{IPC} and made minimal alterations such such that the code ran in reasonable time\footnote{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, visualisation was handled externally.} and output data for analysis.
\todo{Do we want to show that bouncing has no real effect}
For large configuration space exploring runs the code was run using \cite{GNUParallel} to allow for substantially improved throughput.
\todo{Do we want to talk about testing, for example that we get a uniform offset, etc.}
The code was written such that it is reproducible based on a user provided seed for the random number generator, this provided the needed balance between reproducibility and repeated runs.
\todo{Do we have any theory to link for this? Probably in results but worth bearing in mind}
\subsection*{Fractal Dimension Calculation}
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.
\section*{Alteration 1: Probabilistic Sticking}
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.
The first alteration of the system is the introduction of a probabilistic component to the sticking behaviour of the DLA system. Here we introduced a probability $p_{stick}$ to the initial grid based sticking behaviour of the particles, with the particle being given this probability to stick at each site (for example, if the particle was adjacent to two cells in the aggregate, then the probabilistic aspect would apply twice).
\section{Specific Method}
This was also the case used to ground both the minimally altered code, and our new generic system, to ensure they are functioning correctly. The data for both is presented in Figure \ref{sp-fig}.
\begin{enumerate}
\item Choice of maxParticles such that it converges?
\item Use of {convergent} eee
\end{enumerate}
Choice of maxParticles such that it converges?
\section*{Section heading}
\begin{figure}[t]
\begin{figure}
\includegraphics[width=\columnwidth]{newton.png}
\caption{ `Back in the spring of 1720, Sir Isaac Newton owned shares in the South Sea Company, the hottest stock in England. Sensing that the market was getting out of hand, the great physicist muttered that he 'could calculate the motions of the heavenly bodies, but not the madness of the people.' Newton dumped his South Sea shares, pocketing a 100\% profit totaling £7,000. But just months later, swept up in the wild enthusiasm of the market, Newton jumped back in at a much higher price — and lost £20,000 (or more than \$3 million in [2002-2003's] money. For the rest of his life, he forbade anyone to speak the words 'South Sea' in his presence'.}
\label{hyper}
\end{figure}Li Europan lingues es membres del sam familie. Lor separat existentie es un myth. Por scientie, musica, sport etc, litot Europa usa li sam vocabular. Li lingues differe solmen in li grammatica, li pronunciation e li plu commun vocabules. Omnicos directe al desirabilite de un nov lingua franca: On refusa continuar payar custosi traductores.
At solmen va esser necessi far uniform grammatica, pronunciation e plu sommun paroles. Ma quande lingues coalesce, li grammatica del resultant lingue es plu simplic e regulari quam ti del coalescent lingues. Li nov lingua franca va esser plu simplic e regulari quam li existent Europan lingues. It va esser tam simplic quam Occidental in fact, it va esser Occidental.
At solmen va esser necessi far uniform grammatica, pronunciation e plu sommun paroles. Ma quande lingues coalesce, li grammatica del resultant lingue es plu simplic e regulari quam ti del coalescent lingues. Li nov lingua franca va esser plu simplic e regulari quam li existent Europan lingues. It va esser tam simplic quam Occidental in fact, it va esser Occidental. A un Angleso it va semblar un simplificat Angles, quam un skeptic Cambridge amico dit me que Occidental es. Li Europan lingues es membres del sam familie. Lor separat existentie es un myth. Por scientie, musica, sport etc, litot Europa usa li sam vocabular. Li lingues differe solmen in li grammatica, li pronunciation
\begin{equation}
\label{dtheta}
\frac{d\theta}{dt} = \omega
\end{equation}
\begin{equation}
\label{domega}
\frac{d\omega}{dt} = - \frac{GM_{sat}\beta^2}{2R_{H}^{3}}\sin 2(\theta - \phi).
\end{equation}
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. Curabitur ullamcorper ultricies nisi.
Nam eget dui. Etiam rhoncus. Maecenas tempus, tellus eget condimentum rhoncus, sem quam semper libero, sit amet adipiscing sem neque sed ipsum. Nam quam nunc, blandit vel, luctus pulvinar, hendrerit id, lorem. Maecenas nec odio et ante tincidunt tempus. Donec vitae sapien ut libero venenatis faucibus. Nullam quis ante. Etiam sit amet orci eget eros faucibus tincidunt. Duis leo. Sed fringilla mauris sit amet nibh.
\section*{A section}
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.
\begin{figure*}[t]
\centering
\includegraphics[width=0.75\textwidth,height=7cm]{group.jpg}
\caption{This is where you add a caption}
\label{omega_ics}
\end{figure*}
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. Curabitur ullamcorper ultricies nisi. Nam eget dui. Etiam rhoncus. Maecenas tempus, tellus eget condimentum rhoncus, sem quam semper libero, sit amet adipiscing sem neque sed ipsum. Nam quam nunc, blandit vel, luctus pulvinar, hendrerit id, lorem. Maecenas nec odio et ante tincidunt tempus. Donec vitae sapien ut libero venenatis faucibus. Nullam quis ante.
Etiam sit amet orci eget eros faucibus tincidunt. Duis leo. Sed fringilla mauris sit amet nibh. Donec sodales sagittis magna. Sed consequat, leo eget bibendum sodales, augue velit cursus nunc, quis gravida magna mi a libero. Fusce vulputate eleifend sapien. Vestibulum purus quam, scelerisque ut, mollis sed, nonummy id, metus. Nullam accumsan lorem in dui. Cras ultricies mi eu turpis hendrerit fringilla. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; In ac dui quis mi consectetuer lacinia. Nam pretium turpis et arcu.
Duis arcu tortor, suscipit eget, imperdiet nec, imperdiet iaculis, ipsum. Sed aliquam ultrices mauris. Integer ante arcu, accumsan a, consectetuer eget, posuere ut, mauris. Praesent adipiscing. Phasellus ullamcorper ipsum rutrum nunc. Nunc nonummy metus. Vestibulum volutpat pretium libero. Cras id dui. Aenean ut eros et nisl sagittis vestibulum. Nullam nulla eros, ultricies sit amet, nonummy id, imperdiet feugiat, pede. Sed lectus. Donec mollis hendrerit risus. Phasellus nec sem in justo pellentesque facilisis. Etiam imperdiet imperdiet orci. Nunc nec neque.
Phasellus leo dolor, tempus non, auctor et, hendrerit quis, nisi. Curabitur ligula sapien, tincidunt non, euismod vitae, posuere imperdiet, leo. Maecenas malesuada. Praesent congue erat at massa. Sed cursus turpis vitae tortor. Donec posuere vulputate arcu. Phasellus accumsan cursus velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Sed aliquam, nisi quis porttitor congue, elit erat euismod orci, ac placerat dolor lectus quis orci. Phasellus consectetuer vestibulum elit. Aenean tellus metus, bibendum sed, posuere ac, mattis non, nunc. Vestibulum fringilla pede sit amet augue. In turpis. Pellentesque posuere. Praesent turpis. Aenean posuere, tortor sed cursus feugiat, nunc augue blandit nunc, eu sollicitudin urna dolor sagittis lacus. Donec elit libero, sodales nec, volutpat a, suscipit non, turpis. Nullam sagittis. Suspendisse pulvinar, augue ac venenatis condimentum, sem libero volutpat nibh, nec pellentesque velit pede quis nunc. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Fusce id purus. Ut varius tincidunt libero. Phasellus dolor. Maecenas vestibulum mollis
\section*{Also a section}
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. Curabitur ullamcorper ultricies nisi. Nam eget dui. Etiam rhoncus. Maecenas tempus, tellus eget condimentum rhoncus, sem quam semper libero, sit amet adipiscing sem neque sed ipsum. Nam quam nunc, blandit vel, luctus pulvinar, hendrerit id, lorem. Maecenas nec odio et ante tincidunt tempus. Donec vitae sapien ut libero venenatis faucibus. Nullam quis ante.
Etiam sit amet orci eget eros faucibus tincidunt. Duis leo. Sed fringilla mauris sit amet nibh. Donec sodales sagittis magna. Sed consequat, leo eget bibendum sodales, augue velit cursus nunc, quis gravida magna mi a libero. Fusce vulputate eleifend sapien. Vestibulum purus quam, scelerisque ut, mollis sed, nonummy id, metus. Nullam accumsan lorem in dui. Cras ultricies mi eu turpis hendrerit fringilla. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; In ac dui quis mi consectetuer lacinia. Nam pretium turpis et arcu.
\begin{figure}[tb]
\includegraphics[width=\columnwidth]{maxwell.jpg}
\caption{James Clerk Maxwell (Colorized).}
\label{quasiperiodic}
\caption{Sticking probability verThe minimally altered code and new generic system }
\label{sp-fig}
\end{figure}
Phasellus leo dolor, tempus non, auctor et, hendrerit quis, nisi. Curabitur ligula sapien, tincidunt non, euismod vitae, posuere imperdiet, leo. Maecenas malesuada. Praesent congue erat at massa. Sed cursus turpis vitae tortor. Donec posuere vulputate arcu. Phasellus accumsan cursus velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Sed aliquam, nisi quis porttitor congue, elit erat euismod orci, ac placerat dolor lectus quis orci. Phasellus consectetuer vestibulum elit. Aenean tellus metus, bibendum sed, posuere ac, mattis non, nunc. Vestibulum fringilla pede sit amet augue. In turpis. Pellentesque posuere. Praesent turpis. Aenean posuere, tortor sed cursus feugiat, nunc augue blandit nunc, eu sollicitudin urna dolor sagittis lacus. Donec elit libero, sodales nec, volutpat a, suscipit non, turpis. Nullam sagittis. Suspendisse pulvinar, augue ac venenatis condimentum, sem libero volutpat nibh, nec pellentesque velit pede quis nunc. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Fusce id purus. Ut varius tincidunt libero. Phasellus dolor. Maecenas vestibulum mollis
\section*{This is a section}
Phasellus leo dolor, tempus non, auctor et, hendrerit quis, nisi. Curabitur ligula sapien, tincidunt non, euismod vitae, posuere imperdiet, leo. Maecenas malesuada. Praesent congue erat at massa. Sed cursus turpis vitae tortor. Donec posuere vulputate arcu. Phasellus accumsan cursus velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Sed aliquam, nisi quis porttitor congue, elit erat euismod orci, ac placerat dolor lectus quis orci. Phasellus consectetuer vestibulum elit. Aenean tellus metus, bibendum sed, posuere ac, mattis non, nunc. Vestibulum fringilla pede sit amet augue. In turpis. Pellentesque posuere. Praesent turpis. Aenean posuere, tortor sed cursus feugiat, nunc augue blandit nunc, eu sollicitudin urna dolor sagittis lacus. Donec elit libero, sodales nec, volutpat a, suscipit non, turpis. Nullam sagittis. Suspendisse pulvinar, augue ac venenatis condimentum, sem libero volutpat nibh, nec pellentesque velit pede quis nunc. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Fusce id purus. Ut varius tincidunt libero. Phasellus dolor. Maecenas vestibulum mollis
\begin{figure}[tb]
\includegraphics[width=\columnwidth]{noether.jpg}
\caption{ Emmy Noether.}
\label{bifurcation}
\end{figure}
Etiam sit amet orci eget eros faucibus tincidunt. Duis leo. Sed fringilla mauris sit amet nibh. Donec sodales sagittis magna. Sed consequat, leo eget bibendum sodales, augue velit cursus nunc, quis gravida magna mi a libero. Fusce vulputate eleifend sapien. Vestibulum purus quam, scelerisque ut, mollis sed, nonummy id, metus. Nullam accumsan lorem in dui. Cras ultricies mi eu turpis hendrerit fringilla. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; In ac dui quis mi consectetuer lacinia. Nam pretium turpis et arcu.
Duis arcu tortor, suscipit eget, imperdiet nec, imperdiet iaculis, ipsum. Sed aliquam ultrices mauris. Integer ante arcu, accumsan a, consectetuer eget, posuere ut, mauris. Praesent adipiscing. Phasellus ullamcorper ipsum rutrum nunc. Nunc nonummy metus. Vestibulum volutpat pretium libero. Cras id dui. Aenean ut eros et nisl sagittis vestibulum. Nullam nulla eros, ultricies sit amet, nonummy id, imperdiet feugiat, pede. Sed lectus. Donec mollis hendrerit risus. Phasellus nec sem in justo pellentesque facilisis. Etiam imperdiet imperdiet orci. Nunc nec neque.
\section*{A section}
Far far away, behind the word mountains, far from the countries Vokalia and Consonantia, there live the blind texts. Separated they live in Bookmarksgrove right at the coast of the Semantics, a large language ocean. A small river named Duden flows by their place and supplies it with the necessary regelialia. It is a paradisematic country, in which roasted parts of sentences fly into your mouth.
Even the all-powerful Pointing has no control about the blind texts it is an almost unorthographic life One day however a small line of blind text by the name of Lorem Ipsum decided to leave for the far World of Grammar. The Big Oxmox advised her not to do so, because there were thousands of bad Commas, wild Question Marks and devious Semikoli, but the Little Blind Text didn’t listen. She packed her seven versalia, put her initial into the belt and made herself on the way.
When she reached the first hills of the Italic Mountains, she had a last view back on the skyline of her hometown Bookmarksgrove, the headline of Alphabet Village and the subline of her own road, the Line Lane. Pityful a rethoric question ran over her cheek, then she continued her way. On her way she met a copy.
The copy warned the Little Blind Text, that where it came from it would have been rewritten a thousand times and everything that was left from its origin would be the word "and" and the Little Blind Text should turn around and return to its own, safe country. But nothing the copy said could convince her and so it didn’t take long until a few insidious Copy Writers ambushed her, made her drunk with Longe and Parole and dragged her into their agency, where they abused her for their projects again and again. And if she hasn’t been rewritten, then they are still using her.
Far far away, behind the word mountains, far from the countries Vokalia and Consonantia, there live the blind texts. Separated they live in Bookmarksgrove right at the coast of the Semantics, a large language ocean. A small river named Duden flows by their place and supplies it with the necessary regelialia. It is a paradisematic country, in which roasted parts of sentences fly into your mouth. Even the all-powerful Pointing has no control about the blind texts it is an almost unorthographic life One day however a small line of blind text by the name of Lorem Ipsum decided to leave for the far World of Grammar. The Big Oxmox advised her not to do so, because there were thousands of bad Commas, wild Question Marks and devious Semikoli, but the Little Blind Text didn’t listen. She packed her seven versalia, put her initial into the belt and made herself on the way. When she reached the first hills of the Italic Mountains, she had a last view back on the skyline of her hometown Bookmarksgrove, the headline of Alphabet Village and the subline
\begin{equation}
\label{lyexp}
\delta_n \sim e^{n\lambda} \delta_0
\end{equation}
Far far away, behind the word mountains, far from the countries Vokalia and Consonantia, there live the blind texts. Separated they live in Bookmarksgrove right at the coast of the Semantics, a large language ocean. A small river named Duden flows by their place and supplies it with the necessary regelialia. It is a paradisematic country, in which roasted parts of sentences fly into your mouth. Even the all-powerful Pointing has no control about the blind texts it is an almost unorthographic life One day however a small line of blind text by the name of Lorem Ipsum decided to leave for the far World of Grammar. The Big Oxmox advised her not to do so, because there were thousands of bad Commas, wild Question Marks and devious Semikoli, but the Little Blind Text didn’t listen. She packed her seven versalia, put her initial into the belt and made herself on the way. When she reached the first hills of the Italic Mountains, she had a last view back on the skyline of her hometown Bookmarksgrove, the headline of Alphabet Village and the subline of her own road, the Line Lane. Pityful a rethoric question ran over her cheek, then she continued her way.
On her way she met a copy. The copy warned the Little Blind Text, that where it came from it would have been rewritten a thousand times and everything that was left from its origin would be the word "and" and the Little Blind Text should turn around and return to its own, safe country. But nothing the copy said could convince her and so it didn’t take long until a few insidious Copy Writers ambushed her, made her drunk with Longe and Parole and dragged her into their agency, where they abused her for their projects again and again. And if she hasn’t been rewritten, then they are still using her. Far far away, behind the word mountains, far from the countries Vokalia and Consonantia, there live the blind texts. Separated they live in Bookmarksgrove right at the coast of the Semantics, a large language ocean. A small river named Duden flows by their place and supplies it with the necessary regelialia. It is a paradisematic country, in which roasted parts of sentences fly into your mouth.
\section*{Another section}
A wonderful serenity has taken possession of my entire soul, like these sweet mornings of spring which I enjoy with my whole heart. I am alone, and feel the charm of existence in this spot, which was created for the bliss of souls like mine.
I am so happy, my dear friend, so absorbed in the exquisite sense of mere tranquil existence, that I neglect my talents. I should be incapable of drawing a single stroke at the present moment; and yet I feel that I never was a greater artist than now.
When, while the lovely valley teems with vapour around me, and the meridian sun strikes the upper surface of the impenetrable foliage of my trees, and but a few stray gleams steal into the inner sanctuary, I throw myself down among the tall grass by the trickling stream; and, as I lie close to the earth, a thousand unknown plants are noticed by me: when I hear the buzz of the little world among the stalks, and grow familiar with the countless indescribable forms of the insects and flies, then I feel the presence of the Almighty, who formed us in his own image, and the breath
\begin{figure}[tb]
\includegraphics[width=\columnwidth]{schrodinger.jpg}
\caption{ Erwin Schr\"{o}dinger.}
\label{phobo}
\end{figure}
\begin{figure}[tb]
\includegraphics[width=\columnwidth]{leibniz.jpg}
\caption{It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers..}
\label{demo}
\end{figure}
One morning, when Gregor Samsa woke from troubled dreams, he found himself transformed in his bed into a horrible vermin. He lay on his armour-like back, and if he lifted his head a little he could see his brown belly, slightly domed and divided by arches into stiff sections.
The bedding was hardly able to cover it and seemed ready to slide off any moment. His many legs, pitifully thin compared with the size of the rest of him, waved about helplessly as he looked. "What's happened to me? " he thought. It wasn't a dream.
His room, a proper human room although a little too small, lay peacefully between its four familiar walls. A collection of textile samples lay spread out on the table - Samsa was a travelling salesman - and above it there hung a picture that he had recently cut out of an illustrated magazine and housed in a nice, gilded frame. It showed a lady fitted out with a fur hat and fur boa who sat upright, raising a heavy fur muff that covered the whole of her lower arm towards the viewer. Gregor then turned to look out the window at the dull weather. Drops
\section*{Conclusion}
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 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}
\section*{Hexagonal}
% TODO Formatting of these (for one its in american date formats ughhh)
\printbibliography
\section*{Appendix}
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.
\input appendix
\end{document}

20
static.bib Normal file
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@ -0,0 +1,20 @@
@article{GNUParallel,
title = {GNU Parallel - The Command-Line Power Tool},
author = {O. Tange},
address = {Frederiksberg, Denmark},
journal = {;login: The USENIX Magazine},
month = {Feb},
number = {1},
volume = {36},
url = {http://www.gnu.org/s/parallel},
year = {2011},
pages = {42-47}
}
@online{IPC,
author = {Various Physics Lecturers},
title = {{Initially Provided DLA Code Model}},
url = {https://moodle.bath.ac.uk/course/view.php?id=1876&section=3},
urldate = {2023-03-14}
}