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Applied Mathematics Honours Projects
Honours projects in Applied Mathematics
Below you will find some descriptions of Honours projects or areas
of staff interest. If you find a staff member listed below, but no
associated information, you should consider talking to them to find
out more about the opportunities for carrying out an Honours project
with them.
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Professor Nigel Bean
I have supervised honours projects addressing a wide variety of applications
using mathematics from the field of operations research (stochastic
modelling and optimisation). These applications have been in the areas of
telecommunications, scheduling and rostering in industry, auctions and
biology. I have also supervised projects that investigate the mathematical
ideas that support these applications.
If you would like to discuss possible Honours projects with me, then please
email me at nbean@maths.adelaide.edu.au and I will arrange a time to talk
with you.
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Associate Professor David Clements
Please feel free to contact me to discuss possible honours projects.
My areas of interest include:
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Numerical solution of partial differential equations,
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Flow from irrigation channels,
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Mathematical aspects of fracture mechanics,
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Earthquake models,
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Heat flow in solids.
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Dr Liz Cousins
My research interests are primarily in applied optimisation, in
particular, combinatorial optimisation, and the application of random
search methods. Recent honours projects I have been involved with
include:
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Scheduling staff for a 24-hour call centre. This involved many
constraints on the hours staff could work, the lengths of shifts,
and the breaks between them, etc.
- Sequencing cars on an assembly line. There are limitations on which
models of cars can follow others on an assembly line, because of the time
taken to complete the various tasks of fitting windshields, wiring, etc.
The car industry is interested in co nstructing as short a sequence of
cars as possible, without violating constraints on adjacencies.
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Reserve design (choosing those parcels of available land which would
best satisfy biodiversity measures), given various cost constraints. (Each
of these three projects used data from real-life applications.)
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The effect of dam releases on the salinity of the Murray River.
Potential honours students in this area should have an appropriate
background in optimisation, such as can be gained from Optimisation III,
and Mathematical Programming III. Contact me via email
(elizabeth.cousins@adelaide.edu.au) or phone (83035261), or call into my
office, Room 203g, Mathematics Building, to make an appointment.
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Dr Jim Denier
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Freak Waves
The picture below shows a "freak wave" about to
break over the fore-deck of a cargo ship. This wave was estimated to be
20 metres high. Over the past ten years over 200 super-carriers (cargo
ships that are over 200 metres long) have been lost at sea. Many of these
losses have been attributed to an encounter with a freak wave. Recent
data from the European Space Agency's MaxWave experiment detected ten
giant waves (each over 25 metres high) in just a three week period. These wave
are not related to tsunamis. They are thought to result from a
self-interaction process between much smaller amplitude waves that
occur in the ocean. The interaction process serves to produce the
self-focusing behaviour seen in the figure.
A "freak wave" about to hit a cargo ship. The photo was taken from
the wing of the bridge, approximately 17 metres above the level of the
sea. The wave broke above this level!
This project will allow the student to explore current theories for
the generation of such large amplitude, freak waves. It will introduce the
fascinating topic of nonlinear waves, how they are generated and how they
can be described in a very precise mathematical way. Some background in
Differential Equations and Waves would be useful.
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Mathematical Models of the Black Death
Infectious diseases are everywhere and many new ones are classified
(or simply re-discovered) each year. However, the most deadly infectious
disease that has every been recorded is the Plague (the Black Death) that
struck down over a third of the world's population between the 14th and
17th Century. Until recently the cause for this plague been placed at the
feet of the bacterium Yersinia Pestis and spread by the fleas
of the black rat (Rattus rattus). Recent research suggests that
this is not the case, instead the Plague could have been the result of
a viral haemorrhagic fever.
This figure shows the transmission of the plague through Europe in the
14h century.
This project will explore some of the recent theories regarding the
Black Death and its transmission and will consider, in detail, the
general problem of modelling the spatial spread of infectious
diseases. It will be of interest to any student who
would like to combine mathematical skills with some interesting modelling issues.
Although there are no pre-requisites for this project a good grounding
in Differential Equations will prove useful.
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The Mathematics of the Brain
Ever wondered why you think? No, not why you are here, but how does
the brain operate at a most basic and fundamental level? One of the important
aspects behind the very process of thinking is concerned with electrical
signalling (or firing) of neurons in the brain. It was just this problem that
resulted in Hodgkin and Huxley* being award a Nobel Prize in Medicine (of all
things) for their mathematical model of the neuron firing process. This project
will allow the student to explore the Hodgkin-Huxley model (and even simpler
models). At its
very basic level the project is a study in the area of dynamical systems,
exploring such things as bifurcation theory and chaos. At a more ethereal
level it will be an exploration into the mind. Either way, it will be
a lot of fun and you will learn something useful and interesting along the way.
*Hodgkin, A. L. and Huxley, A. F. A Quantitative Description
of Membrane Current and its Application to Conduction and Excitation
in Nerve. Journal of Physiology 117 (1952), 500-544.
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Drag Reduction
With the success of the Australian Swim team at the Athens Olympics,
drag reduction has become a topic that has moved out of the realms of
the aerodynamics industry and entered our every day lives.
The "fast suits" worn by our swimmers are designed to reduce the drag the
swimmers experiences in moving through the water. The technology behind
these swim suits comes from the aerodynamics industry where drag
reduction presents a significant economic problem. Put simply, if you
can reduce the drag an aircraft experiences then you can save
money (and lots of it) on fuel costs.
The figure below shows a new type of fast suit that is designed to increase
the viscous drag felt by a swimmer when moving through water. The
manufacturers believe it provides a higher level of performance when
compared to their competitors fast suits. This claim is contrary to conventional
wisdom and presents an ideal topic of investigation for an honours student.
A new "fast suit" by swimsuit maker Tyr.
This project will introduce the student to the problem of drag
reduction through a study of the topic of turbulence in fluids flows.
The project will involve a review of the state of the art in drag
reduction technologies and can take a variety of directions depending
upon the student's interests and background. Although there are no
pre-requisites for this project some exposure to Fluid Dynamics
may prove useful.
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Dr Janice Gaffney
Please feel free to contact me to discuss possible honours projects.
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Dr Peter Gill
Please feel free to contact me to discuss possible honours projects.
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Dr David Green
My research interests currently include
- Matrix-analytic methods
These are fundamental to the analysis of a rich field of
Markov processes, which have wide applicability in such things as
- Telecommunications networks
- Network protocols
- Computer systems
- Maintenance and reliability
and many other stochastic systems
- Point processes
In particular the use of Markovian models to model traffic streams,
which have direct application to telecommunications systems.
- Simulation modelling
Many real world systems are too complicated to assess performance
measures simply using mathematical analysis, and simulation
modelling is a powerful adjunct in such cases. I am currently
involved with a research venture that uses simulation techniques
in the modelling and design of systems for traffic control and
provision of quality of service.
Some past Honours projects
- TCP congestion control
- Voice over IP
- Mathematics in Bridge
If you would like to discuss doing an honours project with me please
email me at dgreen@maths.adelaide.edu.au to arrange a meeting.
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Professor Charles Pearce
Please feel free to contact me to discuss possible honours projects.
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Dr Matthew Roughan
My research interests are in the area of measurement, modelling and
management of data networks. Some example projects are listed below,
though I am happy to talk about nything in this area.
(1) Non-guassian fractal traffic models.
Internet traffic modeling is a key ingredient in many network design,
and management tasks. In recent years, there has been much research
showing that Internet traffic has fractal characteristics. Typical
traffic models which incorporate such features are Gaussian processes,
with long-memory, such a fractional Gaussian noise. Such processes are
now frequently applied, but Internet traffic, while fractal, does not
always have a Gaussian marginal distribution.
One can distort the marginal distribution to better fit real traffic,
but this alters the fractal characterics of the traffic in a
non-linear manner, related to Hermite polynomials. This project would
determine methods for approximating particular marginal distributions
through non-linear transformations of a Gaussian process, while
maintaining the desired fractal characteristics in the traffic.
(2) Network value at risk
Network reliability is a key issue for most large Internet Service
Providers (ISPs). Providers aim to have downtimes of the order a few
minutes a year. Unfortunately, individual network components have
nowhere near this level of reliability. Reliability is obtained
through redundancy, though at a high cost in terms of
duplication. Reducing the cost, while maintaining reliability is
therefore a key goal for most ISPs.
Interestingly, in the Internet, there are not even good ways of
quantifying overall network reliability. Most metrics that one might
apply are limited in some respect. For instance, it is clearly more
important to maintain high reliability on core backbone links, than
tiny access links, but metrics rarely distinguish the impact of
failures at varying levels. Similarly, when a single failure occurs,
alternative routes can often be used to transmit traffic, but not in
the case of multiple failures.
The aim of this project is to extend ideas from the financial
community to this task. In the financial world, there are concepts
such as the "value at risk", and "conditional value at risk", which
describe the potential damage that is possible to a stock portfolio,
given certain stochastic assumptions. In extending these ideas to
networks, we might then design a minimum cost network, with a
constraint on value at risk.
(3) Search games
In computer science, one of the most common tasks is a search. For
example, one might wish to search a list for a particular element. The
binary search is well known to provide a very good solution, when
searching a sorted list.
However, there are problems where the search involves risks. For
example, in network traffic engineering, we may wish to find a routing
solution that balances traffic over multiple paths, while satisfying
the constraint that we don't send any path more traffic than it can
support. Traditionally, such problems are treated as optimization
problems, with constraints. However, in some problems, we don't know
the constraints initially. These must be estimated by performing the
search, for instance, by sending traffic along the paths, and
receiving feedback about congestion levels. Unfortunately, in doing
so, you may loose traffic to congestion. Thus, we have two objectives
in probing -- firstly to gain information in our search for a viable
solution, and secondly, to avoid loosing too much traffic to
congestion. Thus one has a game, in many respect similar to Poker,
where one must choose how much to bet, to elicit particular
information from other players (about the strength of their hand),
while simultaneously placing value at risk.
A solution is to generalize the binary search algorithm to the space
of possible solutions. We have developed several algorithms which
perform such a search, for the traffic engineering problem. An
interesting question, which this project would address, is how widely
these methods may be generalized to other problems.
(4) Joint models of traffic and topolgy
In Internet modeling, two major efforts are proceeding in parallel --
the first to model Internet traffic, and the second to model the
network topology. Despite great strides in both areas, there has been
little understanding of the fact that these two features of a network
are strongly related. As network routing changes, so changes the
traffic, but also, networks are designed around the traffic they
carry, and so are highly correlated to this traffic.
There is a strong analogy here to hydrological modeling. For instance,
if one examines hydrological data (for instance stream flow rates),
one observes self-similar, or fractal behaviour. Such behaviour is
also observed in Internet traffic flows. Another parallel is drawn
when one considers catchments. River flows are determined by the
rainfall within their catchment, whereas network traffic flows result
from traffic generated by users within a catchment. Similarly, the
water flows over time can alter the shape of a catchment through
erosion, resulting in fractal like landscapes. In the Internet,
changes in the traffic flows result in network redesigns, that then
alter the catchment shapes. Again, much of the recent work on network
modeling has noted fractal structure in the deisng of networks, so the
analogy is quite strong.
In the geological world, the changes made to terrain happen over long
timescales of hundreds to thousands of years. In the Internet, changes
happen overnight, by comparison. Hence, by applying techniques used to
model hydrological processes, we may be able to gain some highly
practical insights that lead to better models for the Internet.
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Dr Yvonne Stokes
My research Interests include
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Fluid Mechanics
In particular very viscous flows, free-surface flows,
computational fluid dynamics.
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Industrial and Biological Mathematics
In particular modelled by
differential equations involving mass
and/or heat transfer.
I am prepared to supervise honours projects in these areas and you are
welcome to discuss your interests with me.
I am located in the Mathematics Building, Room 203d, but I recommend that
you make an appointment either
by email (Yvonne.Stokes@adelaide.edu.au), or by telephone (8303 4808).
In the past I have supervised honours and masters-by-coursework projects in
the following areas:
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Viscous extensional flows under gravity
These are flows which, like honey dripping from an up-turned spoon, exhibit,
elongation,
necking to form a drop suspended by a thin filament, and, finally, pinch-off
of the drop and further
breakup of the filament. Important application areas include fibre
spinning, ink-jet printing, blow-moulding,
and rheometry. Despite considerable research over the last century, the
mechanism(s) which govern where and
when drop pinch-off occurs are still not fully understood.
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Sagging of Viscous Sheets Under the Influence of Gravity
Gravity sagging of viscous fluid sheets is used in the manufacture of car
windscreens and optical lenses;
glass sheets or discs are heated so that they melt and flow under their own
weight. Mathematical modelling
can be used in place of experiments to determine what shape results from
some initial geometrical setup and for
some given temperature distribution. Mathematical modelling is even more
useful for solving the even
more challenging "inverse" problem of determining mould shape and/or
temperature distribution to yield a
required product shape.
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Oxygen diffusion in mammalian oocytes
Evidence suggests that oxygen and nutrient concentrations in a mammalian
oocyte affects its ability to develop, when
fertilised, to full maturity and give rise to a healthy living offspring.
These concentrations cannot, at present,
be directly measured and mathematical modelling to determine concentrations
from other experimentally
vialable data is necessary. This will assist in determining whether
particular oocytes are suitable for use in
assisted reproduction programs.
Another possible project topic is
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Flow in spiral channels
 © 2004
TIOMIN RESOURCES INC. (TIO) All rights reserved.
Spiral-channel flow is important in a number of industrial separation
processes, such as helical-coil distillation of
petroleum products, separation of liquids of different densities (e.g. oil
from seawater), and
particle segregation and concentration in spiral separators used by the
mineral processing industry.
It also has relevance to flows in rivers. Flows in such curved channels
consist of two components: a primary axial
flow and a secondary cross flow. The fluid depth is, typically, small
making experimental investigation
difficult. Mathematical models are therefore of great value for determining
how such flows are influenced
by fluid properties and geometrical parameters.
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Dr Michael Teubner
Before lecturing at The University of Adelaide, I spent 16 years
working as a consulting engineer and program manager in the United
States. During this time, I came across many varied and interesting
projects that could be used as the basis of Honours projects in Applied
Mathematics at Adelaide. Many of the honours students I have supervised
have chosen to study applications of these projects, often leading to
successful jobs in industry or to higher degrees.
Some of these projects include:
- injecting treated Bolivar sewage water into the Northern Adelaide
Plains groundwater system for storage and use in summer
- analysing the effect of groundwater extraction for grape growing on
the groundwater system in the Willunga Basin
- assessing the likelihood of a flood along the Torrens River in
Adelaide
- developing an inverse technique for calibrating fluid flow models
- assessing the effect of drainage ditches on saline groundwater flow
in the southeast of South Australia
- modelling air movement in the attic of a ski resort building to
eliminate ice build-up
- assessing the effect of high city buildings on local winds
My general areas of interest include ground- and surface-water flows,
computational fluid dynamics, modelling brain activity, salinity problems
within the Murray-Darling Basin, and inverse techniques for fluid-flow
modelling.
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Dr John van der Hoek
Please feel free to contact me to discuss possible honours projects.
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