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Vacation scholarships for undergraduates
A scholarship of a tax-free stipend of up to $400 per week is available for undergraduate students in Australia to be involved in cutting-edge research during the summer vacation. It is typically awarded for four weeks in January to February.
How to apply
Applications are now open and will close at 3pm sharp on Friday 24 November 2017.
Please complete and submit the online application form and email the remaining documents to the email address below.
The application process comprises:
- a completed online application form
- a covering letter
- a copy of your academic transcript
- your CV
- contact details and references from two academic referees.
At the completion of the scholarship students will be required to provide a one-page report detailing their experience.
For more information
T: (02) 9850 8947 E: firstname.lastname@example.org
Projects on offer in 2018
Up to six (6) scholarships will be awarded to suitable candidates, with details of eleven (11) possible projects on offer listed below. Please list your top four preferences (in order) on the application form.
|Project title||Project description||Supervisor|
1. Linear Programming Approach to Optimal Control of Nonlinear Dynamical Systems
|The linear programming approach to problems of control of nonlinear dynamical systems is a relatively new technique based on the fact that certain aspects of system’s dynamics can be captured by a system of linear equations. The work on this project will involve learning theoretical foundation of the approach as well as its practical application for finding a numerical solution to a problem of optimal control of a predator-prey model||Vlad Gaitsgory|
2. Numerical Modelling of Stratified Free Surface Flow
|This project focuses on studying water waves caused by potential flow over a submerged obstacle, such as an ocean shelf or trench. This problem is complicated, as the position of the surface (and therefore the shape of the flow domain) is not known, and must be obtained as part of the solution itself. These problems are often studied using iterative numerical methods. In this project, you will apply iterative methods to study flows in which two fluids with different densities separated by a free interface. This can be thought of as a very simple representation of density stratification seen in the ocean. In particular, you will investigate how stratification affects waves on the surface of the flow.||Chris Lustri|
3. Simulation of Travelling Waves through Particle Chains
|Particle chains consist of a string of particles which interact only with their neighbours. These chains can be used to propagate energy or information; however, they are often subject to wave decay due to small imperfections in the chain. This project first involves simulating the behaviour of travelling wave signals sent through ideal particle chains. The second stage of the project is to introduce small imperfections into the system, and study the effect of these imperfections on the propagated waveform.||Chris Lustri|
4. Symmetry and the Hydrogen atom
|The mathematical framework of quantum theory uses techniques from many diverse domains of the mathematical landscape, from the very pure to the highly applied. Group theory in particular, the theory that underlies symmetry, forms a very important and remarkably diverse tool in physical theory. In this project we will explore the non-trivial role that group representation theory plays in constructing physical theories and solving physical problems in general, and in elucidating the spectrum of the Hydrogen atom in particular.||Frank Valckenborgh|
5. Integral Equations
|Just as a differential equation is a mathematical equation that relates some function with its derivatives, an integral equation is one in which the unknown function appears under an integral sign. Many interesting physical problems can be expressed in terms of integral equations: for example, the determination of the distribution of electric charge on a conducting surface from a knowledge of the potential, or the determination of the shape of a surface from a knowledge of the energy scattered by some illuminating field. A linear integral equation can be seen as the continuous analogue of a system of linear algebraic equations. This project will explore ways and means of solving integral equations and their interpretation in physical contexts.||Paul Smith|
6. Mathematics of the brain
The human brain is composed of individual nerve cells, or neurons, whose main function is to transmit and conduct information through the propagation of an action potential. Several mathematical models exist to reproduce certain behaviours of this electrical signalling (or firing) of neurons in the brain. By performing bifurcation analysis and using numerical continuation methods on these systems, we are able to unlock some of the rich dynamics within.
7. Magnetic capture of metal particles
Many food processing systems make use of magnetic extraction techniques to remove small metal particles from powdered food products. These small particles often arise from the abrasive nature of the powders, serving to scour the stainless steel pipe through which they travel. This project will explore some of the issues around how, moving, metal particles can be extracted using magnetic fields. You will get some exposure to fluid mechanics, some physics, some coding, and applying maths to an important industrial problem (no experience in any of these necessary).
8. A viral epidemic in a cluster of bacteria
Bacteriophages are viruses which infect bacteria, and are a frequent cause of bacterial death. When a virus finds a group of bacteria, it can spread very quickly through them leaving only a few survivors. This project will investigate how that occurs, using simulations and equations to model the spread of the virus, and investigate how different factors (such as the ease of infection or the bacteria movement) affect the speed of infection and the number of survivors.
9. The Catalan numbers
The Catalan numbers 1,1,2,5,14,42,... are the solution to many different counting problems; for example, the nth Catalan number counts the number of binary trees with n+1 leaves; or the number of ways of triangulating an (n+2)-sided polygon; or the number of finitely branching plane trees with n+1 vertices. The goal of this project is to explore some of the different structures counted by the Catalan numbers, and the ways in which we can match these seemingly disparate structures together.
10. Solving Laplace's equation on a torus.
Potential theory is a fundamental theory in mathematics which explores the beautiful properties of solutions to Laplace's equation, a partial differential equation of widespread scientific importance. Potential theory is well-understood on simple surfaces such as the sphere, but not on more general surfaces (which might arise in an applications problem, say). Preliminary explicit results in potential theory have been found in the special case of the so-called ring torus, a surface of revolution with a 'hole'. This project will modify existing methods used to derive results in potential theory on the ring torus to include more general non-ring tori. A working knowledge of complex analysis would be an ideal prerequisite for this project.
11. Wedge shape potential well
The potential well is one of more simple and significant example considered in quantum mechanics. In the project, we will use the Airy function to study the discrete spectrum for the wedge shape potential well in a one dimensional model. The project requires only understanding of the basic theory of Ordinary Differential Equations and Linear Algebra.