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How to measure a halo

Conservation fences are a new and challenging method of protecting Australian threatened mammal species, as evidenced in a recent article in The Conversation.At present, fences protect populations of native species behind their walls. In future, we want to use these fences as source populations to restock the surrounding landscape. Extra animals that can't fit into the small space offered by the fences would be released into the surrounding landscape. These released animals would create a "halo-effect", where the benefit of …

Study level
Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

How many species have been saved by national parks?

National parks are the cornerstone of modern conservation efforts. They now cover more than 10% of the Earth’s land surface, and are found on every continent (and sea) on the planet.We can prove that these national parks stop human destruction of habitat, and we can prove that they benefit the lives and livelihoods of people who visit and surround them. However, we cannot yet prove that they have stopped the extinction of a single species. This is not because we …

Study level
PhD, Master of Philosophy, Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Investigating constraints in optimally controlled ODE systems

In an optimal control problem, a system of state equations is formed to model some process. This system of equations is coupled to an objective functional which summarises the goal of the optimisation process and the systemic costs associated with the model. The control is a variable that can be manipulated from outside of the system and could take many forms. The optimal control is the form of the control variable that optimises the objective functional. An example could be …

Study level
Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

The reduction of multi-scale porous electrode models using approximation methods

Two-phase porous electrodes are at the heart of many modern day energy storage technologies such as batteries and solar cells. To effectively simulate the operation of these structures a multi-scale mathematical modelling approach is required. This approach results in a system of stiff, coupled, nonlinear partial differential equations that require numerical solution.

Study level
Master of Philosophy, Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Modelling and simulation of industrial processes and products

Industrial processes and products can be described as 'multi-problems' in that they are often multi-scale, multi-phase and multi-component in nature. The analysis of such problems sits in the exciting nexus of applied mathematics, physical science and engineering science.

Study level
PhD, Master of Philosophy, Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Novel techniques for modelling with partial differential equations in heterogeneous media

Mathematical models involving heterogenous media comprising two or more constituent materials with different physical properties are widespread across scientific and engineering disciplines.For example, modelling the flow of pollutants or water below the earth’s surface involves dealing with a highly heterogeneous geological structure.Solving such mathematical models is particularly challenging when the heterogeneity is explicitly accounted for in the model.As a result this project aims to answer natural questions such as:Can we develop accurate and efficient numerical or semi-analytical methods to solve …

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Computational modelling using exponential integrators

Many physical processes can be modelled using time and space dependent partial differential equations. Solutions to these equations provide researchers/industry with valuable insight into the underlying process and can often be used to explain phenomena that has been observed experimentally.However, due to nonlinearities in the governing equations and the irregular geometries on which they apply, exact analytical solutions are almost always not accessible. In such cases, numerical methods must be called upon to provide an approximate solution.Typically, the first step …

Study level
Master of Philosophy, Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Multiscale computational modelling of heterogeneous transport processes

Computational models of a multiscale nature, whether they involve partial differential equations with fine-scale variation in coefficients or distinct processes at multiple scales, are ubiquitous across engineering and scientific disciplines. For such problems, direct numerical solution of the governing equations is infeasible due to the huge amount of computational resources required to resolve the smaller scale.Such numerical issues motivate the need for either spatial-averaged models that aim to efficiently and accurately approximate the averaged fine-scale solution on a coarser scale …

Study level
PhD, Master of Philosophy, Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Calculating thermal properties of solids from laser flash experiments

Thermal diffusivity is an important property that determines the rate heat is transferred through a material.The most common way to measure the thermal diffusivity of a solid material is to perform the laser flash experiment, which involves subjecting the front surface of a small sample to a heat pulse of radiant energy and recording the resulting temperature rise on the opposite (rear) surface.Recently, Dr Elliot Carr has developed a new method to calculate the thermal diffusivity from the rear-surface temperature …

Study level
Master of Philosophy, Honours
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Accurately and efficiently fitting surfaces to measured data

Many problems in applied mathematics require the reconstruction or extrapolation of a surface based on (limited) measured data points on the surface.An example of this includes reconstructing physical surfaces from information in photographic, point scanner or medical imaging data. Less obvious examples include extending a mathematical surface defined only locally to something defined globally: this has application in modelling moving interfaces in fluids.With these problems it's important to consider how to accurately and efficiently calculate the surface and how to …

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Stochastic patterns of tissue inclusions

Biological tissue growth involves the secretion of new tissue (extracellular matrix, collagen fibers) by cells. This secretion incorporates scattered inclusions such as proteins and minerals into the new tissue. During bone tissue growth, some of the tissue-secreting cells themselves become incorporated into the new tissue. The distribution of these tissue-embedded cells is believed to influence subsequent tissue growth processes.

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

Collisions with evolving surfaces

The density of impacts of particles colliding with an evolving surface is of particular interest for several industrial and biological applications. These include etching and deposition processes [1], the incorporation of molecules in a tissue during its growth, budding cell membranes, and biological tissue growth [2]. Impacts on an evolving surface are generated unevenly depending on the relative velocity between the particles and the surface. The distribution of impacts further evolves in a curvature-dependent manner due to the local distortions …

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Science and Engineering Faculty
Lead unit
School of Mathematical Sciences

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