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Found 7 matching student topics

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Computational modelling using exponential integrators

Many physical processes can be modelled using time and space dependent partial differential equations. The solution of these equations provides 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 the complexity of these processes and the irregular geometries on which they apply, exact analytical solutions to the governing equations are almost always not accessible. In such cases, numerical solution methods must be called upon to …

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

Dynamical systems and theoretical biology

Numerous physical and biological systems involve processes of diffusive and/or advective transport (for example, pollutant dispersal, insect pest infestation, heat) and/or reaction (such as interaction, growth, decay) that vary over space and time. As such they can best be described by coupled systems of partial differential equations.Projects are available that focus on aspects of constructing and validating mathematical models and simulations of tissue growth and repair problems, such as epidermal and corneal wound healing, bone fracture healing and tumour growth.Mathematically, …

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

The mathematics of robustness in molecular communication networks

Robustness, and the ability to function and thrive amid changing and unfavourable environments, is a fundamental requirement for living systems. In the past, it has been a mystery how large and complex biological networks can exhibit robust performance since complexity is generally associated with fragility.Exciting recent research here at QUT has suggested a resolution to this paradox through the discovery that robust adaptive signalling networks must be constructed from a small number of well-defined universal modules ("motifs"). The existence of …

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

Active-transport mechanisms for robust biological patterning

The underlying mechanisms that generate shapes and patterns in biology are characterized by a remarkable robustness, despite the uncontrollable parameter variability. More than half a century ago, Alan Turing published a landmark mathematical study entitled “The Chemical Basis of Morphogenesis” to explain how patterns in biology could be produced via certain classes of reaction-diffusion systems.This mathematical theory proposed the novel idea that two homogeneously dispersed “morphogens” - chemicals that determine a cell’s fate or characteristics - can autonomously generate spatial …

Study level
PhD, 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

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