QUT offers a diverse range of student topics for Honours, Masters and PhD study. Search to find a topic that interests you or propose your own research topic to a prospective QUT supervisor. You may also ask a prospective supervisor to help you identify or refine a research topic.
Found 39 matching student topics
Displaying 25–36 of 39 results
Surrogate models for accurate prediction and inference in mathematical biology
High fidelity mathematical models of biological phenomena are often complex and can require long computational runtimes which can make computational inference for parameter estimation intractable. In this project we will overcome this challenge by working with computationally simple low fidelity models and build a simple statistical model of the discrepancy between the high and low fidelity models. This approach provides the best of both worlds: we obtain high accuracy predictions using a computationally cheap model surrogate.
- Study level
- PhD, Master of Philosophy
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
- Research centre(s)
- Centre for Data Science
Branching processes, stochastic simulations and travelling waves
Branching processes are stochastic mathematical models used to study a range of biological processes, including tissue growth and disease transmission.This project will implement a simple stochastic branching process to generate simulations of biological growth, and then consider differential equation-based description of the stochastic model.Using computation we will compare the two models, and use phase plane and perturbation analysis to analyze the resulting traveling wave solutions.
- Study level
- PhD, Master of Philosophy, Honours
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
- Research centre(s)
- Centre for Data Science
Mathematical and computational models for diffusion magnetic resonance imaging (dMRI)
In 1985, the first image of water diffusion in the living human brain came to life. Since then significant developments have been made and diffusion magnetic resonance imaging (dMRI) has become a pillar of modern neuroimaging.Over the last decade, combining computational modelling and diffusion MRI has enabled researchers to link millimetre scale diffusion MRI measures with microscale tissue properties, to infer microstructure information, such as diffusion anisotropy in white matter, axon diameters, axon density, intra/extra-cellular volume fractions, and fibre orientation …
- Study level
- PhD, Master of Philosophy, Honours
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
- Research centre(s)
- Centre for Data Science
Centre for Biomedical Technologies
Optimisation of piezoelectric materials for robotics applications
Piezoelectricity, which translates to “pressure electricity”, is the phenomenon in which certain materials convert mechanical energy to electrical energy, and vice versa. Such materials are common-place and are used in a variety of applications including sensor, actuator, and energy harvesting technologies. The capabilities of such piezoelectric materials have not yet been fully realised. We plan to use computational structural optimisation to design new piezoelectric materials and components that may contribute to novel sensing technologies for robotics applications. Essentially, robots need …
- Study level
- PhD, Master of Philosophy, Honours
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
Computational methods for multi-scale structural optimisation
Structural optimisation is a powerful computational methodology for finding high-performing designs for structural components or material architectures. For example, what periodic scaffold would provide the highest possible stiffness for its weight?Solving such a problem computationally requires an understanding of the relevant equations required to model the physical properties of interest, as well as efficient implementation of a range of numerical methods including finite elements, finite differences and optimisation.With recent developments in 3D printing technologies it is now becoming possible to …
- Study level
- PhD, Master of Philosophy, Honours
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
Optimising sampling design for model discrimination of coral reef recovery
Natural disturbances including severe storms and bleaching events have devastating impacts on the Great Barrier Reef's health. Unfortunately, the increasing pressures associated with climate change are causing these disturbances to occur more frequently, for a longer duration and with more intensity.It's essential to understand the recovery dynamics between major disturbances so we can manage the health of the Great Barrier Reef under increased environmental pressures. Many studies modelling reef recovery assume a specific form for the growth dynamics. However, the …
- Study level
- PhD, Master of Philosophy, Honours
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
- Research centre(s)
- Centre for Data Science
Creation of fibrous tissue at moving interfaces
Extracellular matrix (ECM) secreted by cells is composed of a meshwork of fibres infiltrated with proteins and/or minerals. This fibre meshwork often matures after its creation by rearranging its structure according to local mechanical clues, or by the infiltration of new molecules.In this project, the fibre meshwork will be represented by a continuous anisotropic field. You will derive evolution equations to describe fibre creation at moving cell membranes and the subsequent maturation of the meshwork.Applications of this model include the:investigation …
- Study level
- PhD, Master of Philosophy, Honours
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
- Research centre(s)
- Centre for Biomedical Technologies
Emergence of curvature-dependent growth in mathematical models of tissue invasion
The growth of biological tissues in 3D-printed scaffold pores occurs under strong geometric controls depending on the shape and size of the pores. How this control emerges from the interaction between spatial constraints and biological processes such as cell migration and cell proliferation remains largely unknown. Existing phenomenological models of tissue growth hypothesise growth laws which directly involve curvature without considering cellular mechanisms.Recently, a reaction–diffusion mathematical model of tissue growth in porous scaffolds was proposed to investigate cell-level behaviour using …
- Study level
- PhD, Master of Philosophy, Honours
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
- Research centre(s)
- Centre for Biomedical Technologies
Moving boundary problems in mathematical biology
Invasion of biological cells or ecological populations involves moving fronts that invade into previously unoccupied regions of space. Such moving fronts are driven by a combination of motility, such as random diffusion, and proliferation, such as logistic growth. Understanding how best to model such invasive fronts is important as moving fronts of cells are associated with wound healing and cancer progression and moving fronts in ecology are associated with the spreading of weeds and invasive species.Previously both continuum and discrete …
- Study level
- PhD, Master of Philosophy, Honours
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
How many species were 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.We can prove that these national parks stop human destruction of habitat. We can prove that they benefit the lives and livelihoods of people who visit and surround them. However, we can't yet prove that they have stopped the extinction of a single species. This isn't because we don’t believe that they've helped. …
- Study level
- PhD, Master of Philosophy, Honours
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
First passage time for diffusion
Mathematical models describing diffusive transport of mass and energy are essential to our understanding of many problems in engineering, physics, biology and chemistry.Classical analysis of mathematical models that describe diffusive transport focus on diffusion in simple geometries, such as lines, discs and spheres composed of homogeneous materials. In contrast, specific applications of diffusive transport theory in more complicated geometries are often explored computationally. This can include geometries with heterogeneous materials.While computational approaches are necessary in certain circumstances, analytical insight is …
- Study level
- PhD, Master of Philosophy, Honours
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
- Research centre(s)
- Centre for Data Science
Equation learning for partial differential equation models of stochastic random walk models
Random walk models are often used to represent the motion of biological cells. These models are convenient because they allow us to capture randomness and variability. However, these approaches can be computationally demanding for large populations.One way to overcome the computational limitation of using random walk models is to take a continuum limit description, which can efficiently provide insight into the underlying transport phenomena.While many continuum limit descriptions for homogeneous random walk models are available, continuum limit descriptions for heterogeneous …
- Study level
- PhD, Master of Philosophy, Honours
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
- Research centre(s)
- Centre for Data Science
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