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 6 matching student topics
Displaying 1–6 of 6 results
Exact and approximate solutions of diffusion on evolving domains
Classical applications of mathematical analysis involve solving partial differential equation models on fixed domains, e.g. 0 < x < L. Applications in biology, however, involve studying diffusive transport on rapidly evolving domains, e.g. 0 < x < L(t), where L(t) represents the length of the evolving tissue. While many problems have been addressed for the case where L(t) increases, less attention has been paid to cases where we consider diffusion on an oscillating domain.In this project we will construct exact …
- Study level
- Master of Philosophy, Honours
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
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
Curvature dependence of reaction-diffusion wave front speed with nonlinear diffusion.
Reaction-diffusion waves describe the progression in space of wildfires, species invasions, epidemic spread, and biological tissue growth. When diffusion is linear, these waves are known to advance at a rate that strongly depends on the curvature of the wave fronts. How nonlinear diffusion affects the curvature dependence of the progression rate of these wavefronts remains unknown.
- Study level
- PhD, Master of Philosophy, Honours
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
- Research centre(s)
- Centre for Biomedical Technologies
Design, derivation, and implementation of mesh-free finite volume solvers based on 3D unit cell morphology to estimate biomass particle effective parameters
The aim of this PhD project is to use lignocellulosic morphological features extracted from high resolution micro-CT images of biomass particles undergoing a dilute acid pretreatment process to perform computational homogenisation over representative unit cell configurations. Mesh-free finite volume solvers will be developed based on 3D point cloud data sets to estimate virtual biomass particle effective parameters, such as diffusivity, thermal conductivity, and permeability. The simulation results will be analysed to provide a fundamental understanding of the impact that changes …
- Study level
- PhD, Master of Philosophy, Honours
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
The role of complex singularities in geometric flows
A popular topic in differential geometry involves studying the singularity structure of geometric flows. The most well-known example is mean curvature flow. In this example, surfaces evolve according to a flow rule that relates the speed of the surface to its curvature. Certain surfaces will evolve until singularities occur in finite time, and these singularities can be studied using similarity solutions and asymptotic analysis.In this project, a different perspective is applied to these problems, namely the use of complex variable …
- Study level
- Master of Philosophy, Honours
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
Weakly nonlinear water waves in the complex plane
Weakly nonlinear waves are described by dispersive pdes, such as the famous Korteweg–De Vries (KdV) equation. These models have applications to a variety of phenomena in physics, including the propagation of water waves, but they are also interesting from a mathematical perspective because they can have special properties.While the KdV equation and its variants are well-studied in the literature, a new approach is to attempt to learn about wave propagation by investigating solution behaviour in complex plane. For example, there …
- Study level
- PhD, Master of Philosophy, Honours
- Faculty
- Faculty of Science
- School
- School of Mathematical Sciences
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