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Found 7 matching student topics

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Forecasting disease spread risk based on human movement patterns

This project aims to forecast the risk of infectious disease spread, such as COVID-19 and dengue, based on human movement patterns. We'll use multiple data sources that describe people movement in order to understand individual and population level mobility patterns, and use empirical disease case data to model the effect of movement on the spread of disease.

Study level
PhD, Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Faculty of Science
School
School of Computer Science

Mathematical models for diffusion magnetic resonance imaging (dMRI)

Mathematical models are becoming increasingly important in magnetic resonance imaging (MRI), as they provide a mechanistic approach for making a link between tissue microstructure and signals acquired using the medical imaging instrument. For example, diffusion Magnetic Resonance Imaging (dMRI) is one of the most important contemporary non-invasive modalities for probing tissue structure at the microscopic scale. However, dMRI signal behaviour at high or ultra-high field strengths has shown increased deviation from the classically expected mono-exponential decay. Characterising the underlying mechanism …

Study level
Vacation research experience scheme
Faculty
Faculty of Science
School
School of Mathematical Sciences

Diffusion and first passage times in random media

Diffusion in homogenous environments is relatively well understood, but the problem becomes more complicated in complex environments - such as wood tissue, cells, filters and catalysts. At QUT there is extensive expertise in using advanced numerical methods to model diffusions and first passage times in complex environments.The ability to combine this expertise with realistic models of random media based on level-sets of Gaussian random field.

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

New mathematical and computational techniques for modelling with partial differential equations

Mathematical models involving partial differential equations (PDEs) are useful for simulating many important physical processes including heat and mass transfer, groundwater flow, pollutant transport and drug delivery. This project will focus on developing new mathematical and computational techniques to solve, approximate and/or analyse PDE models.Potential project topics include:developing new numerical and/or analytical methods for solving PDE modelsbuilding new reduced-order PDE models that are easier to solve, interpret or analyseextracting insight into time scales of PDE models, such as the amount …

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

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, Vacation research experience scheme
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, Vacation research experience scheme
Faculty
Faculty of Science
School
School of Mathematical Sciences
Research centre(s)
Centre for Data Science

Molecular simulation of rotational diffusion in ideal liquids

Rotational tumbling of molecules in a liquid is an important phenomenon in Magnetic Resonance Imaging (MRI) because it determines the spin-relaxation rates of the resident nuclei which can determine MRI contrast.For a relatively simple molecular process, the theoretical description of rotational motion of molecules in liquids remains controversial. The most commonly used model, the Debye model, assumes that:the rotational diffusion propagator of a tumbling molecule is a solution of the diffusion equation on a spherical surfacethis solution is described by …

Study level
PhD, Master of Philosophy, Honours
Faculty
Faculty of Science
School
School of Chemistry and Physics
Research centre(s)
Centre for Materials Science

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