Study level

  • Vacation research experience scheme

Faculty/School

Topic status

We're looking for students to study this topic.

Research centre

Supervisors

Professor Fawang Liu
Position
Professor
Division / Faculty
Faculty of Science

Overview

In recent years, fractional models have attracted considerable interest because of their ability to model many phenomena. Anomalous diffusion phenomena are widely spread in nature and engineering.

This proposal aims to carry out innovative and novel research on developing efficient and accurate computational models for complex fractional dynamical systems.

Potential research projects include:

  • Computational modelling of nanofluids for industrial applications.
  • Time and space nonlocalities underlying fractional-derivative models with application to medical imaging.
  • Fractional dynamic models for MRI to probe tissue microstructure. Explore the utility of multi-term time-space fractional Bloch-Torrey equations to understand the influence of tissue microstructure on model parameters.
  • Time, space, and time-space distributed-order differential equations to model ultraslow diffusion where a plume of particles spreads at a logarithmic rate, to model a mixture of delay sources, to model super-diffusion phenomena.
  • Non-Newtonian modeling of multiphase fluid and multiscale materials, numerical analysis, simulation and applications.
  • Fractional order epidemic models and parameter estimation problems.
  • Computational models of complex fractional dynamical systems and application to finance.

Eligibility criteria

You must have:

  • the potential for, and,
  • an interest in undertaking postgraduate research study (Honours, or MPhil or PhD).

Research activities

Research activities include:

  • fractional dynamical systems
  • numerical methods:
    • finite difference method
    • finite element method
    • finite control volume method
    • meshless method, and,
    • spectral method
  • irregular domains
  • parameter estimation
  • experimental data and applications.

Outcomes

This proposal aims to carry out innovative and novel research on developing robust and accurate computational models for complex fractional dynamical systems and applications.

Skills and experience

It would be useful to have assumed knowledge in:

  • computational mathematics:
    • finite difference methods
    • finite element methods
    • finite volume methods
    • spectral methods, and,
    • meshless methods.
  • MATLAB, or,
  • FORTRAN.

Keywords

Contact

Contact the supervisor for more information.