PhD Scholarship
The Queensland University of Technology

Mathematical Sciences School

Posted on: Thu Apr 10 2014

Project description

The Mathematical Sciences School within the Science and Engineering Faculty at Queensland University of Technology is offering one PhD scholarship to analyse defect driven pattern formation in reaction-diffusion equations and wave equations with possible applications to melanoma modeling. The successful applicant will commence their PhD in 2014 and will contribute to the research project titled: Analysis of defect driven pattern formation in mathematical models, supported by a DISCOVERY EARLY CAREER RESEARCHER AWARD of Dr van Heijster (DE140100741). The key issues that this project addresses are:

  • theoretical and mathematical underpinning of the effect of heterogeneity on pattern formation,
  • characterising the new patterns created by a heterogeneity (existence, stability, dynamics),
  • controlling the new patterns by manipulating the heterogeneity,
  • applying the new theory to a heterogeneous haptotactic model describing melanoma, i.e. skin cancer.

The student will have opportunities to acquire a wide range of research skills and develop advanced knowledge in the area of (applied) mathematics. These include, but are not limited to, Fenichel theory and geometrical singular perturbation techniques for the existence of solutions, the Evans function and the nonlocal eigenvalue problem method for the stability of solutions and the renormalization group method for the interaction of solutions, as well as numerical techniques to implement multi-scale problems. The research topic is highly innovative and it is expected that the student will adopt a `hands on' approach to furthering our understanding of this.

The successful applicant will work at QUT in the Mathematical Sciences School. The applicant would ideally have some knowledge of pattern formation for reaction-diffusion equations and wave equations. More specifically, the applicant would ideally have some knowledge in multi-scale analysis, travelling waves, stability analysis or Hamiltonian methods. Moreover, good communication and mathematical writing skills are expected. While it is not expected that the student will have full knowledge of all the systems and techniques required, it is important that the student is interested and motivated to acquire the necessary knowledge involved with the project.

Application criteria

Candidates will be required to have recently completed a Bachelor of Mathematics with First-class Honours or a Second-class Division A Honours from a recognised institution, or an equivalent degree (for example MSc in Mathematics) from an overseas institute. An affinity with numerical methods is a plus, but definitely not necessary.

Note that this position is NOT RESTRICTED to Australian citizens and a successful international applicant will also be considered for a Higher Degree Research Tuition Fee Sponsorship from the university.

Stipend level

There is a living allowance of $25,392 per annum (tax free and indexed annually) for the duration of 3 years, starting as soon as possible.

For further information

The first step* in applying for this scholarship is submitting a:

  • Cover letter
  • CV
  • Full record of your academic transcript
  • (up to) 2 page summary of your scientific career thus far including
    • a summary of your ``final project";
    • a paragraph on your research interests.
  • Contact details (email, address and phone numbers) of 3 references

For further information, or to discuss this research project, please contact Dr. Peter van Heijster, on +617 3138 1671 or email: .See also

*Note: the second step in the application process is to complete and submit a required application form to confirm that the applicant is eligible for the scholarship. However, only successful candidate(s) from the first round will be asked to fill in this form.

Application closing date

Applications will remain open until a suitable applicant is found.

**Mention you saw it on the AustMS website**