Research scholarships

Full project title: Mathematical modelling of the onset and growth of protuberances in biological cells

The mathematical theory of reaction-diffusion has been remarkably successful in understanding the onset of patterns in biological systems, typically at the level of tissue or organs. A theory has emerged that helps explain cell polarity, that is the mechanism by which cells develop a sense of back and front, and morph into specific shapes.

About the scholarship

This PhD shall consider classes of reaction-diffusion equations that model the dynamics of structural elements that are common to all plant and animal cells, known as G-proteins. The diffusion of the activated form of such proteins on the cell surface is thought to underlie the process by which different cells can develop their specific polarity and shape. Examples include:

• hair cells on the surface of plant root that develop a single soft patch that grows into a long protuberance (the ‘hair’)
• pavement cells on a leaf that develop jigsaw-piece-like blobs and dents in co-operation with their neighbours.

The purpose of this PhD is to analyse such system using mathematical methods that go beyond the usual ‘weakly nonlinear’ theory by introducing two spatial scales:

• on an inner scale there can be a rapid change in concentration, leading to growth
• on an outer scale there is more quiescent behaviour, involving the rapid diffusion of the inactive form of the G-proteins.

There can also be multiple timescales involved.

The work will involve a mixture of mathematical modelling, applied analysis, numerical method development and interdisciplinary interaction with biologists in both institutions.

The aim will be to take simple mathematical theories and adapt them so that they apply in more realistic 2D and 3D geometries, to answer real biological questions about how these important processes are controlled.

Availability

The scholarship is available to candidates eligible to undertake a direct entry PhD program at the University of Bristol (UoB) and Macquarie University, commencing on 11 May 2026.

Admission and scholarship criteria of both universities must be met:

• University of Bristol requirements
• Macquarie University PhD entry and English language requirements, and graduate research scholarship eligibility criteria.

Applicants must not already:

• hold a doctoral degree
• be matriculated for a doctoral degree.

Components

The scholarship comprises the equivalent of a full-fees award and stipend for the normal full-fee paying period of 42 to 48 months.

Scholarship holders will be expected to have submitted their thesis for examination by the end of that period. Students are expected to spend the first 21 or 24 months at UoB, followed by 21 or 24 months at Macquarie. Note that the total duration of the position will be confirmed to the student upon successful application.

The UoB scholarship contribution will include the following components:

• 42 to 48-month tuition fee scholarship for UoB fees
• 21 to 24-month stipend (at UKRI rates) paid pro-rata for the period spent on campus at UoB
• Research Training and Support Grant (RTSG), to contribute towards research-related costs.

The Macquarie scholarship contribution will include the following components:

• 36-month tuition fee scholarship for Macquarie fees. Note that the student registers to the Dual PhD at UoB first, for 42 to 48 months. They register to the equivalent Global PhD (cotutelle) at Macquarie after 6-12 months, for a 36-month period, keeping the program end dates the same at each institution
• 21 to 24-month stipend scholarship at an annual rate of AUD $39,700 (tax exempt, 2026 rate), paid pro-rata for the period spent on campus at Macquarie
• airfare allowance for flights between the UK and Sydney up to AUD $4000.

Unless otherwise specified, the scholarships do not cover:

• any continuation, extension or resubmission period/fees
• a research training grant or another equivalent award for research expenses
• support for travel, immigration, health insurance and related charges between the partner institutions.

How to apply

Call for expressions of interest (EOIs) from students is open now, and closes on 10 December 2025.

Prospective candidates should submit an EOI directly to both supervisors by email:

• Alan Champneys at a.r.champneys@bristol.ac.uk
• Justin Tzou at justin.tzou@mq.edu.au

Use the subject line ‘Mathematical modelling of the onset and growth of protuberances in biological cells’.

Your EOI email must include:

• CV (including information about publications)
• transcripts of most relevant/recent degrees
• information about thesis components (thesis mark, word count, weight/length in comparison to the degree overall)
• a statement of your suitability as a candidate for the project (maximum 500 words)
• an indication that you meet the English language requirements for entry into a PhD program at both universities, or your willingness to obtain relevant English language proficiency test results.

Full application:

• Successful candidates will need to submit a formal application to both institutions (including a research proposal aligned with the project’s scope and a personal statement).
• When making your application:
  • to Macquarie, follow the how to apply instructions.
  • to UoB, use the program title Engineering Mathematics (PhD) (Macquarie), indicate the supervisor name and the project title on the form. Ensure you provide all supporting documents as per the program admissions statement. Learn more about the Dual PhD program.
• Shortlisted candidates will be invited for an interview.
• All relevant entry and immigration requirements for both institutions must be met.

Contact us

Further enquiries about the Global PhD scholarship may be addressed to: