Funded (UK/EU and international students)

Project code



School of Mathematics and Physics

Start dates

October 2021

Application deadline

4 May 2021 (12.00pm GMT)

The PhD will be based in the School of Mathematics and Physics, and will be supervised by Dr Jamie Foster and Dr Marianna Cerasuolo.

Candidates applying for this project may be eligible to compete for a Portsmouth Global PhD scholarship. Successful candidates will receive a scholarship to cover tuition fees at an international rate for three years, a stipend in line with the UKRI rate (£15,609 for 2021/22), and one return flight to London during the duration of the course. Bursary recipients will also receive a £1,500 p.a. for project costs/consumables.

The work on this project could involve:

  • Developing versatile mathematical modelling skills applicable in a broad range of research areas
  • Becoming an expert in growing technology (lithium-ion batteries) providing excellent future employment opportunities
  • Joining a thriving research community (locally at Portsmouth, nationally via the Faraday Institute, internationally via external collaboration including with industry)

Developing cheap and efficient means of storing energy is key to the low-carbon economy. The fastest growing battery design is lithium-ion cells and they are already produced in their billions each year for use in consumer devices. They are the most promising candidates for use in electric vehicles (EVs) but improvements in peak current capabilities and cell lifetime are needed. Their current market value is already $36Bn and this is expected to grow to $92Bn by 2024.

The aims of this project are to carry out the mathematical modelling and analysis required to underpin and inform changes in the current design of battery cells that give rise to the ability to (i) charge quickly, allowing EVs to be refuelled in times comparable to those with traditional combustion engines, and (ii) withstand the chemical and mechanical abuse that occurs during service. The mathematical models that we develop will describe the process occurring with batteries using partial differential equations. The models will be analysed using a combination of analytical (asymptotic) and numerical methods. In collaboration with experimentalists and industrialists we will iteratively refine these models until they are able to accurately reproduce a range of observed phenomena, and the models will then be used to optimise and inform changes in design to improve performance.

The ideal candidate would have some knowledge of the physics of electrical systems as well as some familiarity with asymptotic methods and scientific computing (e.g., in MATLAB or python). The successful applicant will have the benefit of taking part in meetings with both domestic and international collaborators. Furthermore, they will be trained in the workings of a technology that has an extremely promising future, as well as in highly transferable mathematical modelling. The work will be supported internally via the University's Future and Emerging Technology, and Sustainability and the Environment themes.

Entry requirements

You'll need a good first degree from an internationally recognised university (minimum upper second class or equivalent, depending on your chosen course) or a Master’s degree in an appropriate subject. In exceptional cases, we may consider equivalent professional experience and/or qualifications. English language proficiency at a minimum of IELTS band 6.5 with no component score below 6.0.

You should have knowledge of differential equations. Knowledge of asymptotic methods, numerical methods, electrodynamics and electrochemistry is welcomed. 

How to apply

We’d encourage you to contact Dr Jamie Foster ( to discuss your interest before you apply, quoting the project code.

When you are ready to apply, you can use our online application form. Make sure you submit a personal statement, proof of your degrees and grades, details of two referees, proof of your English language proficiency and an up-to-date CV. Our ‘How to Apply’ page offers further guidance on the PhD application process. 

If you want to be considered for this funded PhD opportunity you must quote project code SMAP6010521 when applying.