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Mathematical models for improved lithium-ion batteries


   School of Mathematics and Physics

   Applications accepted all year round  Self-Funded PhD Students Only

About the Project

Applications are invited for a self-funded, 3-year full-time or 6-year part time PhD project.

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

The work on this project could involve:

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

Project description

Developing cheap and efficient means of storing energy is key to the low-carbon economy. The fastest growing battery technology is lithium-ion. Billions of these cells are already produced 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 $68.9Bn and this is expected to grow to $216.5Bn by 2028.

The aims of this project are to carry out the mathematical modelling and analysis required to underpin and inform changes in current design to give rise to batteries that (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 knowledge of both physics and/or electrochemistry as well as familiarity with asymptotic methods and scientific computing (e.g., in MATLAB or python). The successful applicant will benefit from participating in meetings with both domestic and international collaborators, and the Faraday Institution community. Furthermore, they will be trained in a technology with an extremely promising future, and 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.

General admissions criteria

You'll need a good first degree from an internationally recognised university 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.

Specific candidate requirements

Essential is knowledge of differential equations. Desirable knowledge includes asymptotic methods, numerical methods, electrodynamics and electrochemistry.

How to Apply

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

When you are ready to apply, please follow the 'Apply now' link on the Mathematics PhD subject area page and select the link for the relevant intake. 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. 

When applying please quote project code:SMAP5771023.


Funding Notes

Self-funded PhD students only.
PhD full-time and part-time courses are eligible for the UK Government Doctoral Loan (UK students only).

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