This project is an interdisciplinary collaboration between Mathematics and Chemistry. Real-world applications include safe radioactive wate disposal, plutonium stewardship and radiation based cancer care. It will involve simulating phenomena whose outcomes can be measured against real-world data from experiments performed at the Dalton Cumbrian Facility.On the mathematical modelling side, the governing PDEs involved are reaction-diffusion equations. These PDEs are generally well understood in their basic form, but in this project there will be many chemical species which are all interacting nonlinearly in several different ways: within a liquid solution, across a surface in contact with the solution, and even within the material beneath this surface. This makes the modelling and numerical methods challenging. On the computational side, the project will further develop an approximation technique called Fourier extension frames. These are similar to multivariate Fourier series you may have seen before, but with some added flexibility which will allows these nontrivial chemical interactions involving arbitrarily shaped surfaces to be simulated. Much of the methodology has already been implemented in a software package called MIRaCLE (Manchester Inhomogeneous Radiation Chemistry by Linear Expansion), and the project will involve contributing new features to this package to enable the research to be undertaken. Eligibility • Obtained or working towards a 1st class degree in Mathematics, or a closely related discipline with strong mathematical component such as Physics, Engineering, or Chemistry (Master’s level or equivalent) • Background in some or all of the following: scientific computing, partial differential equations, numerical analysis • Good programming skills in a language such as Matlab, Python or Julia • Good communication skills (oral and written) • Openness to working across disciplinesFundingAt Manchester we offer a range of scholarships, studentships and awards at university, faculty and department level, to support both UK and overseas postgraduate researchers applying for competition and self-funded projects. For more information, visit our funding page or search our funding database for specific scholarships, studentships and awards you may be eligible for.Before you apply We strongly recommend that you contact the supervisor(s) for this project before you apply.How to applyApply online through our website: https://uom.link/pgr-apply-fap When applying, you’ll need to specify the full name of this project, the name of your supervisor, if you already having funding or if you wish to be considered for available funding through the university, details of your previous study, and names and contact details of two referees. Your application will not be processed without all of the required documents submitted at the time of application, and we cannot accept responsibility for late or missed deadlines. Incomplete applications will not be considered. After you have applied you will be asked to upload the following supporting documents: Final Transcript and certificates of all awarded university level qualificationsInterim Transcript of any university level qualifications in progressCVContact details for two referees (please make sure that the contact email you provide is an official university/work email address as we may need to verify the reference)English Language certificate (if applicable)If you have any questions about making an application, please contact our admissions team by emailing [email protected]. Equality, diversity and inclusion is fundamental to the success of The University of Manchester, and is at the heart of all of our activities. We know that diversity strengthens our research community, leading to enhanced research creativity, productivity and quality, and societal and economic impact. We actively encourage applicants from diverse career paths and backgrounds and from all sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation and transgender status. We also support applications from those returning from a career break or other roles. We consider offering flexible study arrangements (including part-time: 50%, 60% or 80%, depending on the project/funder).