Mathematics: Fully Funded EPSRC DTP and Swansea University PhD Scholarship: Multiscale spatiotemporal agent-based models with continuous traits (MustABM)

Funding providers: Engineering and Physical Sciences Research Council (EPSRC) DTP and Swansea University's Faculty of Science and Engineering

Subject areas: Mathematics

Project start date: 

• 1 October 2023 (Enrolment open from mid-September)

Project supervisors: 

• Dr Dmitri Finkelshtein ([Email Address Removed])
• Professor Eugene Lytvynov

Aligned programme of study: PhD in Mathematics

Mode of study: Full-time 

Project description: 

Agent-based models are used to study complex phenomena in many fields of science. While simulating agent-based models is often straightforward, predicting their behaviour mathematically has remained a key challenge. Recently developed (by the supervisor with co-authors) mathematical methods allow the prediction of the emerging both spatial and spatiotemporal patterns for a general class of agent-based models. The technique is based on the multiscale approach where the behaviour of the system at the micro-level is approximated by its behaviour at the meso- and macro-levels by using the appropriate correction mechanisms.

Non-trivial agent-based models should naturally consider various traits (marks) reflecting the peculiarities in the agents’ behaviour. The developed methods so far covered the case of discrete traits only. The continuous traits, however, are also extremely important topic, both from pure mathematical and applied perspectives; in particular, to consider models very large number of possible traits (e.g. various genotypes, masses, directions of motion).

The project is aimed to extend the developed methods to the case of continuous traits. Depending on the strengths and background of the prospective applicant, the emphasis may be put on the different levels of the multiscale paradigm: stochastic dynamics, (numerical) analysis of nonlocal equations, mathematical modelling.

Eligibility

Candidates must normally hold an undergraduate degree at 2.1 level or master’s degree with a minimum overall grade at ‘Merit’ (or Non-UK equivalent as defined by Swansea University). 

English Language requirements: If applicable – IELTS 6.0 overall (with at least 5.5 in each individual component) or Swansea recognised equivalent.

Due to funding restrictions, this scholarship is open to applicants eligible to pay tuition fees at the UK rate only, as defined by UKCISA regulations.