Partial Differential Equations Modelling Collective Behaviour (2019)

A three and a half year studentship for a UK or EU student which covers fees and living expenses

Type of award

Postgraduate Research

PhD project

Supervisor: Professor Bertram Duering

A fully-funded 3-and-a-half year PhD position is available in the Department of Mathematics in the School of Mathematical and Physical Sciences at the University of Sussex.

Real-world systems in socio-economics and life sciences often consist of a large number of interacting individuals. These interactions frequently result in formation of complex patterns and collective behaviour, such as aggregation or segregation. Typical real-world applications are congestion models, population dynamics, price and opinion forming.

For large numbers of individuals following the individual dynamics is inefficient and may even be prohibitive. But mathematical methods from kinetic theory and mean-field models allow to describe and analyse the statistical distribution of the individuals and derive macroscopic quantities from them. Then, suitable limit partial differential equations which govern these quantities can be derived, analysed and solved numerically.

The main aims of this project are:

  • To derive mathematical models for real-world complex systems consisting of many interacting individuals;
  • To analyse the interplay of microscopic dynamics and macroscopic observables like the distribution of individuals, opinions or prices, and derive their governing partial differential equations;
  • To develop and implement efficient numerical solvers for the partial differential equations.


You will receive:

  • fully funded tuition fees for 3 and a half years (at the UK/EU rate)
  • a tax-free bursary for living costs for 3 and a half years. For 2018/19 this is £14,777 per year.
  • funds for computing, books, open access publishing, travel to/from the industrial partner and attendance at conferences and workshops.

You may also supplement your income with paid teaching (with your supervisor’s agreement).


To be eligible, you must:

  • be a UK/European Union (EU) student.
  • have or expect to have a UK undergraduate/master’s degree, or equivalent, in Mathematics or equivalent 


9 May 2019 9:46 (GMT)

How to apply

Apply through the postgraduate application system and select the full time PhD in Mathematics with September 2019 start date, depending on your availability. 

Applications will be considered until the position has been filled.

When you apply, you should include:

  • the supervisor’s name (Professor Bertram Duering) in the ‘Suggested supervisor’ section
  • Partial Differential Equations Modelling Collective Behaviour in the ‘Award detail’ section
  • a research proposal/personal statement which describes your suitability for the project
  • 2 academic references
  • your transcripts from any previously obtained degrees. If you have not yet completed your undergraduate degree, you can provide an interim transcript or record of any marks obtained so far.

The position will be filled as soon as a suitable candidate is found so you are encouraged to apply as soon as you are able to. 

Due to the high volume of applications received, you may only hear from us if your application is successful.

Contact us

Email Professor Bertram Duering ( if you have a question about the project

Email if you have a question about applying, funding or eligibility.


At level(s):
PG (research)

Application deadline:
9 May 2019 9:46 (GMT)
the deadline has now expired


The award is available to people from these specific countries: