Fully-funded PhD studentship available under the supervision of Professors. G.A. Pavliotis and Pierre Degond in the Department of Mathematics
This PhD studentship is part of a joint project between Imperial College and the French CNRS jointly led by Pierre Degond (Imperial College) and Louis Casteilla (Stromalab laboratory) entitled "REGEN: Induced self-organized tissue regeneration: a model-data framework". This project aims to explore the different types of self-organization that prevail in healthy and pathological tissues through the combined use of sophisticated mathematical models and high quality data. This project is part of the activity of the joint CNRS - Imperial College International Research Laboratory Abraham de Moivre.
Specifically, in this PhD project, we will describe the tissue as a complex social organization involving different types of agents, such as various categories of cells, fibers and networks which interact one with each other through complex rules. We will start with a multi-agent system approach which has proven successful in the modelling of social systems. Then we will develop mean-field models and view the various interactions between the agents through the viewpoints of control theory and mean-field games. The goal is to decipher the processes that transform a healthy tissue into a pathological one through the concept of phase-transitions triggered by positive feedback loops and to find the ways to prevent these transitions by using concepts from optimal control theory for PDEs. Recent developments in the study of phase transitions and of fluctuations for mean field PDEs, as well as in the development of optimal control methodologies for such systems, will be used.
Within this project, the student will develop a large array of expertise in modelling, mathematical analysis, numerical simulation and applications to life sciences. According to the taste of the student, the project may concentrate more on one particular aspect, but it is expected that all aspects will be covered with different levels of detail during the course of the PhD. Funding is available to support the PhD student’s interactions with the team of biologists in France.
Candidates will have a MSc in Applied or Pure Mathematics or Physics, will need to produce strong records during all their under and post graduate studies. They will need to demonstrate scientific maturity and independence, as well as a strong interest in research at the interface between mathematics and modelling in life sciences. Applications for this studentship are accepted from home and EU students only. The successful candidate will be asked to meet Imperial College’s English language requirements.
The studentship is for 3.5 years and the stipend is around £17,560 per annum. The start date is 01/10/2021.
How to apply
To apply, you can follow the standard College on-line application procedure. The deadline for applications is: 12pm (GMT) 31 January 2021.
D. Peurichard, … , P. Degond, Simple mechanical cues could explain adipose tissue morphology, Journal of Theoretical Biology, 429 (2017), pp. 61-81 (open access).
M.G. Delgadino, R. Gvalani, G.A. Pavliotis, On the diffusive-mean field limit for weakly interacting diffusions exhibiting phase transitions. Archive for Rational Mechanics and Analysis, to appear 2021.
G.A. Pavliotis et al Long-time behaviour and phase transitions for the McKean-Vlasov equation on the torus. Archive for Rational Mechanics and Analysis, 235 (2020) 635-690.
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