The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing in September 2024.
About the Project
- Supervisor: Dr Lennart Dabelow
- Funding:
- Competition funding through QMUL Science and Engineering Studentships, QMUL Engineering and Physical Sciences Research Council (EPSRC) studentships, or S&E Doctoral Research Studentships for Underrepresented Groups 2024/25
- Deadline: 31st January 2024
Project description
This PhD project will explore the collective behaviour of mathematical models for active matter at micro- to nanometre scales, such as bacteria, colloids with catalytic surfaces or liquid crystals in autonomous materials. Their defining characteristic is that they can consume energy from their surroundings and use it to move around deliberately and persistently. Systems of many such active particles exhibit a variety of fascinating emergent phenomena like clustering, swarming and motility-induced phase separation. The principal goal of this project is to find links between such dynamical characteristics and the systems’ thermodynamic properties.
As an example, the recent study [1] identifies the observable irreversibility as a thermodynamic state function and connects it to the pressure that active particles exert on the walls of an enclosing container. Irreversibility [2-3] here is a purely dynamic measure that quantifies how strongly the individual particle trajectories break time-reversal symmetry, without reference to the internal mechanisms of self-propulsion. Relating this irreversibility to thermodynamic properties like the pressure is similar in spirit to the second law of thermodynamics, which identifies the thermodynamic entropy as a quantifier for the (ir)reversibility of transitions between macroscopic equilibrium states.
Within this project, the student will investigate how this fundamental connection between irreversibility and thermodynamics can be adapted to more realistic models of active particles. To this end, they will develop novel approaches to characterize stochastic trajectories and steady-state solutions of such models, bearing in mind experimental constraints such as the fact that the internal processes and chemical reactions underlying the self-propulsion mechanism are typically not directly observable. Furthermore, the student will explore more broadly how collective phenomena in these models, like clustering and swarming, relate to thermodynamic system properties like entropy, pressure, or specific heat, for example.
From a mathematical point of view, this project will
- analyse high-dimensional, non-Markovian stochastic differential equations (SDEs) and especially their stationary solutions;
- adopt and extend analytical path-integral techniques to characterize stochastic trajectories;
- develop numerical estimators for path probabilities and study their convergence properties.
Successful candidates will have
- a first- or upper second-class (or equivalent) degree in mathematics, physics, or a related discipline (by September 2024);
- good foundational knowledge of probability theory and statistics;
- experience with computer programming in a multi-purpose language, for instance C/C++ or Python.
Informal enquiries are encouraged and should be directed to Dr Lennart Dabelow (l.dabelow@qmul.ac.uk).
Funding
For September 2024 entry the following funding sources are available competitively and will provide an annual tax-free maintenance allowance for up to 3.5 years at the UKRI rate (£20,662 in 2023/24, 2024/25 rates tbc):
- QMUL Science and Engineering PhD Studentships. Studentships will cover home tuition fees only.
- QMUL Engineering and Physical Sciences Research Council (EPSRC) studentships. Studentships are open to those with Home and International fee status; however, the number of students with International fee status which can be recruited is capped according to the EPSRC terms and conditions so competition for International places is particularly strong.
- S&E Doctoral Research Studentships for Underrepresented Groups 2024/25. Studentships will cover home tuition fees only.
We also welcome applications for self-funded, or externally funded applicants year-round, for a January, April or September start.
Application
The application procedure is described on the School webpage: www.qmul.ac.uk/maths/postgraduate/postgraduate-research/application-process/. For further inquiries please contact l.dabelow@qmul.ac.uk.
The School of Mathematical Sciences is committed to the equality of opportunities and to advancing women’s careers. As holders of a Bronze Athena SWAN award we offer family friendly benefits and support part-time study.
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