PhD project: Controlling space and time in active matter
Project description
Understanding and controlling how objects move through space and time is at the bedrock of physics, hearkening back to Newton. However, our basic understanding starts to break down when the objects under consideration are actively sustaining their own motion and behaviour, i.e., are far from thermal equilibrium. This departure from equilibrium naturally brings about an arrow of time for active systems: forward and reversed movies of their dynamics look different. Moreover, active matter systems—such as schools of fish, colonies of cells and bacteria, and even robots—interact in complex ways resulting in collective behaviours that are not seen at equilibrium, presenting further theoretical challenges. Despite these challenges, the eventual understanding and control of such rich behaviours opens the door to new “active” machines, actuators, and devices that perform functions beyond that of passive (equilibrium) technologies.
In this project, we will use theoretical frameworks such as stochastic thermodynamics, optimal control theory, and statistical geometry to understand how active constituents explore space and time. We will begin to consider simple active matter models, e.g., self-propelled hard spheres, and then tackle more realistic models. This project involves both mathematical and computational techniques, with scope to include the use of AI.
Reading material:
Entropy production of active particles and for particles in active baths. Pietzonka, P et al. J. Phys. A. (2017)
Automomous engines driven by active matter: Energetics and design principles Pietzonka, P et al. PRX (2019)
Insertion space in repulsive active matter. Davis, L et al. arXiv (2025)
Learning protocols for the fast and efficient control of active matter Casert, C et al. Nat. Comm. (2024)
Active matter under control. Davis, L. et al. PRX (2024)
Project supervisors
- Dr Luke Davis (School of Mathematics)
- Dr Patrick Pietzonka (School of Physics & Astronomy, University of Edinburgh)
The project supervisors welcome informal enquiries about this project.
Find out more about this research area
The links below summarise our research in the area(s) relevant to this project:
- Find out more about Physics of Living Matter.
- Find out more about Statistical Physics and Complexity.
- Find out more about the Institute for Condensed Matter and Complex Systems.
What next?
- Find out how to apply for our PhD degrees.
- Find out about fees and funding and studentship opportunities.
- View and complete the application form (on the main University website).
- Find out how to contact us for more information.
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- Browse other Statistical Physics and Complexity projects.
- Browse other Institute for Condensed Matter and Complex Systems projects.
- Browse all PhD research opportunities in the School of Physics & Astronomy.
- Browse PhD research opportunities elsewhere in the University of Edinburgh.