EPSRC Centre for Doctoral Training in Cross-Disciplinary Approaches to Non-Equilibrium Systems

Lead Research Organisation: King's College London
Department Name: Mathematics


How do we understand whether epidemics will spread, or predict the likelihood of extreme meteorological events? How do we optimize nano-particles to make them efficient vehicles for targeted delivery of drugs in medical applications? Can we predict how a cell in a specific state will evolve in time, for example whether it will stay healthy or become diseased? How do we prevent over-heating in fast electronic devices, or understand how energy conversion in the next-generation of solar cells might work? Can insights into extreme events in the sciences be used to detect whether a network of financial institutions is close to a crash?

These research challenges all relate to non-equilibrium systems. Such systems are typically irreversible, so that if a movie of the system was played backwards it would look very different. For equilibrium systems, on the other hand, a backwards movie would appear much like the original. This lack of an "arrow of time" makes equilibrium systems relatively easy to understand, and indeed most existing methods for predicting e.g. the behaviour of materials are based on the assumption of equilibrium. For non-equilibrium systems, on the other hand, we know much less. They can "age" towards an equilibrium state that is never reached, or exhibit extreme events. The latter are often the result of cascades of collective failure, as illustrated in phenomena ranging from stock market crashes to environmental disasters.

As the examples in the first paragraph show, understanding, predicting and controlling non-equilibrium behaviour is an important challenge in many problems across the physical, mathematical, biological and environmental sciences. The starting point for the proposed interdisciplinary Centre for Doctoral Training is, therefore, that significant progress will require researchers that can exploit and strengthen such links between disciplines. They will need to be trained in how to analyse non-equilibrium systems theoretically, via mathematical models, how to study their behaviour via computer simulations, and how to extract information about them from possibly noisy or incomplete data. They will also need to be aware of the important non-equilibrium problems in different disciplines, to see connections, transfer methods and concepts from one application area to another, and develop new approaches.

The Centre for Doctoral Training in Cross-Disciplinary Approaches to Non-Equilibrium Systems (CANES) will provide the training that such a new generation of researchers will need. In a substantial cohort of at least 10 PhD students per year it will make sure that ideas are exchanged systematically; research projects will be designed to build bridges between different disciplines employing similar methods, or to explore the connections between different approaches that are used to study non-equilibrium systems in the same area. Students will acquire transferable communication and presentation skills, and take part in outreach activities to increase the public understanding of non-equilibrium science. In `open questions sandpits', industry engagement events and dedicated careers events they will also obtain a solid understanding of the priorities of industrial partners working on non-equilibrium systems, and of attractive career paths outside of university. Overall, CANES researchers will emerge with a wide variety of skills that are highly sought after in academia and industry. CANES will also put UK research in non-equilibrium systems on the international map, helping the UK to compete against other countries like the U.S.A. where there is already a significant drive to strengthen research in this area.

Planned Impact

The EPSRC Centre for Doctoral Training in Cross Disciplinary Approaches to Non-Equilibrium Systems (CANES) will provide a high quality doctoral training environment for future research leaders in the area of non-equilibrium systems and processes. Challenges in non-equilibrium systems research exist in a very wide range of disciplines, from environmental science (e.g. extreme events, natural hazards) and socio-economics (failure risks in financial and energy networks) to biomedicine (drug delivery from nano-particles, spread of epidemics) and physics (materials degradation, next-generation photovoltaic cells). The basic premise of CANES is that significant progress can come only from researchers that combine extensive knowledge of non-equilibrium concepts and tools, as developed e.g. in statistical physics and mathematics, with an awareness of the breadth of challenges across application areas. As a result, the potential impact of CANES is very broad.
In addition to significant academic impact, we envisage impact on a wide range of business and industry, the public sector, the general public and schools. In business and industry, CANES-trained researchers will directly enhance research capacity and contribute to the creation of new products and processes; their training will ensure that they are highly numerate with a broad portfolio of research tools and transferable skills. Our industrial partners (e.g. the National Physical Laboratory, or the Saudi Arabian Mineral Oil Company via King Abdullah University of Science and Technology) comment specifically on the fact that the skill set that CANES is designed to provide will be beneficial to industry; further statements of support we have from BP and EDF confirm this. Impacts highlighted are in areas ranging from the response of materials to rapid environmental change, to molecular self-assembly and novel thin film solar cells. CANES will continue to seek out further industrial links, e.g. with companies with whom CANES staff already have connections such as Nestlé, Bosch, and Microsoft Research, and through an active programme of industrial outreach activities.
CANES-trained researchers that go into positions in biomedical research and development will be able to make an impact in the area of health, via optimized drug delivery, the use of molecular modelling for drug discovery, or improved predictions of how protein assemblies lead to pathological cell states. They can create impact in companies dealing with the analysis of genomic data, which can be used to characterize lifestyle or perturbations due to disease. Analytical methods rooted in data-driven approaches or predictive modelling can then be useful to compare across various conditions or environments, and develop appropriate hypotheses for pharmacogenomics applications. In this way CANES graduates will support UK industry sectors that rely on such efficient discovery pipelines, such as the pharmaceutical sector.
In the public sector, CANES graduates and research could have an impact on public policy, where a clearer understanding of the stability of financial or supply networks, or more accurate assessments of natural hazards and extreme environmental events, could improve public policy, regulation and environmental management.
Finally, CANES graduates and our outreach events will impact on the general public and schools, in the area of public understanding of science. Graduates will have been provided with a range of transferable skills, and practical experience, in science communication and public engagement, via dedicated training in the King's College London Graduate School and involvement in taster days, teachers' conferences and the CANES website and social media resources. They will thus be able to play an important role in making the public aware of the importance of non-equilibrium processes in everyday life and the cross-disciplinary science needed to understand, control and harness them.


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