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Fast simulation algorithms for correlated dynamics in condensed matter and data science: from superconducting films to epidemic modelling


Supervisors: Dr. Michael Faulkner (WCPM, Eng.), Prof. Gareth Roberts (Statistics)

Project Partners: Prof. Tom Hase (Phys.), Dr. Sebastiano Grazzi (Statistics), Prof. Zhenzhong Shi (Soochow Physical Science and Technology), Dr. Alice Thorneywork (Oxford Physical Chemistry)


Recent experiments on superconducting films revealed strongly correlated dynamics at the superconducting transition, with evidence for the phenomenon also found in simulations of magnetic films and epidemic models. Modelling these effects is important for high-precision engineering of superconducting and magnetic films – as well as for predicting early-warning signs for epidemics – but this remains unresolved due to the challenges they pose to simulation. Through collaboration with a key Warwick data scientist, this project will develop state-of-the-art simulation algorithms to characterise correlated dynamics in all three systems – which we will corroborate in experiment with collaborators in Soochow (China), Warwick and Oxford.


Many of the most challenging problems in predictive modelling involve strongly correlated system dynamics. These effects freeze systems near random states for disproportionately long times, so that experimental observations disagree with prediction. One cause of correlated dynamics is critical slowing down (CSD). This occurs at continuous phase transitions across statistical science, where it is characterised by some autocorrelation time diverging with system size. For example, recent experiments on superconducting films revealed strong autocorrelations at the superconducting transition [1], and evidence for CSD has also been found in simulations of magnetic films [2] (also implying its existence in colloidal films) and epidemic models [3].

This creates significant challenges for simulation because algorithms are often based on diffusive physical dynamics, so that CSD also freezes simulations at continuous phase transitions. This destroys their predictive power, but recent advances in computational physics and data science have led to new algorithms based on ballistic-style ‘superdiffusive’ dynamics [4], accelerating simulations of both superconducting/magnetic/colloidal films [5] and epidemic models [6].

This project will exploit these algorithms to circumvent CSD and characterise its effects on superconducting, magnetic and colloidal films, working closely with experimental partners in Soochow (Shi) [1], Warwick (Hase) [7] and Oxford (Thorneywork) [8] to corroborate our results with superconducting, magnetic and colloidal-film experiments. We will work in parallel with our key data-science partner at Warwick (Grazzi) to adapt his algorithms for epidemic modelling [6] – allowing us to characterise CSD at the epidemic transition, to ultimately predict early-warning signs for epidemics.

Project Resources:

This project brings together expertise from the Warwick Centre for Predictive Modelling, Warwick Statistics and Warwick Physics, along with various external partners who will provide input on both the advanced simulation algorithms and feedback from experiment. The taught HetSys programme will provide the applicant with the advanced skills required to innovate the superdiffusive algorithms described above, allowing us to tackle this exciting and broadly applicable research project.

Large-scale simulations will be performed on Warwick’s high-performance-computing infrastructure, and the applicant will develop a high level of research software engineering skills over the course of the project. There is also the potential for travel to visit external project partners.

Informal enquiries to are welcome.

Relevant references:

[1] Shi et al., Phys. Rev. B 94, 134503 (2016)
[2] Archambault et al., J. Phys. A 30, 8363 (1997)
[3] Southall, Brett, Tildesley & Dyson, J. R. Soc. Interface 18, 20210555 (2021)
[4] Bernard et al., Phys. Rev. E 80, 056704 (2009); Bierkens & Roberts, Ann. Appl. Probab. 27, 846 (2017)
[5] Faulkner, arXiv:2209.03699 (2022)
[6] Bierkens, Grazzi, Roberts et al. arXiv:2303.08023 (2023)
[7] Arnalds, others, Hase & Hjörvarsson, Appl. Phys. Lett. 105, 042409 (2014)
[8] Thorneywork et al., Phys. Rev. Lett. 118, 158001 (2017)
Are you interesting in applying for this project? Head over to our Study with Us page for information on the application process, funding, and the HetSys training programme

At the University of Warwick, we strongly value equity, diversity and inclusion, and HetSys will provide a healthy working environment, dedicated to outstanding scientific guidance, mentorship and personal development.

HetSys is proud to be a part of the Engineering Department which holds an Athena SWAN Silver award, a national initiative to promote gender equality for all staff and students.