Professor of Mathematics and AI, Lancaster University
Point vortices of both signs in a disc, each mirrored by an image vortex beyond the wall. Raise the mutual friction and dipoles shrink and annihilate while lone vortices drift out. Click inside the disc to add a vortex. Quantum fluids research, related paper
A stochastic SIR model of a planted forest: each tree is susceptible, infected or removed, and infection jumps a short distance to its neighbours. Above a critical planting density a local outbreak becomes an epidemic. Click a tree to infect it. Maths biology research, related paper
Learning where a disease spreads easily from sparse data. An outbreak moves through a landscape whose transmission varies in space, but all we observe is a survey of which sites are infected. A generative diffusion model starts from pure noise and removes it step by step, ending with a map of transmission consistent with the survey. Each sample differs most where the outbreak has not reached, which is where the data say least. Here a simple stand-in plays the part of the trained neural network. Maths biology research
Bottom-heavy swimming algae in the ABC flow, a classic chaotic three-dimensional flow, shown in one periodic cell. Gyrotaxis, the torque that turns the cells upright against gravity, gathers them into helical plumes and suppresses the chaotic mixing that passive particles feel. As the swimming speed rises, chaos is suppressed, returns for speeds just above the flow speed, and is suppressed again, as the inset shows. Drag to rotate. Maths biology research, related paper
A single quantised vortex in superfluid helium, simulated with the vortex filament model. Helical Kelvin waves are driven at the longest wavelengths; their nonlinear interactions pass energy to ever shorter waves until it is lost at the smallest scales, where a real vortex radiates sound. Darker blue marks small-scale waves. The inset compares the spectrum with the two rival predictions, L'vov and Nazarenko's k−5/3 and Kozik and Svistunov's k−7/5; this small simulation is too short in range to tell them apart, which took the much larger simulations of our 2014 paper. Turn the forcing off to watch the cascade decay, or pluck the vortex as a reconnection would. Drag to rotate. Quantum fluids research, 2014 paper, Viewpoint in Physics
I am Professor of Mathematics and AI in MARS: Mathematics for AI in Real-world Systems, part of the School of Mathematical Sciences at Lancaster University, where I am Director of Studies for the MARS degree programme.
My main research interest is turbulence in quantum fluids such as superfluid helium and atomic Bose–Einstein condensates, and how it compares with the classical turbulence we are more familiar with. I also work in mathematical biology, especially the spread of tree and plant disease, combining stochastic epidemic models with statistical and machine-learning inference, and I keep a long-standing interest in mathematical archaeology.
I am always on the lookout for strong PhD students and postdoctoral researchers, and I often have openings for undergraduate summer students. If you are a current student and see me online in Teams, feel free to message or call.
Turbulence in superfluid helium and atomic Bose–Einstein condensates: vortex reconnections, Kelvin-wave cascades, coherent vortex bundles and the motion of point vortices in two dimensions, studied with vortex filament and Gross–Pitaevskii simulations.
[vortex filament method, Gross–Pitaevskii equation, Kelvin waves, vortex reconnections, thermal counterflow, point vortices, dipolar condensates, neutron stars]
How tree and plant diseases spread through landscapes, and how to fit stochastic epidemic models to sparse survey data, alongside collective animal motion, stem cell colonies and the spread of farming in Neolithic Europe.
[plant health, stochastic epidemic models, Bayesian inference, early-warning signals, diffusion models, oak processionary moth, flocking, Neolithic dispersal]
A. W. Baggaley. The turbulent life of a vortex line. Physics 19, 118 (2026).
@article{baggaley2026turbulent,
title = {The turbulent life of a vortex line},
author = {A. W. Baggaley},
journal = {Physics},
volume = {19},
pages = {118},
year = {2026},
}P. Z. Stasiak, Y. Xing, Y. Alihosseini, C. F. Barenghi, A. W. Baggaley, W. Guo et al. Experimental and theoretical evidence of universality in superfluid vortex reconnections. Proceedings of the National Academy of Sciences 122, e2426064122 (2025).
@article{stasiak2025experimental,
title = {Experimental and theoretical evidence of universality in superfluid vortex reconnections},
author = {P. Z. Stasiak and Y. Xing and Y. Alihosseini and C. F. Barenghi and A. W. Baggaley and W. Guo and others},
journal = {Proceedings of the National Academy of Sciences},
volume = {122},
pages = {e2426064122},
year = {2025},
doi = {10.1073/pnas.2426064122},
}I. K. Liu, A. W. Baggaley, C. F. Barenghi, and T. S. Wood. Vortex avalanches and collective motion in neutron stars. The Astrophysical Journal 984, 83 (2025).
@article{liu2025vortex,
title = {Vortex avalanches and collective motion in neutron stars},
author = {I. K. Liu and A. W. Baggaley and C. F. Barenghi and T. S. Wood},
journal = {The Astrophysical Journal},
volume = {984},
pages = {83},
year = {2025},
}L. E. Wadkin, J. Holden, R. Ettelaie, M. J. Holmes, J. Smith, A. Golightly, and A. W. Baggaley. Estimating the reproduction number, R₀, from individual-based models of tree disease spread. Ecological Modelling 489, 110630 (2024).
@article{wadkin2024estimating,
title = {Estimating the reproduction number, R₀, from individual-based models of tree disease spread},
author = {L. E. Wadkin and J. Holden and R. Ettelaie and M. J. Holmes and J. Smith and A. Golightly and A. W. Baggaley},
journal = {Ecological Modelling},
volume = {489},
pages = {110630},
year = {2024},
}A. Golightly, L. E. Wadkin, S. Whitaker, A. W. Baggaley, N. G. Parker, and T. Kypraios. Accelerating Bayesian inference for stochastic epidemic models using incidence data. Statistics and Computing 33, 134 (2023).
@article{golightly2023accelerating,
title = {Accelerating Bayesian inference for stochastic epidemic models using incidence data},
author = {A. Golightly and L. E. Wadkin and S. Whitaker and A. W. Baggaley and N. G. Parker and T. Kypraios},
journal = {Statistics and Computing},
volume = {33},
pages = {134},
year = {2023},
}L. Galantucci, E. Rickinson, A. W. Baggaley, N. G. Parker, and C. F. Barenghi. Dissipation anomaly in a turbulent quantum fluid. Physical Review Fluids 8, 034605 (2023).
@article{galantucci2023dissipation,
title = {Dissipation anomaly in a turbulent quantum fluid},
author = {L. Galantucci and E. Rickinson and A. W. Baggaley and N. G. Parker and C. F. Barenghi},
journal = {Physical Review Fluids},
volume = {8},
pages = {034605},
year = {2023},
doi = {10.1103/PhysRevFluids.8.034605},
}S. Orozco-Fuentes, G. Griffiths, M. J. Holmes, R. Ettelaie, J. Smith, A. W. Baggaley, and N. G. Parker. Early warning signals in plant disease outbreaks. Ecological Modelling 393, 12–19 (2019).
@article{orozcofuentes2019early,
title = {Early warning signals in plant disease outbreaks},
author = {S. Orozco-Fuentes and G. Griffiths and M. J. Holmes and R. Ettelaie and J. Smith and A. W. Baggaley and N. G. Parker},
journal = {Ecological Modelling},
volume = {393},
pages = {12--19},
year = {2019},
eprint = {1802.07562},
archivePrefix = {arXiv},
}A. W. Baggaley and J. Laurie. The Kelvin-wave cascade in the vortex filament model. Physical Review B 89, 014504 (2014).
@article{baggaley2014kelvinwave,
title = {The Kelvin-wave cascade in the vortex filament model},
author = {A. W. Baggaley and J. Laurie},
journal = {Physical Review B},
volume = {89},
pages = {014504},
year = {2014},
doi = {10.1103/PhysRevB.89.014504},
eprint = {1204.4034},
archivePrefix = {arXiv},
}I am happy to supervise PhD projects in quantum fluids and turbulence, in mathematical biology and plant health, and at their interfaces with statistical inference and machine learning. Projects can lean towards large-scale simulation, towards modelling and analysis, or towards inference from data. Please get in touch to discuss ideas. Former students and postdocs are listed on my Bio page.