Dr Robert John Douglas
BSc PhD (Bath)

Dr Robert John Douglas


Department Director of Learning and Teaching

Contact Details


Educated at Pates Grammar School, Cheltenham, and a graduate in Mathematics from Bath University. He obtained his PhD in applied mathematical analysis at Bath, specialising in nonlinear analysis of vortices in ideal fluid flow. Dr. Douglas was a Research Fellow at the Universities of Cambridge and Reading, a Visiting Scientist at the U.K. Meteorological Office, and a Lecturer at the University of Surrey before joining the Mathematics Department at Aberystwyth in February 2000.

His interests include bridge (he has won the Mid Wales Open Pairs and was a member of the first Mid Wales team to win the Perry National Championships), watching cricket and rugby, and reading crime novels.



Dr. Douglas is an applied mathematical analyst; he is interested in innovative modelling of physical problems, but his main focus is proving rigorous results using measure theory and convex analysis (and its generalisations). His previous work proved the Cullen-Norbury-Purser conjecture that identified energy minimising solutions for the semigeostrophic equations, a model for weather front formation, with an extra constraint on the equations. For such flows the trajectory map (for fluid particles) must arise from a polar factorisation (that is a vector-valued mapping written as the composition of the gradient of a convex function with a size-preserving mapping); in collaboration with G.R. Burton (University of Bath), Dr. Douglas established sharp conditions for when such a factorisation is guaranteed to exist, and precisely when it is unique. He has established properties of the relaxation spectrum, which (roughly speaking) describes for how long and to what extent a visco-elastic fluid remembers the past deformation history. With H.R. Whittle Gruffudd (Forest Research in Wales), Dr. Douglas has established non-existence results for relaxation spectra with compact support (using the theory of the Fourier transform in the settings of L^2 and tempered distributions). He is an active participant in the Analysis cluster of the Wales Institute for Mathematical and Computational Sciences.

Current research interests include optimal mass transfer, weather forecast error decomposition (using a combination of L^2 norm and Wasserstein distance), weather front formation and stability of solutions for the semigeostrophic equations, polar inclusions (a generalisation of polar factorisation which was described above), and relaxation spectrum recovery.

Research Groups


Nonexistence results for relaxation spectra with compact supportDouglas, R. J. & Whittle Gruffudd, H. R. 2016 In : Inverse Problems.32, 3, 13 p., 035006
Non-existence of polar factorisations and polar inclusion of a vector-valued mappingDouglas, R. J. 2007 In : International Journal of Pure and Applied Mathematics.41, 3
Generalized semi-geostrophic theory on a sphereCullen, M. J. P., Douglas, R. J., Roulston, I. & Sewell, M. J. 2005 In : Journal of Fluid Mechanics.531, p. 123-15735 p.
Uniqueness of the polar factorisation and projection of a vector-valued mappingBurton, G. R. & Douglas, R. J. 2003 In : Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire.20, 3, p. 405-41814 p.
Large-Amplitude nonlinear stability results for atmospheric circulationsCullen, M. J. P. & Douglas, R. J. 2003 In : Quarterly Journal of the Royal Meteorological Society.129, 591, p. 1969-198820 p.
More publications on the Research Portal