# Dr Robert Douglas BSc PhD (Bath)

Lecturer, Department Director of Learning and Teaching

- LecturerDepartment of Mathematics - Teaching And Research
- Department Director of Learning and TeachingDepartment of Mathematics - Other

#### Department of Mathematics

Physical Sciences Building

Penglais

Aberystwyth

#### Research interests

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.

#### Profile

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.