Ashley Willis

Dr.  Ashley P. Willis

Senior Lecturer of Applied Mathematics

Room H12, Hicks Building

School of Mathematics and Statistics
University of Sheffield
S3 7RH, U.K.

+44 (0)114 2223746


Office hours: I'm usually in H12 or around. Please email to be sure.

School page for APW

Google Scholar page for APW

2010/18-present: Lecturer/Senior Lecturer, School of Mathematics & Statistics, University of Sheffield, U.K.
2008-10: EU Marie Curie Fellow (PI), Laboratoire d'Hydrodynamique (LadHyX), Ecole Polytechnique, Paris, France
2005-08: EPSRC Research Associate, School of Mathematics, University of Bristol, U.K.
2002-05: NERC Research Fellow (RA), School of Earth Sciences, University of Leeds, U.K.
2002: PhD Applied Mathematics, Newcastle University, U.K.

Collaborator's pages 

Elena Marensi , EPSRC Research Assocate, Sheffield, Optimization in Fluid Mechanics ;

Marc Avila Bremen; Predrag Cvitanović Georgia Tech ( ); Yohann Duguet LIMSI, Paris; Dave Gubbins Leeds; Yongyun Hwang Imperial; Rich Kerswell DAMTP, Cambridge; Jeorge Peixinho PIMM, Paris.

Sheffield Fluid Dynamics Group

SoMaS Applied Mathematics Seminars

PhD Projects:

I am looking for motivated students who would like to apply and broaden their mathematical skills. As the focus of my projects is usually on the development of mathematical methods and the study of dynamical systems, I expect you to be familiar with differential equations and vector calculus, but you do not need to have taken advanced courses on fluids.

The modelling of fluid flows is perhaps the traditional test-bed for the development of new methods. Often, even simple-looking setups exhibit all sorts of interesting phenomena, and our understanding of nature is greatly enhanced through numerical simulation and experiments.

I am particularly interested in the appearance of turbulence in fluid flows, and in modelling flows in the interior of planets. The latter is usually responsible for the generation of planetary magnetic fields.

For further information please contact me. The following links to snippets of my work may also be of interest: Turbulence. Dynamos.

Please note that all PhD applications must be made through the university system: School info on PhD places.

Some of my work: 

I am the founder and owner of, a free and fast simulation code for the study of pipe flow, particularly as a dynamical system. Non-problem-specific codes for dynamical systems include...

A Jacobian-free Newton-Krylov (JFNK) code (MATLAB / FORTRAN90) for finding solutions of high-dimensional nonlinear equations (or low-dimensional if you like!).

I've written a Double pendulum android app: with two double-pendula side-by-side, it is specifically designed to show how initially similar states diverge - the chaotic system exhibits sensitivity to initial conditions (SIC). It also shows how the chaotic paths follow particular repeating patterns, periodic orbits.

Publications can be found on my Google Scholar page or here: Publications + preprints

A description of the mathematics behind the following videos can be found here.